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Mitchell Feigenbaum
Mitchell Jay Feigenbaum (December 19, 1944 – June 30, 2019) was an American mathematical physicist whose pioneering studies in chaos theory led to the discovery of the Feigenbaum constants. Early life Feigenbaum was born in Philadelphia, Pennsylvania, to Jewish emigrants from Poland and Ukraine. He attended Samuel J. Tilden High School, in Brooklyn, New York, and the City College of New York. In 1964, he began his graduate studies at the Massachusetts Institute of Technology (MIT). Enrolling for graduate study in electrical engineering, he changed his area of study to physics. He completed his doctorate in 1970 for a thesis on dispersion relations, under the supervision of Professor Francis E. Low. Career After short positions at Cornell University (1970–1972) and the Virginia Polytechnic Institute and State University (1972–1974), he was offered a longer-term post at the Los Alamos National Laboratory in New Mexico to study turbulence in fluids. He was at Cornell ...
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Philadelphia
Philadelphia ( ), colloquially referred to as Philly, is the List of municipalities in Pennsylvania, most populous city in the U.S. state of Pennsylvania and the List of United States cities by population, sixth-most populous city in the United States, with a population of 1,603,797 in the 2020 United States census, 2020 census. The city is the urban core of the Philadelphia metropolitan area (sometimes called the Delaware Valley), the nation's Metropolitan statistical area, seventh-largest metropolitan area and ninth-largest combined statistical area with 6.245 million residents and 7.379 million residents, respectively. Philadelphia was founded in 1682 by William Penn, an English Americans, English Quakers, Quaker and advocate of Freedom of religion, religious freedom, and served as the capital of the Colonial history of the United States, colonial era Province of Pennsylvania. It then played a historic and vital role during the American Revolution and American Revolutionary ...
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Mathematical Physics
Mathematical physics is the development of mathematics, mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories". An alternative definition would also include those mathematics that are inspired by physics, known as physical mathematics. Scope There are several distinct branches of mathematical physics, and these roughly correspond to particular historical parts of our world. Classical mechanics Applying the techniques of mathematical physics to classical mechanics typically involves the rigorous, abstract, and advanced reformulation of Newtonian mechanics in terms of Lagrangian mechanics and Hamiltonian mechanics (including both approaches in the presence of constraints). Both formulations are embodied in analytical mechanics and lead ...
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New Mexico
New Mexico is a state in the Southwestern United States, Southwestern region of the United States. It is one of the Mountain States of the southern Rocky Mountains, sharing the Four Corners region with Utah, Colorado, and Arizona. It also borders the state of Texas to the east and southeast, Oklahoma to the northeast, and shares Mexico-United States border, an international border with the Mexican states of Chihuahua (state), Chihuahua and Sonora to the south. New Mexico's largest city is Albuquerque, and its List of capitals in the United States, state capital is Santa Fe, New Mexico, Santa Fe, the oldest state capital in the U.S., founded in 1610 as the government seat of Santa Fe de Nuevo México, Nuevo México in New Spain. It also has the highest elevation of any state capital, at . New Mexico is the List of U.S. states and territories by area, fifth-largest of the fifty states by area, but with just over 2.1 million residents, ranks List of U.S. states and terri ...
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Los Alamos National Laboratory
Los Alamos National Laboratory (often shortened as Los Alamos and LANL) is one of the sixteen research and development Laboratory, laboratories of the United States Department of Energy National Laboratories, United States Department of Energy (DOE), located a short distance northwest of Santa Fe, New Mexico, in the Southwestern United States, American southwest. Best known for its central role in helping develop the First Atomic bomb, first atomic bomb, LANL is one of the world's largest and most advanced scientific institutions. Los Alamos was established in 1943 as Project Y, a top-secret site for designing nuclear weapons under the Manhattan Project during World War II.The site was variously called Los Alamos Laboratory and Los Alamos Scientific Laboratory. Chosen for its remote yet relatively accessible location, it served as the main hub for conducting and coordinating nuclear research, bringing together some of the world's most famous scientists, among them numerous Nobel ...
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Virginia Polytechnic Institute And State University
The Virginia Polytechnic Institute and State University, commonly referred to as Virginia Tech (VT), is a Public university, public Land-grant college, land-grant research university with its main campus in Blacksburg, Virginia, United States. It was founded as the Virginia Agricultural and Mechanical College in 1872. The university also has educational facilities in six regions statewide, a research center in Punta Cana, Dominican Republic, and a study-abroad site in Riva San Vitale, Switzerland. Through its Virginia Tech Corps of Cadets, Corps of Cadets Reserve Officers' Training Corps, ROTC program, Virginia Tech is a United States Senior Military College, senior military college. Virginia Tech offers 280 undergraduate and graduate degree programs to its 37,000 students; as of 2016, it was the state's second-largest public university by enrollment. It is Carnegie Classification of Institutions of Higher Education, classified among "R1: Doctoral Universities – Very high r ...
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Cornell University
Cornell University is a Private university, private Ivy League research university based in Ithaca, New York, United States. The university was co-founded by American philanthropist Ezra Cornell and historian and educator Andrew Dickson White in 1865. Since its founding, Cornell University has been a Mixed-sex education, co-educational and nonsectarian institution. As of fall 2024, the student body included 16,128 undergraduate and 10,665 graduate students from all 50 U.S. states and 130 countries. The university is organized into eight Undergraduate education, undergraduate colleges and seven Postgraduate education, graduate divisions on its main Ithaca campus. Each college and academic division has near autonomy in defining its respective admission standards and academic curriculum. In addition to its primary campus in Ithaca, Cornell University administers three satellite campuses, including two in New York City, the Weill Cornell Medicine, medical school and ...
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Dispersion Relation
In the physical sciences and electrical engineering, dispersion relations describe the effect of dispersion on the properties of waves in a medium. A dispersion relation relates the wavelength or wavenumber of a wave to its frequency. Given the dispersion relation, one can calculate the frequency-dependent phase velocity and group velocity of each sinusoidal component of a wave in the medium, as a function of frequency. In addition to the geometry-dependent and material-dependent dispersion relations, the overarching Kramers–Kronig relations describe the frequency-dependence of wave propagation and attenuation. Dispersion may be caused either by geometric boundary conditions ( waveguides, shallow water) or by interaction of the waves with the transmitting medium. Elementary particles, considered as matter waves, have a nontrivial dispersion relation, even in the absence of geometric constraints and other media. In the presence of dispersion, a wave does not propagate with ...
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Physics
Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." It is one of the most fundamental scientific disciplines. "Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of ...
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Electrical Engineering
Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems that use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the latter half of the 19th century after the commercialization of the electric telegraph, the telephone, and electrical power generation, distribution, and use. Electrical engineering is divided into a wide range of different fields, including computer engineering, systems engineering, power engineering, telecommunications, radio-frequency engineering, signal processing, instrumentation, photovoltaic cells, electronics, and optics and photonics. Many of these disciplines overlap with other engineering branches, spanning a huge number of specializations including hardware engineering, power electronics, Electromagnetism, electromagnetics and waves, microwave engineering, nanotechnology, electrochemistry, renewable energies, mechatronics/control ...
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Brooklyn
Brooklyn is a Boroughs of New York City, borough of New York City located at the westernmost end of Long Island in the New York (state), State of New York. Formerly an independent city, the borough is coextensive with Kings County, one of twelve original counties established under English rule in 1683 in what was then the Province of New York. As of the 2020 United States census, the population stood at 2,736,074, making it the most populous of the five boroughs of New York City, and the most populous Administrative divisions of New York (state)#County, county in the state.Table 2: Population, Land Area, and Population Density by County, New York State - 2020
New York State Department of Health. Accessed January 2, 2024.

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Samuel J
Samuel is a figure who, in the narratives of the Hebrew Bible, plays a key role in the transition from the biblical judges to the United Kingdom of Israel under Saul, and again in the monarchy's transition from Saul to David. He is venerated as a prophet in Judaism, Christianity, and Islam. In addition to his role in the Bible, Samuel is mentioned in Jewish rabbinical literature, in the Christian New Testament, and in the second chapter of the Quran (although the text does not mention him by name). He is also treated in the fifth through seventh books of '' Antiquities of the Jews'', written by the Jewish scholar Josephus in the first century. He is first called "the Seer" in 1 Samuel 9:9. Biblical account Family Samuel's mother was Hannah and his father was Elkanah. Elkanah lived at Ramathaim in the district of Zuph. His genealogy is also found in a pedigree of the Kohathites (1 Chronicles 6:3–15) and in that of Heman the Ezrahite, apparently his grandson (1 Chro ...
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Ukraine
Ukraine is a country in Eastern Europe. It is the List of European countries by area, second-largest country in Europe after Russia, which Russia–Ukraine border, borders it to the east and northeast. Ukraine also borders Belarus to the north; Poland and Slovakia to the west; Hungary, Romania and Moldova to the southwest; and the Black Sea and the Sea of Azov to the south and southeast. Kyiv is the nation's capital and List of cities in Ukraine, largest city, followed by Kharkiv, Odesa, and Dnipro. Ukraine's official language is Ukrainian language, Ukrainian. Humans have inhabited Ukraine since 32,000 BC. During the Middle Ages, it was the site of early Slavs, early Slavic expansion and later became a key centre of East Slavs, East Slavic culture under the state of Kievan Rus', which emerged in the 9th century. Kievan Rus' became the largest and most powerful realm in Europe in the 10th and 11th centuries, but gradually disintegrated into rival regional powers before being d ...
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