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Displaying 461 – 480 of 787

On the Mathematical Analysis and Optimization of Chemical Vapor Infiltration in Materials Science

Adi Ditkowski, David Gottlieb, Brian W. Sheldon (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we present an analysis of the partial differential equations that describe the Chemical Vapor Infiltration (CVI) processes. The mathematical model requires at least two partial differential equations, one describing the gas phase and one corresponding to the solid phase. A key difficulty in the process is the long processing times that are typically required. We address here the issue of optimization and show that we can choose appropriate pressure and temperature to minimize these...

On the modeling of the transport of particles in turbulent flows

Thierry Goudon, Frédéric Poupaud (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We investigate different asymptotic regimes for Vlasov equations modeling the evolution of a cloud of particles in a turbulent flow. In one case we obtain a convection or a convection-diffusion effective equation on the concentration of particles. In the second case, the effective model relies on a Vlasov-Fokker-Planck equation.

On the modeling of the transport of particles in turbulent flows

Thierry Goudon, Frédéric Poupaud (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

On the motion of a rigid body immersed in a bidimensional incompressible perfect fluid

Jaime Ortega, Lionel Rosier, Takéo Takahashi (2007)

Annales de l'I.H.P. Analyse non linéaire

On the motion of nonviscous compressible fluids in domains with boundary

Paolo Secchi (1992)

Banach Center Publications

On the motion of rigid bodies in a viscous fluid

Eduard Feireisl (2002)

Applications of Mathematics

We consider the problem of motion of several rigid bodies in a viscous fluid. Both compressible and incompressible fluids are studied. In both cases, the existence of globally defined weak solutions is established regardless possible collisions of two or more rigid objects.

On the nonhamiltonian character of shocks in 2-D pressureless gas

Yu. G. Rykov (2002)

Bollettino dell'Unione Matematica Italiana

The paper deals with the 2-D system of gas dynamics without pressure which was introduced in 1970 by Ua. Zeldovich to describe the formation of largescale structure of the Universe. Such system occurs to be an intermediate object between the systems of ordinary differential equations and hyperbolic systems of PDE. The main its feature is the arising of singularities: discontinuities for velocity and d-functions of various types for density. The rigorous notion of generalized solutions in terms of...

On the non-uniqueness of weak solution of the Euler equations

A. Shnirelman (1996)

Journées équations aux dérivées partielles

On the Origin of Chaos in the Belousov-Zhabotinsky Reaction in Closed and Unstirred Reactors

M. A. Budroni, M. Rustici, E. Tiezzi (2010)

Mathematical Modelling of Natural Phenomena

We investigate the origin of deterministic chaos in the Belousov–Zhabotinsky (BZ) reaction carried out in closed and unstirred reactors (CURs). In detail, we develop a model on the idea that hydrodynamic instabilities play a driving role in the transition to chaotic dynamics. A set of partial differential equations were derived by coupling the two variable Oregonator–diffusion system to the Navier–Stokes equations. This approach allows us to shed light on the correlation between chemical oscillations...

On the persistence of decorrelation in the theory of wave turbulence

Anne-Sophie de Suzzoni (2013)

Journées Équations aux dérivées partielles

We study the statistical properties of the solutions of the Kadomstev-Petviashvili equations (KP-I and KP-II) on the torus when the initial datum is a random variable. We give ourselves a random variable $u_{0}$ with values in the Sobolev space $H^{s}$ with $s$ big enough such that its Fourier coefficients are independent from each other. We assume that the laws of these Fourier coefficients are invariant under multiplication by $e^{i θ}$ for all $θ \in ℝ$ . We investigate about the persistence of the decorrelation between the...

On the problem of the Marangoni-to-Prandtl boundary layer transition.

Kuznetsov, V.V. (2000)

Sibirskij Matematicheskij Zhurnal

On the regularity for solutions of the micropolar fluid equations

Elva Ortega-Torres, Marko Rojas-Medar (2009)

Rendiconti del Seminario Matematico della Università di Padova

On the regularization of the pressure field in compressible euler equations

R. Di Lisio, E. Grenier, M. Pulvirenti (1997)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

On the search for singularities in incompressible flows

Diego Córdoba (2006)

Applications of Mathematics

In these notes we give some examples of the interaction of mathematics with experiments and numerical simulations on the search for singularities.

On the second order slip Reynolds equation with molecular dynamics: existence and uniqueness.

Hadi, Khalid Ait, El Bansami, My Hafid (2004)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

On the solution of linear algebraic systems arising from the semi–implicit DGFE discretization of the compressible Navier–Stokes equations

Vít Dolejší (2010)

Kybernetika

We deal with the numerical simulation of a motion of viscous compressible fluids. We discretize the governing Navier–Stokes equations by the backward difference formula – discontinuous Galerkin finite element (BDF-DGFE) method, which exhibits a sufficiently stable, efficient and accurate numerical scheme. The BDF-DGFE method requires a solution of one linear algebra system at each time step. In this paper, we deal with these linear algebra systems with the aid of an iterative solver. We discuss...

On the solvability of some initial boundary value problems of magnetofluidmechanics with Hall and ion-slip effects

Vsevolod A. Solonnikov, Giuseppe Mulone (1995)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

The solvability of three linear initial-boundary value problems for the system of equations obtained by linearization of MHD equations is established. The equations contain terms corresponding to Hall and ion-slip currents. The solutions are found in the Sobolev spaces $W_{p}^{2, 1} (Q_{T})$ with $p > 5 / 2$ and in anisotropic Holder spaces.

On the spatial analyticity of solutions to the Keller-Segel equations

Okihiro Sawada (2008)

Banach Center Publications

The regularizing rate of solutions to the Keller-Segel equations in the whole space is estimated just as for the heat equation. As an application of these rate estimates, it is proved that the solution is analytic in spatial variables. Spatial analyticity implies that the propagation speed is infinite, i.e., the support of the solution coincides with the whole space for any short time, even if the support of the initial datum is compact.

On the spatially homogeneous Boltzmann equation

Stéphane Mischler, Bernst Wennberg (1999)

Annales de l'I.H.P. Analyse non linéaire

On the stability of compressible Navier-Stokes-Korteweg equations

Tong Tang, Hongjun Gao (2014)

Annales Polonici Mathematici

We consider the compressible Navier-Stokes-Korteweg (N-S-K) equations. Through a remarkable identity, we reveal a relationship between the quantum hydrodynamic system and capillary fluids. Using some interesting inequalities from quantum fluids theory, we prove the stability of weak solutions for the N-S-K equations in the periodic domain $Ω =^{N}$ , when N=2,3.

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