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114
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 101 (4 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 40 (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.
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 35 (1 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.
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 25 (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.
Instabilities of Black Strings and Branes
 INVITED REVIEW FOR CLASSICAL AND QUANTUM GRAVITY
, 2007
"... We review recent progress on the instabilities of black strings and branes both for pure Einstein gravity as well as supergravity theories which are relevant for string theory. We focus mainly on GregoryLaflamme instabilities. In the first part of the review we provide a detailed discussion of the ..."
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Cited by 21 (1 self)
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We review recent progress on the instabilities of black strings and branes both for pure Einstein gravity as well as supergravity theories which are relevant for string theory. We focus mainly on GregoryLaflamme instabilities. In the first part of the review we provide a detailed discussion of the classical gravitational instability of the neutral uniform black string in higher dimensional gravity. The uniform black string is part of a larger phase diagram of KaluzaKlein black holes which will be discussed thoroughly. This phase diagram exhibits many interesting features including new phases, nonuniqueness and horizontopology changing transitions. In the second part, we turn to charged black branes in supergravity and show how the GregoryLaflamme instability of the neutral black string implies via a boost/Uduality map similar instabilities for non and nearextremal smeared branes in string theory. We also comment on instabilities of Dbrane bound states. The connection between classical and thermodynamic stability, known as the correlated stability conjecture, is also reviewed and illustrated with examples. Finally, we examine the holographic implications of the GregoryLaflamme instability for a number of nongravitational theories including YangMills theories and Little String Theory.
On the partition function and random maximum aposteriori perturbations
 In Proceedings of the 29th International Conference on Machine Learning
, 2012
"... In this paper we relate the partition function to the maxstatistics of random variables. In particular, we provide a novel framework for approximating and bounding the partition function using MAP inference on randomly perturbed models. As a result, we can use efficient MAP solvers such as graph ..."
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Cited by 20 (5 self)
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In this paper we relate the partition function to the maxstatistics of random variables. In particular, we provide a novel framework for approximating and bounding the partition function using MAP inference on randomly perturbed models. As a result, we can use efficient MAP solvers such as graphcuts to evaluate the corresponding partition function. We show that our method excels in the typical “high signal high coupling ” regime that results in ragged energy landscapes difficult for alternative approaches. 1.
GriffithKellySherman correlation inequalities: a useful tool in the theory of error correcting codes
 IEEE Trans. Inform. Theory
, 2007
"... Abstract—It is shown that a correlation inequality of statistical mechanics can be applied to linear lowdensity paritycheck codes. Thanks to this tool we prove that, under a natural assumption, the exponential growth rate of regular lowdensity paritycheck (LDPC) codes, can be computed exactly by ..."
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Cited by 17 (12 self)
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Abstract—It is shown that a correlation inequality of statistical mechanics can be applied to linear lowdensity paritycheck codes. Thanks to this tool we prove that, under a natural assumption, the exponential growth rate of regular lowdensity paritycheck (LDPC) codes, can be computed exactly by iterative methods, at least on the interval where it is a concave function of the relative weight of code words. Then, considering communication over a binary input additive white Gaussian noise channel with a Poisson LDPC code we prove that, under a natural assumption, part of the GEXIT curve (associated to MAP decoding) can also be computed exactly by the belief propagation algorithm. The correlation inequality yields a sharp lower bound on the GEXIT curve. We also make an extension of the interpolation techniques that have recently led to rigorous results in spin glass theory and in the SAT problem. Index Terms—Correlation inequalities, density evolution, generalized EXIT (GEXIT) curve, growth rate, interpolation technique, iterative decoding, lowdensity paritycheck (LDPC) codes, spin glasses. I.
On the general EricksenLeslie system: Parodi’s relation, wellposedness and stability
 Fakultät für Mathematik, Universität
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Modeling and Optimal Centralized Control of a LargeSize Robotic Population
, 2006
"... Abstract—This paper describes an approach to the modeling and control of multiagent populations composed of a large number of agents. The complexity of population modeling is avoided by assuming a stochastic approach, under which the agent distribution over the state space is modeled. The dynamics ..."
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Cited by 12 (1 self)
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Abstract—This paper describes an approach to the modeling and control of multiagent populations composed of a large number of agents. The complexity of population modeling is avoided by assuming a stochastic approach, under which the agent distribution over the state space is modeled. The dynamics of the state probability density functions is determined, and a control problem of maximizing the probability of robotic presence in a given region is introduced. The Minimum Principle for the optimal control of partial differential equations is exploited to solve this problem, and it is applied to the mission control of a simulated large robotic population. Index Terms—Hybrid automata, multirobot systems, optimal control. I.