The Barnett approximation in the theory of hydrodynamic fluctuations

The Langevin dynamics and fluctuational-dissipative relationships for the hydrodynamic fluctuations for systems which are described in the third Barnett order with respect to the gradients of the hydrodynamic variables are generalized on the basis of a kinetic approach.     

OPTIMAL INVESTMENT IN THE PROTECTION OF A VULNERABLE BIOLOGICAL RESOURCE

It is assumed that the probability of destruction of a biological asset by natural hazards can be reduced through investment in protection. Specifically a model, in which the hazard rate depends on both the age of the asset and the accumulated invested protection capital, is assumed. The protection capital depreciates through time and its effectiveness in reducing the hazard rate is subject to diminishing returns. It is shown how the investment schedule to maximize the expected net present value of the asset can be determined using the methods of deterministic optimal control, with the survival probability regarded as a state variable. The optimal investment pattern involves “bang-bang-singular” control. A numerical scheme for determining jointly the optimal investment policy and the optimal harvest (or replacement) age is outlined and a numerical example involving forest fire protection is given.     

A finite model property for RMImin

It is proved that the variety of relevant disjunction lattices has the finite embeddability property. It follows that Avron's relevance logic RMI _min has a strong form of the finite model property, so it has a solvable deducibility problem. This strengthens Avron's result that RMI _min is decidable. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Double-layer structural-acoustic coupling for cylindrical shell by using a combination of WDA and BIE

This work formulates the double-layer structural-acoustic coupling problem for cylindrical shell by using a combination of the wave-number domain approach (WDA) and the boundary integral equation (BIE). Expressions for the spectral radial velocity of the outer surface of a finite fluid-filled/submerged (FFS) cylindrical thin shell are formulated by means of the transfer matrix equation in wave-number domain. It is shown that the spectral variables on the inner surface of the shell are related to those on the outer surface of the shell. The far field sound radiation from this kind of shell is numerically evaluated for various fluid cases. An experimental verification is performed, and a good correlation between the theoretical results and the experimental results shows that the theoretical study work in this paper is correct.     

Black-hole horizon and metric singularity at the brane separating two sliding superfluids

An analogue of a black hole can be realized in the low-temperature laboratory. The horizon can be constructed for “relativistic” ripplons (surface waves) living on the brane. The brane is represented by the interface between two superfluid liquids, ³He-A and ³He-B, sliding along each other without friction. A similar experimental arrangement was recently used for the observation and investigation of the Kelvin-Helmholtz type of instability in superfluids [1]. The shear-flow instability in superfluids is characterized by two critical velocities. The lowest threshold measured in recent experiments [1] corresponds to the appearance of the ergoregion for ripplons. In the modified geometry, this will give rise to the black-hole event horizon in the effective metric experienced by ripplons. In the region behind the horizon, the brane vacuum is unstable due to interaction with the higher-dimensional world of bulk superfluids. The time of the development of instability can be made very long at low temperature. This will allow us to reach and investigate the second critical velocity—the proper Kelvin-Helmholtz instability threshold. The latter corresponds to the singularity inside the black hole, where the determinant of the effective metric becomes infinite.     

EXPRESSIONS FOR PREDICTING FUNDAMENTAL NATURAL FREQUENCIES OF NON-CYLINDRICAL HELICAL SPRINGS

Numerical and analytical studies are performed for the free vibration analysis of non-cylindrical (conical, barrel and hyperboloidal types) helical springs. The stiffness matrix method is used in the numerical analysis. A total of 12 degrees of freedom (six displacements and six rotations) is described for an element. The exact element stiffness matrix and the exact concentrated element inertia matrix are used in the formulation. The rotary inertia, the shear and extensional deformation effects are considered in the analysis. Comparison of the numerical results with the reported results obtained numerically and experimentally gives satisfactory values. After verification of the numerical frequencies, the non-dimensional fundamental frequencies of fixed-fixed non-cylindrical helical springs with circular section are expressed in a simple formula with a maximum absolute relative error of 5% using those numerical values for the constant helix pitch angles (5°, 10°, and 15°). These expressions restricted to the fundamental frequencies are also verified with ANSYS results.     

Miscibility of bisphenol-A polycarbonate with poly(methyl methacrylate)

The miscibility of bisphenol-A polycarbonate (PC) with poly(methyl methacrylate) (PMMA) has been reexamined using differential scanning calorimetry (DSC) and optical indications for phase separation on heating, i.e., lower critical solution temperature (LCST) behavior. Various methods have been used to prepare the blends including methylene chloride (CH₂Cl₂) and tetrahydrofuran (THF) solution casting, melt mixing, and precipitation of PC and PMMA simultaneously from THF solution by using the nonsolvents methanol and heptane. It is shown that the resulting phase behavior for PC/PMMA blends is strongly affected by the blend preparation method. However, these blends are miscible over the whole blend composition range (unambiguous single composition-dependent T_g's and LCST behavior) when prepared by precipitation from solution using heptane as the nonsolvent. To the contrary, solution-cast and melt-mixed PC/PMMA blends were all phase separated, which may be attributed to the “solvent” effect and LCST behavior, respectively, not discovered in previous reports. Methanol precipitation does not lead to fully mixed blends, which demonstrates the importance of the choice of nonsolvent when using the precipitation method.     

Navier-Stokes approximation and problems of the Chapman-Enskog projection for kinetic equations

The purpose of this paper is to investigate problems of the Navier-Stokes approximation to kinetic equations in terms of the so-called Chapman-Enskog projection. One considers properties of the Chapman-Enskog projection for the Cauchy problem for moment approximations of the kinetic equation and primarily the Chapman-Enskog projection for the Boltzmann-Peierls kinetic equation. The existence of the Chapman-Enskog projection for the Cauchy problem is proved for the phase space of conservative variables (phenomena of nonlinear diffusion) and for the phase space of physical variables (the second sound projection). __________ Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 25, pp. 184–225, 2005.     

Semi‐analytical integration of the 8‐node plane element stiffness matrix using symbolic computation

The semi‐analytical integration of an 8‐node plane strain finite element stiffness matrix is presented in this work. The element is assumed to be super‐parametric, having straight sides. Before carrying out the integration, the integral expressions are classified into several groups, thus avoiding duplication of calculations. Symbolic manipulation and integration is used to obtain the basic formulae to evaluate the stiffness matrix. Then, the resulting expressions are postprocessed, optimized, and simplified in order to reduce the computation time. Maple symbolic‐manipulation software was used to generate the closed expressions and to develop the corresponding Fortran code. Comparisons between semi‐analytical integration and numerical integration were made. It was demonstrated that semi‐analytical integration required less CPU time than conventional numerical integration (using Gaussian‐Legendre quadrature) to obtain the stiffness matrix. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006     

Nonlinear Theory of Spectra of Thermally Stimulated Currents in Complex Crystals with Hydrogen Bonds

The nonlinear theory of thermally stimulated depolarization currents is developed. The theory explains the processes of hetero- and homocharge relaxation in complex crystals with hydrogen bonds and allows the relaxation oscillator parameters to be calculated using the quadratic approximation for the external electric field.