German Americans especially regarding pastries, meats and sausages, and above all, beer. Frankfurters (or "wieners", originating from Frankfurt am Main and Vienna, respectively), hamburgers, bratwurst, sauerkraut, and strudel are common dishes. German bakers introduced the pretzel, which is popular across the United States. Germans introduced America to lager, the most-produced beer style in the United States, and have been the dominant ethnic group in the beer industry since 1850. The oldest extant brewery in the United States is D. G. Yuengling & Son of Pottsville, Pennsylvania (approximately 80 miles northwest of Philadelphia), founded in 1829 by an immigrant from Aldingen in what
Slowly varying envelope approximation Slowly varying envelope approximation In physics, the slowly varying envelope approximation (SVEA, sometimes also called slowly varying amplitude approximation or SVAA) is the assumption that the envelope of a forward-travelling wave pulse varies slowly in time and space compared to a period or wavelength. This requires the spectrum of the signal to be narrow-banded—hence it also referred to as the narrow-band approximation. The slowly varying envelope approximation is often used because the resulting equations are in many cases easier to solve than the original equations, reducing the order of—all or some of—the highest-order partial derivatives. But the validity of the