**1. Introduction**

136 Emerging Informatics – Innovative Concepts and Applications

Tsohou A., Karyda M., Kokolakis S., Kiountouzis E. (2006) "*Formulating information systems*

Whitman, E.M., Mattord, J.H., 2008. *Management of Information Security*, Thomson Course

Computer Security Vol. 14 N° 3

Technology, CANADA, 2nd edition.

*risk management strategies through cultural theory Information"* - Management &

The main applications in the first wave of RFID have been in the supply chain mainly for improving the distribution of physical assets in the systems (Hardgrave and Miller, 2008; Sarma, 2008). The burgeoning use of RFID technology extends its applications to both upstream (supplier management) and downstream (retail and service) of manufacturing supply chains. RFID tags, also called "smart labels", together with other pervasive computing technologies realizes lean thinking in real-life and creates a smarter operating environment through adding *value* not only to customers with user-friendly shopping experience but also to merchants with agile and responsive store operations. Harrison and Hoek (2008), define *value* as relative advantage in general which is specified as *perceived benefit* obtained from the products or services in terms of the final customer, while as *economic profitability* in terms of the management, and the concept can be extended to other supply chain stakeholders as *value stream* which represents the *value-adding processes* beginning as raw materials from suppliers that are progressively converted into finished product bought by end-customers, such as aluminum is converted into one of the constituents of a can of coke. Being one of the management best practices, lean thinking preaches simplification and elimination of wasteful tasks, which is applicable to overly complex and nonintegrated processes that are inefficient and provide little added value. The firms following these practices have seen such dramatic improvement in performance that lean has spread across entire supply chains leading users to map their business processes to drive out *wastes* in operations, and becoming a lean enterprise has the potential to improve operations, reduce costs and deliver services with shorter lead times (King, 2009).

Ohno (1988) identified seven kinds of manufacturing *waste* that need to be eliminated: *overproduction*; *transportation*; *inventory*; *motion*; *defects*; *over-processing*; and *waiting*. These seven wastes represent the most commonly wasted resources and associated wasteful manufacturing activities which do not add value or are unproductive, in which the concept can be applied in non-manufacturing. Womack and Jones (2003) defined the eighth waste, i.e. delivering goods or services *not meeting customer need*, which represents a key attribute of a customer-centric lean enterprise. Lean thinking is proved to be an effective management system for manufacturing to improve overall efficiency and to enhance the work environment, in which the "getting more with less" concept can be applied in any type of business upon value creation (Aikens, 2011; Russell and Taylor, 2009). By offering the benefits of reducing complexity, improving efficiency, speeding delivery, and

RFID, an Emerging Wireless Technology for Sustainable Customer Centric Operations 139

communication technologies (ICT), e.g. RFID technology, add great values to retail sales and operations processes through enabling consumers to find information and alternative products and services more easily online leading to a greener and less wasteful consumption practice by

A RFID system essentially consists of three main components: RFID tag, RFID reader, and backend information system with middleware sitting between reader and backend system for carrying out data capturing, screening and routing (Glover and Bhatt, 2006). An RFID tag is a small object that can be attached to or incorporated into physical asset such as book, clothing, or person. When an RFID tag passes through the electromagnetic zone, it detects the reader's activation signal. The reader decodes the data encoded in the tag's integrated circuit (silicon chip) and the data is passed to the host computer for further processing (Finkenzeller, 2000; Hawrylak *et al.*, 2008; Shepard, 2005). RFID tags generally fall into two categories: passive, and active. Passive tags receive the most publicity and are currently being used by large retailers such as Wal-Mart and Metro to track inventory, and by the U.S. Department of Defense to track supplies (Hawrylak *et al.*, 2008). Unlike active tags, passive tags do not contain onboard power source and derive the power for operation from RFID interrogation signal in the course of communication (Finkenzeller, 2000; Hawrylak *et al.*,

Passive RFID tags communicate using one of two methods: near-field and far-field (Hawrylak *et al.*, 2008). Far-field RFID tags support longer communication range than nearfield tags, but they are comparatively more sensitive to tag orientation. The type of tags required for a RFID system would depend on their business applications, site conditions and system design requirements. In case of supply chain and retail applications, far-field RFID systems are used extensively. According to Hawrylak *et al.* (2008), the sensitivity of the system to RFID tag orientation is critical in many applications. The communication method used by far-field RFID system easily causes false detection and hence the design of middleware and upper layer application software becomes critical in order to effectively

Tracking the movements of product items in operations can be determined by three variables in a three-dimensional space, in which the first two are related to the "time" and "space" of item movement, while the third dimension concerns item identification by using RFID tags that carry Electronic Product Codes (EPCs) (Sarma, 2008). On this ground, RFID reader works with middleware to provide backend information systems with an "inventory snapshot" in its field of view which may cover a small corner of warehouse, distribution centre (DC) or backroom of retail store that essentially provides a series of item management function for improving the efficiency of supply chains including: (1) finding, (2) tracking, (3) tracing, (4) item count, and (5) time-intersections. Through querying of this corpus of data gathering from operations, two key metrics, i.e. *shrinkage* (caused by theft, damage, loss, and etc.) and *lead times* that concern operations visibility are evaluated (Hardgrave and Miller, 2008). In particular for apparel retailing, the "lost sales" causing by (1) misplacement, (2) damage, (3) theft, (4) shipping error, and (5) counterfeit of items can be reduced with the use of RFID which ultimately lead to increased product availability and

screen unwanted RFID signals emitted by nearby irrelevant product items.

**2.2 RFID in enabling sustainable retail operations**

total cost saving (Ustundag and Tanyas, 2009).

helping them to make sustainable choices (UN, 2011).

2008; Shepard, 2005).

understanding customer needs, lean thinking has gained the wide acceptance in nonmanufacturing (Heizer and Render, 2007; Russell and Taylor, 2009). Successful cases of adopting lean thinking in services have been applied in some instances to insurance (Swank, 2003), healthcare (Miller, 2005), government (Gupta, 2004), library (So and Liu, 2007), and retailing (Heizer and Render, 2007; Russell and Taylor, 2009; So and Sun, 2010).

To adopt lean services effectively in operations, firms need to made changes on three aspects: (i) *standardization of tasks and procedures* which can be achieved by, for example, documenting the process flow, training, automating tasks, etc., such that people can be freed to spend more time being creative on value-added work, (ii) *consolidating common processes* to eliminate non-value-added cost and duplicative efforts that customers are not willing to pay for, and (iii) *eliminating loop-backs or delay* which will result in improving productivity levels (Swank, 2003; George and Wilson, 2004; Hanna, 2007). The fast-paced characteristics and changing customer expectations of the markets lead apparel retail to the characteristics of short lifecycle and high impulse purchase which are sensitive to inventory shrinkage and product flow delay in the supply chains. Also, the perception of customers on retail services would affect their purchase decision. Realizing lean thinking in apparel retail operations with RFID technology creates a leaner operating environment which offers not only userfriendly shopping experience to customers but also more agile and responsive store operations to retailers with less wasteful sales and operations process. Adopting lean services in apparel retailing may equally beneficial to this industry with potential of creating both user- and eco-friendly retail environment.

The purpose of this research is to provide management and practitioners with insights on implementing and adopting lean services in contemporary retail environment enabled with RFID, a communication technology that add value to the customer chain in apparel retailing through providing smart and agile service operation. This paper presents supportive literature on the principles and the process of value creating activities based on lean thinking (Womack and Jones, 2003) and CCOR model (SCC, 2010a) aimed at improving profitability. A case study is presented to demonstrate how the convergence of these two management approaches can be applied to an apparel retailer based on a novel RFIDenabled smart apparel system aimed at improving its service operations that lead to increased customer conversion. Lastly, the implications of adopting this new initiative in creating leaner and smarter retail operations are discussed with the purpose to ensure the delivery of maximum value as a strategic tool for apparel retailers.


**Abstract**

Biofilms formed by multidrug resistant (MDR) bacteria like methicillin-resistant *Staphylococcus aureus* (MRSA) and others are the main causes of infections that represent a serious public health issue. Persistent MDR infections are mostly derived from biofilm formation which in turn leads to resistance to conventional antimicrobial therapy. Inhibition of bacterial surface attachment is the new alternative strategy without affecting the bacterial growth. Thus, the discovery of compounds that interfere with biofilm production, virulence factors release and quorum sensing (QS) detection in pathogens is a promising processus. Among these compounds, natural and synthetic molecules are a compelling alternative to attenuate pathogenicity. The combination of these compounds with antibiotics makes the bacteria more vulnerable to the later, once used alone. This combination can restore antibiotic effectiveness against MDR bacteria. Among these molecules, 3-phenylpropan-1-amine (3-PPA) has been found to inhibit *Serratia marcescens* biofilm formation, PAβN has been proven to inhibit biofilm prodcution in *A. baumannii,* while brominated Furanone C-30 has been reported to be a potent inhibitor of the QS system and *P. aeruginosa* biofilm. Therefore, the combination between biofilm-inhibitors and antibiotics represents a promising strategy to mitigate antibiotic resistance in MDR pathogens, which has become a major threat to public healthcare around the globe.

**Keywords:** biofilm inhibitors, antibiotics, association, MDR bacteria, biofilm


*Article* **Is the Urban Form a Driver of Heavy Metal Pollution in Road Dust? Evidence from Mexico City**

**Anahi Aguilera 1,2, Dorian Bautista-Hernández 2,\*, Francisco Bautista 2, Avto Goguitchaichvili 3 and Rubén Cejudo 3**

**Abstract:** Environmental pollution is a negative externality of urbanization and is of great concern due to the fact that it poses serious problems to human health. Pollutants, such as heavy metals, have been found in urban road dust; however, it is unclear whether the urban form has a role in its accumulation, mainly in cases where there is no dominant unique source. We collected 482 samples of road dust, we determined the concentrations of five heavy metals (Cr, Cu, Pb, Zn, and Ni) using inductively coupled plasma optical emission spectrometry (ICP-OES), and then we derived the pollution load index (PLI). After estimating the mostly anthropogenic origin of these pollutants based on global levels of reference, there were two main aims of this study. Firstly, to analyze the spatial correlation of heavy metals, and secondly, to identify the main factors that influenced the heavy metal concentrations in the road dust of Mexico City. We did this by using a spatial autocorrelation indicator (Global Moran's I) and applying ordinary least squares (OLS) and spatial regression models. The results indicated low levels of positive spatial autocorrelation for all heavy metals. Most variables failed to detect any relationship with heavy metals. The median strip area in the roads had a weak (significance level of 90%) but consistent positive relationship with Cr, Cu, Ni, Pb, and the PLI. The distance to the airport had a weak (significance level of 90%) and inverse relationship with Pb. Manufacturing units were associated with an increase in Cu (significance level of 95%), while the entropy index was associated with an increase in Ni (significance level of 95%).

**Keywords:** road dust; heavy metals; Mexico City; urban pollution; urban form

#### **1. Introduction**

The world is becoming increasingly urban. In the developing world, Latin America has already achieved this transition toward an urbanized society. For example, in Mexico, it is estimated that 80% of the population lives in urban areas [1]. The capital, Mexico City, along with its metropolitan area, concentrates around 17.5% of the country's population and has over 40,000 industries and 4 million vehicles that consume more than 40 million liters of fossil fuels per day, releasing, as a result, thousands of tons of pollutants into the urban environment [2]. Environmental pollution is one of the main negative externalities of huge urban agglomerations, especially in the developing context where weak institutions and planning efforts aggravate the problem [3].

Air pollution has attracted a great deal of attention, as it is considered one of the main causes of death in cities [4]; therefore, air pollution has been widely researched. Less attention has been paid to road dust pollution [5]; however, we assume that they are likely interlinked. Research reported that road dust is a sink for polluting emissions,

**Citation:** Aguilera, A.;

Bautista-Hernández, D.; Bautista, F.; Goguitchaichvili, A.; Cejudo, R. Is the Urban Form a Driver of Heavy Metal Pollution in Road Dust? Evidence from Mexico City. *Atmosphere* **2021**, *12*, 266. https://doi.org/10.3390/ atmos12020266

Academic Editor: Dmitry Vlasov

Received: 20 January 2021 Accepted: 14 February 2021 Published: 17 February 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

which are deposited on the surface of streets, sidewalks, and windows [6]. At the same time, road dust is a source of pollutants of atmospheric particulate matter [7]. Studies found that urban structure factors, such as land use, industrial development, and building construction, worsened the pollution in urban areas [8,9]. From a social point of view, aspects such as tax revenue and education level are associated with a decrease in urban pollution [9]. In terms of country-level data, researchers have tested the environmental Kuznets curve (EKC) hypothesis, which states that the relationship between gross domestic product (GDP) per capita and different environmental indicators exhibit an inverted-U curve [10,11].

Heavy metals are some of the major pollutants found in road dust [12–14]. Due to their abundance, toxicity, persistence, and bioaccumulation, heavy metals can cause permanent damage to ecosystems and humans [15]. The severity of health problems due to heavy metal toxicity depends on several factors, such as the type and form of the element, the route and duration of exposure, and to a greater extent, the susceptibility of each person [16]. Low concentrations of non-essential heavy metals (As, Hg, Pb, Cr, and Cd) can be lethal to animals. In Mexico City, the median levels of lead in children's blood were found to be close to the reference level for public health interventions (5.0 μg/dL) [17]. Prenatal lead exposure has been associated with a decrease in child growth [18]. Even essential metals (Zn, Cu, and Ni), required for the proper function of different enzymes, can become toxic in high concentrations, inducing the generation of reactive nitrogen and oxygen species. This can result in the peroxidation of lipids, as well as the functional deterioration of DNA and proteins [19]. Nickel diminishes the protection that taurine provides against neurodegeneration [16].

The sources of heavy metals in road dust can be diverse. In some cities, the origins are very specific to major stationary emitting sources; for example, the smelting industry [13], e-waste recycling [20,21], and mining activities [22]. Natural processes may also be the cause of an increase in the concentrations of trace metals [23]. Using pollutant-tracing approaches, mobile sources of heavy metals have also been identified, such as vehicular emissions [24]. It is considered that Cu, Pb, Zn, and Cr are traffic-related metals [25–27]. The quantities emitted vary, but some metals can be linked to specific vehicle parts. For example, Cu emissions are generally related to brake abrasion [28,29]; Zn is mainly emitted by tire wear [25], as well as from diesel exhaust emissions [27]. Some Zn compounds are used as additives for motor oil [30]. In the case of Cr, this metal can originate from exhaust emissions [26]. Pb can come from brakes and the loss of lead wheel weights [27]; Cr and Pb have been reported to originate also from yellow street paint which contains lead chromate. Paint and pigments crack, peel, and turn to chalk, mobilizing metal particles into the urban environment [31,32]. Ni can come from mixed industrial/fuel-oil combustion [30].

In cities with an economy mostly related to the service sector, there are multiple small and scattered possible sources, which can be mobile or fixed. Therefore, it is vital to determine what characteristics of the urban form act as driving factors of heavy metal pollution in road dust to obtain a better understanding of the cycle in the city. This would bring insights to help plan measures that limit the exposure of the population to these pollutants.

This work goes beyond the description of heavy metals in urban road dust. To the best of our knowledge, this is the first attempt to make systematic statistical inferences regarding the characteristics of the urban form that could influence the concentration of heavy metals in urban road dust. In this paper, we respond to two main questions: (1) Is there a spatial correlation in the heavy metal contents of points sampled across Mexico City? (2) What are the main factors that explain the distribution and concentration of heavy metals in urban road dust? The first question is addressed by applying the Moran's I spatial correlation test to the heavy metal concentrations, and the second question by using linear regression models to analyze the relationship between heavy metals and the urban form.

#### **2. Literature Review**

There have been several approaches to evaluate the effects of the built environment on urban pollution, mainly in the air and taking the city as the unit of analysis. Liang et al. [9] in the Beijing–Tianjin–Hebei urban agglomeration, using a geographically weighted regression model, found that the rate of urbanization, the formation of metropolises, and the level of economic and industrial development, as well as building and road construction aggravate the environmental pollution (measured as an index for air, soil, and water pollution).

Predictors associated with a decrease in urban pollution include the industrial level, tax revenue, education level, and the use of the internet. Implementing taxes to protect the environment promotes the modernization of highly polluting industries, while an increase in resident incomes promotes a shift in the regional economy to low-pollution, knowledgebased industries. An improvement in the educational level drives environmental protection technology, improving the environmental quality.

Jung et al. [8], in Korea, applying a Bayesian spatial regression model, found that the total population, the commercial area, the industrial area, the total area, and the gross domestic product per person are factors associated with worse air pollution (nitrogen oxides, sulfur oxides, PM10, and PM2.5). Zhang et al. [33] in Calgary, Canada, using a land-use regression model, found that the main factors that increased the heavy metal concentrations in airborne particulate matter were industrial point sources.

Industrial and commercial zoning, as well as traffic indicators and population density, were also good predictors for most elements. In the case of specifically addressing the pollution by heavy metals in road dust, Alharbi et al. [14] compared the spatial distribution in two metropolitan cities (a typical corridor city and a compact city) of Saudi Arabia. They found that centrality was an important factor for determining the spatial distribution of heavy metals in road dust, which increased in concentration gradually toward the city center.

In Mexico City, research demonstrated that greenhouse gas emissions, caused by commuting, can be reduced by increasing the mix of residential and economic uses, as well as concentrating jobs near employment centers and economic activity corridors [34]. Studies determined that the sources of heavy metals in the urban road dust in Mexico City must be anthropogenic [35]. Therefore, we hypothesized that factors related to industrial land use, mixed land-use, and job density could be related to the concentrations of heavy metals associated with traffic, like Pb, Cu, and Zn. We hypothesized a negative association with the urban vegetation cover assuming a depuration effect.

#### **3. Study Site**

The Mexico City metropolitan area had a population of around 21,000,000 inhabitants in 2015 and was among the four largest urban agglomerations in the world [36]. The metropolitan area is formed by the urban areas of three states: Mexico City, the State of Mexico, and Hidalgo. Mexico City comprises mostly the central and south parts of the metropolitan area. The metropolitan area is located in a valley at 2240 m.a.s.l. The unique topography, with mountains surrounding the metropolis, results in thermal inversions preventing the dispersion of pollutants during the winter season from November to April.

Sierra del Ajusco's mountains in the southwest prevent the passage of the prevailing winds (northeast to southwest direction) and, thus, the dispersion of pollutants [37]. The land use geography in Mexico City is complex, but as a general description, Rodríguez-Salazar et al. [38] stated that the main industrial center, with a high population density, is located in the northern part of the city. The central part includes the historical and business center of the city, with high commercial activity.

The southern area has been dominated by residential and commercial activities. It was in the 1980s with the liberation of the economy that a process of absolute and relative deindustrialization related to the global economy began in the metropolis [39]. Factories were obligated to settle beyond the limits of Mexico City (formerly called the Federal District) and the consolidation of light manufacturing began; overall, the tertiarization of the economy led to commercial and services activities beginning to dominate the economy in the city [40].

#### **4. Materials and Methods**

#### *4.1. Data Collection*

We collected 482 road dust samples associated with 482 sampling points for this study in a semi-grid pattern of approximately 1-km-wide squares across the urban area of Mexico City (Figure 1). The project was executed only within this political jurisdiction given that this was a project funded by the government. Thus, this sampling can be considered systematic, which covered the urban and peri-urban parts of the city. The collection of samples was done during the dry season in April and May (30 days) of 2017. The atmospheric conditions were stable; the temperature was between 15 and 20 ◦C, with winds in a north to south direction and speeds between 4 and 8 km/h [41]. During the sample collection campaign, there were no rains. All samples were collected under the same conditions: in a square meter of area on the pavement, below the sidewalk, the distance from the pedestrian area was between 0 and 1 m. All samples were taken in horizontal streets and without sedimentary traps (holes or potholes) to avoid biases. Because the sampling was systematic, the distance to the traffic lights was not considered. The urban road dust was sampled by brushing it from a 1 m2 area at each point. The dust load in each sample point is defined as the amount of dust (<250 μm) per area of street space—in this case, 1 m2—after the coarse material is removed [42,43]. Particles of less than 250 micrometers are most likely to adhere to hands and therefore be involuntarily ingested [44]. This particle size can be easily obtained in the laboratory using a sieve, which is very useful when analyzing a large number of samples.

The concentrations (mg/kg) of 14 elements were determined via inductively coupled plasma optical spectrometer (ICP-OES), which is a methodology used previously to this end [20,45,46]. However, only the most polluting metals identified in a previous study [47] were considered in the present work. Those elements were Chromium (Cr), Copper (Cu), Nickel (Ni), Lead (Pb), and Zinc (Zn). The concentrations were determined by digesting 0.4 g of each sample with 20 mL of concentrated HNO3, using Teflon PFA beakers, in an ETHOS Easy microwave digestion system (Millestone Inc, Milan, Italy). The temperature was brought to 175 ± 5 ◦C in approximately 5 min and was kept for 4.5 min. After cooling, the digested samples were filtered with Whatman No. 42 paper, transferred into 50 mL flasks, and graduated with water type A (US-EPA method 3051A). Quality controls for the acid digestion method included reagent blanks and sample duplicates. The quality assurance and quality control (QA/QC) results showed no signs of contamination or loss in any of the analyzes. An Agilent Technologies 5100 ICP-OES (US: EPA method 6010C), sourced from Santa Clara, CA, USA, was used to analyze, in triplicate, the digestions and quality controls. A multi-elemental QCS-26R reference certified material was used (high purity brand) to prepare the calibration curve. The radiofrequency power (RF power) was 1.2 kW, the nebulization flow was 0.7 L/min, and the argon plasma flow was 12.0 L/min.

The pollution load index (PLI) was calculated as the geometric average of the Cr, Cu, Ni, Pb, and Zn results divided by their corresponding background value [48]. The contamination factors were obtained by dividing the concentrations of each heavy metal at each sampling point by the background value. We used the world background values for soils [49], which were obtained by determining heavy metal concentration in soils from places with the least anthropic disturbance possible. A PLI value close to 1 indicates that the heavy metal load was close to the naturally occurring level, while a PLI > 1 indicates contamination [48,50]. In Table 1, we can see the descriptive statistics of the dependent variables. The concentration of Pb in one sample was below the detection limit (Pb = 3.75 mg/kg). We took that limit as the Pb content in the sample because the statistical analysis requires numerical variables.

**Figure 1.** The study site and sampling point locations.

Note: 1 Kabata-Pendias (2011); 2 unitless; 3 Amount of dust <250 μm in 1 m2 of the street (g/m2).

Different explanatory variables were measured at each sampling point (Table 2). The population density was measured as inhabitants per hectare at the census tract level using the 2010 census data from the National Institute of Statistics and Geography [51]. The population density can determine the intensity of various socioeconomic activities that worsen air pollution [8]. Job density considered the number of jobs per hectare within the traffic analysis zone (TAZ) according to the 2017 Household Origin-Destination Survey [52]. Jobs were estimated according to the number of trips to work to a certain TAZ.

**Table 2.** Descriptive statistics of the covariates in the analysis. n = 482.

Note: A minimum value of zero is expected when the covariate is not present at any of the road dust sampling points.

For the rest of the covariates, we considered a 300 m ring buffer around each sampling site. Street intersections were identified using the street network shapefiles from the official geostatistical framework [51], and, with the network analysis tool in ArcGis 10.0, we counted all intersections within the buffers. The road surface was estimated using this same layer. Street classification is not consistent between the municipalities of Mexico City; thus, for simplicity, we assumed three types of roads and their dimensions: local streets as 7 m wide, intermediate roads as 15 m wide, and highways as 25 m wide. We propose that this classification produces a conservative estimation of the road surface in each buffer.

Based on the 2014 urban geostatistical framework, we calculated the total area of polygons corresponding to large concrete surfaces, such as civil airfields, malls, markets, aviation tracks, and electrical substations. We called these surfaces "gray areas". The median strip area, which is usually covered with vegetation, was estimated using this same dataset, which has polygons explicitly categorized with this name, road median strip. The distance to the city center was calculated using the Euclidean distance (the straight line that connect two points assuming there are no obstacles in the space) from each sampling point to the historical center of downtown (also called Zócalo-Tenochtitlán).

The distance to the airport also considered the Euclidean distance to the Benito Juarez International Airport. The number of manufacturing units in each buffer was calculated based on those classified by the North American industry classification system in 2018. The number of potentially polluting units considered the economic units related to mining, construction, and pipelines in the National Statistical Directory of Economic Units (Directorio Nacional de Unidades Económicas, DENUE) [53].

We calculated the entropy index as a measure of the land-use mix, considering the relative percentages of different land-use types within an area. The entropy index varied from 0 to 1, with 0 indicating a homogeneous area with only one land-use type, and the mix level increasing as the index increases. Here, *Pj* is the percentage of each land-use type j in the area, and *k* ≥ 2 is the number of land-use types j.

$$ENT = -\left[\sum\_{j=1}^{k} P^j \ln\left(P^j\right)\right] / \ln(k) \tag{1}$$

The entropy index was calculated using information from the publicly available urban data website "Portal de Datos de la Ciudad de México" [54]. Each land-use polygon was georeferenced as a data point, and information about the land use type and the area was provided. Thus, all polygons whose centroid lay within the 300 m buffer were considered

in the estimation. There were 113 categories of land-use descriptions, and two categories were excluded (no zoning—"sin zonificación"—and existing uses—"usos existentes").

Then, the 111 categories were simplified to six general categories: (1) green areas, parks, open spaces, and agricultural areas; (2) residential; (3) office and commercial; (4) industrial; (5) mixed-use; and (6) institutional and public facilities. The official information did not provide concrete and clear definitions of the 111 initial categories; thus, a series of assumptions were made in the collapsing process. For example, land use corresponding to residential and low-scale retail was considered residential. It is very common that, in middle and low-income neighborhoods, small-scale retail coexists with residential uses.

Every original category that includes office and services, was counted in category 3. The mixed-use category included all polygons that were explicitly considered as this on the website as well as those centers of traditional towns and suburbs called "Centros de Barrio". Different land uses, such as residential, commercial, office, and open spaces, converge in these places. The column open area was used for those polygons lacking information about their area. Other corrections were made through a visual inspection on Google Earth for polygons with an important area within the buffer but not initially taken into account when their centroid was not within the buffer.

We calculated the mean normal difference vegetation index (NDVI) in each buffer zone from satellite images (March to May 2017) obtained from Planet Scope for Mexico City to estimate the urban vegetation. A supervised classification was made from the NDVI raster file in the QGIS version 3.4 software, using the "Semi-automatic Classification Plugin" tool. Two classes were determined: (1) vegetation, for the highest NDVI values (>0.6); and (2) no vegetation or the remainder of the urban area. Subsequently, the results of the classification were transformed into a shapefile to obtain the vegetation polygons and to calculate their area.

The vegetation polygons intersecting the buffers were summed up to obtain the total area of vegetation within each buffer. Finally, the total vegetation area was divided by the buffer surface and multiplied by 100 to obtain the percentage of vegetation present in each buffer, referred to here as "vegetation (%)". Another variable related to vegetation is the Euclidean distance from the sampling point to the closest vegetation polygon. Finally, as a measure of the socioeconomic characteristics, the index of marginalization was extracted at the census tract level for each sampling point. This index can have negative and positive values; the highest positive values correspond to the highest levels of marginalization [55].

We considered local variables as those related to characteristics of the immediate urban environment that surrounds the sample point. Examples of these are population density, percentage of vegetation, and the number of potentially polluting units. On the other hand, regional variables were those that characterize a sample with respect to a metropolitan point of reference. Examples are the distance from the city center, and the distance to the airport.

#### *4.2. Spatial Autocorrelation*

The univariate spatial autocorrelation was examined using Moran's *I* statistics for global measurements of spatial dependence [56]. The formula for standard correlation is expanded to incorporate a spatial weight matrix. Thus, its formula is defined as:

$$I = \frac{n}{S\_o} \frac{\sum\_{i=1}^{n} \sum\_{j=1}^{n} w\_{i,j} z\_i z\_j}{\sum\_{i=1}^{n} z\_i^2} \tag{2}$$

where *n* is the number of sample points indexed by *i* and *j*, *Zi* is the deviation of an attribute (in this case, the heavy metal content) for point *i* from its mean, *Wi,j* is the spatial weight between point *i* and *j*, while So is the aggregate of all spatial weights.

We defined neighbors as those spatial units within a specific distance threshold. For this analysis, we tested different thresholds of contiguity (1600, 5000, 10,000, and 15,000 m). All neighbors were weighted equally and then row standardized. This means that it

depends on the number of neighbors to determine the final weight, as the larger the number, the lower the weights.

The range of Moran's I varies with the weights matrix, but it is usually expected to vary from −1 to 1. The sign corresponds to the type of autocorrelation, i.e., positive or negative. Values close to 1 indicate high spatial autocorrelation while values close to zero mean null spatial autocorrelation. The Moran's test for spatial autocorrelation uses the spatial weights matrix and tests the null hypothesis statement of 'no spatial autocorrelation'. In other words, the alternative hypothesis is if the Moran's I is greater than zero. Then, a *p*-value lower than 0.05 means there is strong evidence to reject the randomization null hypothesis in favor of an alternative hypothesis. We used the function "moran.test" of the R Project program to test the spatial autocorrelation. These results were compared with a Moran Monte Carlo permutations test and also using an inverse distance criterion to determine weights for neighbors. These results were relatively consistent with the moran.test function.

#### *4.3. Regression Models*

When two variables are close to a perfect linear combination of one another, it is called collinearity. Thus, when more than two variables are involved, it is called multicollinearity. This represents a problem when applying linear regression models given that it can result in unstable regression estimates with high standard errors. Variance inflation factors (VIF) measure how much the variance of the estimated regression coefficient is inflated by the existence of correlation among the predictor variables. The general rule of thumb is that VIFs exceeding 4 warrant further investigation, while VIFs exceeding 10 signify serious multicollinearity requiring correction. Thus, the variance inflation factor (VIF) was used to test the multicollinearity between the factors.

Ordinary least squares (OLS) regressions were tested for all response variables, i.e., the heavy metals contents. Due to a lack of normality evaluated through the Shapiro test, all covariates and dependent variables were log-transformed using a natural logarithm. Some variables with zero values were transformed using the natural logarithm of 1+x. An OLS model can be described in the form:

$$
\Upsilon = \emptyset \mathcal{X} + \ \varepsilon \tag{3}
$$

where Y is the dependent variable, X is the independent variable, and β its coefficient. If we consider several covariates, then we have a vector of X and β. Finally, ε is the error term. Coefficients of log-log regression models can be interpreted in the following way, given a coefficient in the form "0.X". We expect about X increase in heavy metal content when the covariate increases by 10%.

After that, a spatial diagnostic of the OLS residuals was applied to select the appropriate spatial regression model for each of these dependent variables [57,58]. There are two main sources of spatial dependence: (1) spatial diffusion, which occurs when spatially proximate units are influenced by the behavior of their neighbors. This was modeled via a Lagrange multiplier spatial lag model (LMlag), estimated by the maximum likelihood; and (2) the geographic clustering of covariates, also called attributional dependence. This was modeled via a spatial error model (LMerror), estimated either with the maximum likelihood or with the generalized method of moments.

The Spatial lag model takes the form:

$$\mathbf{Y} = \beta \mathbf{X} + \rho \mathbf{W} \mathbf{y} + \varepsilon \tag{4}$$

Here, to the OLS equation it is added a W term that stands for the spatial weights matrix and the ρ coefficient.

In the case of the Spatial error model, this takes the form:

$$
\varepsilon = \lambda \mathbf{W} \varepsilon + \mathbf{v} \tag{5}
$$

We can see that this model is related to the error term, where W is also the spatial weights matrix, it is included the lambda coefficient and v is an uncorrelated additional error term.

Lagrange multiplier diagnostics for spatial dependence in R use the regression object and the object of neighbors and weights. In the case of the Spatial lag model, we test for a missing spatially lagged dependent variable, in other words, the null hypothesis is that rho = 0. In the case of the Spatial error model, the null hypothesis is that lambda (λ) = 0. The first step was to run the non-robust LMlag and LMerror diagnostic tests, the results of which can lead to three different paths: (1) if none of these diagnostic tests are statistically significant, then the OLS estimates are sufficient to model the dependent variable; (2) if only one of the diagnostics determined the presence of spatial dependence, the corresponding model was estimated; (3) if both diagnostic tests were significant, then both the robust LMlag and the robust LMerror diagnostics were tested, and the model with the largest value was used [58]. All the statistical analyses were done with the R Studio program, version 3.6.1.

#### **5. Results**

The median concentrations of the heavy metals were higher than the global background value in the soils, except for Cr. In the case of Ni, the median concentration is only 6 units above the global background level. Indeed, 91.5% of the samples had a pollution load index (PLI) greater than 1 (median=2) (see above Table 1). We propose that this is an important indication of the anthropogenic origin of the heavy metals found in the road dust from Mexico City. The dust load varied considerably from 5.4 to 173.3 g/m2. As it is very difficult to control aspects related to the deposition of dust in the points of sampling, we decided to work with the heavy metal concentrations instead of the total heavy metal contents as dependent variables.

The mean concentrations of the heavy metals reported here are lower than those reported in a previous study in Mexico City (sampling in 2011) [35]. Even though there are not yet maximum permissible levels in urban road dust, the content of heavy metals in the samples is fortunately still lower than the closest regulation, i.e., the content of heavy metals in soils from residential areas. Therefore, it is important to continue monitoring for long-term fluctuations to avoid an increase in these pollutants and prove the good performance of the environmental policies.

#### *5.1. Spatial Autocorrelation*

Moran's I was significant for Cr only at a vicinity distance of 5000 m; however, the coefficient of autocorrelation was only 0.03. Therefore, a general pattern of clustering was not expected (Table 3). Cu had a significant Moran's I at all vicinity distances, but, again, the coefficient was very small. Moran's I for Ni became significant at a distance of 10,000 m and was even more significant at 15,000 m; however, the coefficient was only 0.01.

Contrary to Ni, Moran's I for Pb was significant at short distances (1600 and 5000 m), but, again, the coefficients were smaller than 0.1. Zn had a significant Moran's I at all distances, except at 5000 m, with the coefficient smaller than 0.1. Moran's I for the PLI was significant at all distances, and it was greater than 0.1 at 1600 m; hence, a general pattern of clustering could be expected at a short vicinity distance. The dust load had a significant Moran's I at all distances; thus, the coefficients (and consequently the autocorrelation) decreased as the distance increased.

As the global Moran's I was very close to 0 for all heavy metals, indicating low levels of positive spatial autocorrelation, it was not necessary to explore the local version of this index to identify any spatial clustering pattern. This is an initial sign that the local aspects are more relevant than any regional process in determining the concentrations of these metals.

**Table 3.** The global Moran's I and test of statistical significance at different vicinity distances (1600, 5000, 10,000, and 15,000 m).

\* Significance at 95% confidence, \*\* 99% confidence, and \*\*\* 99.9% confidence.

In Table 4, we can see the *p*-values of the diagnostic tests of the OLS residuals. All non-robust tests were non-significant. In the case of the robust versions, for Cu, Ni, Zn, the PLI, and the dust load, the tests were also non-significant, which indicates that OLS is a suitable modeling approach. For Pb, the spatial error model was significant (alpha at 5%); thus, for this metal, the results of the spatial error regression model were analyzed.

**Table 4.** *p*-values of the diagnosis of the ordinary least squares (OLS) regression residuals.

\* Significance at 95% confidence.

#### *5.2. Factors Influencing the Heavy Metal Concentrations*

The VIF indicators were below 4.3 for our vector of covariates, which indicates a low risk of multicollinearity that could bias the coefficient estimations. Overall, there were few significant relationships between the covariates and the heavy metal concentrations, including the road dust load (Table 5). Population density had a null association with all of the heavy metals, which indicates that the number of people in the surroundings of the sample point was not relevant to explain the presence of our dependent variables.

#### **Table 5.** Results of the ordinary least squares regressions.

**Table 5.** *Cont*.

beta is the slope; *p* represents the *p*-value; **.** Significance at 90% confidence, \* 95% confidence, \*\* 99% confidence, and \*\*\* 99.9% confidence.

Job density had a weak positive association (significance level of 90%) with Cu. However, there was not any significant relationship with the rest of the metals. Our initial expectation was that in places with high job density, the heavy metal concentrations would be high due to an increased number of trips to work and, therefore, increased levels of polluting emissions. Thus, the association found between job density and Cu supports our initial hypothesis since the emission of this metal from vehicles has been associated with tire wear and brake abrasion [29] With the dust load, job density had a significant inverse association (significance level of 99%). We could expect about a 1.6% increase in the dust load when the job density decreased by 10%. This could be explained if we consider that employment centers in Mexico City are related to tertiary types (offices and commerce) that are not necessarily highly polluting activities. These workplaces tend to be better cared for and cleaner than lower-class areas.

The street intersections variable was not significant with any metal. The initial expectation was that this variable could represent the emissions of heavy metals due to car braking, with the higher the number of street intersections representing higher braking frequency. However, the braking emissions are likely not large enough to be detected through street intersections.

The road surface had a weak positive relationship with Zn (significance level of 90%). The emissions of Zn from vehicles have been associated with the combustion of lubricating oil [30], tire wear [25], and diesel exhaust emissions [27]. Therefore, this result supports the expectation that the road surface is a suitable proxy variable for traffic flow as a determinant of Zn in the road dust. On the other hand, there was a significant inverse association between the road surface and the dust load (significance level of 95%). We could expect about a 3% increase in the dust load when the road surface decreased by 10%. These surfaces are likely maintained and cleaned as brigades of cleaning workers sweep the larger roads.

The distance to the airport had a positive but weak relationship with Ni (significance level of 90%). Higher concentrations of this metal were found further away from the airport; therefore, the airport might not be an important source of this metal. An inverse weak association (significance level of 90%) was found for Pb and the distance to the airport in the spatial error model (Table 6). The coefficient tells us that we could expect about

a 2% increase in the Pb content when the distance to the airport decreased by 10%. Our hypothesis is that tire wear in the aircraft take-off and landing could emit dust particles containing Pb. In the case of the distance to the city center, there was a null association with the other heavy metals.

**Table 6.** Spatial error model results for Pb.

Note: AIC (Akaike Information Criterion), lower AIC value suggest a better fit.

Manufacturing units had a positive significant association with Cu with an alpha level of 5%. We could expect about a 1% increase in Cu when manufacturing units increased by 10%. It is very likely that behind this variable there are a variety of chemical processes in the manufacturing; therefore, there could be several sources of Cu from these processes as well as traffic-related emissions. The relationship with PLI was also positive but less significant (significance level of 90%). Potentially polluting units failed to show any association with the heavy metals. This means that possible major pollutant units were not properly identified with our variable. Thus, other alternatives must be tackled in future research such as the use of other classification schemes to differentiate potentially polluting units from the whole census of economic units. Only in the case of the dust load was there a positive significant association at the 90% significance level. Thus, these units are associated with an increase in dust, but are not associated with an increase in the heavy metal content.

The gray area variable also failed to detect any association with the heavy metals. Our initial expectation was that this variable could be related to heavy metals due to the polluting emissions of activities related to large concrete surfaces (markets, aviation tracks, and electrical substations). The null association of the gray areas could be due to the huge diversity of activities considered in the covariate. The entropy index had a positive relationship at the alpha level of 5% with Ni. We could expect about a 4% increase in Ni when the entropy index increased by 10%. A high entropy index means a similar proportion of the six land uses considered; thus, these places could have a variety of potential sources of Ni together, such as sites of fuel combustion.

There was also a weak positive relation (alpha level of 10%) of the entropy index with the dust load. The difficulty in obtaining a clear relationship between the land-use covariates and heavy metal contents in urban dust in México City could be related to the tertiary-oriented economy. We assume that mobile sources of traffic emissions would be more relevant but also more difficult to trace. In the case of air pollution, industrial point emissions have been identified as the source of pollution, such as in the studies of Zhang et al. [33] in Alberta, Canada, and Jung et al. [8] in Korea, where commercial and industrial areas were associated with increased particulate matter pollution.

The percentage of vegetation in the buffer and the distance to the closest vegetation spot failed to show any association with the heavy metal content. In the case of the former, there was a significant negative association (significance level of 99%) with the dust load, which indicates that vegetated areas tended to have less dust but not necessarily a higher heavy metal content. The median strip area had a weak (significance level of 90%) but consistent positive relationship with Cr, Cu, Ni, Pb, and PLI. This led us to hypothesize that these areas may act as sinks of pollution in the roads, acting as places of heavy metal accumulation. For example, during the sweeping of the road, the dust may be dumped there. The positive relationship between the median strip area and Pb remained for the spatial error model at the alpha level of 10% (Table 6).

Initially, we considered the median strip area part of the vegetation area because it frequently has a vegetation cover. After testing the initial models, the previous vegetation area covaried positively with Pb and Cr. That result was unexpected, and we therefore decided to separate the components of the vegetation covariation and, finally, identified that only the median strip area was positively related to Cr, Pb, Zn, and the PLI. It will be important to untangle the relationship between heavy metals and the median strip area to define the best way to manage such areas. It is important to clarify that covariates of urban form do not necessarily represent specific detailed sources of heavy metals. They represent general characteristics (places) of the urban environment where these pollutants could be being emitted or places of concentration (sinks of pollution (from other mobile or fixed sources of pollution)).

Finally, there was no differential exposition to heavy metals according to the socioeconomic status of households, as we found a null association with the marginalization index. The good news is that road dust is not an important source of exposure to Pb for those in low-income areas, as they are at higher risk of developing health problems [59]. However, attention should be paid to keep the streets clean, because marginalized areas tended to be dustier than middle-income and affluent areas.

The study of the relationships between the urban form and heavy metals is incipient; further investigation is needed to develop a conceptual framework that guides the development of more robust models. The present study is an exploratory analysis in this sense, and we tested the group of covariates that we considered the most relevant. Although some of these variables did not show any association, the inclusion was supported by a deep reflection of what we considered could be the route of heavy metals in the urban environment.

The study of temporal variation in the short term is also important to design better sampling processes that minimize and control the effects of potential confounding factors. For example, natural cleaning mechanisms, such as rain and air currents, and the different practices of street sweeping. From a methodological point of view, we propose to test smaller buffers, which might be at 100 or 150 m around the sampling points, since the characteristics of the immediate surroundings are very important. A better characterization of the urban form might also benefit from more consistent and refined publicly available data regarding the urban environment. The characterization of the local urban environment is key to devising the sampling strategy. Further research lines also include the application of other modeling approaches and inter-city comparisons to test if the phenomena studied here present similar behavior in cities of different sizes and economic conditions. Furthermore, we suggest the inclusion of covariates related to atmospheric processes as well as covariates with more detailed georeferenced data about emission sources.

#### **6. Conclusions**

According to the global Moran's I, there were low levels of positive spatial autocorrelation in all the heavy metals analyzed. We interpret this as an indication of the greater relevance of the local aspects over regional processes as determinants of the heavy metal

content in urban road dust. Any mapping exercise based on statistical interpolation would not be reliable. A lack of major unique sources of these pollutants could also cause a lack of spatial autocorrelation. In our regression exercise, the most striking finding was that the median strip area in urban roads had a weak but consistent positive relationship with Cr, Cu, Ni, Pb, and the Pollution Load Index. Other significant positive relationships were found for Cu with the manufacturing units, and Ni with the entropy index. More disaggregated indicators would be relevant to unveil the nature of these associations.

Certain variables failed to show any association with the heavy metals, such as the population density, street intersections, distance to the city center, gray area, distance to vegetation, and marginalized areas. Other variables that failed to be associated with heavy metals but showed an association with the dust load were the potentially polluting units (significance level of 90%) and vegetation (significance level of 99%), positive in the former and negative in the latter. The job density (significance level of 99%) and road surface (significance level of 95%) significantly reduced the dust load as well. For Pb, the spatial error model showed the correct specification, unlike the other metals where OLS was found to be appropriate. In this model, distance to the airport had a weak (significance level of 90%) and an inverse association with Pb. This presents an important suggestion to consider this place as a potential source of this metal in urban dust.

Thus, we can conclude that some features of the urban form, as described above, are important drivers of heavy metal pollution in the road dust. A better understanding of how road dust pollution is associated with the urban form will be important to design measures that mitigate the exposure of people to those pollutants.

**Author Contributions:** A.A.: data cleaning, calculations, statistical analysis, wrote the manuscript. D.B.-H.: original idea, data cleaning, calculations, statistical analysis, directed the research, trained the student, and wrote the final version of the manuscript. F.B.: project coordinator, coordinated the chemical analyzes, proposed the idea, and revised the previous texts. A.G.: project coordinator, reviewed the final version of the manuscript. R.C.: collected the urban dust samples and prepared them for analysis. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by grant number 283135 SEP-CONACYT.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data about heavy metal content in the sampling points presented in this study are available on request from the corresponding author. This data are not publicly available due to belong to the funding agency. The rest of the data comes from publicly available datasets. This data can be found here: https://www.inegi.org.mx/programas/ccpv/2010/; http: //en.www.inegi.org.mx/programas/eod/2017/default.html#Microdata (accessed 28 October 2020).

**Acknowledgments:** We are grateful to Gutiérrez-Ruiz, M.E., Ceniceros-Gómez, A.E., López-Santiago, N.R. for support in the chemical analysis of the dust samples. We would like to thank the four anonymous reviewers for their valuable feedback in the review process.

**Conflicts of Interest:** We declare no conflicts of interest.

#### **References**


**Possible consequences**

• Output of samples with wrong clinical data ! cause error results

• Lack of time

*Risk Management in Biobanks*

**Possible consequences**

• Longer period to find samples

*DOI: http://dx.doi.org/10.5772/intechopen.91463*

• Waste of biobank resources

**Possible coping strategies**

• "Four-eye principle"

**Possible reasons**

• Lack of time

• No well-trained staff

**Possible consequences**

**Possible coping strategies**

• Precise working

**91**

• Samples are not usable for projects

• Regular process monitoring

• Further development of concepts

• Expanding of personnel resources

*<IP_ADDRESS> Improper handling of samples in processing*

data

• High error rate of systems for storage of samples or for input of sample-related

• Staff training according to Standard Operation Procedures of the biobank

• Cryosamples may defrost (long handling time, transport, long shipping time)

• Waste of biobank resources (storage capacity, liquid nitrogen, etc.)

• Staff training according to Standard Operation Procedures of the biobank

• Valuable samples get lost and cannot be used for projects

• Precise working while handling with samples

• Automated identification and process of samples

• Tissue could get damaged during the freezing process

• Image loss


**5. Conclusion**

The presence of antibiotics in aquatic ecosystems, although considered less than other contaminants, can alter the microbiota of these environments and favor the emergence of multi-resistant bacterial populations. Considering the importance of water bodies for human subsistence and due to the risk of bacterial spread, strategies for controlling the disposal of these contaminants must be evaluated, as well as the other agents that impact aquatic environments.


**4.3. Optimization of a differential amplifier**

For the analysis of Simulated Annealing options and the influence over the automatic sizing procedure of analog basic blocks, we will explore different configurations of temperature schedule, state generation function and reannealing for global optimization and further local optimization. Due to the random nature of some parameters of SA, an statistic analysis is needed to understand the search behavior. We performed 1000 optimization runs for each temperature schedule function described before: Boltzman, Exponential and Fast. The state generation function was kept fixed as *gBoltz*(*X*) (Eq. 2). Each execution started with a different seed for the random number generator function. The same parameters were used for the three functions, including the same random number vector for a fair comparison. A MATLAB script was implemented and the native SA method (simulannealbnd) was used as the main bound constrained optimization function.

Fig. 6 shows a graph comparing the 3 temperature schedules, considering only the optimum solutions obtained in relation to the optimization time. It is possible to notice the very attractive results for Boltzman, which achieved 400 optimum solutions (over a set of 1000 executions) in about 25 seconds of execution time. After this time, the number of optimal solutions does not grow considerably, saturating in 430 at 37 seconds. The same saturation behavior happens with Exponential and Fast temperature schedules, but with a very lower

Simulated Annealing to Improve Analog Integrated Circuit Design: Trade-Off s and Implementation Issues 273

Optimal Results versus Execution Time

0 5 10 15 20 25 30 35 40

Time (s)

**Figure 6.** Optimal results versus execution time for the global optimization of a differential amplifier,

In order to improve the results obtained by global optimization with Simulated Annealing, we apply a local optimization algorithm over the previous set of solutions generated by SA with the three temperature schedule functions. We choose the interior point algorithm [18], which is suitable for linear and non-linear convex design spaces. We suppose that the design space region near the solution provided by the global optimization and evolving the global optimum solution is convex and can be explored by this method. The algorithm was implemented by using the MATLAB native function fmincon. The results can be seen in Tab. 4 . It is clear the improvement obtained by the local optimization. The mean final cost of the 1000 executions for the three temperature schedules are close to the known global optimum of −1.960306. The total execution time (including global followed by local execution times) was increased by

number of optimal solutions and at early execution time.

TBoltz TExp TFast

0

considering 3 different temperature schedule functions.

about 50%, but it is still in a reasonable value, near 20 seconds.

*4.3.2. Global followed by local optimization*

50

100

150

200

250

Optimal Results

300

350

400

450

### *4.3.1. Global optimization*

Table 2 shows the mean of the optimal cost function found after 1000 executions of the optimization procedure for each temperature schedule function. The Boltzman schedule achieved the best values, with a mean final cost *f* ∗ *c* of −1.960306, right near the optimal global solution of −1.9623. It means that most of the solutions provided by the procedure with Boltzman are near the global optimum. Exponential and Fast temperature schedules demonstrate worst results in terms of cost. Boltzman result was obtained at expense of a higher execution time and total number of iterators.

The free variables *W* and *L* found by the three temperature schedule functions are shown in Tab. 3. Again, Boltzman demonstrates the best results, with the mean values near the optimal solution. Fast schedule presents the worst results in this configuration.

**Table 3.** Mean *W* and *L* values achieved by global optimization procedure of the differential amplifier after 1000 runs for each different temperature schedule function.

Fig. 6 shows a graph comparing the 3 temperature schedules, considering only the optimum solutions obtained in relation to the optimization time. It is possible to notice the very attractive results for Boltzman, which achieved 400 optimum solutions (over a set of 1000 executions) in about 25 seconds of execution time. After this time, the number of optimal solutions does not grow considerably, saturating in 430 at 37 seconds. The same saturation behavior happens with Exponential and Fast temperature schedules, but with a very lower number of optimal solutions and at early execution time.

**Figure 6.** Optimal results versus execution time for the global optimization of a differential amplifier, considering 3 different temperature schedule functions.

#### *4.3.2. Global followed by local optimization*

12 Will-be-set-by-IN-TECH

For the analysis of Simulated Annealing options and the influence over the automatic sizing procedure of analog basic blocks, we will explore different configurations of temperature schedule, state generation function and reannealing for global optimization and further local optimization. Due to the random nature of some parameters of SA, an statistic analysis is needed to understand the search behavior. We performed 1000 optimization runs for each temperature schedule function described before: Boltzman, Exponential and Fast. The state generation function was kept fixed as *gBoltz*(*X*) (Eq. 2). Each execution started with a different seed for the random number generator function. The same parameters were used for the three functions, including the same random number vector for a fair comparison. A MATLAB script was implemented and the native SA method (simulannealbnd) was used as the main bound

Table 2 shows the mean of the optimal cost function found after 1000 executions of the optimization procedure for each temperature schedule function. The Boltzman schedule

global solution of −1.9623. It means that most of the solutions provided by the procedure with Boltzman are near the global optimum. Exponential and Fast temperature schedules demonstrate worst results in terms of cost. Boltzman result was obtained at expense of a

> Boltzman -1.960306 16.32 1777.44 Exponential -1.834720 9.57 1043.89 Fast -1.579269 12.99 1416.36

**Table 2.** Mean values of differential amplifier global optimization procedure for different temperature

The free variables *W* and *L* found by the three temperature schedule functions are shown in Tab. 3. Again, Boltzman demonstrates the best results, with the mean values near the optimal

Temperature schedule *W* (*μm*) *L* (*μm*)

Boltzman 8.07 20.57 Exponential 11.47 23.00 Fast 34.46 26.32

Optimum value 8.00 20.00

**Table 3.** Mean *W* and *L* values achieved by global optimization procedure of the differential amplifier

solution. Fast schedule presents the worst results in this configuration.

after 1000 runs for each different temperature schedule function.

*c* of −1.960306, right near the optimal

*c* Execution time (*s*) Iterations

**4.3. Optimization of a differential amplifier**

achieved the best values, with a mean final cost *f* ∗

higher execution time and total number of iterators.

Temperature schedule *f* ∗

constrained optimization function.

schedule functions after 1000 executions.

*4.3.1. Global optimization*

In order to improve the results obtained by global optimization with Simulated Annealing, we apply a local optimization algorithm over the previous set of solutions generated by SA with the three temperature schedule functions. We choose the interior point algorithm [18], which is suitable for linear and non-linear convex design spaces. We suppose that the design space region near the solution provided by the global optimization and evolving the global optimum solution is convex and can be explored by this method. The algorithm was implemented by using the MATLAB native function fmincon. The results can be seen in Tab. 4 . It is clear the improvement obtained by the local optimization. The mean final cost of the 1000 executions for the three temperature schedules are close to the known global optimum of −1.960306. The total execution time (including global followed by local execution times) was increased by about 50%, but it is still in a reasonable value, near 20 seconds.

In terms of the number of optimal solutions found over the 1000 executions, the local search also demonstrate an improvement. Fig. 7 shows the results obtained, in which we can see that, for Boltzman schedule, almost 90% of the final solutions are optimal, an improvement of more than 50% over the global optimization. The same occurs for the other temperature

Simulated Annealing to Improve Analog Integrated Circuit Design: Trade-Off s and Implementation Issues 275

We can observe the improvement in the number of optimal solutions with local search in Fig. 8, which presents the frequency histogram of the resulting final cost provided by global search (Fig. 8(a)) and global search followed by local search (Fig. 8(b)) for the 3 different temperature schedules. Besides the increase in the number of optimal solutions found, the inclusion of local search after global search also approximated the remaining non-optimal solutions in the

For the analysis of the influence of reannealing in the optimization process, we performed some experiments executing Simulated Annealing with reannealing intervals of 200, 450, 700 and 950 iterations. Again, 1000 executions were done in order to guarantee a statistical

Fig. 9 shows the relation between the number of optimal solutions found by Boltzman schedule function versus the execution time for reannealing intervals from 200 to infinite (*i.e.*, no reannealing). Reannealing interval affects the number of optimal solutions in this case. As the interval decrease, the number of optimal solutions decrease too. The best configuration is with no reannealing, demonstrating that it is not interesting to use reannealing with *TBoltz*. It happens because the temperature decreases slowly at the beginning of the annealing process. With the reannealing, the temperature increases for higher values before the search in the

When the temperature schedule function is modified to Exponential, the behavior is opposite. As the reannealing interval decreases, more optimal solutions are found. Fig. 10 shows the relation between optimal solutions found and execution time for this temperature schedule

The same occurs for the Fast temperature schedule function, shown in Fig. 11. As the reannealing interval diminishes, the number of optimal solutions increases. This behavior is maintained for ever small intervals. A high improvement in the number of optimal solutions is obtained for reannealing intervals in the order of 100 iterations, as shown in Fig. 12. As the temperature decreases very fast, the reannealing allows to avoid local minima. Thus, it increases the chances of finding the correct path to the optimum solution. Also, we can observe the existence of an optimum value for the reannealing interval which returns the

The variation of the state generation function is also a factor that can change the convergence of the Simulated Annealing algorithm. Two of these functions are analyzed here: Boltzman and Fast. The combinations of temperature schedule function and state generation function produce distinct results for the synthesis of the differential amplifier. Fig. 13 shows

analysis for the three temperature schedule functions described before.

design space reaches a path trending to the optimal solution.

schedules.

configuration.

direction to the best known value.

*4.3.3. Global optimization with reannealing*

maximum number of optimal solutions.

*4.3.4. Analysis of state generation function*

**Table 4.** Mean values of differential amplifier after local optimization over the results obtained by global optimization shown in Tab. 2.

The mean values found for the free variables after the local search are shown in Tab. 5 . Comparing to the previous values provided by the global optimization, it is possible to note the great improvement of the Exponential temperature schedule, whose mean *W* and *L* approached very near to the global optimum.

**Table 5.** Mean *W* and *L* values achieved by local optimization procedure of the differential amplifier over the results obtained by global optimization shown in tab. 3.

**Figure 7.** Optimal results versus execution time for the global optimization of a differential amplifier, considering 3 different temperature schedule functions - global and local.

In terms of the number of optimal solutions found over the 1000 executions, the local search also demonstrate an improvement. Fig. 7 shows the results obtained, in which we can see that, for Boltzman schedule, almost 90% of the final solutions are optimal, an improvement of more than 50% over the global optimization. The same occurs for the other temperature schedules.

We can observe the improvement in the number of optimal solutions with local search in Fig. 8, which presents the frequency histogram of the resulting final cost provided by global search (Fig. 8(a)) and global search followed by local search (Fig. 8(b)) for the 3 different temperature schedules. Besides the increase in the number of optimal solutions found, the inclusion of local search after global search also approximated the remaining non-optimal solutions in the direction to the best known value.


**Bioactive Polysaccharides of American Ginseng**  *Panax quinquefolius* **L. in Modulation of Immune Function: Phytochemical and Pharmacological Characterization**

Edmund M. K. Lui, Chike G. Azike, José A. Guerrero-Analco, Ahmad A. Romeh, Hua Pei, Sherif J. Kaldas, John T. Arnason and Paul A. Charpentier

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/50741

**1. Introduction**

Ginseng has a long history of use as a traditional medicine; and it is one of the top selling medicinal herbs in the world. It is a multi-action herb with a wide range of pharmacological effects on the central nervous system, cardiovascular system and endocrine secretion, and the reproductive and immune systems [1]. Ginseng is a deciduous, perennial plant of the Araliaceae family. There are two major species of ginseng: *Panax ginseng and Panax quinquefolius*; and the roots are primarily used for medicinal benefits. Ginseng's wide range of pharmacological activities is believed to be due to the presence of a host of bioactive compounds. The primary ones are the ginsenosides, which are steroidal saponins conjugated to different sugar moieties and polysaccharides (PS) which account for 10-20% by weight of ginseng.

Polysaccharide components of ginseng have received much attention recently because of the emergence of different biological activities, such as immunomodulatory, antibacterial, antimutagenic, radioprotective, anti-oxidative, anti-ulcer, antidepressant, anti-septicaemic and anti-inflammatory activities [2]. Specifically, the polysaccharide fraction of ginseng has been shown to have immunomodulatory effects in both preclinical and clinical studies [3-6], although they are poorly characterized.

Several polysaccharides have been identified in *P. ginseng* and *P. notoginseng* but these compounds, including arabinogalactan, pectins, and acidic polysaccharides, have been

© 2012 Lui et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

rarely studied in the North American species. They are made up of a complex chain of monosaccharides rich in L-arabinose, D-galactose, L-rhamnose, D-galacturonic acid, Dglucuronic acid and D-galactosyl residues [7]. The actual structural characteristics and the heterogeneity of PS components are poorly understood due to a lack of methodologies for separation as well as quantitative and qualitative analysis.

Most studies have focused on Asian ginseng PS and mostly *in vitro* experimental models. In this chapter, we will focus on *Panax quinquefolius* (American ginseng). The use of gel permeation chromatography (GPC) with multiple detectors has provided enhanced resolution for phytochemical analysis. And we have used both *in vivo* and *in vitro* models to evaluate its immunomodulatory activity.


**5. Therapy**

Therapeutic approach to the tachycardia-induced cardiomyopathy includes two steps: 1. tachyarrhythmia correction as it represents causal therapeutic intervention and 2. heart failure treatment.

Due to the potential reversibility of hemodynamic and structural changes in tachycardiainduced cardiomyopathy, all efforts should be made to achieve **heart rate correction or appropriate rate control.** Rhythm or rate control may be achieved using both pharmacological and non-pharmacological tools. Depending on the type of arrhythmia and presence/absence of concomitant structural heart disease, various antiarrhytmic drugs may be used to terminate the arrhythmia or to achieve adequate rate control. Especially, betablockers and class III antiarrhythmics play an irreplaceable role regarding this treatment. It is very important to avoid drugs with higher pro-arrhythmic effect (e.g. flecainide) in the presence of systolic dysfunction or drugs that may contribute to further progression of systolic dysfunction (e.g. disopyramide). Most arrhythmias that lead to tachycardia-induced cardiomyopathy are currently treatable using catheterization ablation, success rate of which reaches 60–90% depending on the type of arrhythmia. This therapeutic approach should be therefore consid‐ ered as a first-line treatment in the absence of contraindication.

In atrial fibrillation, rate and rhythm control strategy have been shown to be comparable with respect to quality of life, mortality or stroke rate [64, 69]. The decision to favor rhythm control over rate control should thus be made on an individual basis, and discussed with the patient [70]. In case rate control strategy is chosen, repeated long-term ECG monitoring is instrumental to decide whether the selected treatment is appropriate and ensures acceptable rate control (strict rate control requires 60–80 bpm at rest and 90–115 bpm at moderate exercise; lenient rate control requests resting rate < 110 bpm). Atrial arrhythmias are often refractory to antiarrhythmic drugs and an acceptable rate control may be then achieved only with higher doses of AV nodal blocking agent. In such cases, catheter ablation is an option. By other supraventricular tachyarrhythmias, which lead to tachycardia-induced cardiomyopathy, restoration of sinus rhythm is usually preferred. Rhythm correction may be achieved through either pharmacological or electrical cardioversion or (preferably) via catheter ablation of the arrhythmia in these patients.

In rare cases, failing to restore sinus rhythm (even using catheter ablation) and to achieve adequate ventricular control, an ablation of AV node with insertion of a permanent pacemaker may be considered. Because of the present ventricular dysfunction prior to pacemaker insertion, biventricular systems are usually favored [71].

**Treatment of heart failure** symptoms due to tachycardia-induced cardiomyopathy includes standard regimen and drug spectrum as in heart failure of other origin, i.e. ACE inhibitors, beta-blockers, angiotensin-receptor blockers, diuretics and digoxin.


**2. Numerical Formulation**

The 3D numerical analysis of multi degrees of freedom electromechanical devices represents a challenging, still open problem, which poses several critical issues. Several commercial codes, typically based on the Finite Elements Method (FEM), provide packages for coupled electro-mechanical analysis, but they seem to be not very effective with multiple degrees of freedom and with sliding contacts. Moving conductors and sliding contacts usually require remeshing of the domains with consequent increase of computational times and potential numerical instabilities.

Integral Formulations (e.g., the Method of Moments) seem to work quite well with moving domains since they require the discretization of the active regions only (namely conductors and ferromagnetic materials), so avoiding the problem of coupling meshes with different speeds. Integral formulations implicitly enforce the far field boundary conditions, and are able to produce accurate results by using coarse discretization (when compared with those required by FEM).

The numerical investigation of the complete launch system has been performed by the research code EN4EM. It is based on an integral formulation, and it is under continuous development by the authors for investigating electromechanical systems [27–34].

EN4EM applied to the launch package is able to simulate the whole system considering the characteristics of the two devices and taking into account their "strong interaction". Figure 1 shows the steps of a conceptual flow chart of the numerical formulation: discretization in elementary volumes, writing and integration of Ohm's law, arrangement in an electric network and writing of the governing electro-mechanical equations. The usual notations for the electromagnetic quantities in Figure 1 are adopted according to the Table 1.

With reference to the inset in the bottom right of Figure 1, Ohm's law is written in the conductive elementary volumes where a uniform current distribution is assumed (row #1 of the inset). The additive properties of the integrals with respect to the integration domain allows expressing the fields and potentials in the *k*-th conductive elementary volume as a summation of contribution due to the currents in the other volumes (row #2 of the inset). Finally integration on the *k*-th elementary volume leads to an equation that can be seen as the voltage-current relationship of a branch that is a series connection of a resistor, an inductor coupled with other inductors, and a voltage generator controlled by the currents in other elementary volumes (row #3). The equivalent network of the device is built by connecting the terminals of the branches so obtained. In case of a multi-device system, the code is able to model separately the different devices by their equivalent networks. Then, all these networks are connected together according to the relative positions of the corresponding elementary volumes and to the presence of electrical contacts between them. The described procedure has been applied to model the launcher and the compulsator, obtaining a whole model composed of thousands of branches.

**Figure 1.** Conceptual flow chart of the numerical formulation. (Reproduced with permission from [30], IEEE, 2017).

**Table 1.** Notations.

Mesh analysis yields to the governing equations written in matrix form:

$$\mathbf{L}\left(\mathbf{C}(t)\right)\frac{d\dot{\mathbf{i}}}{dt} + \left(\mathbf{R} + \mathbf{K}\{\mathbf{C}(t), \dot{\mathbf{C}}(t)\}\right)\dot{\mathbf{i}} = \mathbf{e}(t) \tag{1}$$

The values of the elements of the matrices in (1) are function of the system configuration *C*(*t*) and its derivative . *C*(*t*) (i.e., the relative positions and velocities of the elementary volumes used to discretize the devices respectively). Coupling between electrical and mechanical equations is achieved by the terms *vk*(*t*) × *Bk*(*t*) that, once integrated on the elementary volumes, are assembled to form the matrix of the motional terms *K*, and by the terms *jk*(*t*) × *Bk*(*t*) which are integrated to provide the forces and the torques on the moving parts of the device. The mechanical equation for the armature of the launcher is:

$$m\ddot{\mathbf{x}}\_{\rm G} = F(\mathbf{i}, \mathcal{C}(\mathbf{t})) \tag{2}$$

while the equation for the compulsator are:

$$\mathbf{I}\_{\mathbf{G}}\dot{\boldsymbol{\omega}} + \hat{\boldsymbol{\omega}}\mathbf{I}\_{\mathbf{G}}\boldsymbol{\omega} = \mathbf{M}\_{\mathbf{G}}(\mathbf{i}, \mathbf{C}(t)) \tag{3}$$

In the above equations *F* represents the resultant force on the launcher armature and *m* is its mass, *MG* is the resultant torque on the rotor of the compulsator and *IG* is its inertia tensor. The coupled

differential equations for electrical and mechanical equilibrium are time varying, and the resulting system is nonlinear; integration is carried out as described in [27,28].

It is worth to mention that the currents in the branches of the equivalent network are not fictitious currents. The current in a branch of the equivalent network is in correspondence with one component of the current density of an elementary volumes as shown by the insets in the upper right and in the lower left corners in Figure 1. By the above described equivalent network the distribution of all the relevant electromechanical quantities can be evaluated everywhere in the whole system. In particular, the expression of the force by the term *jk*(*t*) × *Bk*(*t*) allows to evaluate its distribution in each elementary volumes and to determine the contribution to the total dynamical action in materials that are usually heavily stressed when used in EML technology.

Simultaneous analysis of interacting devices simply requires building a bigger equivalent network constituted by the properly connected equivalent networks of the components. This implements a "strong interaction" between devices for which a "strong coupled" analysis is performed.

If the devices can be assumed magnetically uncoupled (i.e., leakage magnetic fluxes from a device that links the others are negligible) independent networks are built, linked together at the common terminals and simultaneously solved. It is worth to remark that the topology of the resultant network is the same than that of the more general case of magnetically coupled devices. The only difference lies in the filling of the inductance matrix *L* and of the motional terms matrix *K*, which are more densely populated in the latter case.

Coupling of the equivalent network so far described with external circuits is straightforward and this will be performed in the next section to investigate the "weak interaction" between the rail launcher and the compulsator.

The presence of sliding contacts has been taken into account by introducing an auxiliary network [20]. Considering that the motion in the rail launcher is characterized by a straight trajectory, all the possible contacts between elementary volumes on the rails and on the armature are known a priori. A new branch is set for each couple of volumes (one on the inner parts of the rails and the other on the faced outer surfaces of the armature) that can have a contact during the motion.

Figure 2 shows an example of a set of auxiliary branches that take into account the sliding contacts. The circuit elements in the auxiliary branches are function of the shared portion of the faces (if any) between the two volumes. When the shared portion is zero, the auxiliary branch opens. The proposed model of the sliding contacts is coherent with the adopted formulation based on an equivalent network of the entire system.

**Figure 2.** Example of the auxiliary network used for taking into account the presence of sliding contacts. (**a**) All the branches are shown. (**b**) Only the branches that are not open circuits are evidenced.

Finally the introduction of the equivalent network allows the use of advanced analysis techniques for the evaluation of the sensitivity of the response with respect to parameter variation [35]. This represents an important tool in gradient based optimization processes.

EN4EM was validated by comparison with results produced by other numerical codes and with experimental data [5,6,27,28,31,32].

#### **3. Weak Interaction Analysis**

In this section the analysis based on the "weak interaction" between rail launcher and compulsator will be critically reviewed and the difficulties of the equivalent circuit extraction will be discussed.

Figure 3 shows the active parts of a single-phase, two-pole compulsator with selective passive compensation provided by a discontinuous conductive shield. The inner part of the device consists of two stationary field coils which produce a magnetic flux density distribution whose axis is in the vertical direction (Figure 3b). The two series connected armature windings are located on the rotor which is the outer part of the machine. Figure 3c shows the stationary compensating shields that are in the central part of the machine. Figure 3a shows a 3D view of the device. A more detailed description is reported in [29].

**Figure 3.** An example of the modeling of a compulsator by EN4EM. Snapshot of (**a**) the 3D view; (**b**) cross section of the machine; (**c**) discretization of the compensating shield. (Reproduced with permission from [29], IEEE, 2017).

When using a compulsator to feed a rail launcher, its rotor has to be preliminarily driven to a proper angular speed at no load conditions; part of the stored kinetic energy of the rotor will be delivered to the railgun armature. At the firing instant, the armature windings of the compulsator are connected to the rails of the launcher. During the launch, the rail armature accelerates and at the same time, the rotating part of the compulsator decreases its angular speed. The rates of change of the speeds of both the moving parts (and consequently their positions) are not known a-priori and substantially depend on the delivered current.

Since the simultaneous 3D analysis of the two electromechanical devices can be very time consuming, a common practice is to substitute one or both the device with equivalent circuits. This procedure may lead to significant error in the current flowing in the devices because of the difficulties in the determination of the topology and of the parameter extraction of the equivalent circuit.

Referring to the compulsator, when looking for a lumped equivalent circuit, we have to distinguish between the two compensation techniques usually adopted. When compensation is achieved by the use of shorted discrete coils, we can consider the self and mutual inductances of all windings (field, armature and compensating ones). Considering that the values of the mutual inductances depend on relative angular positions only, the lumped equivalent circuit of the compulsator is able to give accurate results; its building is a matter of evaluation (experimental or by computations) of self and mutual coefficients and EN4EM can be used as an extraction tool.

Things go in a different way when non-uniform (discontinuous) compensating shields are used. In these devices, the extraction of the values of the equivalent internal inductance *L* is not as straightforward as with shorted discrete coils, since it is function of the position of the rotor, as well as of the speed of the rotor, which is not known and varies during the system operation.

In fact, the speed of the rotor imposes the frequency of the electrical quantities in the shield, which in turn determines the path and the amplitude of the induced currents and their shielding effects which contribute to the internal equivalent inductance. Figure 4 shows an example of eddy currents distribution on one of the discontinuous compensating shields of the compulsator above described whose operating conditions are reported in [29]. In particular the compulsator was loaded with a simple lumped R-L equivalent circuit representing the rail launcher. The rectangle in Figure 4 represents the flattened cylindrical surface shown Figure 3c.

**Figure 4.** Eddy current distribution on the conductive compensating shield. (Reproduced with permission from [29], IEEE, 2017.)

The equivalent internal inductance of the compulsator, as well as the electromotive force at the terminals of the machine, are functions of the distribution of the currents on the shields. Expressing these functional dependencies represents a challenging problem.

Similar difficulties arise when looking for an equivalent circuit of the rail launcher. Figure 5 shows a rail launcher fed by an ideal voltage source whose waveform is given by *e*(*t*) = 50 1 − *e* −*t* τ *V*. Details about the geometry are in Table 2. In this figure, 20 elementary volumes located near the launcher breech are shown. The device was analyzed by EN4EM and the current density waveforms in the evidenced volumes are reported in Figure 6. The solid curves are associated with the labelled sections in reported in the inset of Figure 5; the greatest current density occurs in the section #5 in the inner part of the rail. The peak values became smaller as the outer boundary of the rail is approached. The reported waveforms put into evidence the uneven current density distribution in the rail section for most of the launch time, the ratio between the maximum and the minimum value is greater than two. This behavior is a consequence of the skin and proximity effects; also, the velocity skin effect has an heavy impact on the current distribution, which is a function of the rate of change of the electrical quantities imposed by the generator and the rate of change of the mechanical quantities i.e., the speed of the armature [36,37]. Both these quantities change during the launch.

**Figure 5.** A sketch a rail launcher. The inset put into evidence the cross section of half of the upper rail. The labelled rectangles represent the cross section of the inner layer of the elementary volumes, i.e., those involved in the sliding contacts with the armature.

**Table 2.** Description of the devices.

The basic equivalent circuit of the railgun, here shown in Figure 7, is usually composed of three elements. A resistor and an inductor, both varying with the distance travelled by the armature, and another resistor, that takes into account the motional induced electromagnetic force, is related to the inductance gradient and its resistance depends on the speed of the armature.

In the light of the above discussion, these circuital components should be function of the frequency which influences the effective current density distributions in both the rails and the armature, as well as of the time, because of the speed and of the distance travelled by the armature. Some lumped equivalent circuits of the rail launchers adopt simplified expressions of the form: *R*(*z*, *f*) = *Ra* + *R*0 + *R z* and *L*(*z*, *f*) = *L*0 + *L z*, where *R* = *dR dz* is the rail resistance gradient, *L* = *dL dz* is the rail inductance gradient, *Ra* is the armature resistance and *R*0 and *L*0 are the resistance and the inductance due to the connection wires [1]. All these expressions discard the dependence of these parameters on the frequency and are

not able to take into account the velocity skin effect. On the other hand, the formal definition of the parameters as shown in Figure 7 and their estimate pose complex problems.

**Figure 6.** Time waveforms of the *z*-axis component of current density in the rail at the feeding end. Uneven distribution occurs for about 80% of the launch time.

**Figure 7.** Basic equivalent lumped parameter circuit of a rail launcher. The presence of f (frequency) among the independent variables means that the circuit parameters are function of the rate of change of the electromagnetic phenomena.