Variational Principle for Nonequilibrium Steady States Tested by Molecular Dynamics Simulation of Model Liquid Crystal Systems PDF Download
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Author: Sten Sarman
Publisher:
ISBN:
Category : Electronic books
Languages : en
Pages : 0
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Book Description
The purpose of the work presented in this chapter is to test a recently proven variational principle according to which the irreversible energy dissipation rate is minimal in the linear regime of a nonequilibrium steady state. This test is carried out by performing molecular dynamics simulations of liquid crystals subject to velocity gradients and temperature gradients. Since the energy dissipation rate varies with the orientation of the director of the liquid crystal relative to these gradients and is minimal at certain orientations, this is a stringent test of the variational principle. More particularly, a nematic liquid crystal model based on the Gay-Berne potential, which can be regarded as a Lennard-Jones fluid generalized to elliptical molecular cores, is studied under planar Couette flow, planar elongational flow, and under a temperature gradient. It is found that the director of a nematic liquid crystal consisting of rod-like molecules lies in the vorticity plane at an angle of about 20° to the stream lines in the planar Couette flow. In the elongational flow, it is parallel to the elongation direction, and it is perpendicular to the temperature gradient in a heat flow. These orientations are the ones where the irreversible energy dissipation rate is minimal, so that the variational principle is fulfilled in these three cases.
Author: Sten Sarman
Publisher:
ISBN:
Category : Electronic books
Languages : en
Pages : 0
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Book Description
The purpose of the work presented in this chapter is to test a recently proven variational principle according to which the irreversible energy dissipation rate is minimal in the linear regime of a nonequilibrium steady state. This test is carried out by performing molecular dynamics simulations of liquid crystals subject to velocity gradients and temperature gradients. Since the energy dissipation rate varies with the orientation of the director of the liquid crystal relative to these gradients and is minimal at certain orientations, this is a stringent test of the variational principle. More particularly, a nematic liquid crystal model based on the Gay-Berne potential, which can be regarded as a Lennard-Jones fluid generalized to elliptical molecular cores, is studied under planar Couette flow, planar elongational flow, and under a temperature gradient. It is found that the director of a nematic liquid crystal consisting of rod-like molecules lies in the vorticity plane at an angle of about 20° to the stream lines in the planar Couette flow. In the elongational flow, it is parallel to the elongation direction, and it is perpendicular to the temperature gradient in a heat flow. These orientations are the ones where the irreversible energy dissipation rate is minimal, so that the variational principle is fulfilled in these three cases.
Author: Albert S. Kim
Publisher: BoD – Books on Demand
ISBN: 1839680776
Category : Science
Languages : en
Pages : 198
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Book Description
All engineering processes are processes of non-equilibrium because one or all of heat, mass, and momentum transfer occur in an open system. The pure equilibrium state can be established in an isolated system, in which neither mass nor heat is transferred between the system and the environment. Most engineering transport analyses are based on the semi-, quasi-, or local equilibrium assumptions, which assume that any infinitesimal volume can be treated as a box of equilibrium. This book includes various aspects of non-equilibrium or irreversible statistical mechanics and their relationships with engineering applications. I hope that this book contributes to expanding the predictability of holistic engineering consisting of thermo-, fluid, and particle dynamics.
Author: Pawel Pieranski
Publisher: John Wiley & Sons
ISBN: 1789450403
Category : Science
Languages : en
Pages : 370
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Book Description
This book on liquid crystals reports on the new perspectives that have been brought about by the recent expansion of frontiers and overhaul of common beliefs. First, it explores the interaction of light with mesophases, when the light or matter is endowed with topological defects. It goes on to show how electrophoresis, electro-osmosis and the swimming of flagellated bacteria are affected by the anisotropic properties of liquid crystals. It also reports on the recent progress in the understanding of thermomechanical and thermohydrodynamical effects in cholesterics and deformed nematics and refutes the common belief that these effects could explain Lehmann’s observations of the rotation of cholesteric droplets subjected to a temperature gradient. It then studies the physics of the dowser texture, which has remarkable properties. This is of particular interest in regards to nematic monopoles, which can easily be generated, set into motion and collided within it. Finally, this book deals with the spontaneous emergence of chirality in nematics made of achiral molecules, and provides a brief historical context of chirality
Author: Albert Kim
Publisher:
ISBN: 9781839680786
Category :
Languages : en
Pages : 183
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Book Description
Author: B. L. Moiseiwitsch
Publisher: Courier Corporation
ISBN: 0486150496
Category : Mathematics
Languages : en
Pages : 534
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Book Description
This graduate-level text's primary objective is to demonstrate the expression of the equations of the various branches of mathematical physics in the succinct and elegant form of variational principles (and thereby illuminate their interrelationship). Its related intentions are to show how variational principles may be employed to determine the discrete eigenvalues for stationary state problems and to illustrate how to find the values of quantities (such as the phase shifts) that arise in the theory of scattering. Chapter-by-chapter treatment consists of analytical dynamics; optics, wave mechanics, and quantum mechanics; field equations; eigenvalue problems; and scattering theory. 1966 edition. Bibliography. Index.
Author: E.G. Virga
Publisher: Routledge
ISBN: 1351405640
Category : Mathematics
Languages : en
Pages : 284
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Book Description
Essentially there are two variational theories of liquid crystals explained in this book. The theory put forward by Zocher, Oseen and Frank is classical, while that proposed by Ericksen is newer in its mathematical formulation although it has been postulated in the physical literature for the past two decades. The newer theory provides a better explanation of defects in liquid crystals, especially of those concentrated on lines and surfaces, which escape the scope of the classical theory. The book opens the way to the wealth of applications that will follow.
Author: Billy D. Todd
Publisher: Cambridge University Press
ISBN: 0521190096
Category : Science
Languages : en
Pages : 371
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Book Description
This coherent collection of theory, algorithms, and illustrative results presents the field of nonequilibrium molecular dynamics in detail.
Author: Loris Bennett
Publisher:
ISBN: 9783896853110
Category :
Languages : en
Pages : 98
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Book Description
Author: Christian Maes
Publisher: Springer
ISBN: 3319677802
Category : Science
Languages : en
Pages : 56
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Book Description
This book introduces and discusses both the fundamental aspects and the measurability of applications of time-symmetric kinetic quantities, outlining the features that constitute the non-dissipative branch of non-equilibrium physics. These specific features of non-equilibrium dynamics have largely been ignored in standard statistical mechanics texts. This introductory-level book offers novel material that does not take the traditional line of extending standard thermodynamics to the irreversible domain. It shows that although stationary dissipation is essentially equivalent with steady non-equilibrium and ubiquitous in complex phenomena, non-equilibrium is not determined solely by the time-antisymmetric sector of energy-entropy considerations. While this should not be very surprising, this book provides timely, simple reminders of the role of time-symmetric and kinetic aspects in the construction of non-equilibrium statistical mechanics.
Author: B. D. Vujanovic
Publisher: Academic Press
ISBN: 0080926428
Category : Mathematics
Languages : en
Pages : 383
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Book Description
This book provides a comprehensive survey of analytic and approximate solutions of problems of applied mechanics, with particular emphasis on nonconservative phenomena. Include
