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1.
A. Cemal Eringen 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2005,56(3):529-547
A continuum theory is introduced for viscous fluids carrying dense suspensions (such as blood) or emulsions of arbitrary shape and inertia. Suspended particles possess microinertia that make the mixture an anisotropic fluid whose viscosity changes with motion and orientation of suspensions. The microinertia balance law coupled with the equations of motion of an anisotropic fluid govern the ultimate outcome. By means of the second law of thermodynamics, constitutive equations are obtained in terms of the frame-independent tensors. In a special case, a theory of bar-like suspensions is obtained. The field equations, boundary and initial conditions are given for both the arbitrarily-shaped suspensions and the bar-like suspensions. The theory is demonstrated with the solution of the channel flow problem. The mean viscosity of the fluid with suspensions is determined. The motions of suspensions down flow are demonstrated. 相似文献
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A. C. Eringen 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2002,4(5):1026-1037
Abstract. A continuum theory of superconductivity is formulated for a mixture consisting of three species: a superelectron fluid, a conducting fluid, and a conducting elastic solid. Each one of the three species is subject to their own electro-magnetic (E-M) fields and motions. Irreversible thermodynamics are used to obtain constitutive equations. Field equations, boundary and initial conditions are given. A special case is obtained, suitable for mathematical analysis and applications. The Pippard theory of superconductivity is shown to be a special case of the present theory. 相似文献
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W.T. Ingram 《Topology and its Applications》2006,153(10):1530-1539
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Kenneth A. Kline Stuart J. Allen 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1968,19(6):898-905
Zusammenfassung Das vonAllen, DeSilva undKline [1] vorgeschlagene Kontinuumsmodell richtungsorientierter Flüssigkeiten wird auf die TheorieEricksens [2, 3] undHands [4] zurückgeführt. Es wird die Suspension fester Drehkörper in Flüssigkeiten und solche sphärischer Partikel unter elastischer Verformung behandelt. 相似文献
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Convection of a scalar quantity by a compressible velocity field may give rise to unbounded solutions or nonphysical overshoots at the continuous and discrete level. In this paper, we are concerned with solving continuity equations that govern the evolution of volume fractions in Eulerian models of disperse two-phase flows. An implicit Galerkin finite element approximation is equipped with a flux limiter for the convective terms. The fully multidimensional limiting strategy is based on a flux-corrected transport (FCT) algorithm. This nonlinear high-resolution scheme satisfies a discrete maximum principle for divergence-free velocities and ensures positivity preservation for arbitrary velocity fields. To enforce an upper bound that corresponds to the maximum-packing limit, an FCT-like overshoot limiter is applied to the converged convective fluxes at the end of each time step. This postprocessing step imposes an additional physical constraint on the numerical solution to the unconstrained mathematical model. Numerical results for 2D implosion problems illustrate the performance of the proposed limiting procedure. 相似文献
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Franco Barragán 《Topology and its Applications》2010,157(3):597-1205
In 1979 Sam B. Nadler, Jr. defined the hyperspace suspension of a continuum. We define the n-fold symmetric product suspensions of a continuum using n-fold symmetric products. We study some properties of this hyperspace: unicoherence, local connectedness, arcwise connectedness. 相似文献
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《Applied Mathematical Modelling》2005,29(9):805-817
Heat and mass transport is modeled in convective flow of a dilute binary mixture of a continuous fluid with mono-dispersed particles (PCM suspensions), in which solid–liquid phase change can take place. The model is based on the mixture continuum approach together with an approximate enthalpy formulation, in which the temporal and spatial variations of phase change fraction in the particles are considered explicitly. Derivations are given for a set of equations governing conservation of mass, momentum, species, and energy of the suspensions, as well as the evolution of phase change fraction of the dispersed particles. 相似文献
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We analyze the evolution of the plastic distortion and the nucleation and accumulation of dislocations within a model bicrystal with one active slip system in each single crystal (symmetric with respect to the interface), which is subject to prescribed displacements of plane–strain shear and extension, and we present closed–form analytical solutions. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
12.
Yu. Z. Povstenko 《Journal of Mathematical Sciences》1992,62(1):2524-2530
We give a survey of the theory of dislocations and disclinations in moment media. We study the theory of incompatible deformations of three- and two-dimensional Cosserat continua. In the context of a differential-geometric approach we give a physical interpretation of the geometric quantities in terms of the continuous theory of defects.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 27, 1988, pp. 34–40. 相似文献
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We discuss qualitative aspects of a continuum theory for thin films rigorously derived in [B. Schmidt, On the passage from atomic to continuum theory for thin films, preprint 82/2005, Max-Planck Institut für Mathematik in den Naturwissenschaften, Leipzig]. The stored energy density is examined for convexity properties and limiting behavior under large and small strains. A study of the dependence of the theory on relaxation parameters leads to the result that the scale of convergence used in [B. Schmidt, On the passage from atomic to continuum theory for thin films, preprint 82/2005, Max-Planck Institut für Mathematik in den Naturwissenschaften, Leipzig] is the only scale for which a limiting theory that also accounts for atomic relaxation effects is non-trivial. 相似文献
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We apply the nonlinear dislocation theory to the problem of antiplane constrained shear in a single crystal with one slip system. By taking dissipation into account, the relaxed energy functional has to be minimized. We show that, up to a threshold strain, no dislocations are nucleated and therefore the plastic slip is zero. Since this threshold value depends on the width of the specimen, a size effect takes place. The stress strain curve turns out to be a hysteresis loop exhibiting the work hardening due to the dislocation pile-up. It is shown that the Bauschinger effect holds true. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
15.
Wei Ma 《Annals of Operations Research》2018,271(2):787-809
This note generalizes Gul and Pesendorfer’s random expected utility theory, a stochastic reformulation of von Neumann–Morgenstern expected utility theory for lotteries over a finite set of prizes, to the circumstances with a continuum of prizes. Let [0, M] denote this continuum of prizes; assume that each utility function is continuous, let \(C_0[0,M]\) be the set of all utility functions which vanish at the origin, and define a random utility function to be a finitely additive probability measure on \(C_0[0,M]\) (associated with an appropriate algebra). It is shown here that a random choice rule is mixture continuous, monotone, linear, and extreme if, and only if, the random choice rule maximizes some regular random utility function. To obtain countable additivity of the random utility function, we further restrict our consideration to those utility functions that are continuously differentiable on [0, M] and vanish at zero. With this restriction, it is shown that a random choice rule is continuous, monotone, linear, and extreme if, and only if, it maximizes some regular, countably additive random utility function. This generalization enables us to make a discussion of risk aversion in the framework of random expected utility theory. 相似文献
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Summary A quadrilateral continuum-basedC
0 shell element is presented, which relies on extensible director kinematics and incorporates unmodified three-dimensional
constitutive models. The shell element is developed from the nonlinear enhanced assumed strain (EAS) method advocated by Sino
& Armero [1] and formulated in curvilinear coordinates. Here, the EAS-expansion of the material displacement gradient leads
to the local interpretation of enhanced covariant base vectors that are superposed on the compatible covariant base vectors.
Two expansions of the enhanced covariant base vectors are given: first an extension of the underlying single extensible shell
kinematic and second an improvement of the membrane part of the bilinear element. Furthermore, two assumed strain modifications
of the compatible covariant strains are introduced such that the element performs well even in the case of very thin shells.
This paper is dedicated to the memory of Juan C. Simo
In honour of Professor Juan Simo who had significant collaboration with our institute and contributed important insights to
our research work.
This paper was solicited by the editors to be part of a volume dedicated to the memory of Juan Simo. 相似文献
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V. A. Ganov 《Siberian Mathematical Journal》1973,14(5):666-680
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First‐order phase transitions are modelled by a non‐homogeneous, time‐dependent scalar‐valued order parameter or phase field. The time dependence of the order parameter is viewed as arising from a balance law of the structure order. The gross motion is disregarded and hence the body is regarded merely as a heat conductor. Compatibility of the constitutive functions with thermodynamics is exploited by expressing the second law through the classical Clausius–Duhem inequality. First, a model for conductors without memory is set up and the order parameter is shown to satisfy a maximum theorem. Next, heat conductors with memory are considered. Different evolution problems are established through a system of differential equations whose form is related to the manner in which the memory property is represented. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
20.
A characterization of dense languages 总被引:2,自引:0,他引:2
H. J. Shyr 《Semigroup Forum》1984,30(1):237-240