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Sep 18, 2013
09/13

by
P. Meurs; C. Van den Broeck

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Recently, a thermal Brownian motor was introduced [Van den Broeck, Kawai and Meurs, Phys. Rev. Lett. (2004)], for which an exact microscopic analysis is possible. The purpose of this paper is to review some further properties of this construction, and to discuss in particular specific issues including the relation with macroscopic response and the efficiency at maximum power.

Source: http://arxiv.org/abs/cond-mat/0505753v2

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71

Jul 20, 2013
07/13

by
M. Copelli; C. Van den Broeck

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We study a model of unsupervised learning where the real-valued data vectors are isotropically distributed, except for a single symmetry breaking binary direction $\bm{B}\in\{-1,+1\}^{N}$, onto which the projections have a Gaussian distribution. We show that a candidate vector $\bm{J}$ undergoing Gibbs learning in this discrete space, approaches the perfect match $\bm{J}=\bm{B}$ exponentially. Besides the second order ``retarded learning'' phase transition for unbiased distributions, we show...

Source: http://arxiv.org/abs/cond-mat/9910365v2

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45

Sep 24, 2013
09/13

by
V. Balakrishnan; C. Van den Broeck

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In the context of the problem of heat conduction in one-dimensional systems, we present an analytical calculation of the instantaneous energy transfer across a tagged particle in a one-dimensional gas of equal-mass, hard-point particles. From this, we obtain a formula for the steady-state energy flux, and identify and separate the mechanical work and heat conduction contributions to it. The nature of the Fourier law for the model, and the nonlinear dependence of the rate of mechanical work on...

Source: http://arxiv.org/abs/cond-mat/0412317v1

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31

Sep 21, 2013
09/13

by
C. Van den Broeck; R. Kawai

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Onsager symmetry implies that a Brownian motor, driven by a temperature gradient, will also perform a refrigerator function upon loading. We analytically calculate the corresponding heat flux for an exactly solvable microscopic model and compare it with molecular dynamics simulations.

Source: http://arxiv.org/abs/cond-mat/0602153v2

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2.0

Jun 30, 2018
06/18

by
C. Van den Broeck; R. Toral

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We introduce multi-kangaroo Markov processes and provide a general procedure for evaluating a certain type of stochastic functionals. We calculate analytically the large deviation properties. Applications include zero-crossing statistics and stochastic thermodynamics.

Topics: Statistical Mechanics, Condensed Matter

Source: http://arxiv.org/abs/1401.2154

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31

Sep 18, 2013
09/13

by
B. Cleuren; C. Van den Broeck

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An asymmetric object, undergoing dissipative collisions with surrounding particles, acquires a nonzero average velocity. The latter is calculated analytically by an expansion of the Boltzmann equation and the result is compared with Monte Carlo simulations.

Source: http://arxiv.org/abs/cond-mat/0611283v1

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Sep 24, 2013
09/13

by
J. Farago; C. Van den Broeck

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We calculate analytically the phase boundary for a nonequilibrium phase transition in a one-dimensional array of coupled, overdamped parametric harmonic oscillators in the limit of strong and weak spatial coupling. Our results show that the transition is reentrant with respect to the spatial coupling in agreement with the prediction of the mean field theory.

Source: http://arxiv.org/abs/cond-mat/0103104v1

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Sep 19, 2013
09/13

by
C. Van den Broeck; B. Cleuren

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In their recent paper [Phys. Rev. Lett. 98, 094101 (2007)], A. Porporato et al. studied the irreversibility and fluctuation theorem for stationary time series. In this comment, we point out that the fluctuation theorem is in fact the trivial outcome of a symmetry operation, and hence its physical contect is less convincing.

Source: http://arxiv.org/abs/cond-mat/0703213v1

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Sep 18, 2013
09/13

by
B. Cleuren; C. Van den Broeck

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The fluctuation theorem is verified for black-body radiation, provided the bunching of photons is taken into account appropriately.

Source: http://arxiv.org/abs/0705.4248v1

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5.0

Jun 27, 2018
06/18

by
C. Van den Broeck; R. Toral

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Stochastic thermodynamics is formulated for variables that are odd under time reversal. The invariance under spatial rotation of the collision rates due to the isotropy of the heat bath is shown to be a crucial ingredient. An alternative detailed fluctuation theorem is derived, expressed solely in terms of forward statistics. It is illustrated for a linear kinetic equation with kangaroo rates.

Topics: Condensed Matter, Statistical Mechanics

Source: http://arxiv.org/abs/1503.08118

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3.0

Jun 30, 2018
06/18

by
T. Becker; T. Willaert; B. Cleuren; C. Van den Broeck

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Detailed fluctuation theorems are statements about the probability distribution for the stochastic entropy production along a trajectory. It involves the consideration of a suitably transformed dynamics, such as the time reversed, the adjoint, or a combination of these. We identify specific, typically unique, initial conditions, called echo states, for which the final probability distribution of the transformed dynamics reproduces the initial distribution. In this case the detailed fluctuation...

Topics: Statistical Mechanics, Condensed Matter

Source: http://arxiv.org/abs/1405.6064

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41

Sep 20, 2013
09/13

by
Kevin Wood; C. Van den Broeck; R. Kawai; Katja Lindenberg

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We derive an exact expression for entropy production during effusion of an ideal gas driven by momentum transfer in addition to energy and particle flux. Following the treatment in Phys. Rev. E Vol. 74, 021117 (2006), we construct a master equation formulation of the process and explicitly verify the thermodynamic fluctuation theorem, thereby directly exhibiting its extended applicability to particle flows and hence to hydrodynamic systems.

Source: http://arxiv.org/abs/physics/0612167v2

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Sep 17, 2013
09/13

by
M. van den Broek; C. Van den Broeck

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We present the exact analysis of a chiral Brownian motor and heat pump. Optimization of the construction predicts, for a nanoscale device, frequencies of the order of kHz and cooling rates of the order of femtojoule per second.

Source: http://arxiv.org/abs/0711.1758v1

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Sep 22, 2013
09/13

by
I. Bena; C. Van den Broeck; R. Kawai; Katja Lindenberg

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We derive explicit results for the asymptotic probability density and drift velocity in systems driven by dichotomous Markov noise, including the situation in which the asymptotic dynamics crosses {\em unstable} fixed points. The results are illustrated on the problem of the rocking ratchet.

Source: http://arxiv.org/abs/cond-mat/0307336v1

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Sep 23, 2013
09/13

by
B. Cleuren; C. Van den Broeck; R. Kawai

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We elucidate the connection between various fluctuation theorems by a microcanonical version of the Crooks relation. We derive the microscopically exact expression for the work distribution in an idealized Joule experiment, namely for an object, convex but otherwise of arbitrary shape, moving at constant speed through an ideal gas. Analytic results are compared with molecular dynamics simulations of a hard disk gas.

Source: http://arxiv.org/abs/cond-mat/0511653v1

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50

Sep 18, 2013
09/13

by
B. Cleuren; C. Van den Broeck; R. Kawai

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The probability distribution of the entropy production for the effusion of an ideal gas between two compartments is calculated explicitly. The fluctuation theorem is verified. The analytic results are in good agreement with numerical data from hard disk molecular dynamics simulations.

Source: http://arxiv.org/abs/cond-mat/0606141v1

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51

Sep 22, 2013
09/13

by
I. Bena; R. Kawai; C. Van den Broeck; Katja Lindenberg

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Stochastic Stokes' drift and hypersensitive transport driven by dichotomous noise are theoretically investigated. Explicit mathematical expressions for the asymptotic probability density and drift velocity are derived including the situation in which particles cross unstable fixed points. The results are confirmed by numerical simulations.

Source: http://arxiv.org/abs/cond-mat/0501499v1

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Sep 18, 2013
09/13

by
Kevin Wood; C. Van den Broeck; R. Kawai; Katja Lindenberg

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Synchronization of stochastic phase-coupled oscillators is known to occur but difficult to characterize because sufficiently complete analytic work is not yet within our reach, and thorough numerical description usually defies all resources. We present a discrete model that is sufficiently simple to be characterized in meaningful detail. In the mean field limit, the model exhibits a supercritical Hopf bifurcation and global oscillatory behavior as coupling crosses a critical value. When...

Source: http://arxiv.org/abs/cond-mat/0606073v1

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37

Sep 21, 2013
09/13

by
P. Meurs; C. Van den Broeck; A. Garcia

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We calculate the systematic average speed of the adiabatic piston and a thermal Brownian motor, introduced in [Van den Broeck, Kawai and Meurs, \emph{Microscopic analysis of a thermal Brownian motor}, to appear in Phys. Rev. Lett.], by an expansion of the Boltzmann equation and compare with the exact numerical solution.

Source: http://arxiv.org/abs/cond-mat/0407180v1

31
31

Sep 19, 2013
09/13

by
I. Bena; C. Van den Broeck; R. Kawai; Katja Lindenberg

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Dichotomous noise appears in a wide variety of physical and mathematical models. It has escaped attention that the standard results for the long time properties cannot be applied when unstable fixed points are crossed in the asymptotic regime. We show how calculations have to be modified to deal with these cases and present as a first application full analytic results for hypersensitive transport.

Source: http://arxiv.org/abs/cond-mat/0209298v2

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45

Sep 21, 2013
09/13

by
B. Cleuren; K. Willaert; A. Engel; C. Van den Broeck

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The probability distribution of the entropy production for the effusion of a relativistic ideal gas is calculated explicitly. This result is then extended to include particle and anti-particle pair production and annihilation. In both cases, the fluctuation theorem is verified.

Source: http://arxiv.org/abs/0709.3801v1

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47

Sep 19, 2013
09/13

by
R. Kawai; J. M. R. Parrondo; C. Van den Broeck

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We show, through a refinement of the work theorem, that the average dissipation, upon perturbing a Hamiltonian system arbitrarily far out of equilibrium in a transition between two canonical equilibrium states, is exactly given by $ = < W > -\Delta F =kT D(\rho\|\widetilde{\rho})= kT < \ln (\rho/\widetilde{\rho})>$, where $\rho$ and $\widetilde{\rho}$ are the phase space density of the system measured at the same intermediate but otherwise arbitrary point in time, for the forward...

Source: http://arxiv.org/abs/cond-mat/0701397v1

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33

Sep 20, 2013
09/13

by
R. Brito; M. J. Renne; C. Van den Broeck

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An adiabatic piston, separating two granular gases prepared in the same macroscopic state, is found to eventually collapse to one of the sides. This new instability is explained by a simple macroscopic theory which is furthermore in qualitative agreement with hard disk molecular dynamics.

Source: http://arxiv.org/abs/cond-mat/0506152v1

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33

Sep 18, 2013
09/13

by
Kevin Wood; C. Van den Broeck; R. Kawai; Katja Lindenberg

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We study synchronization in populations of phase-coupled stochastic three-state oscillators characterized by a distribution of transition rates. We present results on an exactly solvable dimer as well as a systematic characterization of globally connected arrays of N types of oscillators (N=2, 3, 4) by exploring the linear stability of the nonsynchronous fixed point. We also provide results for globally coupled arrays where the transition rate of each unit is drawn from a uniform distribution...

Source: http://arxiv.org/abs/cond-mat/0611757v1

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44

Sep 18, 2013
09/13

by
M. van den Broek; C. Van den Broeck

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This paper provides some comprehensive calculations supporting the results in Phys. Rev. Lett. 100, 130601 (2008) [arXiv:0711.1758].

Source: http://arxiv.org/abs/0803.4105v1

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31

Sep 18, 2013
09/13

by
M. van den Broek; C. Van den Broeck

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We extend the analysis of a thermal Brownian motor reported in Phys. Rev. Lett. 93, 090601 (2004) by C. Van den Broeck, R. Kawai, and P. Meurs to a three-dimensional configuration. We calculate the friction coefficient, diffusion coefficient, and drift velocity as a function of shape and present estimates based on physically realistic parameter values.

Source: http://arxiv.org/abs/0803.0689v1

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27

Sep 23, 2013
09/13

by
V. Balakrishnan; C. Van den Broeck; I. Bena

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We present analytical expressions for the time-dependent and stationary probability distributions corresponding to a stochastically perturbed one-dimensional flow with critical points, in two physically relevant situations: delayed evolution, in which the flow alternates with a quiescent state in which the variate remains frozen at its current value for random intervals of time; and interrupted evolution, in which the variate is also re-set in the quiescent state to a random value drawn from a...

Source: http://arxiv.org/abs/cond-mat/0109028v1

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35

Sep 23, 2013
09/13

by
M. van den Broek; R. Eichhorn; C. Van den Broeck

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We present a generic formalism to describe Brownian motion of particles with intrinsic asymmetry and give predictions for the drift behavior in unbiased time-dependent force fields. Our findings are supported by molecular dynamics simulations.

Source: http://arxiv.org/abs/0810.1898v1

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0.0

Jun 29, 2018
06/18

by
R. Toral; C. Van den Broeck; D. Escaff; Katja Lindenberg

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We verify the finite time fluctuation theorem for a linear Ising chain at its ends in contact with heat reservoirs. Analytic results are derived for a chain consisting of only two spins. The system can be mapped onto a model for particle transport, namely the symmetric exclusion process, in contact with thermal and particle reservoirs. We modify the symmetric exclusion process to represent a thermal engine and reproduce universal features of the efficiency at maximum power.

Topics: Statistical Mechanics, Condensed Matter

Source: http://arxiv.org/abs/1611.08188

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44

Sep 20, 2013
09/13

by
I. Bena; C. Van den Broeck; R. Kawai

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We illustrate the Jarzynski equality on the exactly solvable model of a one-dimensional ideal gas in uniform expansion or compression. The analytical results for the probability density $P(W)$ of the work $W$ performed by the gas are compared with the results of molecular dynamics simulations for a two-dimensional dilute gas of hard spheres.

Source: http://arxiv.org/abs/cond-mat/0506289v1

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28

Sep 23, 2013
09/13

by
C. Van den Broeck; R. Kawai; P. Meurs

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We study a genuine Brownian motor by hard disk molecular dynamics and calculate analytically its properties, including its drift speed and thermal conductivity, from microscopic theory.

Source: http://arxiv.org/abs/cond-mat/0312701v2

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67

Sep 23, 2013
09/13

by
I. Bena; M. Copelli; C. Van den Broeck

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We derive the explicit analytic expression for the Stokes' drift in one dimension in the presence of a dichotomic Markov forcing. For small amplitudes of the forcing, the drift is enhanced, but the enhancement is reduced with increasing frequency of the forcing. On the other hand, a reduction of the drift or even a flux reversal can be induced at larger amplitudes, while the flux is now found to be an increasing function of the perturbation frequency.

Source: http://arxiv.org/abs/cond-mat/9908338v2

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31

Sep 23, 2013
09/13

by
V. Balakrishnan; I. Bena; C. Van den Broeck

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We consider the motion of a test particle in a one-dimensional system of equal-mass point particles. The test particle plays the role of a microscopic "piston" that separates two hard-point gases with different concentrations and arbitrary initial velocity distributions. In the homogeneous case when the gases on either side of the piston are in the same macroscopic state, we compute and analyze the stationary velocity autocorrelation function C(t). Explicit expressions are obtained...

Source: http://arxiv.org/abs/cond-mat/0109025v1

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41

Jul 20, 2013
07/13

by
M. Copelli; C. Van den Broeck; M. Opper

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We study a simple model of unsupervised learning where the single symmetry breaking vector has binary components $\pm 1$. We calculate exactly the Bayes-optimal performance of an estimator which is required to lie in the same discrete space. We also show that, except for very special cases, such an estimator cannot be obtained by minimization of a class of variationally optimal potentials.

Source: http://arxiv.org/abs/cond-mat/9906356v3

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51

Sep 18, 2013
09/13

by
Kevin Wood; C. Van den Broeck; R. Kawai; Katja Lindenberg

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We investigate both continuous (second-order) and discontinuous (first-order) transitions to macroscopic synchronization within a single class of discrete, stochastic (globally) phase-coupled oscillators. We provide analytical and numerical evidence that the continuity of the transition depends on the coupling coefficients and, in some nonuniform populations, on the degree of quenched disorder. Hence, in a relatively simple setting this class of models exhibits the qualitative behaviors...

Source: http://arxiv.org/abs/0707.2996v1

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50

Sep 22, 2013
09/13

by
A. Gomez-Marin; J. M. R. Parrondo; C. Van den Broeck

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We reformulate the result for the entropy production given in Phys. Rev. Lett. 98, 080602 (2007) in terms of the relative entropy of microscopic trajectories. By a combination with the Crook's theorem, we identify the path variables that are sufficient to fully identify irreversibility. We show that work saturates the relative entropy, and derive the entropy production for stochastic descriptions.

Source: http://arxiv.org/abs/0805.4703v1

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Sep 23, 2013
09/13

by
R. Kawai; X. Sailer; L. Schimansky-Geier; C. Van den Broeck

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Bistability generated via a pure noise-induced phase transition is reexamined from the view of bifurcations in macroscopic cumulant dynamics. It allows an analytical study of the phase diagram in more general cases than previous methods. In addition using this approach we investigate patially-extended systems with two degrees of freedom per site. For this system, the analytic solution of the stationary Fokker-Planck equation is not available and a standard mean field approach cannot be used to...

Source: http://arxiv.org/abs/cond-mat/0312688v1

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35

Jul 22, 2013
07/13

by
A. Gomez-Marin; J. M. R. Parrondo; C. Van den Broeck

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By different coarse-graining procedures we derive lower bounds on the total mean work dissipated in Brownian systems driven out of equilibrium. With several analytically solvable examples we illustrate how, when, and where the information on the dissipation is captured.

Source: http://arxiv.org/abs/0807.1027v1

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0.0

Jun 30, 2018
06/18

by
T. Becker; K. Nelissen; B. Cleuren; B. Partoens; C. Van den Broeck

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We expand on a recent study of a lattice model of interacting particles [Phys. Rev. Lett. 111, 110601 (2013)]. The adsorption isotherm and equilibrium fluctuations in particle number are discussed as a function of the interaction. Their behavior is similar to that of interacting particles in porous materials. Different expressions for the particle jump rates are derived from transition state theory. Which expression should be used depends on the strength of the inter-particle interactions....

Topics: Statistical Mechanics, Condensed Matter

Source: http://arxiv.org/abs/1410.3360

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0.0

Jun 30, 2018
06/18

by
T. Becker; K. Nelissen; B. Cleuren; B. Partoens; C. Van den Broeck

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We study the adsorption and desorption kinetics of interacting particles moving on a one-dimensional lattice. Confinement is introduced by limiting the number of particles on a lattice site. Adsorption and desorption are found to proceed at different rates, and are strongly influenced by the concentration-dependent transport diffusion. Analytical solutions for the transport and self-diffusion are given for systems of length 1 and 2 and for a zero-range process. In the last situation the self-...

Topics: Statistical Mechanics, Condensed Matter

Source: http://arxiv.org/abs/1406.7164

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Jul 20, 2013
07/13

by
M. Copelli; M. Bouten; C. Van den Broeck; B. Van Rompaey

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We show that the center of mass of Ising vectors that obey some simple constraints, is again an Ising vector.

Source: http://arxiv.org/abs/cond-mat/9902102v2

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1.0

Jun 30, 2018
06/18

by
J. Meidam; M. Agathos; C. Van Den Broeck; J. Veitch; B. S. Sathyaprakash

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The Einstein Telescope (ET), a proposed third-generation gravitational wave observatory, would enable tests of the no-hair theorem by looking at the characteristic frequencies and damping times of black hole ringdown signals. In previous work it was shown that with a single $500 - 1000\,M_\odot$ black hole at distance $\lesssim 6$ Gpc (or redshift $z \lesssim 1$), deviations of a few percent in the frequencies and damping times of dominant and sub-dominant modes would be within the range of...

Topic: General Relativity and Quantum Cosmology

Source: http://arxiv.org/abs/1406.3201

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Sep 19, 2013
09/13

by
W. Zhao; C. Van Den Broeck; D. Baskaran; T. G. F. Li

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A design study is currently in progress for a third generation gravitational-wave (GW) detector called Einstein Telescope (ET). An important kind of source for ET will be the inspiral and merger of binary neutron stars (BNS) up to $z \sim 2$. If BNS mergers are the progenitors of short-hard $\gamma$-ray bursts, then some fraction of them will be seen both electromagnetically and through GW, so that the luminosity distance and the redshift of the source can be determined separately. An important...

Source: http://arxiv.org/abs/1009.0206v4

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Sep 23, 2013
09/13

by
M. Malek Mansour; C. Van den Broeck; I. Bena; F. Baras

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Particle simulations of the Kolmogorov flow are analyzed by the Landau-Lifshitz fluctuating hydrodynamics. It is shown that a spurious diffusion of the center of mass corrupts the statistical properties of the flow. The analytical expression for the corresponding diffusion coefficient is derived.

Source: http://arxiv.org/abs/cond-mat/0109086v1

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1.0

Jun 30, 2018
06/18

by
T. Becker; K. Nelissen; B. Cleuren; B. Partoens; C. Van den Broeck

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In a recent paper Arita et al. [Phys. Rev. E 90, 052108 (2014)] consider the transport properties of a class of generalized exclusion processes. Analytical expressions for the transport-diffusion coefficient are derived by ignoring correlations. It is claimed that these expressions become exact in the hydrodynamic limit. In this Comment, we point out that (i) the influence of correlations upon the diffusion does not vanish in the hydrodynamic limit, and (ii) the expressions for the self- and...

Topics: Statistical Mechanics, Condensed Matter

Source: http://arxiv.org/abs/1412.6324

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44

Sep 19, 2013
09/13

by
I. Bena; R. Kawai; C. Van den Broeck; M. Copelli; K. Lindenberg

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We revisit the mean field model of globally and harmonically coupled parametric oscillators subject to periodic block pulses with initially random phases. The phase diagram of regions of collective parametric instability is presented, as is a detailed characterization of the motions underlying these instabilities. This presentation includes regimes not identified in earlier work [I. Bena and C. Van den Broeck, Europhys. Lett. {\bf 48}, 498 (1999)]. In addition to the familiar parametric...

Source: http://arxiv.org/abs/cond-mat/0102113v1

3
3.0

Jun 27, 2018
06/18

by
C. Van Den Broeck; for the LIGO Scientific Collaboration; the Virgo Collaboration

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Advanced LIGO and Advanced Virgo are expected to make the first direct detections of gravitational waves (GW) in the next several years. Possible types of GW emission include short-duration bursts, signals from the coalescence of compact binaries consisting of neutron stars or black holes, continuous radiation from fast-spinning neutron stars, and stochastic background radiation of a primordial nature or resulting from the superposition of a large number of individually unresolvable sources. We...

Topic: General Relativity and Quantum Cosmology

Source: http://arxiv.org/abs/1505.04621

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28

Sep 23, 2013
09/13

by
A. Gomez-Marin; J. M. R. Parrondo; C. Van den Broeck

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We generalize to stochastic dynamics the exact expression for average dissipation along an arbitrary non-equilibrium process, given in Phys. Rev. Lett. 98, 080602 (2007). We then derive lower bounds by various coarse-graining procedures and illustrate how, when and where the information on the dissipation is captured in models of over- and underdamped Brownian particles.

Source: http://arxiv.org/abs/0710.4290v1

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105

Sep 23, 2013
09/13

by
T. G. F. Li; W. Del Pozzo; S. Vitale; C. Van Den Broeck; M. Agathos; J. Veitch; K. Grover; T. Sidery; R. Sturani; A. Vecchio

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In this paper we elaborate on earlier work by the same authors in which a novel Bayesian inference framework for testing the strong-field dynamics of General Relativity using coalescing compact binaries was proposed. Unlike methods that were used previously, our technique addresses the question whether one or more 'testing coefficients' (e.g. in the phase) parameterizing deviations from GR are non-zero, rather than all of them differing from zero at the same time. The framework is well-adapted...

Source: http://arxiv.org/abs/1111.5274v2

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99

Sep 23, 2013
09/13

by
T. G. F. Li; W. Del Pozzo; S. Vitale; C. Van Den Broeck; M. Agathos; J. Veitch; K. Grover; T. Sidery; R. Sturani; A. Vecchio

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Coalescences of binary neutron stars and/or black holes are amongst the most likely gravitational-wave signals to be observed in ground based interferometric detectors. Apart from the astrophysical importance of their detection, they will also provide us with our very first empirical access to the genuinely strong-field dynamics of General Relativity (GR). We present a new framework based on Bayesian model selection aimed at detecting deviations from GR, subject to the constraints of the...

Source: http://arxiv.org/abs/1110.0530v2