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Birch–Murnaghan Equation Of State
The Birch–Murnaghan isothermal equation of state, published in 1947 by Albert Francis Birch of Harvard, is a relationship between the volume of a body and the pressure to which it is subjected. Birch proposed this equation based on the work of Francis Dominic Murnaghan of Johns Hopkins University published in 1944, so that the equation is named in honor of both scientists. Expressions for the equation of state The third-order Birch–Murnaghan isothermal equation of state is given by P(V)=\frac \left left(\frac\right)^ - \left(\frac\right)^\right\left\. where ''P'' is the pressure, ''V''0 is the reference volume, ''V'' is the deformed volume, ''B''0 is the bulk modulus, and ''B''0' is the derivative of the bulk modulus with respect to pressure. The bulk modulus and its derivative are usually obtained from fits to experimental data and are defined as B_0 = -V \left(\frac\right)_ and B_0' = \left(\frac\right)_ The expression for the equation of state is obtained by expandi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Francis Birch (geophysicist)
Francis Birch (August 22, 1903 – January 30, 1992) was an American geophysicist. He is considered one of the founders of solid Earth geophysics. He is also known for his part in the atomic bombing of Hiroshima and Nagasaki. During World War II, Birch participated in the Manhattan Project, working on the design and development of the gun-type nuclear weapon known as Little Boy. He oversaw its manufacture, and went to Tinian to supervise its assembly and loading into ''Enola Gay'', the Boeing B-29 Superfortress tasked with dropping the bomb. A graduate of Harvard University, Birch began working on geophysics as a research assistant. He subsequently spent his entire career at Harvard working in the field, becoming an Associate Professor of Geology in 1943, a professor in 1946, and Sturgis Hooper Professor of Geology in 1949, and professor emeritus in 1974. Birch published over 100 papers. He developed what is now known as the Birch-Murnaghan equation of state in 1947. In 1952 h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harvard
Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher learning in the United States and one of the most prestigious and highly ranked universities in the world. The university is composed of ten academic faculties plus Harvard Radcliffe Institute. The Faculty of Arts and Sciences offers study in a wide range of undergraduate and graduate academic disciplines, and other faculties offer only graduate degrees, including professional degrees. Harvard has three main campuses: the Cambridge campus centered on Harvard Yard; an adjoining campus immediately across Charles River in the Allston neighborhood of Boston; and the medical campus in Boston's Longwood Medical Area. Harvard's endowment is valued at $50.9 billion, making it the wealthiest academic institution in the world. Endowment inco ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Francis Dominic Murnaghan (mathematician)
Francis Dominic Murnaghan (August 4, 1893 – March 24, 1976) was an Irish mathematician and former head of the mathematics department at Johns Hopkins University. His name is attached to developments in group theory and mathematics applied to continuum mechanics ( Murnaghan and Birch–Murnaghan equations of state). Biography Frank Murnaghan was born in Omagh, Co. Tyrone, Ireland, seventh of the nine children of George Murnaghan, a Nationalist MP representing Mid Tyrone constituency. He graduated from Irish Christian Brothers secondary school in 1910, and University College Dublin with first-class honours BSc in Mathematical Sciences in 1913. Following an MSc in 1914, he was awarded a National University of Ireland (NUI) Travelling Studentship, which funded him to pursue his doctorate at Johns Hopkins University. In 1916, after just two years working under department chair Frank Morley's new PhD student Harry Bateman, he was awarded the Ph.D. He then lectured at Rice Univers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Johns Hopkins University
Johns Hopkins University (Johns Hopkins, Hopkins, or JHU) is a private university, private research university in Baltimore, Maryland. Founded in 1876, Johns Hopkins is the oldest research university in the United States and in the western hemisphere. It consistently ranks among the most prestigious universities in the United States and the world. The university was named for its first benefactor, the American entrepreneur and Quaker philanthropist Johns Hopkins. Hopkins' $7 million bequest to establish the university was the largest Philanthropy, philanthropic gift in U.S. history up to that time. Daniel Coit Gilman, who was inaugurated as :Presidents of Johns Hopkins University, Johns Hopkins's first president on February 22, 1876, led the university to revolutionize higher education in the U.S. by integrating teaching and research. In 1900, Johns Hopkins became a founding member of the American Association of Universities. The university has led all Higher education in the U ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Albert Francis Birch
Francis Birch (August 22, 1903 – January 30, 1992) was an American geophysicist. He is considered one of the founders of solid Earth geophysics. He is also known for his part in the atomic bombing of Hiroshima and Nagasaki. During World War II, Birch participated in the Manhattan Project, working on the design and development of the gun-type nuclear weapon known as Little Boy. He oversaw its manufacture, and went to Tinian to supervise its assembly and loading into ''Enola Gay'', the Boeing B-29 Superfortress tasked with dropping the bomb. A graduate of Harvard University, Birch began working on geophysics as a research assistant. He subsequently spent his entire career at Harvard working in the field, becoming an Associate Professor of Geology in 1943, a professor in 1946, and Sturgis Hooper Professor of Geology in 1949, and professor emeritus in 1974. Birch published over 100 papers. He developed what is now known as the Birch-Murnaghan equation of state in 1947. In 1952 h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Murnaghan Equation Of State
The Murnaghan equation of state is a relationship between the volume of a body and the pressure to which it is subjected. This is one of many state equations that have been used in earth sciences and shock physics to model the behavior of matter under conditions of high pressure. It owes its name to Francis D. Murnaghan who proposed it in 1944 to reflect material behavior under a pressure range as wide as possible to reflect an experimentally established fact: the more a solid is compressed, the more difficult it is to compress further. The Murnaghan equation is derived, under certain assumptions, from the equations of continuum mechanics. It involves two adjustable parameters: the modulus of incompressibility ''K''0 and its first derivative with respect to the pressure, ''K''′0, both measured at ambient pressure. In general, these coefficients are determined by a regression on experimentally obtained values of volume ''V'' as a function of the pressure ''P''. These exper ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuum Mechanics
Continuum mechanics is a branch of mechanics that deals with the mechanical behavior of materials modeled as a continuous mass rather than as discrete particles. The French mathematician Augustin-Louis Cauchy was the first to formulate such models in the 19th century. Explanation A continuum model assumes that the substance of the object fills the space it occupies. Modeling objects in this way ignores the fact that matter is made of atoms, and so is not continuous; however, on length scales much greater than that of inter-atomic distances, such models are highly accurate. These models can be used to derive differential equations that describe the behavior of such objects using physical laws, such as mass conservation, momentum conservation, and energy conservation, and some information about the material is provided by constitutive relationships. Continuum mechanics deals with the physical properties of solids and fluids which are independent of any particular coordinate sy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
