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Subrahmanyan Chandrasekhar
Subrahmanyan Chandrasekhar (; ) (19 October 1910 – 21 August 1995) was an Indian-American theoretical physicist who spent his professional life in the United States. He shared the 1983 Nobel Prize for Physics with William A. Fowler for "...theoretical studies of the physical processes of importance to the structure and evolution of the stars". His mathematical treatment of stellar evolution yielded many of the current theoretical models of the later evolutionary stages of massive stars and black holes. Many concepts, institutions, and inventions, including the Chandrasekhar limit and the Chandra X-Ray Observatory, are named after him. Chandrasekhar worked on a wide variety of problems in physics during his lifetime, contributing to the contemporary understanding of stellar structure, white dwarfs, stellar dynamics, stochastic process, radiative transfer, the quantum theory of the hydrogen anion, hydrodynamic and hydromagnetic stability, turbulence, equilibrium and the stabi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lahore
Lahore ( ; pnb, ; ur, ) is the second most populous city in Pakistan after Karachi and 26th most populous city in the world, with a population of over 13 million. It is the capital of the province of Punjab where it is the largest city. Lahore is one of Pakistan's major industrial and economic hubs, with an estimated GDP ( PPP) of $84 billion as of 2019. It is the largest city as well as the historic capital and cultural centre of the wider Punjab region,Lahore Cantonment globalsecurity.org and is one of Pakistan's most , progressiv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anne Barbara Underhill
Anne Barbara Underhill FRSC (June 12, 1920 - July 3, 2003) was a Canadian astrophysicist. She is most widely known for her work on early-type stars and was considered one of the world's leading experts in the field. During her lifetime she received many awards for her contributions to astronomy and astrophysics. Early life Underhill grew up in Vancouver, British Columbia. She was the only girl of five children born to European immigrants Irene Anna (née Creery) and civil engineer Frederic Clare Underhill. She was awarded the Lieutenant Governor's medal in high school for her outstanding school performance. She was close with her twin brother and three younger brothers, and helped to raise them following the death of her mother when she was 18. In 1944 her twin brother was killed in World War II. Education Underhill graduated from the University of British Columbia in 1942 with a BA Hons in chemistry. She continued her education at the University and received a master's d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chandrasekhar Virial Equations
In astrophysics, the Chandrasekhar virial equations are a hierarchy of moment equations of the Euler equations, developed by the Indian American astrophysicist Subrahmanyan Chandrasekhar, and the physicist Enrico Fermi and Norman R. Lebovitz. Mathematical description Consider a fluid mass M of volume V with density \rho(\mathbf,t) and an isotropic pressure p(\mathbf,t) with vanishing pressure at the bounding surfaces. Here, \mathbf refers to a frame of reference attached to the center of mass. Before describing the virial equations, let's define some moments. The density moments are defined as : M = \int_V \rho \, d\mathbf, \quad I_i = \int_V \rho x_i \, d\mathbf, \quad I_ = \int_V \rho x_i x_j \, d\mathbf, \quad I_ = \int_V \rho x_i x_j x_k \, d\mathbf, \quad I_ = \int_V \rho x_i x_j x_k x_\ell \, d\mathbf, \quad \text the pressure moments are :\Pi = \int_V p \, d\mathbf, \quad \Pi_i = \int_V p x_i \, d\mathbf, \quad \Pi_ = \int_V p x_i x_j \, d\mathbf, \quad \Pi_ = \int_V p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chandrasekhar Potential Energy Tensor
In astrophysics, Chandrasekhar potential energy tensor provides the gravitational potential of a body due to its own gravity created by the distribution of matter across the body, named after the Indian American astrophysicist Subrahmanyan Chandrasekhar. The Chandrasekhar tensor is a generalization of potential energy in other words, the trace of the Chandrasekhar tensor provides the potential energy of the body. Definition The Chandrasekhar potential energy tensor is defined as :W_ = -\frac \int_V \rho \Phi_ d\mathbf =\int_V \rho x_i \frac d\mathbf where :\Phi_(\mathbf) = G \int_V \rho(\mathbf) \frac d\mathbf, \quad \Rightarrow \quad \Phi_ = \Phi = G \int_V \frac d\mathbf where *G is the Gravitational constant *\Phi(\mathbf) is the self-gravitating potential from Newton's law of gravity *\Phi_ is the generalized version of \Phi *\rho(\mathbf) is the matter density distribution *V is the volume of the body It is evident that W_ is a symmetric tensor from its definition. The tr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chandrasekhar–Page Equations
Chandrasekhar–Page equations describe the wave function of the spin-½ massive particles, that resulted by seeking a separable solution to the Dirac equation in Kerr metric or Kerr–Newman metric. In 1976, Subrahmanyan Chandrasekhar showed that a separable solution can be obtained from the Dirac equation in Kerr metric. Later, Don Page extended this work to Kerr–Newman metric, that is applicable to charged black holes. In his paper, Page notices that N. Toop also derived his results independently, as informed to him by Chandrasekhar. By assuming a normal mode decomposition of the form e^ for the time and the azimuthal component of the spherical polar coordinates (r,\theta,\phi), Chandrasekhar showed that the four bispinor components can be expressed as product of radial and angular functions. The two radial and angular functions, respectively, are denoted by R_(r), R_(r) and S_(\theta), S_(\theta). The energy as measured at infinity is \omega and the axial angular momentum is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chandrasekhar–Fermi Method
Chandrasekhar–Fermi method or CF method or Davis–Chandrasekhar–Fermi method is a method that is used to calculate the mean strength of the interstellar magnetic field that is projected on the plane of the sky. The method was described by Subrahmanyan Chandrasekhar and Enrico Fermi in 1953 and independently by Leverett Davis Jr in 1951. According to this method, the magnetic field B in the plane of the sky is given by :B = Q\sqrt \frac where \rho is the mass density, \delta v is the line-of-sight velocity dispersion In astronomy, the velocity dispersion (''σ'') is the statistical dispersion of velocity, velocities about the Arithmetic mean, mean velocity for a group of astronomical objects, such as an open cluster, globular cluster, galaxy, galaxy cluster, or ... and \delta \phi is the dispersion of polarization angles and Q is an order unity factor, which is typically taken it to be Q\approx 0.5. The method is also employed for prestellar molecular clouds.Crutcher, R. M., ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Emden–Chandrasekhar Equation
In astrophysics, the Emden–Chandrasekhar equation is a dimensionless form of the Poisson equation for the density distribution of a spherically symmetric isothermal gas sphere subjected to its own gravitational force, named after Robert Emden and Subrahmanyan Chandrasekhar. The equation was first introduced by Robert Emden in 1907. The equation reads :\frac \frac\left(\xi^2 \frac\right)= e^ where \xi is the dimensionless radius and \psi is the related to the density of the gas sphere as \rho=\rho_c e^, where \rho_c is the density of the gas at the centre. The equation has no known explicit solution. If a polytropic fluid is used instead of an isothermal fluid, one obtains the Lane–Emden equation. The isothermal assumption is usually modeled to describe the core of a star. The equation is solved with the initial conditions, :\psi =0, \quad \frac =0 \quad \text \quad \xi=0. The equation appears in other branches of physics as well, for example the same equation appears in the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chandrasekhar's H-function
In atmospheric radiation, Chandrasekhar's ''H''-function appears as the solutions of problems involving scattering, introduced by the Indian American astrophysicist Subrahmanyan Chandrasekhar.Sparrow, Ephraim M., and Robert D. Cess. "Radiation heat transfer." Series in Thermal and Fluids Engineering, New York: McGraw-Hill, 1978, Augmented ed. (1978). The Chandrasekhar's ''H''-function H(\mu) defined in the interval 0\leq\mu\leq 1, satisfies the following nonlinear integral equation :H(\mu) = 1+\mu H(\mu)\int_0^1 \fracH(\mu') \, d\mu' where the characteristic function \Psi(\mu) is an even polynomial in \mu satisfying the following condition :\int_0^1\Psi(\mu) \, d\mu \leq \frac. If the equality is satisfied in the above condition, it is called ''conservative case'', otherwise ''non-conservative''. Albedo is given by \omega_o= 2\Psi(\mu) = \text. An alternate form which would be more useful in calculating the ''H'' function numerically by iteration was derived by Chandrasekhar as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chandrasekhar–Kendall Function
Chandrasekhar–Kendall functions are the axisymmetric eigenfunctions of the curl operator derived by Subrahmanyan Chandrasekhar and P. C. Kendall in 1957 while attempting to solve the force-free magnetic fields. The functions were independently derived by both, and the two decided to publish their findings in the same paper. If the force-free magnetic field equation is written as \nabla\times\mathbf=\lambda\mathbf, where \mathbf is the magnetic field and \lambda is the force-free parameter, with the assumption of divergence free field, \nabla\cdot\mathbf=0, then the most general solution for the axisymmetric case is :\mathbf = \frac\nabla\times(\nabla\times\psi\mathbf) + \nabla \times \psi \mathbf where \mathbf is a unit vector and the scalar function \psi satisfies the Helmholtz equation, i.e., :\nabla^2\psi + \lambda^2\psi=0. The same equation also appears in Beltrami flows from fluid dynamics where, the vorticity vector is parallel to the velocity vector, i.e., \nabla\times\math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chandrasekhar Friction
In astrophysics, dynamical friction or Chandrasekhar friction, sometimes called ''gravitational drag'', is loss of momentum and kinetic energy of moving bodies through gravitational interactions with surrounding matter in space. It was first discussed in detail by Subrahmanyan Chandrasekhar in 1943. Intuitive account An intuition for the effect can be obtained by thinking of a massive object moving through a cloud of smaller lighter bodies. The effect of gravity causes the light bodies to accelerate and gain momentum and kinetic energy (see slingshot effect). By conservation of energy and momentum, we may conclude that the heavier body will be slowed by an amount to compensate. Since there is a loss of momentum and kinetic energy for the body under consideration, the effect is called ''dynamical friction''. Another equivalent way of thinking about this process is that as a large object moves through a cloud of smaller objects, the gravitational effect of the larger object pulls ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chandrasekhar Number
The Chandrasekhar number is a dimensionless quantity used in magnetic convection to represent ratio of the Lorentz force to the viscosity. It is named after the Indian astrophysicist Subrahmanyan Chandrasekhar. The number's main function is as a measure of the magnetic field, being proportional to the square of a characteristic magnetic field in a system. Definition The Chandrasekhar number is usually denoted by the letter \ Q, and is motivated by a dimensionless form of the Navier-Stokes equation in the presence of a magnetic force in the equations of magnetohydrodynamics: :: \frac\left(\frac\ +\ (\mathbf \cdot \nabla) \mathbf\right)\ =\ - p\ +\ \nabla^2 \mathbf\ +\frac \ ( \wedge \mathbf) \wedge\mathbf, where \ \sigma is the Prandtl number, and \ \zeta is the magnetic Prandtl number. The Chandrasekhar number is thus defined as:N.E. Hurlburt, P.C. Matthews and A.M. Rucklidge, "Solar Magnetoconvection," ''Solar Physics'', 192, p109-118 (2000) :: \ =\ \frac where \ \m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
