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54
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 42 (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
"Theoretical mathematics”: Toward a cultural synthesis of mathematics and theoretical physics
 BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY
, 1993
"... Is speculative mathematics dangerous? Recent interactions between physics and mathematics pose the question with some force: traditional mathematical norms discourage speculation, but it is the fabric of theoretical physics. In practice there can be benefits, but there can also be unpleasant and de ..."
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Cited by 24 (1 self)
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Is speculative mathematics dangerous? Recent interactions between physics and mathematics pose the question with some force: traditional mathematical norms discourage speculation, but it is the fabric of theoretical physics. In practice there can be benefits, but there can also be unpleasant and destructive consequences. Serious caution is required, and the issue should be considered before, rather than after, obvious damage occurs. With the hazards carefully in mind, we propose a framework that should allow a healthy and positive role for speculation.
Myosin learns to walk
 J Cell Sci
, 2001
"... Recent experiments, drawing upon singlemolecule, solution kinetic and structural techniques, have clarified our mechanistic understanding of class V myosins. The findings of the past two years can be summarized as follows: (1) Myosin V is a highly efficient processive motor, surpassing even convent ..."
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Cited by 11 (0 self)
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Recent experiments, drawing upon singlemolecule, solution kinetic and structural techniques, have clarified our mechanistic understanding of class V myosins. The findings of the past two years can be summarized as follows: (1) Myosin V is a highly efficient processive motor, surpassing even conventional kinesin in the distance that individual molecules can traverse. (2) The kinetic scheme underlying ATP turnover resembles those of myosins I and II but with rate constants tuned to favor strong binding to actin. ADP release precedes dissociation from actin and is ratelimiting in the cycle. (3) Myosin V walks in strides averaging ~36 nm, the long pitch pseudorepeat of the actin helix, each step coupled to a single ATP hydrolysis. Such a unitary displacement, the largest molecular step size measured to date, is required for a processive myosin motor to follow a linear trajectory along a helical actin track.
Lattice Boltzmann simulations of contact line motion
 II. Binary fluids. Phys. Rev. E
"... We use a lattice Boltzmann algorithm for liquid–gas coexistence to investigate the steady state interface profile of a droplet held between two shearing walls. The algorithm solves the hydrodynamic equations of motion for the system. Partial wetting at the walls is implemented to agree with Cahn the ..."
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Cited by 11 (0 self)
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We use a lattice Boltzmann algorithm for liquid–gas coexistence to investigate the steady state interface profile of a droplet held between two shearing walls. The algorithm solves the hydrodynamic equations of motion for the system. Partial wetting at the walls is implemented to agree with Cahn theory. This allows us to investigate the processes which lead to the motion of the threephase contact line. We confirm that the profiles are a function of the capillary number and a finite size analysis shows the emergence of a dynamic contact angle, which can be defined in a region where the interfacial curvature tends to zero.
The Blackholic energy and the canonical GammaRay Burst
 in XIIth Brazilian School of Cosmology and Gravitation, edited by
"... Abstract. GammaRay Bursts (GRBs) represent very likely “the ” most extensive computational, theoretical and observational effort ever carried out successfully in physics and astrophysics. The extensive campaign of observation from space based Xray and γray observatory, such as the Vela, CGRO, Bep ..."
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Cited by 7 (6 self)
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Abstract. GammaRay Bursts (GRBs) represent very likely “the ” most extensive computational, theoretical and observational effort ever carried out successfully in physics and astrophysics. The extensive campaign of observation from space based Xray and γray observatory, such as the Vela, CGRO, BeppoSAX, HETEII, INTEGRAL, Swift, RXTE, Chandra, XMM satellites, have been matched by complementary observations in the radio wavelength (e.g. by the VLA) and in the optical band (e.g. by VLT, Keck, ROSAT). The net result is unprecedented accuracy in the received data allowing the determination of the energetics, the time variability and the spectral properties of these GRB sources. The very fortunate situation occurs that these data can be confronted with a mature theoretical development. Theoretical interpretation of the above data allows progress in three different frontiers of knowledge: a) the ultrarelativistic regimes of a macroscopic source moving at Lorentz gamma factors up to ∼ 400; b) the occurrence of vacuum polarization process verifying some of the yet untested regimes of ultrarelativistic quantum field theories; and c) the first evidence for extracting, during the process of gravitational collapse leading to the formation of a black hole, amounts of energies up to 10 55 ergs of blackholic energy — a new form of energy in physics and astrophysics. We outline how this progress leads to the confirmation of three interpretation paradigms for GRBs proposed in July 2001. Thanks mainly to the observations by Swift and the optical observations by VLT, the outcome
Dynamic System Evolution and Markov Chain Approximation
 Discrete Dynamics in NS, Gordon & Breach
, 1998
"... In this paper computational aspects of the mathematical modelling of dynamic system evolution have been considered as a problem in information theory. The construction of such models is treated as a decision making process with limited available information. The solution of the problem is associated ..."
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Cited by 4 (4 self)
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In this paper computational aspects of the mathematical modelling of dynamic system evolution have been considered as a problem in information theory. The construction of such models is treated as a decision making process with limited available information. The solution of the problem is associated with a computational model based on heuristics of a Markov Chain in a discrete spacetime of events. A stable approximation of the chain has been derived and the limiting cases are discussed. An intrinsic interconnection of constructive, sequential, and evolutionary approaches in related optimization problems provides new challenges for future work. Key words: decision making with limited information, optimal control theory, hyperbolicity of dynamic rules, generalized dynamic systems, Markov Chain approximation. 1 Introduction Many mathematical problems in information theory and optimal control related to dynamic system studies can be formulated in the following generic form. A decision...
New Hierarchic theory of condensed matter and its computerized application to water and ice
 In the Archives of LosAlamos: http://arXiv.org/abs/physics/0102086
, 2001
"... This work contains review of original quantum Hierarchic theory of condensed matter, general for liquids and solids and its numerous branches. Computer program (copyright, 1997, Kaivarainen), based on new theory, was used for comprehensive simulations of water and ice physical properties. Condensed ..."
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Cited by 3 (3 self)
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This work contains review of original quantum Hierarchic theory of condensed matter, general for liquids and solids and its numerous branches. Computer program (copyright, 1997, Kaivarainen), based on new theory, was used for comprehensive simulations of water and ice physical properties. Condensed matter is considered as gas of 3D standing waves (collective excitations) of different nature: thermal de Broglie waves (waves B), IR photons and thermal phonons. Quantitative interrelation between microscopic, mesoscopic (as intermediate) and macroscopic properties of condensed matter are demonstrated. New theories of total internal energy, including contributions of kinetic and potential energy, heat capacity, surface tension, vapor pressure, thermal conductivity, viscosity and selfdiffusion are described. Hierarchic theory of osmotic pressure, based on new state equation, new theories of light refraction, Brillouin light scattering and Mössbauer effect are presented also in article and compared with available experimental data for water and ice. Lot of hidden parameters, inaccessible for experiment, describing the dynamic and spatial properties of 24 quantum collective excitations of matter, can be calculated also, as demonstrated on examples of water and ice. Total number of physical parameters of liquids and solids in wide Tinterval, including that of phase transitions, to be possible to evaluate using CAMP computer program, is about 300. The agreement between theoretical and available experimental results is very good. The evidence of highT mesoscopic molecular Bose condensation (BC) in water and ice in form of coherent clusters is obtained. The new mechanisms of the 1st and 2nd order phase transitions, related to such clusters formation/melting, their assembly/disassembly and symmetry change is proposed. Theory unifies dynamics and thermodynamics on microscopic, mesoscopic and macroscopic scales in terms of quantum physics. The idea of new optoacoustic device: Comprehensive Analyzer of Matter Properties (CAMP) with huge informational possibilities, based on computer program, elaborated and its multisided applications are described. This work may be considered as a
Counting in Lattices: Combinatorial Problems from Statistical Mechanics
, 1994
"... In this thesis we consider two classical combinatorial problems arising in statistical mechanics: counting matchings and selfavoiding walks in lattice graphs. The first problem arises in the study of the thermodynamical properties of monomers and dimers (diatomic molecules) in crystals. Fisher, Kas ..."
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Cited by 2 (1 self)
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In this thesis we consider two classical combinatorial problems arising in statistical mechanics: counting matchings and selfavoiding walks in lattice graphs. The first problem arises in the study of the thermodynamical properties of monomers and dimers (diatomic molecules) in crystals. Fisher, Kasteleyn and Temperley discovered an elegant technique to exactly count the number of perfect matchings in two dimensional lattices, but it is not applicable for matchings of arbitrary size, or in higher dimensional lattices. We present the first efficient approximation algorithm for computing the number of matchings of any size in any periodic lattice in arbitrary dimension. The algorithm is based on Monte Carlo simulation of a suitable Markov chain and has rigorously derived performance guarantees that do not rely on any assumptions. In addition, we show that these results generalize to counting matchings in any graph which is the Cayley graph of a finite group. The second problem is countin...
LongTime Behavior of Macroscopic Quantum Systems: Commentary Accompanying the English Translation of John von Neumann’s 1929 Article on the Quantum Ergodic Theorem
, 2010
"... The renewed interest in the foundations of quantum statistical mechanics in recent years has led us to study John von Neumann’s 1929 article on the quantum ergodic theorem. We have found this almost forgotten article, which until now has been available only in German, to be a treasure chest, and to ..."
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Cited by 2 (2 self)
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The renewed interest in the foundations of quantum statistical mechanics in recent years has led us to study John von Neumann’s 1929 article on the quantum ergodic theorem. We have found this almost forgotten article, which until now has been available only in German, to be a treasure chest, and to be much misunderstood. In it, von Neumann studied the longtime behavior of macroscopic quantum systems. While one of the two theorems announced in his title, the one he calls the “quantum Htheorem, ” is actually a much weaker statement than Boltzmann’s classical Htheorem, the other theorem, which he calls the “quantum ergodic theorem, ” is a beautiful and very nontrivial result. It expresses a fact we call “normal typicality ” and can be summarized as follows: For a “typical ” finite family of commuting macroscopic observables, every initial wave function ψ0 from a microcanonical energy shell so evolves that for most times t in the long run, the joint probability distribution of these observables obtained from ψt is close to their microcanonical distribution. PACS: 05.30.d. Key words: quantum statistical mechanics; approach to thermal equilibrium; macroscopic observable; microcanonical energy shell; typical longtime behavior.