How to get Airy disc from Airy pattern

Airy pattern is formed by diffraction of a plane wave through a circular aperture in the far field with certain side lobes. It is shown that Airy pattern can be truncated at the first dark ring by a circular aperture to pick up the center spot (called Airy disc) without causing additional diffraction fringes, even in the very far field. This may be called zero field truncation technique. And is very useful in practice, for example, as a good quality optical source.     

Static anisotropic fluid spheres in general relativity with nonuniform density

An Ansatz developed by Maharaj and Maartens is used to obtain solutions of Einstein's field equations for static anisotropic fluid spheres with nonuniform density. These solutions are matched with the Schwarzschild exterior solution.     

Kinetic theory of hard spheres

Kinetic equations for the hard-sphere system are derived by diagrammatic techniques. A linear equation is obtained for the one-particle-one particle equilibrium time correlation function and a nonlinear equation for the one-particle distribution function in nonequilibrium. Both equations are nonlocal, noninstantaneous, and extremely complicated. They are valid for general density, since statistical correlations are taken into account systematically. This method derives several known and new results from a unified point of view. Simple approximations lead to the Boltzmann equation for low densities and to a modified form of the Enskog equation for higher densities.     

Generalization and applications of the Sasakawa theory

The Sasakawa theory of scattering is phrased in the form of a Fredhohn reduction technique for integral equations possessing a fixed-point singularity in their kernels. This permits the generalization of this theory to a large variety of scattering integral equations. Some specific applications include the two-particle off-shell and multichannel scattering problems. In the first instance a rank-three approximation to the fully off-shell transition matrix is derived which is exact on and half-off shell, satisfies off-shell unitarity, and which possesses no unphysical singularities. In the second problem it is shown how the method leads to the generation of a unitary approximation to the multichannel amplitudes.     

Application of the scaled particle theory to the glass transition of hard spheres

In a previous article [1], an improved approach to the scaled particle theory of Reiss et al. was presented. As a result, we obtained a Padé-like expression of the compressibility factor of the fluid state. That expression contains two parameters p ₁ and p ₂, which we were able to calculate. In this paper we find other sets of values for p ₁ and p ₂. Two of these sets yield equations of state which agree with the simulation results of the glassy states obtained by Woodcock and Speedy. The calculations are based on two assumptions: firstly, that second order phase transitions may occur and secondly, that a hard sphere glass contains a fluid-like and a solid-like part. As an additional result, we found an upper and a lower limit for the fluid densities at which glass transitions may occur.     

Bounce of spheres in Einstein-Cartan theory

It is pointed out that an Einstein-Cartan sphere must bounce outside the Schwarzschild radius, if it bounces at all. Except in extreme cases the presence of torsion does not appreciably alter the conditions of the gravitational collapse of stars.     

Charged dust spheres in the general theory of relativity

Tolman's problem for charged dust is solved in quadratures. The external solution (Reisner-Nordstrom) is obtained in the natural reference frames of charged test particles. The conditions for matching a charged dust sphere with a vacuum over a fixed Lagrangian sphere are formulated. They are equivalent to boundary conditions on the initial data.Translated from Izvestiya Uchebnykh Zavedenii, Fizika, No. 4, pp. 107–113, April, 1976.The author is deeply grateful to his colleagues K. A. Bronnikov and M. A. Koval'chuk for discussion of this article and a number of valuable remarks.     

Charged dust spheres in the general theory of relativity

The problem of the physical time singularities of charged dust spheres is investigated on the basis of the quadratures of the Einstein-Maxwell equations derived in Part I. Two versions are enumerated for the initial conditions which result in completely nonsingular models.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 106–111, July, 1976.     

Generalization of Haag's theorem in scattering theory

A simple proof of Haag's theorem for the Jost model is given. Our method, different from the known ones, enables us to generalize the Haag's theorem in a sense that the inversitibility property of W_±(t) mappings for any fixed time and its boundedness, instead of the unitarity requirement, is already sufficient to make a theory physically trivial.     

The structure of Lennard-Jones dimerizing spheres near a hard wall from the nonuniform wertheim Ornstein-Zernike equation

A dimerizing model of Lennard-Jones particles near a hard wall is studied using the inhomogeneous or second order Wertheim Ornstein-Zernike equation and the inhomogeneous associative Percus-Yevick closure. We investigate the influence of the degree of dimerization on the shape of the density profiles and on inhomogeneous pair correlation functions. This work was supported in parts by KBN of Poland (the Grant No. 3T09A 06210) and by Cray Research, Inc., of Mexico under its University Research and Development Grant Program. Garcia.     

Generalization of the Hutson and White theory to the case of piezosemiconductors with mixed conductivity

The Hutson-White theory is extended to the case when there are mobile charge carriers of both signs in a piezeosemiconductor. Expressions are obtained for the damping and velocity of the longitudinal sound wave being propagated along the z axis in the piezosemiconductor as a function of the magnitude of the longitudinal electrical field, as well as for the constant current density originating here. It is shown that the acoustic wave changes the conductivity of a piezosemiconductor with mixed conductivity. A method is proposed for determining the mobility simultaneously of both the positive and negative carriers in an intrinsic piezosemiconductor.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 55–58, November, 1984.     

A partitioned density functional theory of freezing: application to soft spheres

A non-perturbative density functional theory (DFT) for inhomogeneous fluids is developed by partitioning the functional into short range (‘entropic’) and long range (‘energetic’) contributions. The short range part is treated using standard weighted density functional techniques and the long range contribution is evaluated exactly. This method, which is a generalization of a method due to Likos, C., and Senatore, G., 1995, J. Phys.: Condens. Matter, 7, 6797, does not require the use of a reference system. Results are presented for the calculation of the crystal-/fluid phase coexistence for systems interacting with inverse-power potentials of the form r ^-n , where n = 4, 6 and 12. These results show that this non-perturbative DFT is capable of predicting the freezing of long range inverse power systems (n = 4, 6) into a body-centredcubic lattice. Improvements over earlier methods also are noted in the current results for the solid structure as measured by the Lindemann ratio.     

Charged static fluid spheres in Einstein-Cartan theory

We give exact interior solutions of the Einstein-Cartan equations describing charged perfect fluid distribution in general relativity. Results previously unknown for the uncharged case are deduced and we find that the pressure is discontinuous at the boundary of the fluid sphere.     

Kinetic theory of field effects in nonuniform molecular gases

Effects of magnetic and electric fields on transport phenomena in dilute polyatomic gases are reviewed within the framework of first order Enskog theory. The established technique of approximate operator inversion is used to give first order approximations of the transport coefficients. Instead of the customary expansion of polarization into orthogonal polynomials a more general treatment is chosen here so as to accomodate recent experimental observations. The polarizations produced by macroscopic fluxes are assumed to be eigenfunctions of the collision operator within the subspace of functions anisotropic in angular momentum. The formalism is extended to mixtures in a way to let the final expressions assume the same form as for pure gases. The obtained transport coefficients obey several symmetry relations and inequalities. Additional inequalities are now also derived for the matrix describing the saturated field effects.     

On the theory of phase transformations with a nonuniform nucleation rate

An expression for the phase volume fraction in a system with a nonuniform nucleation rate is derived by using the geometrical-probabilistic approach. Examples of such systems considered here are (1) a plane layer (with nucleation in the midplane) and random planes in space, (2) an infinitely long cylinder (with nucleation on the axis) and random lines in space, and (3) a sphere (with nucleation at the center) and nucleation at random points. In each case, an expression for the phase volume fraction is derived for the time-dependent rates of nucleation and growth. The equivalence of homogeneous nucleation and nucleation at points is established.     

Generalization of the momentum-space subtraction procedure for renormalized perturbation theory

The momentum-space subtraction procedure for defining renormalized Feynman integrals is modified to allow for subtraction operators more general than the usual Taylor operators. The added generality permits one to assign subtraction degree less than four to some terms of the unperturbed Lagrangian.