**1. Introduction**

Multiple-phase composites possess admirable mechanical properties and service life. Combining softer matrix with harder islands [1], multiple-phase materials demonstrate the strong structure and ductility, such as in dual-phase steel (DP steel) [2], metal matrix composites, and other advanced steel [3]. The material properties of the multiphase materials depend on the microstructural attributes, such as the size, shape, composition, and distribution of the second phase within the matrix [4]. The effect of these attributes is interdependent and plays a key role in defining the deformation and damage behavior under varying loading conditions [5,6], i.e., strain rate, temperature, and loading direction. Numerical simulation models provide an interesting outlook for targeted material development by avoiding the expensive and time-consuming experimentation of every iterative modification in the material microstructure [7–9].

There are different numerical simulation models, i.e., empirical, analytical, datadriven, and hybrid [10,11]. Although they are useful in the general modeling of material deformation and damage behavior, they lack the fundamental dependence on the local microstructural attributes [12,13]. Fast Fourier transformation-based crystal plasticity models provide a comprehensive and accurate solution for modeling the multiphase

**Citation:** Tseng, S.; Qayyum, F.; Guk, S.; Chao, C.; Prahl, U. Transformation of 2D RVE Local Stress and Strain Distributions to 3D Observations in Full Phase Crystal Plasticity Simulations of Dual-Phase Steels. *Crystals* **2022**, *12*, 955. https:// doi.org/10.3390/cryst12070955

Academic Editors: Pavel Lukác and ˇ Wojciech Polkowski

Received: 28 April 2022 Accepted: 6 July 2022 Published: 8 July 2022

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**Copyright:** © 2022 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/).

material's dependence on the microstructural attributes [14,15]. The RVEs in such models comprise all the necessary phase compositions, size, orientation, and distribution that represent the actual material [16]. Therefore, the model's accuracy and applicability largely depend on the constructed RVE for such simulations.

Different simple and sophisticated models for accurate RVE development have been proposed previously, i.e., single-step Voronoi tessellation, multi-step Voronoi tessellation, and artificial neural networks yielding accurate results that are usually 3D. According to the RVE [17] method, both 2D (2-dimension) [18] and 3D (3-dimension) [19] microstructures have been constructed by random grain size, orientation, phase, and texture or measured from electron backscatter diffraction (EBSD) data [20]. Based on EBSD patterns from the serial-sectioning experiments, 3D polycrystalline microstructures were constructed by Groeber et al. [21,22]. Recently, DREAM-3D [23] was used to construct realistic RVEs from virtual or real statistical grain size, orientation, and texture data. Applying DREAM-3D and DAMASK [24], the performance of multilayer composites can be evaluated under mechanical loading by the crystal plasticity material model.

Compared to the simulation and experimental data for DP steels, Ramazani et al. [25] discovered that the 2D model displayed underestimated behavior, while the 3D result demonstrated a quantitative description of the flow curve in comparison to the experimental data. Qayyum et al. [26,27] studied the local deformation and transformation behavior of transformation-induced plasticity (TRIP) steel. In these articles, the simulation results of global stress and strain behavior were compared to the experimental result. Nevertheless, the validation of local distribution in 3D has a challenge to discuss, owing to the inconsistency between experiment and simulation results. Diehl et al. [28] analyzed the effect of "columnarity" and studied the influence of the nearby environment on stress and strain in DP microstructures. It was discovered that the local stress and strain distributions are strongly influenced by both the nearby grain shape and grain orientation. Due to this effect, the 2D simulations of heterogeneous microstructures could be definitely misleading for the damage prediction [29] of crack initiation and propagation.

The CP models are also largely dependent on several physical and a few fitting parameters. These parameters are obtained by comparing averaged numerical simulation results with experimental stress and strain curves [26,30]. Although a certain set of fitted parameters seems to accurately represent the overall deformation behavior, a slightly different set of fitted parameters is also expected to yield similar global results with a significant change in local results. This reliability of such models on the globally calibrated parameters can lead to incorrect local results. In the recent past, researchers have developed algorithms for automated sensitivity analyses and parametric identifications from global stress and strain curves [31,32]. A more reliable way of calibrating and validating the CP model parameters can be through direct local comparison of experimental in situ and simulation results.

The local strain measurement is experimentally possible now due to the advancement of in situ measurement and data processing tools, which can accurately capture local strain distribution and local microstructural attributes [33–35]. However, constructing an accurate 3D RVE of the same specimen is a paradox as 3D EBSD requires polishing, slicing, and measurement throughout the specimen. Moreover, different phases frequently cause false detection at the measurement surfaces and the grain boundaries [36].

Therefore, to carry out such a comparison, the 2D RVE results from CP simulation should be reliably transformed to keep the global results the same while transforming the local stress and strain distributions for comparison with the results of the 3D material surface. It is a mathematical challenge that can yield a model for transforming 2D RVE simulation results of local strain distribution for comparison with strain measurements on the surface of a 3D specimen. Recently, Qayyum et al. [37,38] investigated the stress and strain distribution between 2D and 3D RVEs with different total grain numbers. It was shown that the global distribution of the flow curve is similar across different RVEs. However, the local distribution showed obvious variation. The numerical finding of

Qayyum et al. [37,38] underlines the different stress and strain distribution in 2D and 3D via random distribution of grain size and orientation. In the current article, the previous study is carried one step further, and a corresponding local 3D stress and strain distribution on the RVE surface is achieved by transforming 2D stress and strain. The work is based on the alternative error and least square method. The transformation of the ferrite phase stress and strain from the 2D result is iteratively achieved. The iterative constants for different cases of magnification, strain levels, and volume fractions are presented and compared. The proposed new numerical approach is helpful in iteratively transforming the 2D stress and strain if the 3D outcome is known. To analyze and compare the derived 3D distribution with actual results, a statistical analysis of the obtained data is carried out.

The following Section 2 presents the detail of the numerical simulation model, including grain size, boundary condition, and material parameter of crystal plasticity. Then, the proposed iterative method, which is adopted in the current work, is explained in Section 3. Next, the derived 3D local stress and strain distribution calculated using the proposed method are displayed. Meanwhile, similarities between derived and exact 3D distribution are provided by statistical analysis in Section 4. Finally, the discussion and conclusion are presented in Sections 5 and 6.

#### **2. Numerical Simulation Model**

The material adopted in the current investigation is DP steel, which comprises two distinct phases, i.e., soft ferrite matrix and hard martensite island. This large local microstructural heterogeneity yields significant local strain contrast during deformation. The microstructural distribution, grain size, material properties, and grain orientation are adopted from previously published work [39–41]. This article investigates different parameters for varying the overall number of grains, strain levels, and volume fractions. Table 1 demonstrates the grain size distribution of ferrite and martensite, number of total grains, volume fractions, and strain levels for each model. For cases 1 to 3, the varying parameter is the total number of grains; for cases 4 to 6, the varying parameter is strain level; For cases 7 to 9, the varying parameter is volume fraction. Note that the unit of grains size is μm and total grain is a dimensionless value. Based on experimental observation [42], the smaller average grain sizes of ferrite and martensite were assigned as 6.35 and 4.6 in RVE-A, whereas the larger average grain sizes were 14.0 and 12.8 in RVE-C during the crystal plasticity simulation. Hence, the total grains of RVE-A are more than RVE-C.

**Table 1.** Grain size distribution, number of total grain, volume fraction, and strain level for the microstructure [37].

A cubic equiaxed crystal structure and ellipsoid grain shape are assigned to both ferrite and martensite phases. 100 × 100 × 100 voxels RVEs are systematically constructed using DREAM-3D for the sizes as shown in Table 1. Figure 1 shows a schematic diagram and flow chart in this article. The blue arrows indicate the steps involved in carrying out this work. In the beginning, 2D and 3D simulations for different RVEs are carried out. Both ferrite (F) and martensite (M) phases are then individually analyzed. Combined with the

least square and alternative error method, the iterative constants (*a*1, *b*1, *a*2, and *b*2, ... ) of the linear equation are calculated while transforming the 2D results into 3D.

**Figure 1.** The schematic diagram represents the flow chart of the current work. The upper half (yellow background) indicates the flow chart of crystal simulation, and the bottom half (blue background) represents numerical analysis. The blue arrow indicates the flow of data. The red arrow represents tensile loading, and the yellow arrow separates the ferrite (F) and martensite (M) phases.

The principal aim of this ongoing study is to develop a robust methodology for deriving the 3D surface stress and strain distribution from the 2D RVE result for ferrite and martensite phases. This work brings us one step closer to that aim. As a representation,

RVE-C in inverse pole figure (IPF) colors is shown in Figure 2a (h = 1), where h indicates the length of z-direction normalized total length of z-direction. Following Qayyum et al. [37], 50- (h = 0.5) and 1-layer (h = 0.01) RVE were sliced from the initial microstructure and regarded as 3D and 2D RVE, respectively. The simulation results for 1- and 50-layers have been selected and defined as 2D and 3D results of the local stress and strain distribution. There are 10,000 Gaussian mesh elements in one layer, meaning 2D and 3D possess 10,000 and 500,000 elements, respectively. All the constructed RVEs were sliced into similar geometries with 1-layer (h = 0.01) RVE and shown in terms of texture style in Figure 2b.

**Figure 2.** (**a**) The resulting RVE-C initial microstructure colored according to the inverse pole figure (IPF). (**b**) All RVE models (RVE-A to RVE-F) were sliced into geometries with 1-layer (h = 0.01) RVE in terms of texture style.

The ferrite and martensite are defined as elastic–viscoplastic deformable phases. The elastic stiffness, shear resistance, hardening behavior, and curve fitting parameter are adapted from previously published work [38] and presented in Table 2.

**Table 2.** Mechanical properties of multiphase (ferrite and martensite) were adopted from [37] for simulation modeling.

The crystallographic orientation, mechanical properties, and phase of ferrite and martensite are included in the RVE geometry definition. A uniaxial load along the x-direction is defined using mixed boundary conditions as follows:

$$
\dot{F}\_{ij} = \begin{bmatrix} 1 & 0 & 0 \\ 0 & \* & 0 \\ 0 & 0 & \* \end{bmatrix} \times 10^{-3} \cdot s^{-1} \tag{1}
$$

$$P\_{ij} = \begin{bmatrix} \* & \* & \* \\ \* & 0 & \* \\ \* & \* & 0 \end{bmatrix} Pa \tag{2}$$

where *Fij* is the coefficients of the macroscopic rate of the deformation gradient, *Pij* is the first Piola–Kirchhoff stress. . *F*11 = 1/*s* indicates tensile condition, 0 is represented as restricted, and \* is an arbitrary value during the simulation. It should be noted that the strain rate of all simulations is assumed to be 1 × 10−3/*s* in conjunction with periodic boundary conditions in all three directions. The simulations are performed in plain strain mode, where 2D RVE is interpreted as a columnar grain structure.

The spectral method via fast Fourier transform [43] is used to solve the continuum mechanics formulation mentioned above. After completing simulations, the 2D and 3D data are statistically analyzed. The 3D numerical results are used as a reference for iteratively modifying the 2D results by combining the least square and alternative error methods via Matlab programs (2019b, The MathWorks Inc., Natick, MA, USA).


**2.4. Combined effects of pH, cinnamic, and vanillic acids on the viable count of the strain 13M**

The strain 13M was used as target; it was inoculated into MSM broth to 6–7 log cfu/ml. The amounts of cinnamic and vanillic acids and pH varied according to a 2k experimental (Table 1). The samples were stored at 30°C and periodically analyzed to evaluate the viable count and phenol content (up to 12 days).

**Table 1.** Combinations of 2k design.

The analyses were performed in duplicate and the results of viable count analyzed through a multiple regression approach by using the option DoE/2k design of the software Statistica for Windows.


**Preface**

This Special Issue reprint includes one review and fifteen research articles. The review by Palyanova et al. (2023) summarized the available information on the palladian gold and proposed classifying the types of deposits based on the fineness, content, and set of impurities in palladian gold and minerals intergrown with it. Fifteen articles focused on the typomorphic features of native gold from gold deposits in Russia, India, Chile, Scotland, and Canada. This Special Issue aims to identify and generalize the reasons for variations in the compositions of native gold. I hope all the articles in this Special Issue will be helpful and valuable resources for anyone who is interested in native gold and gold deposits. I thank the Authors and Reviewers for their efforts and contributions. I am also grateful to the Editor-in-Chief, Editors and Assistant Editors of *Minerals* for their help.

**Galina Palyanova**

*Editor*


3.2.2. Activity: Preclinical Studies

Curcumin inhibits proinflammatory cytokines, TNF–α, ICAM–1, NOX2 and cyclo– oxygenase–2 expressions, and reduces the leucocyte-endothelium interaction in diabetesinduced rat vascular inflammatory models [100,101]. Curcumin has been widely evaluated with respect to the modulation of endothelial function [102]. Curcumin also presents a neuroprotective potential in the pathogenesis of Alzheimer's disease [103–105]. The many described biological activities of curcumin have been linked to its chemical instability that leads to the rapid autoxidation responsible for its antioxidant behavior. The oxidation of curcumin produces intermediate metabolites that conduct to a final bicyclopentadione [106,107]. Moreover, it has been demonstrated that electrophilic metabolites can covalently adduct to cellular protein targets, in particular those of the NF–κB pathway, which explains the anti-inflammatory activity of the natural compound. The methoxy groups of the molecule have also been shown to possess a role in its anti-inflammatory biological activity [108].

Ischemia and reperfusion injury in skeletal muscles, obtained by clamping the femoral artery and vein, is an experimental model that can provide information on the damage occurring in ischemic events of the limbs. Rats subjected to 4 h femoral occlusion followed by 2 h reperfusion, which received curcumin (100 mg/kg i.p., 1 h before reperfusion), presented a preservation of superoxide dismutase and catalase activities, as well as of the glutathione content in muscle tissues, compared to injured but not treated animals [109]. In the same context, the muscle and plasma levels of malondialdehyde and protein oxidation were reduced, as well as the plasma levels of inflammatory cytokines (TNF–α and IL–1β). The data suggest that curcumin has protective activity against the ischemic damage of skeletal muscles [109].

Using a mouse model of hindlimb ischemia obtained by the ligation of the left femoral artery, Liu et al. observed that curcumin (100 mg/kg, i.p. administration 1 h before the ligation surgery) is capable of improving the running capacity on a treadmill of injured mice compared to the controls, evaluated 1 and 2 weeks following injury [110]. A histological examination of skeletal-muscle sections from the curcumin-treated group showed less muscle degeneration and fibrosis than in the control mice; also, curcumin treatment was able to significantly reduce macrophage infiltration and ischemia- induced inflammation. The regulation of the tissue inflammatory response has been associated with a decrease in the proinflammatory cytokines TNF–α, IL–1β and IL–6 as a result of the diminished expression of NF–κB, namely, of the subunit p65 [110]. These data suggest that curcumin could be a promising agent used against diseases of the ischemic limbs. Another in vivo experiment conducted on streptozotocin-induced diabetic mouse that received hindlimb ischemic surgery demonstrated that curcumin (1000 mg/kg in olive oil, applied by gavage for 14 days) can promote the significant recovery of blood flow detected by laser Doppler imaging, 7 and 14 days after ischemic surgery; histology evidenced neogenic capillary formation, as a consequence of improved angiogenesis and the proliferation of endothelial progenitor cells [111]. Zhang et al. studied the role of curcumin in an experimental PAD model of murine hindlimb ischemia obtained with surgical ligation and the excision of the femoral artery. Mice received 1000 mg/kg of curcumin (in 300 μL of olive oil, gavage) once a day for two weeks [112]. In animals treated with curcumin, the laser Doppler perfusion imaging system showed perfusion recovery 14, 21 and 28 days after ischemia induction, significantly better than in the control. Histology of the ischemic gastrocnemius muscle after 28 days revealed a significant increase in capillary density. Furthermore, 7 days after surgery, a 5-fold increase in the expression of microRNA (miR)–93 (a mediator of neovascularization in PAD) was detected in the muscle tissue, suggesting the role of curcumin in angiogenesis [112].

Another possible favorable mechanism of action of curcumin in the damage of large arteries could be the inhibition of hypoxia-inducible factor 1α (HIF–1α), implicated in the progression of atherosclerosis. Ouyang et al. demonstrated that in a culture of human macrophages, the protein level of HIF–1α, induced by hypoxia, is reduced in a concentration-dependent way by treatment with curcumin (20–40 μM), which acts in a proteasome-dependent manner without affecting the mRNA level of the factor [113]. Moreover, it has been shown that curcumin causes the inhibition of the expression of HIF–1α through ERK signaling pathway. Following HIF–1α inhibition, curcumin also affects macrophage apoptosis induced by hypoxia; also, it significantly reduces the hypoxiainduced release of proinflammatory cytokines IL–6 and TNF–α from macrophages [113].

Curcumin has been evaluated under the aspect of AGEs inhibition, a process that is strictly related to arterial senescence and degeneration. A review has recently taken into account this issue [114]. Curcumin has been shown to reduce in vitro the generation of AGEs, as well as to counteract in vivo AGE formation. The possible mechanisms involved include methylglyoxal trapping, but also the capacity to prevent AGE formation, due to the antioxidant activity and clearance of free radicals. Curcumin can also act on the expression of AGE receptors by suppressing RAGE (a receptor that mediates the detrimental effects of AGEs) and enhancing AGE–R1 (a distinct receptor that mediates the detoxification of AGEs) [115]. It should be mentioned that curcumin may act as favorable modulator of PAD also influencing several pathways linked to DM, the disease whose complications often evolve toward vascular manifestations. A recent overview has considered by bioinformatic methodology the many targets that can be affected by curcumin due to its antioxidant and anti-inflammatory properties, which can modulate the disease's progression [116].

#### 3.2.3. Activity: Clinical Studies

From a strict, clinical point of view, the data on the effectiveness of curcumin in PAD are limited. A meta-analysis of 5 randomized clinical trials conducted on a total of 192 healthy subjects with doses of curcumin ranging from 25 to 200 mg, showed that curcumin supplementation is able to improve vascular function, determined as the flow-mediated dilation of the brachial artery [117]. Alidadi et al. reported 7 randomized clinical trials conducted on humans, ranging from healthy subjects to obese people and type 2 diabetic patients, with a sample size ranging from 21 to 88 subjects [118]. Curcumin doses ranged from 150 mg/day to 2 g/day, over periods of 8–16 weeks. In healthy subjects, curcumin appeared to improve endothelial function, determined by a non-invasive ultrasoundbased technique that measured flow-mediated dilation. On the contrary, in pathological conditions, curcumin treatment did not show an appreciable improvement in endothelial function, also due to the limited number of patients evaluated [118].

Despite its interesting biological properties, curcumin has the limitation of being poorly absorbed by the gastrointestinal tract due to its high hydrophobicity [119]. Several formulations were investigated to enhance curcumin bioavailability [120,121], in particular micro- and nano-formulations. An optimized curcumin formulation was developed and investigated [122]. It consisted of poly (propylene sulfide) (PPS) microparticles used for curcumin encapsulation and the delivery of the active principle on demand at the site of oxidative stress. An oil-in-water emulsion was obtained, which permitted, in the presence of ROS, the transition of hydrophobic PPS into more hydrophilic sulfoxide and sulfone, thus releasing curcumin. Following an in vitro evaluation of the system, the authors tested the formulation in vivo (curcumin-loaded PPS microspheres: 5 mg/kg of curcumin with 10.3 mg/kg of PPS, administered i.m. in the gastrocnemius and adductor muscles) in a streptozotocin-induced mouse model of DM in which hindlimb ischemia was induced [122]. The results show that curcumin microspheres were able to selectively reduce ROS levels in the tissue of the ischemic limbs, significantly increasing blood perfusion and the length of the vasculature, providing evidence for a favorable action of curcumin in the treatment of diabetic PAD. Another more recent attempt to produce "on demand" treatment for PAD has been reported [123]. It consists of PVAX (vanillyl alcohol-incorporated copolyoxalate) nanoparticles loaded with curcumin that release the drug at a pathologically elevated level of H2O2, as occurs at an ischemic site. After optimizing in vitro the formulation of curcumin–PVAX nanoparticles and demonstrating their antioxidant, anti-inflammatory and angiogenic activities, the authors evaluated the activity of the product in a mouse model of unilateral hindlimb ischemia. The in vivo results, obtained with the i.m. injection of curcumin–PVAX nanoparticles into the ischemic area on days 0, 3 and 7, showed significant blood-flow recovery and neovascularization, with almost complete blood-flow restoration 12 days after ischemia. The histological examination demonstrated the suppression of tissue damage and inflammatory responses, with an extensive expression of angiogenic factor CD31 [123]. Several other formulations of curcumin, including nano-formulations or encapsulation, have appeared on the market to ensure the optimal intake of the active compound [124,125].

#### 3.2.4. Safety Profile

Regarding curcumin toxicity, the compound is considered safe and has a good tolerability profile in humans [126–128]. The reported side effects mainly include gastrointestinal disturbances. However, in Italy, several cases of acute hepatitis have been reported to be associated with formulations that provide high bioavailability and high doses of curcumin [129]. In fact, the availability of many different formulations of curcumin with an enhanced bioavailability profile has focused on the question of safety. For instance, Fuloria et al. considered the curcumin toxicity profile that emerged during the most recent preclinical and clinical studies; excessive amounts of curcumin may lead to alterations in testosterone levels in men, influence blood clotting and contrast iron absorption [125].

In VigiBase curcumin has 71 potential side effects [95], such as gastrointestinal disorders (i.e., diarrhea and nausea), nervous system disorders (e.g., asthenia and others) and hepatobiliary disorders (e.g., acute liver failure, increase in alanine aminotransferase and aspartate aminotransferase, and others). More trials are needed to understand the safety of curcumin for pharmacological use, also reducing the number of additives, and considering customized microencapsulation [125].


**Comparison of Modern and Pleistocene (MIS 5e) Coastal Boulder Deposits from Santa Maria Island (Azores Archipelago, NE Atlantic Ocean)**

**Sérgio P. Ávila 1,2,3,4,\*, Markes E. Johnson 5, Ana Cristina Rebelo 1,3,6,7, Lara Baptista 1,3,4 and Carlos S. Melo 1,3,8,9**

Received: 21 April 2020; Accepted: 26 May 2020; Published: 28 May 2020

**Abstract:** Modern and palaeo-shores from Pleistocene Marine Isotope Substage 5e (MIS 5e) featuring prominent cobble/boulder deposits from three locations, on the southern and eastern coast of Santa Maria Island in the Azores Archipelago, were compared, in order to test the idea of higher storminess during the Last Interglacial. A total of 175 basalt clasts from seven transects were measured manually in three dimensions perpendicular to one another. Boulders that exceeded the minimum definitional diameter of 25 cm contributed to 45% of the clasts, with the remainder falling into the category of large cobbles. These were sorted for variations in shape, size, and weight pertinent to the application of two mathematical formulas to estimate wave heights necessary for traction. Both equations were based on the "Nott-Approach", one of them being sensitive to the longest axis, the other to the shortest axis. The preponderance of data derived from the Pleistocene deposits, which included an intertidal invertebrate fauna for accurate dating. The island's east coast at Ponta do Cedro lacked a modern boulder beach due to steep rocky shores, whereas raised Pleistocene palaeo-shores along the same coast reflect surged from an average wave height of 5.6 m and 6.5 m. Direct comparison between modern and Pleistocene deposits at Ponta do Castelo to the southeast and Prainha on the island's south shore produced contrasting results, with higher wave heights during MIS 5e at Ponta do Castelo and higher wave heights for the modern boulder beach at Prainha. Thus, our results did not yield a clear conclusion about higher storminess during the Last Interglacial compared to the present day. Historical meteorological records pit the seasonal activity of winter storms arriving from the WNW-NW against the scant record of hurricanes arriving from the ESE-SE. The disparity in the width of the marine shelf around Santa Maria Island with broad shelves to the north and narrow shelves to the south and east suggested that periodic winter storms had a more regular role in coastal erosion, whereas the rare episodic recurrence of hurricanes had a greater impact on southern and southeastern rocky shores, where the studied coastal boulder deposits were located.

**Keywords:** coastal boulder deposits; storm surge; hydrodynamic equations; Holocene; Pleistocene; MIS 5e (Marine Isotope Substage 5e); NE Atlantic Ocean

#### **1. Introduction**

Survey models regarding the level of storm intensity during the Last Interglacial stage of the Pleistocene, specifically the Marine Isotope Substage 5e (MIS 5e), have been conducted on a global scale [1], but studies organized on a more regional scale provide the potential for higher resolution. Localized studies on the propensity for storms in the Bahamas and Bermuda (Western Atlantic) [2,3] reveal patterns in agreement with global results. However, for higher latitudes in the North Atlantic Ocean (e.g., the Azores Archipelago), such analyses have been scarce [4]. Climatological reconstructions are of utmost importance because they allow the scientific community, policymakers, and the general public to better predict and plan for future hazardous events. With a worldwide extension of 500,000 km, coastlines are highly complex and dynamic geomorphological features [5] that commonly correspond to areas of high-density human habitation [6]. With ongoing conditions of global warming, there is even more urgency for increased knowledge about the deep history of storm patterns associated with oceanic circulation.

The shorelines of volcanic oceanic islands are highly dynamic in nature as a result of volcanism, mass wasting, and exposure to the energetic action of the open sea [7–10]. Exposure to wave action is the primary factor that shapes coastlines, as wave surge crossing island shelves acts continuously, but at different levels of energy [11]. In the Azores Archipelago, all islands are subject to the direct action of waves [11]. Unprotected by the absence of barriers (e.g., reefs) and with narrow insular shelves [12], erosion rates are high [6]. The result is the production of variable amounts of detrital materials that are readily shaped and transported, commonly including coastal boulder deposits (CBDs). Sometimes, transported materials are configured in peculiar geomorphologies, such as fajãs [13]. In the Azores, processes that lead to the production of modern CBDs allow for comparisons with morphologies deposited during the Last Pleistocene Interglacial episode (MIS 5e). Santa Maria is the only island in the Azores with marine fossiliferous sequences that date back to the Pliocene and late Pleistocene (MIS 5e) [14–16]. The presence of such sequences makes this island an ideal place for studies testing the postulated higher storminess and inferred palaeo-wave heights that affected the wider archipelago approximately 125,000 years ago.

Inference on palaeo-wave-heights through measurements of eroded blocks in Pleistocene settings has been conducted by Johnson et al. [17–19] at localities in the Mexican Gulf of California, providing a useful methodology for application elsewhere. Here, we adapted the program using mathematical formulas to compare the storminess during the Last Interglacial (MIS 5e) and the modern situation, deduced from storms imprinted in the CBDs. Herein, we presented the first estimations for palaeo-wave heights from the Pleistocene (MIS 5e) in the Azores. Data on the shape, size, and calculated weight of palaeo-shore boulders from Santa Maria Island had the advantage of being sourced from well-dated MIS 5e outcrops containing thermophile fauna typical of the Last Interglacial. Crucially, estimates on wave heights from MIS 5e CBDs might be compared with adjacent modern beach boulders. Work was limited to localities on the island's south and east coast, where marine shelves were narrower. The island's broader northern shelf provided the basis for conjecture on differences in storm patterns that led to that outcome.

#### **2. Geographical and Geological Setting**

#### *2.1. Position and Geotectonic Setting*

The Azores is an oceanic volcanic archipelago with nine islands, found in the NE North Atlantic Ocean, between latitudes 36◦55 and 49◦43 N and longitudes 24◦46 and 31◦16 W, and spreading along a distance of 650 km (Figure 1a). Seated on the Azores Plateau, the archipelago straddles a triple junction between the Eurasian, North American, and Nubian (African) tectonic plates [20]. Santa Maria Island is the most southeastern and oldest among these and is seated on the Nubian plate. It exhibits a geologic record, marking the earliest emergence from the sea due to Surtseyan volcanic activity approximately 6 million years ago [8]. Much of the ensuing rock record, which includes intercalated sedimentary strata and extensive volcanic flows, is restricted to the Pliocene Epoch [21,22]. Island uplift, which commenced 2.8 million years ago, has resulted in more than 200 m of tectonic rise, as a result of which older Pliocene marine strata are well exposed in sea cliffs on all sides of the island, but most accessible along the south and eastern shores [23]. Santa Maria ranks seventh in size compared to the other islands in the Azores Archipelago, with an area of 97 km2 and a coastal circumference of 53 km. The island presents a peculiar orography, with a flatter Western part and a rougher Eastern part, as a result of its unusual geological evolution (i.e., different erosional rates and off-center volcanism during a rejuvenated stage, mostly located on the eastern section of the older edifice [8,24]; Figure 1b). In terms of bathymetry, the island is much reduced in size with an asymmetrical marine shelf that is broadest to the north and narrowest to the south and east [24]. The shelf is also characterized by a suite of submerged terraces, all presumably younger than ~1 Ma, which are more developed and preserved in wider and low-gradient sectors (Figure 1b) [25]. During the Last Interglacial epoch of the Pleistocene, extensive boulder beds were emplaced all around the island that incorporates marine fossils attributed to the MIS 5e [4]. Three localities, including Prainha and Ponta do Castelo on the south shore and Ponta do Cedro on the east coast, were chosen to highlight lateral variations in Pleistocene boulder size together with a review of the associated fauna. Comparisons were drawn with modern boulder beds at the two southern localities, whereas the plunging coastal cliffs at Ponta do Cedro lacked any such development of a coastal boulder deposit (CBD) at or close to modern sea level.

**Figure 1.** Maps covering the Azores Archipelago in the NE Atlantic Ocean: (**a**) Geographic and geotectonic setting of the Azores Archipelago (modified from [26–28]). NA—North American plate; Eu—Eurasian plate; Nu—Nubian (African) plate; MAR – Mid Atlantic Ridge; TR—Terceira Rift (grey area); EAFZ—East Azores Fracture Zone; GF—Gloria Fault; (**b**) Topography/bathymetry of Santa Maria Island. Black stars mark the studied sites. The bathymetric data was extracted from GEBCO 2019 (https://www.gebco.net); subaerial topography was generated from a 1:5000 scale digital altimetric database.

#### *2.2. Sources and Shaping of the Boulders*

The Prainha site is situated within a bay, thus affording a higher potential for the deposition of clasts and finer sediments. The analysis of local currents showed a confluence of waves to the south coast of the island (https://www.ipma.pt/pt/maritima/hs/index.jsp?area=acores-east) that explains how during the summer season the nearby coastlines collect extensive (on a local scale) sand beaches. The area is also the river-mouth of some streams. As the archipelago's climate is classified as "Warm Temperate" [29], higher precipitation events are common. Such events are responsible for the

transport of varying amounts of boulders and sand to the intertidal zone. As rough seas are commonly registered in the archipelago, the boulders are easily rounded and shaped.

At the southeasternmost tip of the island, Ponta do Castelo presents the most complex wave regime from the three sites studied. In the area, perpendicular (in direction) wave currents interact, promoting rougher seas, even under fair-weather conditions. As a result of this exposure, no fine sediment is deposited, and only a well-developed CBD is present.

In Ponta do Cedro, however, despite being found inside a bay, like Prainha, a plunging coastline allows for no accumulation of sandy deposits, and a modern CBD also is absent. Ponta do Cedro and Ponta do Castelo, however, share the same type of boulder source resulting from erosion of the area's high sea cliffs. Both these sites are situated in the rough eastern end of the island, where sea cliffs are impressive in height.

#### *2.3. Wave Energy and Direction*

The Azores occupies a region in the NE Atlantic Ocean encompassing approximately 22,500 km2 (Figure 1a) and is characterized by a high level of marine storm activity. Hurricanes rarely cross through the region during the annual Atlantic hurricane season, although tropical cyclones are common. Such storms arrive from a zone off the west coast of Africa in the vicinity of the Cabo Verde Archipelago, located at a lower 17◦ N latitude. Notwithstanding, extreme storm events tend to arrive once every seven years, on average [6,30]. In contrast and as a result of the exposure to the strong NW North Atlantic winds – the Westerlies [31], the northern exposures of islands are subject to winter storms. The archipelago is also in the pathway the Gulf Stream makes from the North American coasts towards the central zone of the North Atlantic [32,33], being so a source of many instability processes, meanders, and eddies [34]. The main wave direction that affects the archipelago comes from WNW-NW [5,8,23]. Such predominance is reflected in the island's bathymetrical morphology that shows higher erosional rates on the W and N coasts. According to Rusu and Soares [11], and using the closest station to Santa Maria Island (P18), present-day mean wave heights during summer is 1.75 and during winter is 3.20 m. For the Azores archipelago, Santa Maria presents the lowest values regarding the mean values for both seasons, and Corvo presents the highest. This variation in values has been related to the shadow effect promoted mainly by São Miguel Island (North of Santa Maria), protecting it from the high wave energy [13].

#### **3. Methods**


4.7.2. Discussion on the Findings of the Full Implementation of IFRS in Cameroon

The findings with respect to Cameroon's ability to implement the IFRS revealed that accounting practitioners are actually positive about the IFRS implementation irrespective of the limited time for the law to take effect. However, the results were insignificant, indicating that most of those interviewed believe that Cameroon does not have the necessary infrastructure as well as proper accounting knowledge of IFRS to implement IIFSR in the system fully. This is unlike Barth et al. (2008), who found that the application of International Accounting standards was associated with higher accounting quality in 21 countries that adopted IAS from 1994 to 2003. The author also compared the accounting quality for IAS firms before and after they adopted the IAS and concluded that accounting quality has improved between the pre- and post-adoption periods. The period before and after they adopted IAS showed that accounting quality was enhanced between the pre- and post-adoption periods.


**Acknowledgements**

This work is supported by the African Institute for Mathematical Sciences, www. nexteinstein.org, with financial support from the Government of Canada, provided through Global Affairs Canada, www.international.gc.ca, and the International Development Research Centre, www.idrc.ca.

This research was carried out through the West African Science Service Centre on Climate Change and Adapted Land Use (WASCAL) initiative supported by the German Federal Ministry of Research and Education.

We acknowledge that the results of this research were achieved using computational resources at the German Climate Computing Center (DKRZ). The ERA-Interim dataset was downloaded from the European Centre for Medium – Range Weather Forecasts (ECMWF) (available online http://apps.ecmwf.int/datasets/data/interimfull-daily/levtype=sfc/). The CFSv2 dataset was downloaded from the Environmental Modeling Center at NCEP (available online ftp://nomads.ncdc.noaa.gov/modeldata/ cfsv2\_analysis\_flxf).


**12. Conclusion**

• Sponge.

202 Family Planning

• Diaphragm.

• Spermicides.

**11.13. Innovations**

• Contraception. • Menorrhagia.

**11.14. Side effects**

**11.15. Mirena**

ectopic pregnancies.

Aims of intrauterine devices:

• Endometrial protection.

spotting, especially in the first months [69].

• Birth control rings.

condom with a failure rate of 18% [68].

contains 52 mg levonorgestrel and yields 20 μg/24 h for 5 years.

They can cause amenorrhea or oligomenorrhea.

**11.12. Intrauterine contraception**

From contraceptive barrier methods, the most widespread, economic, easy to use, well accepted by both partners, with the greatest contraceptive success and the greatest protection against sexually transmitted diseases is the male condom, 75% of adolescents report using a

Copper intrauterine device is the most effective reversible method of contraception in terms of cost-effectiveness which is the first method of contraception with a coil used in the world. Mirena, which was released in 1997, is a type of intrauterine device with levonorgestrel that

Forming new IUD with less levonorgestrel that will be easily applied to nulliparous women (Femilis and Femilis slim) are under construction and they are another IUD without side

The use of IUD can cause tempοrarily edema, headache, tenderness, depression and breast tenderness, acne or other skin lesions. There are may also be appeared: abdominal pain in the lower part of the abdomen, vaginal discharge, nausea, functional ovarian cysts and rarely

Mirena is an intrauterine device effective in relation to the main indication of its usage which is contraception. It could be also used as a reliable therapeutic method of menorrhagia. In many cases, reduce dysmenorrhea. It reduces the risk of pelvic inflammatory disease and

arms, for easy adjustment to various sizes of uterus IUD (SPRM) (ulipristol).

From the above mentioned, we conclude that with the preventative gynecological control in females of young age, a prompt diagnosis and appropriate treatment, in particular congenital abnormalities of the genitals and investigation of clinical symptoms of these individuals, can be made.

Early diagnosis and treatment of ovarian tumors despite their small incidence of genital cancers up to 18 years of age is of major clinical importance because they are not always accompanied by a characteristic clinical picture.