75 research outputs found
A Theorem on the origin of Phase Transitions
For physical systems described by smooth, finite-range and confining
microscopic interaction potentials V with continuously varying coordinates, we
announce and outline the proof of a theorem that establishes that unless the
equipotential hypersurfaces of configuration space \Sigma_v ={(q_1,...,q_N)\in
R^N | V(q_1,...,q_N) = v}, v \in R, change topology at some v_c in a given
interval [v_0, v_1] of values v of V, the Helmoltz free energy must be at least
twice differentiable in the corresponding interval of inverse temperature
(\beta(v_0), \beta(v_1)) also in the N -> \infty and the
{\Sigma_v}_{v > v_c}, which is the consequence of the existence of critical
points of V on \Sigma_{v=v_c}, that is points where \nabla V=0.Comment: 10 pages, Statistical Mechanics, Phase Transitions, General Theory.
Phys. Rev. Lett., in pres
Characterisation and categorisation of the diversity in viscoelastic vibrational properties between 98 wood types
International audienceContext Increased knowledge on diversity in wood properties would have implications both for fundamental research and for promoting a diversification of uses as material. *Aims The objective is to contribute to overcoming the critical lack of data on the diversity of wood dynamic mechanical/viscoelastic vibrational properties, by testing lesser-known species and categorizing sources of variability. *Methods Air-dry axial specific dynamic modulus of elasticity (E'/γ) and damping coefficient (tanδ) were measured on a wide sampling (1792 specimens) of 98 wood types from 79 species. An experimental device and protocol was designed for conducting systematic (i.e. rapid and reproducible) characterizations. *Results Diversity at the specimens' level corroborates the "standard" relationship between tanδ and E'/γ, which is discussed in terms of orientation of wood elements and of chemical composition. Diversity at the species level is expressed on the basis of results for normal heartwood, with specific gravity (γ) ranging from 0.2 to 1.3. Axial E'/γ ranges from 9 to 32 GPa and tanδ from 4×10-3 to 19×10-3. Properties distribution follows a continuum, but with group characteristics. The lowest values of tanδ are only found in certain tropical hardwoods. Results can also suggest alternative species for musical instruments making
Macroscopic fluctuation theory
Stationary non-equilibrium states describe steady flows through macroscopic
systems. Although they represent the simplest generalization of equilibrium
states, they exhibit a variety of new phenomena. Within a statistical mechanics
approach, these states have been the subject of several theoretical
investigations, both analytic and numerical. The macroscopic fluctuation
theory, based on a formula for the probability of joint space-time fluctuations
of thermodynamic variables and currents, provides a unified macroscopic
treatment of such states for driven diffusive systems. We give a detailed
review of this theory including its main predictions and most relevant
applications.Comment: Review article. Revised extended versio
Electrical current distribution across a metal-insulator-metal structure during bistable switching
Combining scanning electron microscopy (SEM) and electron-beam-induced
current (EBIC) imaging with transport measurements, it is shown that the
current flowing across a two-terminal oxide-based capacitor-like structure is
preferentially confined in areas localized at defects. As the thin-film device
switches between two different resistance states, the distribution and
intensity of the current paths, appearing as bright spots, change. This implies
that switching and memory effects are mainly determined by the conducting
properties along such paths. A model based on the storage and release of charge
carriers within the insulator seems adequate to explain the observed memory
effect.Comment: 8 pages, 7 figures, submitted to J. Appl. Phy
The Hitting Times with Taboo for a Random Walk on an Integer Lattice
For a symmetric, homogeneous and irreducible random walk on d-dimensional
integer lattice Z^d, having zero mean and a finite variance of jumps, we study
the passage times (with possible infinite values) determined by the starting
point x, the hitting state y and the taboo state z. We find the probability
that these passages times are finite and analyze the tails of their cumulative
distribution functions. In particular, it turns out that for the random walk on
Z^d, except for a simple (nearest neighbor) random walk on Z, the order of the
tail decrease is specified by dimension d only. In contrast, for a simple
random walk on Z, the asymptotic properties of hitting times with taboo
essentially depend on the mutual location of the points x, y and z. These
problems originated in our recent study of branching random walk on Z^d with a
single source of branching
Spectroscopy of the transition-rate matrix for molecular junctions: dynamics in the Franck-Condon regime
The quantum master equation applied to electronic transport through
nanoscopic devices provides information not only on the stationary state but
also on the dynamics. The dynamics is characterized by the eigenvalues of the
transition-rate matrix, or generator, of the master equation. We propose to use
the spectrum of these eigenvalues as a tool for the study of nanoscopic
transport. We illustrate this idea by analyzing a molecular quantum dot with an
electronic orbital coupled to a vibrational mode, which shows the Franck-Condon
blockade if the coupling is strong. Our approach provides complementary
information compared to the study of observables in the stationary state.Comment: 13 pages, 13 figure
Gibbsian Method for the Self-Optimization of Cellular Networks
In this work, we propose and analyze a class of distributed algorithms
performing the joint optimization of radio resources in heterogeneous cellular
networks made of a juxtaposition of macro and small cells. Within this context,
it is essential to use algorithms able to simultaneously solve the problems of
channel selection, user association and power control. In such networks, the
unpredictability of the cell and user patterns also requires distributed
optimization schemes. The proposed method is inspired from statistical physics
and based on the Gibbs sampler. It does not require the concavity/convexity,
monotonicity or duality properties common to classical optimization problems.
Besides, it supports discrete optimization which is especially useful to
practical systems. We show that it can be implemented in a fully distributed
way and nevertheless achieves system-wide optimality. We use simulation to
compare this solution to today's default operational methods in terms of both
throughput and energy consumption. Finally, we address concrete issues for the
implementation of this solution and analyze the overhead traffic required
within the framework of 3GPP and femtocell standards.Comment: 25 pages, 9 figures, to appear in EURASIP Journal on Wireless
Communications and Networking 201
Temporal-Difference Reinforcement Learning with Distributed Representations
Temporal-difference (TD) algorithms have been proposed as models of reinforcement learning (RL). We examine two issues of distributed representation in these TD algorithms: distributed representations of belief and distributed discounting factors. Distributed representation of belief allows the believed state of the world to distribute across sets of equivalent states. Distributed exponential discounting factors produce hyperbolic discounting in the behavior of the agent itself. We examine these issues in the context of a TD RL model in which state-belief is distributed over a set of exponentially-discounting “micro-Agents”, each of which has a separate discounting factor (γ). Each µAgent maintains an independent hypothesis about the state of the world, and a separate value-estimate of taking actions within that hypothesized state. The overall agent thus instantiates a flexible representation of an evolving world-state. As with other TD models, the value-error (δ) signal within the model matches dopamine signals recorded from animals in standard conditioning reward-paradigms. The distributed representation of belief provides an explanation for the decrease in dopamine at the conditioned stimulus seen in overtrained animals, for the differences between trace and delay conditioning, and for transient bursts of dopamine seen at movement initiation. Because each µAgent also includes its own exponential discounting factor, the overall agent shows hyperbolic discounting, consistent with behavioral experiments
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