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38
Quasiincompressible Cahn–Hilliard fluids and topological transitions
 Proc. R. Soc. Lond. A
, 1998
"... One of the fundamental problems in simulating the motion of sharp interfaces between immiscible fluids is a description of the transition that occurs when the interfaces merge and reconnect. It is well known that classical methods involving sharp interfaces fail to describe this type of phenomena. F ..."
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Cited by 38 (3 self)
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One of the fundamental problems in simulating the motion of sharp interfaces between immiscible fluids is a description of the transition that occurs when the interfaces merge and reconnect. It is well known that classical methods involving sharp interfaces fail to describe this type of phenomena. Following some previous work in this area, we suggest a physically motivated regularization of the Euler equations which allows topological transitions to occur smoothly. In this model, the sharp interface is replaced by a narrow transition layer across which the fluids may mix. The model describes a flow of a binary mixture, and the internal structure of the interface is determined by both diffusion and motion. An advantage of our regularization is that it automatically yields a continuous description of surface tension, which can play an important role in topological transitions. An additional scalar field is introduced to describe the concentration of one of the fluid components and the resulting system of equations couples the Euler (or Navier–Stokes) and the Cahn–Hilliard equations. The model takes into account weak nonlocality (dispersion) associated with an internal length scale and localized dissipation due
The lattice Boltzmann equation method: Theoretical interpretation, numerics and implications
 Int. Multiphase Flow, J
, 2003
"... During the last ten years the Lattice Boltzmann Equation (LBE) method has been developed as an alternative numerical approach in computational fluid dynamics (CFD). Originated from the discrete kinetic theory, the LBE method has emerged with the promise to become a superior modeling platform, both c ..."
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Cited by 14 (0 self)
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During the last ten years the Lattice Boltzmann Equation (LBE) method has been developed as an alternative numerical approach in computational fluid dynamics (CFD). Originated from the discrete kinetic theory, the LBE method has emerged with the promise to become a superior modeling platform, both computationally and conceptually, compared to the existing arsenal of the continuumbased CFD methods. The LBE method has been applied for simulation of various kinds of fluid flows under different conditions. The number of papers on the LBE method and its applications continues to grow rapidly, especially in the direction of complex and multiphase media. The purpose of the present paper is to provide a comprehensive, selfcontained and consistent tutorial on the LBE method, aiming to clarify misunderstandings and eliminate some confusion that seems to persist in the LBErelated CFD literature. The focus is placed on the fundamental principles of the LBE approach. An excursion into the history, physical background and details of the theory and numerical implementation is made. Special attention is paid to advantages and limitations of the method, and its perspectives to be a useful framework for description of complex flows and interfacial (and multiphase) phenomena. The computational performance of the LBE method is examined, comparing it to other CFD methods, which directly solve for the transport equations of the macroscopic variables.
Critical Region for Droplet Formation in the TwoDimensional Ising Model
, 2002
"... We study the formation/dissolution of equilibrium droplets in finite systems at parameters corresponding to phase coexistence. Specifically, we consider the 2D Ising model in volumes of size L inverse temperature # > # c and overall magnetization conditioned to take the value m vL , wher ..."
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Cited by 10 (6 self)
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We study the formation/dissolution of equilibrium droplets in finite systems at parameters corresponding to phase coexistence. Specifically, we consider the 2D Ising model in volumes of size L inverse temperature # > # c and overall magnetization conditioned to take the value m vL , where # 1 c is the critical temperature, m (#) is the spontaneous magnetization and vL is a sequence of positive numbers. We find that the critical scaling for droplet formation/dissolution is when v L L 2 tends to a definite limit. Specifically, we identify a dimensionless parameter #, proportional to this limit, a nontrivial critical value # c and a function ## such that the following holds: For # < # c , there are no droplets beyond log L scale, while for # > # c , there is a single, Wulffshaped droplet containing a fraction ## # c = 2/3 of the magnetization deficit and there are no other droplets beyond the scale of log L. Moreover, ## and # are related via a universal equation that apparently is independent of the details of the system.
Modelling Pinchoff and Reconnection in a HeleShaw Cell I: The Models and their Calibration
, 2000
"... This is the first paper in a twopart series in which we analyze two model systems to study pinchoff and reconnection in binary fluid flow in a HeleShaw cell. The systems stem from a simplification of a general system of equations governing the motion of a binary fluid (NSCH model [69]) to flow ..."
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Cited by 10 (1 self)
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This is the first paper in a twopart series in which we analyze two model systems to study pinchoff and reconnection in binary fluid flow in a HeleShaw cell. The systems stem from a simplification of a general system of equations governing the motion of a binary fluid (NSCH model [69]) to flow in a HeleShaw cell. The system takes into account the chemical diffusivity between different components of a fluid mixture and the reactive stresses induced by inhomogeneity. In one of the systems we consider (HSCH), the binary fluid may be compressible due to diffusion. In the other system (BHSCH), a Boussinesq approximation is used and the fluid is incompressible. In this paper, we motivate, present and calibrate the HSCH/BHSCH equations so as to yield the classical sharp interface model as a limiting case. We then analyze their equilibria, one dimensional evolution and linear stability. In the second paper (Part II [66]), we analyze the behavior of the models in the fully nonline...
Correlation of entropy with similarity and symmetry
 Journal of Chemical Information and Computer Sciences
, 1996
"... Informational entropy is quantitatively related to similarity and symmetry. Some tacit assumptions regarding their correlation have been shown to be wrong. The Gibbs paradox statement (indistinguishability corresponds to minimum entropy, which is zero) has been rejected. All their correlations are b ..."
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Cited by 8 (4 self)
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Informational entropy is quantitatively related to similarity and symmetry. Some tacit assumptions regarding their correlation have been shown to be wrong. The Gibbs paradox statement (indistinguishability corresponds to minimum entropy, which is zero) has been rejected. All their correlations are based on the relation that less information content corresponds to more entropy. Higher value of entropy is correlated to higher molecular similarity. The maximum entropy of any system (e.g., a mixture or an assemblage) corresponds to indistinguishability (total loss of information), to perfect symmetry or highest symmetry, and to the highest simplicity. This conforms without exception to all the experimental facts of both dynamic systems and static structures and the related information loss processes. 1.
A survey on the continuous nonlinear resource allocation problem
 Eur. J. Oper. Res
, 2008
"... Our problem of interest consists of minimizing a separable, convex and differentiable function over a convex set, defined by bounds on the variables and an explicit constraint described by a separable convex function. Applications are abundant, and vary from equilibrium problems in the engineering a ..."
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Cited by 6 (1 self)
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Our problem of interest consists of minimizing a separable, convex and differentiable function over a convex set, defined by bounds on the variables and an explicit constraint described by a separable convex function. Applications are abundant, and vary from equilibrium problems in the engineering and economic sciences, through resource allocation and balancing problems in manufacturing, statistics, military operations research and production and financial economics, to subproblems in algorithms for a variety of more complex optimization models. This paper surveys the history and applications of the problem, as well as algorithmic approaches to its solution. The most common techniques are based on finding the optimal value of the Lagrange multiplier for the explicit constraint, most often through the use of a type of line search procedure. We analyze the most relevant references, especially regarding their originality and numerical findings, summarizing with remarks on possible extensions and future research. 1 Introduction and
Roughening instability of broken extremals
"... We derive a new general jump condition on a broken WeierstrassErdmann extremal of a vectorial variational problem. Such extremals, containing surfaces of gradient discontinuity, are ubiquitous in shape optimization and in the theory of elastic phase transformations. The new condition, which does no ..."
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Cited by 4 (4 self)
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We derive a new general jump condition on a broken WeierstrassErdmann extremal of a vectorial variational problem. Such extremals, containing surfaces of gradient discontinuity, are ubiquitous in shape optimization and in the theory of elastic phase transformations. The new condition, which does not have a one dimensional analog, reflects the stationarity of the singular surface with respect to twoscale variations that are nontrivial generalizations of Weierstrass needles. The overdeterminacy of the ensuing free boundary problem suggests that typical stable configurations must involve microstructures or chattering controls. 1
Convergence of a low order nonlocal NavierStokesKorteweg
, 2013
"... system: the orderparameter model ..."
Maxallent: Maximizers of all entropies and uncertainty
"... journal homepage: www.elsevier.com/locate/camwa ..."