Wave Interactions and Stability of Riemann Solutions of the Aw–Rascle Model for Generalized Chaplygin Gas

In this paper, we mainly study the interactions of the elementary waves of the Aw–Rascle model for the generalized Chaplygin gas. With the characteristic analysis method, the solutions are obtained constructively when the initial data are three piecewise constant states. Moreover, by studying the limits of the perturbed Riemann solutions as the perturbed parameter \(\varepsilon\) tends to zero, we find that the Riemann solutions are stable for such perturbations on the initial data.     

Approaching Chaplygin pressure limit of solutions to the Aw–Rascle model

This paper studies the limit of solutions to the Aw–Rascle model as the pressure tends to the Chaplygin gas pressure. For concreteness, the pressure is taken as a modified Chaplygin gas pressure. Firstly, the Riemann problem for the Aw–Rascle model with the modified Chaplygin gas pressure is solved constructively. Secondly, it is shown that as the pressure tends to the Chaplygin gas pressure, some Riemann solutions containing a shock and a contact discontinuity tend to a delta-shock solution, whose propagation speed and strength are different from those of delta-shock solution to the Aw–Rascle model with a Chaplygin gas pressure. Besides, it is also proven that the rest Riemann solutions converge to a two-contact-discontinuity solution, which is exactly the solution to the Aw–Rascle model with a Chaplygin gas pressure. Thirdly, some numerical results are presented to exhibit the process of formation of delta-shocks.     

Numerical Solution of the Baer–Nunziato Relaxation Model Using the Discontinuous Galerkin Method

Differential Equations - We propose a numerical method for solving problems of two-phase two-velocity hydrodynamics in the framework of the Baer–Nunziato model with relaxation. The model...     

Localized Solutions of a Piecewise Linear Model of the Stationary Swift–Hohenberg Equation on the Line and on the Plane

In this paper we study a simplified model of the stationary Swift–Hohenberg equation, where the cubic nonlinearity is replaced by a piecewise linear function with similar properties. The main goal is to prove the existence of so-called localized solutions of this equation, i.e., solutions decaying to a homogeneous zero state with unbounded increase of the space variable. The following two cases of the space variable are considered: one-dimensional (on the whole line) and two-dimensional; in the latter case, radially symmetric solutions are studied. The existence of such solutions and increase of their number with change in the equation parameters are shown.     

Flow near the two-dimensional stagnation-point on an infinite permeable wall with a homogeneous–heterogeneous reaction

This paper studies the effects of mass transfer (suction and injection) on the problem of steady-state boundary layer flow near the forward stagnation-point of an infinite permeable wall with a homogeneous (bulk) reaction given by isothermal cubic autocatalator kinetics and the heterogeneous (surface) reaction by first-order kinetics. The case of an impermeable wall has been considered by Chaudhary and Merkin (1994) [1]. It is found that the mass transfer parameter considerably affects the flow characteristics.     

Bayesian Semiparametric Density Estimation and Model Verification Using a Logistic–Gaussian Process

This article proposes a semiparametric model, which consists of parametric and nonparametric components, for density estimation. The parametric component represents the researcher's a priori beliefs about a likely family of density functions. The nonparametric component, which is modeled by a logistic–Gaussian process, allows the predictive distribution to deviate from the parametric family if it is inadequate. Bayesian hypothesis testing is used to examine the adequacy of the parametric model relative to the flexible alternative provided by the semiparametric model. The article presents a Markov chain Monte Carlo algorithm that efficiently handles the large number of parameters.     

Validation of a Computational Algorithm Based on the Discontinuous Galerkin Method for the Baer–Nunziato Relaxation Model

Differential Equations - The Runge–Kutta/Discontinuous Galerkin (RK/DG) method is considered to simulate the dynamics of two-phase media in the framework of a completely nonequilibrium...     

Applicability Indicators and Identification Techniques for a Nonlinear Maxwell–Type Elastoviscoplastic Model Using Loading–Unloading Curves

Mechanics of Composite Materials - A physically nonlinear Maxwell-type constitutive relation with two material functions for nonaging materials is studied analytically in order to reveal the set of...     

Multilayered Attack–Defense Model on Networks

Computational Mathematics and Mathematical Physics - The classical Germeier’s attack–defense game is generalized for the case of defense in depth (multilayered defense) that has a...     

Existence of a Phase Transition for the Potts p-adic Model on the Set ℤ

We consider the Potts model on the set in the field Q _p of p-adic numbers. The range of the spin variables (n), , in this model is . We show that there are some values q=q(p) for which phase transitions occur.     

Evolution of the Perturbation of a Circle in the Stokes–Leibenson Problem for the Hele-Shaw Flow

Among the initial contours of the Sobolev class H ¹ close to a circle, we distinguish the set of those for which the Stokes–Leibenson problem in the case of a source has a solution, moreover, this solution is unique. The contour corresponding to this solution is defined for all t > 0 and tends to a circle as t .     

BV Estimates on Lax–Friedrichs' Scheme or a Model of Radiating Gas

In this article, we give a uniform BV estimates and L ¹-stability of solutions to the Lax–Friedrichs' scheme for a model of radiating gas when the strict C–F–L (Courant–Friedrichs–Levy) condition is satisfied. This result implies that the approximate solutions generated by the Lax–Friedrichs' scheme converge to the solution given by the method of vanishing viscosity [C. Lattanzio and P. Marcati (2003 Lattanzio, C and Marcati, P. 2003. Global well-posedness and relaxation limits of a model for radiating gas. Journal of Differential Equations, 190: 439–465. [Crossref], [Web of Science ®] , [Google Scholar]). Global well-posedness and relaxation limits of a model for radiating gas. Journal of Differential Equations, 190, 439–465].     

A Method for Predicting the Parameters of Plastic Deformation of Dispersedly Reinforced Materials by Using a Modified Mori–Tanaka Model

Mechanics of Composite Materials - A modified Mori–Tanaka model to predict the average mechanical characteristics for dispersedly reinforced materials considering the physical nonlinearity,...     

Extremality of Gibbs Measures for the $$HC$$ -Blume–Capel Model on the Cayley Tree

Mathematical Notes - In this paper, we consider translation-invariant Gibbs measures (TIGMs) for the $$HC$$ -Blume–Capel model in case of “wands” with chemical potential with...     

Note on “Obtaining the Maximum Likelihood Estimates in Incomplete R × C Contingency Tables Using a Poisson Generalized Linear Model”

Abstract

This note extends the construction of the design matrix used for estimating cell probabilities with ignorable missing data described by Lipsitz, Parzen, and Molenberghs. A reformulation for the general case of an n-way table is described and implemented in a SAS macro program. The macro constructs this design matrix and offset variable, estimates the cell probabilities, and returns a table with the estimates, their standard errors, and fitted cell frequencies.     

Model of quark–antiquark interaction in quantum chromodynamics on the light front

We formulate a model of quark–antiquark interaction related to the limit transition to the light-front Hamiltonian in quantum chromodynamics. As ultraviolet regularization, we use a lattice in the space of transverse coordinates, and we additionally introduce a longitudinal light-front coordinate cutoff and also corresponding periodic boundary conditions. We regard the zero mode with respect to this coordinate as an independent dynamical variable. The state space of the model is limited to a quark and an antiquark that interact only via the zero mode of the gluon field on the light front. In this framework, we obtain a discrete mass spectrum of bound states. This spectrum is determined by an equation that with respect to the longitudinal coordinate turns out to be analogous to the’ t Hooft equation in two-dimensional quantum chromodynamics. The equation also contains a quark–antiquark potential that ensures confinement in the transverse space.