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77
Nonequilibrium critical phenomena and phase transitions into absorbing states
 ADVANCES IN PHYSICS
, 2000
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Statistical mechanics of neocortical interactions: A scaling paradigm applied to electroencephalography
 PHYS. REV. A
, 1991
"... A series of papers has developed a statistical mechanics of neocortical interactions (SMNI), deriving aggregate behavior of experimentally observed columns of neurons from statistical electricalchemical properties of synaptic interactions. While not useful to yield insights at the single neuron lev ..."
Abstract

Cited by 47 (41 self)
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A series of papers has developed a statistical mechanics of neocortical interactions (SMNI), deriving aggregate behavior of experimentally observed columns of neurons from statistical electricalchemical properties of synaptic interactions. While not useful to yield insights at the single neuron level, SMNI has demonstrated its capability in describing largescale properties of shortterm memory and electroencephalographic (EEG) systematics. The necessity of including nonlinear and stochastic structures in this development has been stressed. In this paper, a more stringent test is placed on SMNI: The algebraic and numerical algorithms previously developed in this and similar systems are brought to bear to fit large sets of EEG and evoked potential data being collected to investigate genetic predispositions to alcoholism and to extract brain “signatures” of shortterm memory. Using the numerical algorithm of Very Fast Simulated ReAnnealing, it is demonstrated that SMNI can indeed fit this data within experimentally observed ranges of its underlying neuronalsynaptic parameters, and use the quantitative modeling results to examine physical neocortical mechanisms to discriminate between highrisk and lowrisk populations genetically predisposed to alcoholism. Since this first study is a control to span relatively long time epochs, similar to earlier attempts to establish such correlations, this discrimination is inconclusive because of other neuronal activity which can mask such effects. However, the SMNI model is shown to be consistent
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
Relativistic viscous hydrodynamics, conformal invariance, and holography
 JHEP
"... Abstract: We consider secondorder viscous hydrodynamics in conformal field theories at finite temperature. We show that conformal invariance imposes powerful constraints on the form of the secondorder corrections. By matching to the AdS/CFT calculations of correlators, and to recent results for Bj ..."
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Cited by 36 (1 self)
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Abstract: We consider secondorder viscous hydrodynamics in conformal field theories at finite temperature. We show that conformal invariance imposes powerful constraints on the form of the secondorder corrections. By matching to the AdS/CFT calculations of correlators, and to recent results for Bjorken flow obtained by Heller and Janik, we find three (out of five) secondorder transport coefficients in the strongly coupled N = 4 supersymmetric YangMills theory. We also discuss how these new coefficents can arise within the kinetic theory of weakly coupled conformal plasmas. We point out that the MüllerIsraelStewart theory, often used in numerical simulations, does not contain all allowed secondorder terms and, frequently, terms required by conformal invariance. Contents
Towards a unified brain theory
, 1981
"... An approach to collective aspects of the neocortical system is formulated by methods of modern nonequilibrium statistical mechanics. Microscopic neuronal synaptic interactions are first spatially averaged over columnar domains. These spatially ordered domains include well formulated fluctuations th ..."
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Cited by 29 (27 self)
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An approach to collective aspects of the neocortical system is formulated by methods of modern nonequilibrium statistical mechanics. Microscopic neuronal synaptic interactions are first spatially averaged over columnar domains. These spatially ordered domains include well formulated fluctuations that retain contact with the original physical synaptic parameters. They also are a suitable substrate for macroscopic spatialtemporal regions described by FokkerPlanck and Lagrangian formalisms. This development clarifies similarities and differences among previous studies, suggests new analytically supported insights into neocortical function and permits future approximation or elaboration within current paradigms of collective systems.
TwoPhase Binary Fluids and Immiscible Fluids Described By an Order Parameter
, 1996
"... A unified framework for coupled NavierStokes/CahnHilliard equations is developed using, as a basis, a balance law for microforces in conjunction with constitutive equations consistent with a mechanical version of the second law. As a numerical application of the theory, we consider the kinetics ..."
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Cited by 23 (1 self)
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A unified framework for coupled NavierStokes/CahnHilliard equations is developed using, as a basis, a balance law for microforces in conjunction with constitutive equations consistent with a mechanical version of the second law. As a numerical application of the theory, we consider the kinetics of coarsening for a binary fluid in two spacedimensions. Typeset using REVT E X 1 I. INTRODUCTION The CahnHilliard equation [1] 1 ' . = m\Delta [f 0 (') \Gamma ff\Delta'] (1) is central to materials science, as it characterizes important qualitative features of twophase systems. This equation is based on a free energy /('; grad') = f(') + 1 2 ffjgrad'j 2 ; (2) with f(') a doublewell potential whose wells define the phases, and leads to an interfacial layer within which the density ' suffers large variations. The standard derivation of the CahnHilliard equation begins with the mass balance ' . = \Gammadiv h (3) and the constitutive equation 1 Notation. Tensors ar...
EulerPoincaré dynamics of perfect complex fluids
, 2000
"... Lagrangian reduction by stages is used to derive the EulerPoincaré equations for the nondissipative coupled motion and micromotion of complex fluids. We mainly treat perfect complex fluids (PCFs) whose order parameters are continuous material variables. These order parameters may be regarded geomet ..."
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Cited by 18 (9 self)
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Lagrangian reduction by stages is used to derive the EulerPoincaré equations for the nondissipative coupled motion and micromotion of complex fluids. We mainly treat perfect complex fluids (PCFs) whose order parameters are continuous material variables. These order parameters may be regarded geometrically either as objects in a vector space, or as coset spaces of Lie symmetry groups with respect to subgroups that leave these objects invariant. Examples include liquid crystals, superfluids, YangMills magnetofluids and spinglasses. A LiePoisson Hamiltonian formulation of the dynamics for perfect complex fluids is obtained by Legendre transforming the EulerPoincaré formulation. These dynamics are also derived by using the Clebsch approach. In the Hamiltonian and Lagrangian formulations of perfect complex fluid dynamics Lie algebras containing twococycles arise as a characteristic feature. After discussing these geometrical formulations of the dynamics of perfect complex fluids, we give an example of how to introduce defects into the order parameter as imperfections (e.g., vortices) that carry their own momentum. The defects may move relative to the Lagrangian fluid material and thereby produce additional reactive forces and stresses.
Conservative multigrid methods for Cahn–Hilliard fluids
 J. Comput. Phys
"... We develop a conservative, second order accurate fully implicit discretization in two dimensions of the NavierStokes NS and CahnHilliard CH system that has an associated discrete energy functional. This system provides a diffuseinterface description of binary fluid flows with compressible or inco ..."
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Cited by 15 (3 self)
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We develop a conservative, second order accurate fully implicit discretization in two dimensions of the NavierStokes NS and CahnHilliard CH system that has an associated discrete energy functional. This system provides a diffuseinterface description of binary fluid flows with compressible or incompressible flow components [44,4]. In this work, we focus on the case of flows containing two immiscible, incompressible and densitymatched components. The scheme, however, has a straightforward extension to multicomponent systems. To efficiently solve the discrete system at the implicit timelevel, we develop a nonlinear multigrid method to solve the CH equation which is then coupled to a projection method that is used to solve the NS equation. We analyze and prove convergence of the scheme in the absence of flow. We demonstrate convergence of our scheme numerically in both the presence and absence of flow and perform simulations of phase separation via spinodal decomposition. We examine the separate effects of surface tension and external flow on the decomposition. We find surface tension driven flow alone increases coalescence rates through the retraction of interfaces. When there is an external shear flow, the evolution
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.