A finite element-spherical harmonics radiation transport model for photon migration in turbid media

In this paper, we solve the steady-state form of the Boltzmann transport equation in homogeneous and heterogeneous tissue-like media with a finite element-spherical harmonics (FE-P_N) radiation transport method. We compare FE-transport and diffusion solutions in terms of the ratio of absorption to reduced scattering coefficient, (μ_a/μ_s′) and the anisotropy factor g. Two different scattering phase function formulas are employed to model anisotropic scattering in the slab media with high g-value. Influence of void-like heterogeneities, and of their boundaries with the surrounding medium on the transport of photons are also examined.     

Planar Pyrochlore,Quantum Ice and Sliding Ice

We study quantum antiferromagnetism on the highly frustrated planar pyrochlore lattice, also known as the square lattice with crossings. The quantum Heisenberg antiferromagnet on this lattice is of interest as a two-dimensional analogue of the pyrochlore lattice magnet. By combining several approaches we conclude that this system is most likely ordered for all values of spin, S, with a two-fold degenerate valence-bond solid being the ground state for small S. We show next that the Ising antiferromagnet with a weak four-spin exchange, equivalent to square ice with the leading quantum dynamics, exhibits analogous plaquette order. As a byproduct of this analysis we obtain, in the system of weakly coupled ice planes, a sliding phase with XY symmetry; at intermediate couplings, long range “anti-ferroelectric” order is stabilized.     

Sagnac Effect of Gödel's Universe

We present exact expressions for the Sagnac effect of Gödel's Universe. For this purpose we first derive a formula for the Sagnac time delay along a circular path in the presence of an arbitrary stationary metric in cylindrical coordinates. We then apply this result to Gödel's metric for two different experimental situations: First, the light source and the detector are at rest relative to the matter generating the gravitational field. In this case we find an expression that is formally equivalent to the familiar nonrelativistic Sagnac time delay. Second, the light source and the detector are rotating relative to the matter. Here we show that for a special rotation rate of the detector the Sagnac time delay vanishes. Finally we propose a formulation of the Sagnac time delay in terms of invariant physical quantities. We show that this result is very close to the analogous formula of the Sagnac time delay of a rotating coordinate system in Minkowski spacetime.     

Geometric algebra techniques for general relativity

Geometric (Clifford) algebra provides an efficient mathematical language for describing physical problems. We formulate general relativity in this language. The resulting formalism combines the efficiency of differential forms with the straightforwardness of coordinate methods. We focus our attention on orthonormal frames and the associated connection bivector, using them to find the Schwarzschild and Kerr solutions, along with a detailed exposition of the Petrov types for the Weyl tensor.     

Mathematical modeling of the Magnus effect in the geometrical optics approximation

The Magnus effect in multimode fibers with triangular and parabolic refractive index profiles (RIPs) is simulated in the geometrical optics approximation. The calculations confirm the linear relation between the angle of rotation Δ? and the fiber length z. The results of calculations for a spiral path with constant radius are compared with the analytical solution obtained. For a fiber with a parabolic RIP, the value of Δ? obtained in this work is one-half the result obtained in the wave approach.     

Computer processing of electronic absorption spectra of rare-earth elements in inorganic laser media

Algorithms and program modules are developed for calculation of the Judd-Ofelt parameters on modern computers. These programs can be used to perform numerical analysis of the energy absorption by rareearth ions in laser media.     

Some inhomogeneous magnetized viscous-fluid cosmological models with varyingΛ

Some cylindrically symmetric inhomogeneous viscous-fluid cosmological models with electromagnetic field are obtained. To get a solution a supplementary condition between metric potentials is used. The viscosity coefficient of bulk viscous fluid is assumed to be a power function of mass density. Without assuming anyad hoc law, we obtain a cosmological constant as a decreasing function of time. The behaviour of the electromagnetic field tensor together with some physical aspects of the model are also discussed.     

An interference method for studying a substance in the vicinity of its critical point

An interference method for measuring certain parameters of a substance in the vicinity of the critical state is proposed. The essence of the method is to decipher the interference pattern arising upon grazing incidence of a laser beam on a curved liquid-vapor interface. The deciphering allows one to determine the difference between the refractive indices of the two phases and the scaling factor of the wetting meniscus shape. This, in turn, makes it possible to calculate the critical exponents for the temperature dependences of the surface tension and the difference in the densities of the two phases. The ratio of these critical exponents for xenon, measured in the paper, is 3.81±0.03.     

On two functionals connected to the Laplacian in a class of doubly connected domains in space-forms

LetB ₁ be a ball of radiusr ₁ inS ⁿ (ℍⁿ), and letB ₀ be a smaller ball of radiusr ₀ such thatB ₀ ⊂B ₁ . ForS ⁿ we considerr ₁ π. Let u be a solution of the problem- δm = 1 in Ω :=B ₁ /B ₀ vanishing on the boundary. It is shown that the associated functionalJ (Ω) is minimal if and only if the balls are concentric. It is also shown that the first Dirichlet eigenvalue of the Laplacian on Ω is maximal if and only if the balls are concentric.