Exact solutions inU 4 gravity. I. The ansatz for self double dual curvature

We investigate the energy-momentum and spin field equations of gravity theory on a Riemann-Cartan space-time (including metric and torsion,U ₄-manifold). The structure of the rather complicated nonlinear differential equations of second order is made considerably easier to survey by decomposing curvature into its self and anti-self double dual parts. This leads to an obvious ansatz for the self double dual curvature, whereby the field equations are reduced to Einstein's equations with cosmological term. To solve the double dual ansatz, we choose proper variables adopted to its double duality, and perform a (3+1)-decomposition of exterior calculus. We examine these equations further on a Kerr background with cosmological constant for the Riemannian geometry.     

Effects of stenosis on arterial rheology through a mathematical model

The paper presents an analytical study of blood flow through a stenosed artery using a suitable mathematical model. The artery is modelled as an anisotropic viscoelastic cylindrical tube containing a non-Newtonian viscous incompressible fluid representing blood. The blood flow is assumed to be characterized by the Herschel–Bulkley model. The effect of the surrounding connective tissues on the motion of the arterial wall has been incorporated. Initially, the relevant solutions of the boundary value problem are obtained in the Laplace transform space, through the use of a suitable finite difference technique. Laplace inversion is carried out by employing suitable numerical techniques. Finally, the variations of the vascular wall displacements, the velocity distribution of the blood flow, the flux, the resistance to flow and the wall shear stress in the stenotic region are quantified through numerical computations and presented graphically.     

Atomistic packing models for experimentally investigated swelling states induced by CO2 in glassy polysulfone and poly(ether sulfone)

Atomistic packing models have been created, which help to better understand the experimentally observed swelling behavior of glassy polysulfone and poly (ether sulfone), under CO₂ gas pressures up to 50 bar at 308 K. The experimental characterization includes the measurement of the time‐dependent volume dilation of the polymer samples after a pressure step and the determination of the corresponding gas concentrations by gravimetric gas‐sorption measurements. The models obtained by force‐field‐based molecular mechanics and molecular dynamics methods allow a detailed atomistic analysis of representative swelling states of polymer/gas systems, with respect to the dilation of the matrix. Also, changes of free volume distribution and backbone mobility are accessible. The behavior of gas molecules in unswollen and swollen polymer matrices is characterized in terms of sorption, diffusion, and plasticization. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1874–1897, 2006     

High-pressure effect on the crystal and magnetic structure of LuMnO3: Correlation between a distortion of the triangular lattice and the symmetry of the magnetic state in hexagonal frustrated manganites

The effect of a high pressure (up to 6 GPa) on the crystal and magnetic structure of the hexagonal manganite LuMnO₃ is studied by neutron diffraction in the temperature range 10–295 K. It is found that, as the pressure increases, the ordered magnetic moment of Mn ions at T = 10 K decreases noticeably from 2.48 (0 GPa) to 1.98 μ_B (6 GPa). This decrease is due to an enhancement of the geometrical frustration effects on the triangular lattice. At the same time, the symmetry of the triangular antiferromagnetic state (the irreducible representation Γ₂) remains unchanged. A correlation is revealed between the distortion parameter of the triangular lattice formed by Mn ions and the symmetry of the antiferromagnetic state of hexagonal manganites RMnO₃. Based on this correlation, a generalized magnetic phase diagram of these compounds is constructed. The obtained phase diagram provides an explanation for the changes observed in the magnetic state of hexagonal manganites caused by high pressure and chemical substitution.     

On algebras of Toeplitz fuzzy matrices

In this paper, necessary and sufficient conditions are given for a product of Toeplitz fuzzy matrices to be Toeplitz. As an application, a criterion for normality of Toeplitz fuzzy matrices is derived and conditions are deduced for symmetric idempotency of Toeplitz fuzzy matrices. We discuss similar results for Hankel fuzzy matrices. Keywords: Fuzzy matrix, Toeplitz and Hankel matrices.     

Influence of focusing depth on the microfabrication of waveguides inside silica glass by femtosecond laser direct writing

We studied the influence of focusing depth on the index change threshold and damage threshold of silica glass irradiated by a focused 120 fs laser beam. Both thresholds increased with the focusing depth. The aspect ratio of the waveguide cross section can be selected by changing the focusing depth. A 5 mm long waveguide was written at the depth of 2100 μm, which was single mode at 632.8 nm and exhibited propagation loss of 0.56 dB/cm. The refractive index change was calculated to be ∼2.47×10^-3. The influence of the focusing depth should be considered in multi-layer devices as shown in the fabrication of a 3×3 waveguide array. PACS 42.62.-b; 42.82.Et; 81.05.Kf     

On the stability of the output characteristics of a grazing incidence grating dye laser transversely pumped by a copper vapor laser

The output characteristics of a high repetition rate pulsed dye laser has both short-term fluctuations and long-term drift. In high power high repetition rate lasers flow induced variations dominate over those due to other factors. In this paper it is shown by dye laser measurements that bandwidth fluctuations can be traced to the effective changes of the resonator dispersion due to fluctuations in the penetration depth of the pump beam in the dye medium. Short-term wavelength fluctuations can be traced to instantaneous deflection of the dye laser axis by the refractive index changes due to absorption of the pump beam. The fluctuations in both the bandwidth and the wavelength decreases with increasing flow rates within a laminar region. A copper vapor laser operating at 5.6 kHz repetition rate pumped the Rhodamine 6G dye laser used. The wavelength fluctuation of ±0.0035, 0.0030, 0.0004 nm and the bandwidth fluctuation of ±710, 132, 45 MHz over approx. 60 minutes were observed at 1.2, 3.7, 5.5 lpm flow rates respectively.     

Representations of symmetric groups with maximal dimension

Results of numerical modeling connected with the study of the asymptotics of representations of the symmetric group S_N for largeN which are of maximal dimension are given.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova, Akad. Nauk SSSR, Vol. 172, pp. 160–166, 1989.