Transport in ordered and disordered porous media V: Geometrical results for two-dimensional systems

In this paper we continue the geometrical studies of computer generated two-phase systems that were presented in Part IV. In order to reduce the computational time associated with the previous three-dimensional studies, the calculations presented in this work are restricted to two dimensions. This allows us to explore more thoroughly the influence of the size of the averaging volume and to learn something about the use of anon-representative region in the determination of averaged quantities.

Nomenclature

Roman Letters A interfacial area of the– interface associated with the local closure problem, m² - a _i i=1, 2, gaussian probability distribution used to locate the position of particles - l unit tensor - characteristic length for the-phase particles, m - ⁰ reference characteristic length for the-phase particles, m - characteristic length for the-phase, m - _i i=1,2,3 lattice vectors, m - m convolution product weighting function - m _V special convolution product weighting function associated with a unit cell - n _i i=1, 2 integers used to locate the position of particles - n unit normal vector pointing from the-phase toward the-phase - r _p position vector locating the centroid of a particle, m - r gaussian probability distribution used to determine the size of a particle, m - r ₀ characteristic length of an averaging region, m - V averaging volume, m³ - V volume of the-phase contained in the averaging volume,V, m³ - x position of the centroid of an averaging area, m - x ₀ reference position of the centroid of an averaging area, m - y position vector locating points in the-phase relative to the centroid, m Greek Letters V /V, volume average porosity - _{a i} standard deviation ofa _i - _r standard deviation ofr - intrinsic phase average of      

Transport in Porous Media

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Transport in Porous Media     

Transport in diffusion-substitution systems

The class of two-component diffusion-substitution processes including thermodynamic cross-effects is examined analytically. The diffusor approach, a physical decoupling procedure in two effective diffusion processes according to the eigenstates of the diffusivity-matrix is worked out for the linear regime of such systems explicitly. Some peculiarities of these transport processes are discussed in detail. Received on 1 September 1998     

Bending-induced extension in two-dimensional crystals

We find by ab initio simulations that significant overall tensile strain can be induced by pure bending in a wide range of two-dimensional crystals perpendicular to the bending moment, just like an accordion being bent to open. This bending-induced tensile strain increases in a power law with bent curvature and can be over 20% in monolayered black phosphorus and transition metal dichalcogenides at a moderate curvature of 2 nm?1 but more than an order weaker in graphene and hexagon boron nitride. This accordion effect is found to be a quantum mechanical effect raised by the asymmetric response of chemical bonds and electron density to the bending curvature.     

Transport in Porous Media

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Transport in Porous Media     

Transport in Porous Media

Table of Contents

Transport in Porous Media     

Integral equations in two-dimensional airfoil theory

A system of integral equations is obtained for the tangential components of the velocities on the upper and lower surfaces of a profile which does not have a parametric singularity connected with the thickness of the airfoil. An example of the solution of these equations by the discrete vortex method is given. This shows that they are highly effective for solving problems of flow over an airfoil of any, including arbitrarily small, thickness.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.4, pp. 173–177, July–August, 1992.     

Transition radiation in two-dimensional elastic systems

Institute of Mechanical Engineering, Russian Academy of Sciences, Nizhnii Novgorod 603024. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 36, No. 3, pp. 170–178, May–June, 1995.     

Scaling and intermittency in two-dimensional turbulence

In this paper we discuss several properties of two-dimensional decaying turbulence. In particular we analyze the intermittency of the vorticity field and the entrophy dissipation field. We find that strong intermittency acts upon the system which cannot be explained within an entrophy cascade. We propose different explanations based on the geometry of isovorticity lines and on conformal field theory.

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Sommario In questo lavoro vengono discusse alcune proprietà della turbolenza bidimensionale in decadimento. In particolare sono analizzate l'intermittenza del campo di vorticità e della dissipazione di enstrofia. Esiste una forte intermittenza della dissipazione di enstrofia che non può essere spiegata con una cascata di enstrofia simile a quanto avviene in tre dimensioni. Viene proposto un differente meccanismo basato sulla geometria delle linee di isovorticità e sulla teoria conforme.

     

Contaminant contraction in two-dimensional oscillatory flows

If the vertically-mixing time is comparable with that of period oscillatory current,the contaminant contraction may occur.The coefficient of shear dispersion is negative(singularity).According to the two-dimensional delay-diffusion equation derived by theauthor:where u(t),v(t)are vertically-averaged velocities,the equations for X(t),Y(t),central displacement,dispersion tensor,had been derived.αD_(ij)/τis positivewhenτis small.If theτis large,the memory functions may be negative.Also theexpressions for D_(ij)and X,Y had been obtained.     

Free tides in two-dimensional uniform-depth basins

The problem of free tidal wave propagation in two-dimensional uniform-depth basins is considered. To solve the problem, a numerical algorithm, a version of the Babenko method, is developed. The algorithm makes it possible to solve the problem in a singly-connected domain admitting conformal mapping onto a circle. A solution can be obtained for both nonrotating and rotating basins. The first natural frequencies are determined for elliptic basins with different eccentricities and angular velocities and certain characteristic natural shapes demonstrating the distinctive features of tidal flows in elliptic basins are constructed. The time evolution of modes in a rotating elliptic basin is studied.Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, 2004, pp. 119–130. Original Russian Text Copyright © 2004 by Ivanov.     

Partial control of delay-coordinate maps

Nonlinear Dynamics - Delay-coordinate maps have been widely used recently to study nonlinear dynamical systems, where there is only access to the time series of one of their variables. Here, we...     

Lyapunov exponent for Lipschitz maps

Nonlinear Dynamics - It is well known that the Lyapunov exponent plays a fundamental role in dynamical systems. In this note, we propose a definition of Lyapunov exponent for Lipschitz maps, which...     

Transport phenomena in dissociating gases

On the basis of the Chapman—Enskog method, a mathematical formalism of kinetic theory is developed for investigating transport phenomena in rarefied gases with allowance for an equilibrium dissociation reaction. The contribution of the dissociation collision integrals to the transport coefficients is estimated. The results of the estimate show that the presence of dissociation collisions in the gas does not have an appreciable influence on the coefficients of shear viscosity, thermal conductivity, and diffusion. On the other hand, the influence of the equilibrium dissociation reaction on the coefficient of bulk viscosity must be appreciable.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 168–173, July–August, 1981.     

Symbolic dynamics of Belykh-type maps

The symbolic dynamics of a Belykh-type map (a two-dimensional discontinuous piecewise linear map) is investigated. The admissibility condition for symbol sequences named the pruning front conjecture is proved under a hyperbolicity condition. Using this result, a symbolic dynamics model of the map is constructed according to its pruning front and primary pruned region. Moreover, the boundary of the parameter region in which the map is chaotic of a horseshoe type is given.