The Experts below are selected from a list of 39 Experts worldwide ranked by ideXlab platform
Peter Palffy-muhorayt - One of the best experts on this subject based on the ideXlab platform.
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SMECTIC A-NEMATIC PHASE TRANSITION*
2020Co-Authors: M. Carme, Peter Palffy-muhoraytAbstract:We consider free energy functionals to model equilibrium smectic A liquid crystal configurations in the neighborhood of the nematic phase transition. We begin with the functional proposed by de Gennes based on the Ginzburg-Landau model for superconductivity and consider its covariant formulations. Exploring qualitative analogies with the nonlinear elastic bar of Ericksen, we motivate a revision of the liquid crystal energy so as to include a Nonconvex constraint. We study boundary-value problems corresponding to Neumann and Dirichlet boundary condi- tions for smectic A liquid crystals confined between two parallel plates. We show that the Nonconvex Term of the free energy density causes the presence in the solutions of nematic defects known to occur near the phase transition from smectic A to nematic. The latter are reminiscent of the dislocations occurring in higher dimensional configurations. We also deTermine parameter values that give rise to nucleation of nematic defects for boundary conditions consistent with externally imposed winding of the smectic phase field. The resulting energy also allows us to sort out liquid-like and solid-like behaviors, respectively. predictions concerning bulk properties of the smectic phase remain largely unaffected, the new constraint Term may prove relevant in the modeling of local effects such as dislocations. We consider boundary-value problems for the Euler-Lagrange equations corresponding to the newly formulated free energy functional and study static con- figurations of a liquid crystal confined between two plates. We construct solutions of the governing system that present arrays of nematic defects and dislocations. In particular, we deTermine the critical value of the prescribed winding number of the boundary conditions such that singular fields satisfy the governing system. With the decrease of temperature most nematic liquid crystals experience a tran- sition to the smectic A phase when the temperature reaches a critical value, TNA. Smectic A configurations are characterized by a modulation of the density, p, that gives the appearance of layers. The corresponding value of the wave length, q, of the structure depends on the material properties and the temperature. One of the fea- tures that distinguishes the smectic A phase from other lower temperature phases with higher degree of order is the fact that, in the former, the molecules remain mostly aligned perpendicularly to the layers; i.e., the director, n, may be assumed
Peter Palffy-muhoray - One of the best experts on this subject based on the ideXlab platform.
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Ericksen's bar and modeling of the smectic a-nematic phase transition
Siam Journal on Applied Mathematics, 2000Co-Authors: M. Carme Calderer, Peter Palffy-muhorayAbstract:We consider free energy functionals to model equilibrium smectic A liquid crystal configurations in the neighborhood of the nematic phase transition. We begin with the functional proposed by de Gennes based on the Ginzburg--Landau model for superconductivity and consider its covariant formulations. Exploring qualitative analogies with the nonlinear elastic bar of Ericksen, we motivate a revision of the liquid crystal energy so as to include a Nonconvex constraint. We study boundary-value problems corresponding to Neumann and Dirichlet boundary conditions for smectic A liquid crystals confined between two parallel plates. We show that the Nonconvex Term of the free energy density causes the presence in the solutions of nematic defects known to occur near the phase transition from smectic A to nematic. The latter are reminiscent of the dislocations occurring in higher dimensional configurations. We also deTermine parameter values that give rise to nucleation of nematic defects for boundary conditions consis...
M. Carme - One of the best experts on this subject based on the ideXlab platform.
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SMECTIC A-NEMATIC PHASE TRANSITION*
2020Co-Authors: M. Carme, Peter Palffy-muhoraytAbstract:We consider free energy functionals to model equilibrium smectic A liquid crystal configurations in the neighborhood of the nematic phase transition. We begin with the functional proposed by de Gennes based on the Ginzburg-Landau model for superconductivity and consider its covariant formulations. Exploring qualitative analogies with the nonlinear elastic bar of Ericksen, we motivate a revision of the liquid crystal energy so as to include a Nonconvex constraint. We study boundary-value problems corresponding to Neumann and Dirichlet boundary condi- tions for smectic A liquid crystals confined between two parallel plates. We show that the Nonconvex Term of the free energy density causes the presence in the solutions of nematic defects known to occur near the phase transition from smectic A to nematic. The latter are reminiscent of the dislocations occurring in higher dimensional configurations. We also deTermine parameter values that give rise to nucleation of nematic defects for boundary conditions consistent with externally imposed winding of the smectic phase field. The resulting energy also allows us to sort out liquid-like and solid-like behaviors, respectively. predictions concerning bulk properties of the smectic phase remain largely unaffected, the new constraint Term may prove relevant in the modeling of local effects such as dislocations. We consider boundary-value problems for the Euler-Lagrange equations corresponding to the newly formulated free energy functional and study static con- figurations of a liquid crystal confined between two plates. We construct solutions of the governing system that present arrays of nematic defects and dislocations. In particular, we deTermine the critical value of the prescribed winding number of the boundary conditions such that singular fields satisfy the governing system. With the decrease of temperature most nematic liquid crystals experience a tran- sition to the smectic A phase when the temperature reaches a critical value, TNA. Smectic A configurations are characterized by a modulation of the density, p, that gives the appearance of layers. The corresponding value of the wave length, q, of the structure depends on the material properties and the temperature. One of the fea- tures that distinguishes the smectic A phase from other lower temperature phases with higher degree of order is the fact that, in the former, the molecules remain mostly aligned perpendicularly to the layers; i.e., the director, n, may be assumed
M. Carme Calderer - One of the best experts on this subject based on the ideXlab platform.
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Ericksen's bar and modeling of the smectic a-nematic phase transition
Siam Journal on Applied Mathematics, 2000Co-Authors: M. Carme Calderer, Peter Palffy-muhorayAbstract:We consider free energy functionals to model equilibrium smectic A liquid crystal configurations in the neighborhood of the nematic phase transition. We begin with the functional proposed by de Gennes based on the Ginzburg--Landau model for superconductivity and consider its covariant formulations. Exploring qualitative analogies with the nonlinear elastic bar of Ericksen, we motivate a revision of the liquid crystal energy so as to include a Nonconvex constraint. We study boundary-value problems corresponding to Neumann and Dirichlet boundary conditions for smectic A liquid crystals confined between two parallel plates. We show that the Nonconvex Term of the free energy density causes the presence in the solutions of nematic defects known to occur near the phase transition from smectic A to nematic. The latter are reminiscent of the dislocations occurring in higher dimensional configurations. We also deTermine parameter values that give rise to nucleation of nematic defects for boundary conditions consis...
Christodoulos A. Floudas - One of the best experts on this subject based on the ideXlab platform.
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The α BB Global Optimization Algorithm for Nonconvex Problems: An Overview
Nonconvex Optimization and Its Applications, 2020Co-Authors: Claire S. Adjiman, Christodoulos A. FloudasAbstract:The αBB algorithm, a deTerministic global optimization algorithm for constrained twice-differentiable NLPs, is presented. It is based on a branch-and-bound approach in which a convex relaxation of the original Nonconvex problem is obtained through a dual procedure. First, all Nonconvex Terms of special structure (i.e., bilinear, trilinear, fractional, fractional trilinear, univariate concave) are replaced by customized tight convex lower bounding functions. Second, valid convex underestirnators are generated for general Nonconvex Terms by using a diagonal shift matrix A. A is related to the Hessian matrix of the Nonconvex Term and four rigorous methods, based on the interval Hessian matrix, are proposed for its computation. Branching variable selection strategies that improve the quality of the convex relaxations are presented. Variable bound updates are also found to affect the convergence rate positively. An implementation of the algorithm is used to solve three examples: a small but highly Nonconvex problem, a stability problem and a large-scale problem involving the design of batch plant under uncertainty.