A numerical computation of a non-dimensional form of stream water quality model with hydrodynamic advection–dispersion–reaction equations

Mathematical models of water quality assessment problems often arise in environmental science. The modelling often involves numerical methods to solve the equations. In this research, two mathematical models are used to simulate pollution due to sewage effluent in the nonuniform flow of water in a stream with varied current velocity. The first is a hydrodynamic model that provides the velocity field and elevation of the water flow. The second is a dispersion model, where the commonly used governing factor is the one-dimensional advection–dispersion–reaction equation that gives the pollutant concentration fields. In the simulation processes, we used the Crank–Nicolson method system of a hydrodynamic model and the backward time central space scheme for the dispersion model. Finally, we present a numerical simulation that confirms the results of the techniques.     

Effect of two photon absorption on nonlinear pulse propagation in gain medium

The effects of two photon absorption (TPA) and gain dispersion on soliton propagation in amplified medium are investigated. For finite gain bandwidth, the effect of gain dispersion becomes significant along with TPA and is treated as perturbation in fundamental soliton propagation. Including these perturbing effects an analytical expression of integrated intensity is formulated applying a completely new methodology by adopting Rayleigh’s dissipation function in the framework of variational approach. With classical analogy, the Euler–Lagrange equation in non-conservative system is used to solve the problem analytically. In order to justify the analytical prediction a numerical verification is made by split-step beam propagation method following Ginzburg–Landau equation.     

Comparison of dispersion properties of some difference schemes for the system of two-dimensional equations of acoustics

We analyze the dispersion properties of three difference schemes approximating the system of two-dimensional equations of acoustics. Comparison of the principal terms in the expansion of the dispersion error indicates that the dispersion properties of the centered scheme proposed by the authors are superior to those of other schemes, including the well-known Lax—Wedroff scheme. Computational results are reported supporting the theoretical conclusions.Kiev University. Nukus University. Translated from Vychislitel'naya i Prikladnaya Matematika, No. 75, pp. 43–50, 1991.     

Mechanical characteristics of oriented glass-reinforced plastics in shear

The mechanical characteristics of oriented glass-reinforced plastics stressed in shear are considered. Various methods of determining them are compared. The dispersion of the shear strength is characterized and the possibility of glass-reinforced plastics elements failing as a result of low interlaminar shear strength is discussed.Moscow Aviation Technological Institute. Translated from Mekhanika Polimerov, No. 6, pp. 1008–1013, November–December, 1969.     

Random creation and dispersion of mass

Consider evolution of density of a mass or a population, geographically situated in a compact region of space, assuming random creation-annihilation and migration, or dispersion of mass, so the evolution is a random measure. When the creation-annihilation and dispersion are diffusions the situation is described formally by a stochastic partial differential equation; ignoring dispersion make approximations to the initial density by atomic measures and if the corresponding discrete random measures converge “in law” to a unique random measure call it a solution. To account for dispersion Trotter's product formula is applied to semiflows corresponding to dispersion and creation-annihilation. Existence of solutions has been a conjecture for several years despite a claim in ([2], J. Multivariate Anal. 5, 1–52). We show that solutions exist and that non-deterministic solutions are “smeared” continuous-state branching diffusions.     

Effect of loading on the vibrations of the molecules of certain polymers with a plane zigzag skeleton

The main-chain vibrational frequency shifts are calculated on the basis of a simplified model for a series of loaded polymers with a plane zigzag skeleton. The dispersion curves and distribution functions for the free and loaded molecules are compared.A. F. Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 6, pp. 971–978, November–December, 1970.     

Production and characterization of UHMWPE fibers/LDPE composites

The production of unidirectionally fiber-reinforced composites (tapes) consisting of high-strength/high-modulus UHMWPE fibers and LDPE matrix is described. Two production techniques are applied: impregnation by aqueous powder dispersion and dry powder impregnation. The produced composites exhibit excellent mechanical properties. Depending on the fiber volume content which can be obtained: tensile strength (in fiber direction) 460–1100 MPa, elastic modulus 11–22 GPa, and elongation at break 4.9–8.3%.Presented at the Ninth International Conference on the Mechanics of Composite Materials, Riga, October, 1995.Technical University of Berlin. Institute of Nonmetallic Materials. Polymer Physics Group.-Englishe Str. 20, D-10587 Berlin. Germany. Published in Mekhanik Kompozitnykh Materialov, Vol. 32, No. 6. pp. 719–728, November–December, 1996.     

Propagation of elastic waves along the fibers in oriented glass-reinforced plastics

The dispersion equation is derived for axisymmetric (longitudinal and torsional) normal vibrations in oriented glass-reinforced plastics. The low-frequency case is examined in detail. The frequency limits of applicability of the method of substituting a homogeneous medium for the composite (GRP) are estimated. The dependence of the vibration propagation velocity on glass content is calculated.Leningrad Zonal Scientific-Research Institute of Experimental Design of Public and Residential Buildings. Translated from Mekhanika Polimerov, No. 6, pp. 976–983, November–December, 1973.     

Spectral method in the theory of wave propagation in cellular periodic waveguides

The spectral method is substantiated for the particular example of normal wave determination in a corrugated waveguide with rectangular-profile ribs. We establish the rib conditions, prove an analog of the Paley—Wiener theorem for Fourier series, and use the theorem to prove equivalence of the solutions of the original boundary-value problem and the dispersion equation. Some topics connected with the existence of the characteristic value of the dispersion equation and with the convergence of the approximate method are explored.Translated from Vychislitel'naya Matematika i Matematicheskoe Obespechenie EVM, pp. 186–198, 1985.     

The effect of the concentration and dispersion of quartz on the physicomechanical properties of polyvinylacetate films

Data are given from a study of the effect of the concentration and dispersion of quartz on the structure, the coefficient of thermal expansion, the elastic modulus, the strength, and the extension under tension of polyvinylacetate films. The change in the properties of these films is associated with a change in the structure of the polymer on filling.Institute of Physical Chemistry, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 1, pp. 63–67, January–February, 1972.     

A higher-order moment method of the lattice Boltzmann model for the conservation law equation

In this paper, we proposed a higher-order moment method in the lattice Boltzmann model for the conservation law equation. In contrast to the lattice Bhatnagar–Gross–Krook (BGK) model, the higher-order moment method has a wide flexibility to select equilibrium distribution function. This method is based on so-called a series of partial differential equations obtained by using multi-scale technique and Chapman–Enskog expansion. According to Hirt’s heuristic stability theory, the stability of the scheme can be controlled by modulating some special moments to design the third-order dispersion term and the fourth-order dissipation term. As results, the conservation law equation is recovered with higher-order truncation error. The numerical examples show the higher-order moment method can be used to raise the accuracy of the truncation error of the lattice Boltzmann scheme for the conservation law equation.     

Determination of the complex dielectric constant of polymeric materials from the polarization current

A method of determining the frequency dependence of the complex dielectric constant of polymeric materials from the polarization current is considered; the basic relations of the phenomenological theory of dielectric losses and permittivity, from which the dielectric dispersion of solid dielectrics can be calculated, are given. The region of application of the method is analyzed and the principal existing computation methods are examined.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 507–511, May–June, 1976.     

The acoustic properties of polymers with an asymmetric potential barrier at liquid-helium temperatures

The pulse-phase compensation method has been used to measure the propagation velocities of longitudinal and shear waves in polyvinyl chloride, polyvinyl fluoride, and polystyrene at frequencies of 1 and 5 MHz on the temperature interval 2.1–240°K. It has been established that as the temperature falls to 2.1°K the speed of ultrasound in these polymers monotonically increases, the dispersion (frequency dependence) of the speed of sound being preserved over the entire temperature interval. Two possible causes of the viscoelastic relaxation observed in the investigated polymers in the region of helium temperatures are considered.Scientific-Research Institute of Plastics, Moscow. Translated from Mekhanika Polimerov, No. 4, pp. 749–751, July–August, 1973.     

Fundamentals of the statistical mechanics of composite systems

Conclusions The proposed variant of the statistical theory of composite media makes it possible to derive relations between the effective parameters of the medium and the dispersion characteristics of the structure, and also to account for the effect of specimen shape and variable structural heterogeneity on these parameters. In the limiting case of an infinitely large specimen, all relationships comply with the results of the traditional theory of composite systems.Presented at the Sixth All-Union Conference on the Mechanics of Polymer and Composite Materials (Riga, November, 1986).Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 21–30, January–February, 1988.     

Influence of an electric field on the rheological behavior of a dilute suspension of dipolar dumbbells in a viscoelastic oldroyd liquid

Conclusions 1. Rheological equations of state of a dilute suspension of dipolar dumbbels in a viscoelastic Oldroyd liquid have been obtained for a stationary orientation of suspended particles in steady flows and electric fields.2. Study of the rheological properties of such a medium in simple shear flow in the presence of an electric field, the intensity vector of which lies in the shear plane and is perpendicular to the velocity vector, has shown that the medium examined conducts itself as a viscoelastic liquid. This is the result of both the viscoelastic properties of the dispersion medium and the orientation of the suspended particles under the action of frictional forces and the electric field. The effective viscosity of the suspension and difference in normal stresses resulting from the presence of the suspended particles are greater if one does not take the elastic properties of the dispersion medium into account.T. G. Shevchenko Kiev State University. Translated from Mekhanika Polimerov, No. 3, pp. 519–524, May–June, 1978.     

Wave triplets in two-phase composites

The possibility of an appearance of wave triplets in composites is studied. It is shown that a resonant interaction in industrial composites is possible. It is stated graphically only in two classic examples of layered and fiber reinforced composites that dispersion curves of the materials allow a resonant wave interaction. The quadratic nonlinear theory of two-phase mixtures is built as the variant of a microstructure theory of composite materials. Triplets of harmonic waves are studied in the framework of this theory.Published in Mekhanika Kompozitnykh Materialov, Vol. 31, No. 5, pp. 660–670, September–October, 1995.     

Dispersion of strength properties and reliability of glued joints

The effect of various factors on the dispersion of the strength characteristics of glued joints is examined. A study of aluminum alloys bonded with type EPTs-1 cold-cured epoxy adhesive has shown that such factors as the presence of a filler, the filler particle size, and supplementary heat treatment of the glued joint have a considerable effect on the dispersion of the strength characteristics. It is established that a decrease in filler particle size and supplementary heat treatment reduce the dispersion of the strength characteristics and, correspondingly, increase the reliability of the joints. The experimental data are analyzed by the methods of mathematical statistics.Mekhanika Polimerov, Vol. 1, No. 5, pp. 78–84, 1965     

Investigation of the dispersion equation for an acoustics problem in a borehole

One gives the results of the analytic and numerical analysis of the roots of the dispersion equation for a model of a log borehole. One investigates the effect of the elastic parameters and of the densities on the dispersion and the damping of the waves in the case of radial oscillations.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 128, pp. 89–94, 1983.     

Investigation of the roots of the dispersion equation for a layered,transversally isotropic medium

To investigate the propagation of normal and damped waves in a layered, transversally isotropic medium, it is necessary to determine the complex and pure imaginary roots of the dispersion equation. The dispersion equation considerably simplifies in the case of large and small wave numbers. It is therefore possible to determine the initial and final points of all roots and to trace the entire motion of the roots between these points.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 99, pp. 104–122, 1980.     

Temperature-frequency dependence of the elastic constants of certain resins

The authors present the results of an experimental investigation of the elastic constants of certain crosslinked and linear polymers in the temperature range from –50 to +110° C and the frequency range from 10¹ to 10⁵ Hz. The elastic constants were determined by both quasi-static and dynamic methods. The range of application of the different methods are characterized with respect to a time scale. It is shown that when certain experimental conditions are observed (strain rate, frequency), the values of the constants obtained by the different methods almost coincide. On the basis of temperature measurements it is postulated that rigid epoxies have a secondary low-temperature dispersion region.Mekhanika Polimerov, Vol. 3, No. 1, pp. 60–65, 1967