Browsing Faculty Works, Department of Mathematics by Issue Date
Now showing items 120 of 182

expansionfree electromagnetic solutions of KerrSchild class
(AIP Publishing, 197407)Starting with the general Kerr_Schild form of the metric tensor,d s2=_+l_l (where l is null and _ is flat space_time), a study is made for those solutions of the Einstein_Maxwell equations in which l is geodesic, shear_free, ... 
power statistics for wave propagation in onedimension and comparison with radiative transporttheory. II.
(AIP Publishing, 197412)We consider the one_dimensional problem of a slab having a random index of refraction and illuminated from within by a point source. We compute the expected value and the fluctuations of both the total power and power flux. ... 
conditional entropy in microcanonical ensemble
(AIP Publishing, 197508)The existence of the configurational microcanonical conditional entropy in classical statistical mechanics is proved in the thermodynamic limit for a class of long_range multiparticle observables. This result generalizes ... 
functional calculus for symmetric multigroup transport operator
(AIP Publishing, 197602)A rigorous treatment of the symmetric multigroup transport equation is given by developing the functional calculus for the transport operator. Von Neumann spectral theory is applied to nonorthogonal cyclic subspaces, and ... 
Case eigenfunction expansion for a conservative medium
(AIP Publishing, 197602)By using the resolvent integration technique introduced by Larsen and Habetler, the one‐speed, isotropic scattering,neutron transport equation is treated in the infinite and semi‐infinite media. It is seen that the results ... 
solution of multigroup transport equation in Lp spaces
(AIP Publishing, 197611)The isotropic multigroup transport equation is solved in L p , p_1, for both half range and full range problems, using resolvent integration techniques. The connection between these techniques and a spectral decomposition ... 
Vlasov theory of plasma oscillations: linearapproximation
(AIP Publishing, 1977)A functional analytic approach to the linearized collisionless Vlasov equation is presented utilizing a resolvent integration technique on the resolvent of the transport operator evaluated at a particular point. Formulae ... 
multiplescales spacetime analysis of a randomly perturbed onedimensional waveequation
(AIP Publishing, 197710)An initial value problem for one_dimensional wave propagation is considered; the medium is assumed to be randomly perturbed as a function of both space and time. The stochastic perturbation theory of Papanicolaou and Keller ... 
interaction function and lattice duals
(AIP Publishing, 197710)An interaction function is defined for lattice models in statistical mechanics. A correlation function expansion is derived, giving a direct proof of the duality relations for correlation functions. 
uniqueness of solutions to linearized Boltzmann equation
(AIP Publishing, 197801)Uniqueness theorems are proved for the linearized Boltzmann equation for both the ’’exterior’’ and ’’interior’’ problems under generalized Maxwellboundary conditions. The solution space is a weighted L p space, and agrees ... 
transverse plasma oscillations
(AIP Publishing, 1979)An operator theoretic approach is used to solve the linearized Vlasov–Maxwell equations for transverse plasma oscillations. In particular, the special cases of simple and second‐order real zeros of the plasma dispersion ... 
resolvent integration techniques for generalized transport equations
(AIP Publishing, 197906)A generalized class of ’’transport type’’ equations is studied, including most of the known exactly solvable models; in particular, the transport operator K is a scalar type spectral operator. A spectral resolution for K ... 
Pulse propagation in a randomly perturbed ocean: Single pulse statistics
(Acoustical Society of America, 198010)A statistical theory of broadband single pulse propagation in a random ocean is presented. The mutual coherence function of the received signal is derived using an analysis based upon coupled mode theory. As propagation ... 
analytical solutions of model equations for two phase gas mixtures: Transverse velocity perturbations
(AIP Publishing, 1984)Model equations for a dilute binary gas system are derived, using a linear BGK scheme. Complete analytical solutions for the stationary half_space problem are obtained for transverse velocity perturbations. The method of ... 
the effect of surface tension on the shape of a HeleShaw cell bubble
(AIP Publishing, 198611)Numerical and asymptotic solutions are found for the steady motion of a symmetrical bubble through a parallel‐sided channel in a Hele–Shaw cell containing a viscous liquid. The degeneracy of the Taylor–Saffman zero ... 
The thinlayer effect and interfacial stability in a twolayer Couette flow with similar liquids
(AIP Publishing, 198706)The linear stability of Couette flow composed of two layers of immiscible fluids, one lying on top of the other, is considered for the special case when the two fluids have similar mechanical properties. The interfacial ... 
viscosity and density stratification in vertical Poiseuille flow
(AIP Publishing, 198706)The linear stability of plane three_layer vertical Poiseuille flow is considered. The layers are composed of two immiscible fluids, one next to the walls and one centrally located. The fluids have different viscosities and ... 
exact behavior of Jost functions at lowenergy
(AIP Publishing, 198801)For Schrödinger operators with central potential q(r) and angular momentuml, the behavior of the Jost function F l (k) as k→0 is investigated. It is assumed that ∫∞ 0 d r (1+r)σ‖q(r)‖<∞, where σ≥1. Situations where q is ... 
the semiclassical limit of quantum dynamics. I. time evolution
(AIP Publishing, 198802)The ℏ→0 limit of the quantum dynamics determined by the Hamiltonian H(ℏ) =−(ℏ2/2m)Δ+V on L 2(R n ) is studied for a large class of potentials. By convolving with certain Gaussian states, classically determined asymptotic ... 
Couette flow of a binary gas mixture
(AIP Publishing, 198803)The linearized binary model described by Hamel [Phys. Fluids 8, 418 (1964)] is used to obtain a set of kinetic equations and boundary conditions for the Couette flow problem. The derived set of two coupled integrodifferential ...