Shock structure and multiple sub-shocks in Grad 10-moment binary mixtures of monoatomic gases

The problem of sub-shock occurrence within a shock structure solution is investigated for an inert binary mixture of monoatomic gases, modelled by a Grad 10-moment approximation of the Boltzmann equations. The main purpose of this paper is to show by numerical simulations the existence of discontinuous shock structure solutions for values of the shock speed below the maximum unperturbed characteristic velocity. Moreover, for suitable concentrations of the two species, and for shock velocities beyond the maximum unperturbed characteristic velocity, each constituent of the mixture generates a jump discontinuity, and the shock structure solution exhibits two sub-shocks.

     

Global Well-Posedness of Strong Solutions of Doi Model with Large Viscous Stress

We study models of dilute rigid rod-like polymer solutions. We establish the global well-posedness of the Doi model for large data and for arbitrarily large viscous stress parameter. The main ingredient in the proof is the fact that the viscous stress adds dissipation to high derivatives of velocity.

     

Modeling the influence of mineral content and porosity on ultrasound parameters in bone by using synthetic phantoms

Model composite media − 10×15×80 mm³ bone tissue phantoms based on an epoxy resin with fillers—were made to study the influence of porosity and mineral content on ultrasound velocity and attenuation. The pores were simulated by ∼ 1 mm³ particles of a soft rubber, while the mineral content was imitated by a mineral residue of natural bone obtained by burning and grinding. The porosity and mineral content were varied in the range of 0–70% by volume with a step of 10%. The velocity, attenuation, and prevalent frequency of ultrasound were measured by the pulse transition method, using transducers with nominal frequencies 0.1, 0.2, 0.5, and 1.0 MHz. It was experimentally found that the ultrasound velocity decreased nearly exponentially with growth in porosity, while the velocity dispersion was negligible at frequencies >0.2 MHz; the ultrasound attenuation increased linearly with growth in porosity and strongly depended on the frequency; the velocity increased nonlinearly with growth in mineral content above 40%; the attenuation did not exhibit a distinct dependence on the mineral content; the porosity provoked a shift in the prevalent frequency of transducers, tending to the common value of 0.2 MHz, while the mineral content did not excite similar changes. The complex measurement of velocity, frequency-dependent attenvation, and prevenlent frequency of ultrasound is proposed in ultrasonic diagnostics of bone for more precise determination of the influence of the porosity and the degree of mineralization on the bone condition.     

Modeling the influence of mineral content and porosity on ultrasound parameters in bone by using synthetic phantoms

Model composite media – 10×15×80 mm³ bone tissue phantoms based on an epoxy resin with fillers—were made to study the influence of porosity and mineral content on ultrasound velocity and attenuation. The pores were simulated by 1 mm³ particles of a soft rubber, while the mineral content was imitated by a mineral residue of natural bone obtained by burning and grinding. The porosity and mineral content were varied in the range of 0–70% by volume with a step of 10%. The velocity, attenuation, and prevalent frequency of ultrasound were measured by the pulse transition method, using transducers with nominal frequencies 0.1, 0.2, 0.5, and 1.0 MHz. It was experimentally found that the ultrasound velocity decreased nearly exponentially with growth in porosity, while the velocity dispersion was negligible at frequencies >0.2 MHz; the ultrasound attenuation increased linearly with growth in porosity and strongly depended on the frequency; the velocity increased nonlinearly with growth in mineral content above 40%; the attenuation did not exhibit a distinct dependence on the mineral content; the porosity provoked a shift in the prevalent frequency of transducers, tending to the common value of 0.2 MHz, while the mineral content did not excite similar changes. The complex measurement of velocity, frequency-dependent attenvation, and prevenlent frequency of ultrasound is proposed in ultrasonic diagnostics of bone for more precise determination of the influence of the porosity and the degree of mineralization on the bone condition.Published in Mekhanika Kompozitnykh Materialov, Vol. 35, No. 2, pp. 211–220, March–April, 1999.     

On the Cauchy Problem for a Class of Linear Weakly Hyperbolic Operators

Abstract

We study a class of linear weakly hyperbolic operators with anisotropic degeneracy on their characteristic manifold and we give sufficient conditions for the well-posedness of the related Cauchy problem.     

Forward and Inverse Viscoacoustic Modelling in a Tunnel Environment

In this work, the goal is to model forward acoustic waves in a tunnel environment with attenuation and to do full waveform inversion. In reality, there is no material without attenuation. Some materials, such as rocks, have so low attenuation that, in a small domain, the waves are almost not damped at all. At the same time, there are materials with high attenuation. In an environment with such materials, the attenuation has to be taken into account in order to model the waves properly. In this study, attenuation effect is integrated into acoustic equation by using Kolsky-Futterman model ( [1], [2]) which only replaces velocity field with a complex-valued field in frequency domain. Apart from attenuation, another objective is to consider an inhomogeneous density field. Mainly, acoustic equation with a constant density field is referred to in many studies. In many cases, it may suffice to model waves appropriately. However, in reality, the density field of ground can be highly inhomogeneous. The objective is to investigate the effect of the inhomogeneity in waves, and to search for density field ρ and attenuation parameter Q as well as pressure wave velocity c using full waveform inversion. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Closed-Form Pricing of Two-Asset Barrier Options with Stochastic Covariance

Abstract

Single and double barrier options on more than one underlying with stochastic volatility are usually priced via Monte Carlo simulation due to the non-existence of closed-form solutions for their value. In this paper, for a special dependence structure, the prices of some two-asset barrier derivatives, like double-digital options and correlation options can be derived analytically using generalized Fourier transforms and some conditions on the characteristic functions. We study the influence of the various parameters on these prices and show that these formulas can be easily and quickly computed. We also extend our approach to further allow for a random correlation structure.     

Expected invariants of simplicial complexes obtained from random point samples

In this paper, we study the expectation values of topological invariants of the Vietoris–Rips complex and ?ech complex for a finite set of sample points on a Riemannian manifold. We show that the Betti number and Euler characteristic of the complexes are Lipschitz functions of the scale parameter and that there is an interval such that the Betti curve converges to the Betti number of the underlying manifold.

     

Asymptotic Stability for a Class of Equations of Neutral Type

Under study is the problem of asymptotic but exponential stability for a class of linear autonomous neutral functional differential equations. We demonstrate that the asymptotic stability of an equation of the class takes place for all integrable initial functions if the roots of the characteristic equation lie on the left of and approach the imaginary axis.

     

Uniqueness of twisted linear periods and twisted Shalika periods

Let k be a local field of characteristic zero.Letπbe an irreducible admissible smooth representation of GL2 n(k).We prove that for all but countably many charactersχ’s of GLn(k)×GLn(k),the space ofχ-equivariant(continuous in the archimedean case)linear functionals onπis at most one dimensional.Using this,we prove the uniqueness of twisted Shalika models.     

Propagation of non-planar weak and strong shocks in a non-ideal relaxing gas

In this article, the kinematics of one-dimensional motion have been applied to construct evolution equations for non-planar weak and strong shocks propagating into a non-ideal relaxing gas. The approximate value of exponent of shock velocity, at the instant of shock collapse, obtained from systematic approximation method is compared with those obtained from characteristic rule and Guderley’s scheme. Computation of exponent is carried out for different values of van der Waals excluded volume. Effects of non-ideal and relaxation parameters on the wave evolution, governed by the evolution equations, are analyzed.

     

Automorphic equivalence in the varieties of representations of Lie algebras

Abstract

In this paper, we consider the wide class of subvarieties of the variety of all representation of Lie algebras over a field k of characteristic 0. We study the relation between the geometric equivalence and automorphic equivalence of the representations from these subvarieties.     

Nonlinear stability in microfluidic porous convection problems

This paper investigates classes of thermal convection problems which display effects which are predominant at small scales, i.e. at the microfluidic level. We concentrate on two effects. The first is the effect of local thermal non-equilibrium (LTNE), where the temperature of the saturating fluid may be different from the temperature of the solid skeleton of the porous body. The second is the effect of anisotropy where differences in the flow direction may change strongly depending on the inertia, permeability, thermal conductivity, and on the diffusion coefficient. The class of porous materials analysed are those of Forchheimer type. However, we employ a Forchheimer law recently in vogue in the literature where the nonlinear term which accounts for the variation from linear in the velocity—pressure gradient relationship is cubic in the velocity field as opposed to the classical quadratic one.

     

Resonance waves in media with unwelded boundaries

It is shown that in layered media with weakened interfaces, resonance waves (Kr-waves) arise. Such waves have characteristic frequencies, and many other kinematic and dynamic features distinguish them from well-known Love and Rayleigh type waves. Comparison of theoretical results with experimental seismic data indicates that Kr-waves can be formed in real geological sections. We show theoretically and numerically that in a sedimentary basin of finite lateral extent, a horizontal Kr-wave can be trapped and resonates. This wave has a number of interesting properties: the wave spectrum has a resonance frequency, the wave group velocity is equal to an intermediate value between the shear and longitudinal velocities; the attenuation of the wave increases as the frequency varies from the resonance value. Bibliography: 5 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 354, 2008, pp. 150–156.     

Wave features of a hodograph-like transformation for quasilinear hyperbolic systems

We study the properties of a variables transformation for a 2×2 quasilinear hyperbolic nonhomogeneous system of first order, related to wave propagation. The considered variables transformation transforms characteristic curves of the original system, into characteristic curves of the transformed system. We make use of this property to study the propagation of weak discontinuities (acceleration waves) compatible with the quasilinear system (1.1). Finally a special class of rate-type media is considered and asymptotic solutions are investigated.

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Sommario Si studiano le proprietà di una trasformazione di variabili per un sistema quasilineare iperbolico del primo ordine non omogeneo. La trasformazione considerata trasforma curve caratteristiche del sistema originale in curve caratteristiche del sistema trasformato. Utilizzando queste proprietà si studia la propagazione delle onde di discontinuità (onde di accelerazione) compatibile con il sistema quasilineare iperbolico considerato e si cercano soluzioni asintotiche.

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This work was supported by the C.N.R. through the G.N.F.M. and partially under contract No. 88. 01855.01.     

Second sound near lambda transition in presence of quantum vortices

In this paper, temperature waves (also known as second sound) are considered, with their respective coupling with waves in the order parameter describing the transition from normal phase to superfluid phase, and with waves in the vortex length density. We analyze the coupling between these three kinds of waves and explore its relevance in situations not far from the lambda transition. In particular, the expressions for the second sound speed and second sound attenuation are explicitly obtained within some approximations, showing the influence of the order parameter and the vortex length density, which is decisive close to the transition.

     

Three-dimensional zeropotent algebras over an algebraically closed field of characteristic two

Abstract

We previously classified three-dimensional zeropotent algebras over an algebraically closed field of any characteristic except for two. The exceptional case of characteristic two is special because some of the previous transformation matrices to verify isomorphism are unavailable. In this paper, we give new transformation matrices peculiar to characteristic two and then achieve classification in the exceptional case. We thus accomplish a classification of three-dimensional zeropotent algebras over an algebraically closed field of any characteristic.     

Phase Separation in the Advective Cahn–Hilliard Equation

The Cahn–Hilliard equation is a classic model of phase separation in binary mixtures that exhibits spontaneous coarsening of the phases. We study the Cahn–Hilliard equation with an imposed advection term in order to model the stirring and eventual mixing of the phases. The main result is that if the imposed advection is sufficiently mixing, then no phase separation occurs, and the solution instead converges exponentially to a homogeneous mixed state. The mixing effectiveness of the imposed drift is quantified in terms of the dissipation time of the associated advection–hyperdiffusion equation, and we produce examples of velocity fields with a small dissipation time. We also study the relationship between this quantity and the dissipation time of the standard advection–diffusion equation.