Fluctuation theorem: A critical review.

Fluctuation theorem for entropy production is revisited in the framework of stochastic processes. The applicability of the fluctuation theorem to physico-chemical systems and the resulting stochastic thermodynamics were analyzed. Some unexpected limitations are highlighted in the context of jump Markov processes. We have shown that these limitations handicap the ability of the resulting stochastic thermodynamics to correctly describe the state of non-equilibrium systems in terms of the thermodynamic properties of individual processes therein. Finally, we considered the case of diffusion processes and proved that the fluctuation theorem for entropy production becomes irrelevant at the stationary state in the case of one variable systems.

Validity of path thermodynamic description of reactive systems: Microscopic simulations.

Traditional stochastic modeling of reactive systems limits the domain of applicability of the associated path thermodynamics to systems involving a single elementary reaction at the origin of each observed change in composition. An alternative stochastic modeling has recently been proposed to overcome this limitation. These two ways of modeling reactive systems are in principle incompatible. The question thus arises about choosing the appropriate type of modeling to be used in practical situations. In the absence of sufficiently accurate experimental results, one way to address this issue is through the microscopic simulation of reactive fluids, usually based on hard-sphere dynamics in the Boltzmann limit. In this paper, we show that results obtained through such simulations unambiguously confirm the predictions of traditional stochastic modeling, invalidating a recently proposed alternative.

Reply to "Comment on 'Validity of path thermodynamic description of reactive systems: Microscopic simulations' ".

The Comment's author argues that a correct description of reactive systems should incorporate an explicit interaction with reservoirs, leading to a unified system-reservoir entity. However, this proposition has two major flaws. First, as we will emphasize, this entity inherently follows a thermodynamic equilibrium distribution. In the Comment, no indication is provided on how to maintain such a system-reservoir entity in a nonequilibrium state. Second, contrary to the author's claim, the inclusion of a system-reservoir interaction in the traditional stochastic modeling of reactive systems does not automatically alter the limited applicability of path thermodynamics to problematic reactive systems. We will provide a simple demonstration to illustrate that certain elementary reactions may not involve any changes in reservoir components, which seem to have been overlooked by the author.

Molecular Dynamics Studies in Nanojoining: Self-Propagating Reaction in Ni/Al Nanocomposites.

Reactive joining with Ni/Al nanocomposites is an innovative technology that provides an alternative to more common bonding techniques. This work focuses on a class of energetic material, produced by high energy ball milling and cold rolling. The initial microstructure is more complex than that of reactive multilayer nanofoils, produced by magnetron sputtering, in which the bilayer thickness is constant. Typical samples are composed of reactive nanocomposite particles that are numerically modelized by randomly distributed layered grains. The self-propagating reaction was studied by means of molecular dynamics simulations. We determined the front characteristics and investigated the elemental mechanics that trigger propagation. Both dissolution of Ni in amorphous Al and sustained crystallization of the B2-NiAl intermetallic compound were found to contribute to the heat delivered during the process.

Dynamical and statistical properties of high-temperature self-propagating fronts: an experimental study.

We present a detailed experimental study of high-temperature self-propagating fronts using image processing techniques. The intrinsic features of the wave propagation are investigated as a function of the combustion temperature TC for a model system made of titanium and silicon powders. Different front behavior is realized by changing the molar ratio x of the mixture Ti+xSi. Outside the range x=[0.3,1.5], no thermal front is propagating while inside, three regimes are observed: steady-state combustion which is characterized by a flat front propagating at constant velocity and two unsteady regimes. The combustion temperature (or the corresponding ratio x) is thus playing the role of bifurcation parameter leading from stationary state to complex behavior. In the titanium-rich mixture, the position of the front oscillates and hot spots propagate along the external border of the sample. At lower amounts of Ti, localized bright regions appear randomly and deform the front profile. The associated dynamical behavior is a relay-race mechanism which becomes more pronounced close to the combustion limit. Methods are developed to characterize the structural and dynamical properties of thermal waves near instabilities, with a special emphasis on the statistical aspects. It is clearly demonstrated that the mesoscopic scale phenomena interfere significantly with the macroscopic behavior. The experiments reveal front behaviors that cannot be described using the usual macroscopic theories.

Hydrodynamic description of the adiabatic piston.

A closed macroscopic equation for the motion of the two-dimensional adiabatic piston is derived from standard hydrodynamics. It predicts a damped oscillatory motion of the piston towards a final rest position, which depends on the initial state. In the limit of large piston mass, the solution of this equation is in quantitative agreement with the results obtained from both hard disk molecular dynamics and hydrodynamics. The explicit forms of the basic characteristics of the piston's dynamics, such as the period of oscillations and the relaxation time, are derived. The limitations of the theory's validity, in terms of the main system parameters, are established.

Three-state model for cooperative desorption on a one-dimensional lattice.

We develop a master equation approach to the dynamics of immobile reactants on a one-dimensional lattice, in the presence of two different species undergoing cooperative desorption. A common feature of all the schemes studied is the strong dependence of the final coverage on the initial conditions, associated with the lack of ergodicity of the invariant state. Our approach leads to full agreement with Monte Carlo simulations, both asymptotically and transiently.

Oscillatory reactive dynamics on surfaces: a lattice limit cycle model.

Complex reactive dynamics on low-dimensional lattices is studied using mean-field models and Monte Carlo simulations. A lattice-compatible reactive scheme that gives rise to limit cycle behavior is constructed, involving a quadrimolecular reaction step and bimolecular adsorption and desorption steps. The resulting lattice limit cycle model is dissipative and, in the mean-field limit, exhibits sustained oscillations of the species concentrations for a wide range of parameter values. Lattice Monte Carlo simulations of the lattice limit cycle model show locally the emergence of sustained oscillations of the species concentrations. Random fluctuations of the concentrations, clustering between homologous species, and competition between the various clusters/species cause the in-phase oscillations of neighboring sites. Distant regions oscillate out of phase and spatial correlations decay exponentially with the distance. The amplitude and period of the local oscillations depend on the system parameters.

Comparing cephaloauricular and scaphaconchal angles in prominent ear patients and control subjects.

Approximately 5% of 1-year-old children have prominent ears. The most common findings are underdevelopment or lack of the antihelical fold, overdevelopment of the concha, a scapha-conchal angle greater than 130 degrees, and a protruding lobule. This study compared the cephaloauricular and scaphaconchal angles of 15 patients with prominent ears and 15 patients in a control group. Alginate was used to create a mold of each patient's right ear. Afterward the molds were cut transversally for measurement of the angles. The first cut was made at the middle of the ear's cephalocaudal length. The second cut was made in the superior piece midway between the first cut and the superior extremity of the ear. The cephaloauricular angle was defined as the intersection of a straight line running through the tragus insertion and the lateral portion of the mastoid region with a straight line that running through the tragus and the middle of the helix. The scaphaconchal angle was obtained in the second cut by measurement of the angles formed by these two structures molded in the posterior aspect of the ear. The Student's t test was used for statistical analysis. The average cephaloauricular angle was 47.7 degrees for the study group and 31.1 degrees for the control group. The average scaphaconchal angle was 132.6 degrees for the study group and 106.7 degrees for the control group. This study presents a new method for evaluating the angles of the ear, confirming that both measured angles (cephaloauricular and scaphaconchal) are greater in patients with prominent ears (p < 0.005).

Reaction-controlled cooperative desorption in a one-dimensional lattice: a dynamical approach.

The spinlike dynamics of immobile reactants in a one-dimensional lattice is analyzed for two representative systems involving cooperative desorption. An exact combinatorial approach is worked out. Its failure to reproduce the results of microscopic simulations is shown to be associated with the lack of sufficiently strong ergodic properties, as a result of which the final state depends strongly on the initial conditions. A dynamical approach to the problem based on the Master equation description is subsequently developed, leading to full agreement with the microscopic simulations.

Hydrodynamic fluctuations in the Kolmogorov flow: linear regime.

The Landau-Lifshitz fluctuating hydrodynamics is used to study the statistical properties of the linearized Kolmogorov flow. The relative simplicity of this flow allows a detailed analysis of the fluctuation spectrum from near equilibrium regime up to the vicinity of the first convective instability threshold. It is shown that in the long time limit the flow behaves as an incompressible fluid, regardless of the value of the Reynolds number. This is not the case for the short time behavior where the incompressibility assumption leads in general to a wrong form of the static correlation functions, except near the instability threshold. The theoretical predictions are confirmed by numerical simulations of the full nonlinear fluctuating hydrodynamic equations.

Hydrodynamic fluctuations in the kolmogorov flow: nonlinear regime

In a previous paper [I. Bena, M. Malek Mansour, and F. Baras, Phys. Rev. E 59, 5503 (1999)] the statistical properties of linearized Kolmogorov flow were studied, using the formalism of fluctuating hydrodynamics. In this paper the nonlinear regime is considered, with emphasis on the statistical properties of the flow near the first instability. The normal form amplitude equation is derived for the case of an incompressible fluid and the velocity field is constructed explicitly above (but close to) the instability. The relative simplicity of this flow allows one to analyze the compressible case as well. Using a perturbative technique, it is shown that close to the instability threshold the stochastic dynamics of the system is governed by two coupled nonlinear Langevin equations in Fourier space. The solution of these equations can be cast into the exponential of a Landau-Ginzburg functional, which proves to be identical to the one obtained for the case of an incompressible fluid. The theoretical predictions are confirmed by numerical simulations of the nonlinear fluctuating hydrodynamic equations.