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A physical model for a structured tetrameric pore is studied. The pore is modeled as a device composed of four subunits, each one exhibiting two possible states (open and closed). The pore is located within a membrane that separates two reservoirs with ionic solutions. All variables of the model follow physical dynamical equations accounting for the internal structure of the pore, derived from a single energy functional and supplemented with thermal noises. An extensive study of the resulting ionic intensity is performed for different values of the control parameters, mainly membrane potential and reservoir ion concentrations. Two possible physical devices are studied: voltage-gated (including a voltage sensor in each subunit) and non-voltage-gated pores. The ionic flux through the pore exhibits several distinct dynamical configurations, in particular subconductance states, which indicate very different dynamical internal states of the subunits. Such subconductance states become much easier to observe in sensorless pores. These results are compared with available experimental data on tetrameric K channels and analytical predictions., Comment: 29 pages, 15 figures

We consider the numerical integration of Langevin equations for particles in a channel, in the presence of boundary conditions fixing the concentration values at the ends. This kind of boundary condition appears for instance when considering the diffusion of ions in molecular channels, between the different concentrations at both sides of the cellular membrane. For this application the overdamped limit of Brownian motion (leading to a first order Langevin equation) is most convenient, but in previous works some difficulties associated with this limit were found for the implementation of the boundary conditions. We derive here an algorithm that, unlike previous attempts, does not require the simulation of particle reservoirs or the consideration of velocity variables or adjustable parameters. Simulations of Brownian particles in simple cases show that results agree perfectly with theory, both for the local concentration values and for the resulting particle flux in nonequilibrium situations. The algorithm is appropriate for the modeling of more complex ionic channels and, in general, for the treatment of analogous boundary conditions in other physical models using first order Langevin equations. ***This version corrects misprints in two equations of the published paper***, Comment: 8 pages, 5 figures

Neuronal cells present periodic trains of localized voltage spikes involving a large amount of different ionic channels. A relevant question is whether this is a cooperative effect or it could also be an intrinsic property of individual channels. Here we use a Langevin formulation for the stochastic dynamics of a pair of Na and K ionic channels. These two channels are simple gated pore models where a minimum set of degrees of freedom follow standard statistical physics. The whole system is totally autonomous without any external energy input, except for the chemical energy of the different ionic concentrations across the membrane. As a result it is shown that a unique pair of different ionic channels can sustain membrane potential periodic spikes. The spikes are due to the interaction between the membrane potential, the ionic flows and the dynamics of the internal parts (gates) of each channel structures. The spike involves a series of dynamical steps being the more relevant one the leak of Na ions. Missing spike events are caused by the altered functioning of specific model parts. The time dependent spike structure is comparable with experimental data., Comment: 8 pages, 11 figures

Experiments on single ionic channels have contributed to a large extent to our current view on the function of cell membrane. In these experiments the main observables are the physical quantities: ionic concentration, membrane electrostatic potential and ionic fluxes, all of them presenting large fluctuations. The classical theory of Goldman--Hodking--Katz assumes that an open channel can be well described by a physical pore where ions follow statistical physics. Nevertheless real molecular channels are active pores with open and close dynamical states. By skipping the molecular complexity of real channels, here we present the internal structure and calibration of two active pore models. These models present a minimum set of degrees of freedom, specifically ion positions and gate states, which follow Langevin equations constructed from an unique potential energy functional and by using standard rules of statistical physics. Numerical simulations of both models are implemented and the results show that they have dynamical properties very close to those observed in experiments of Na and K molecular channels. In particular a significant effect of the external ion concentration on gating dynamics is predicted, which is consistent with previous experimental observations. This approach can be extended to other channel types with more specific phenomenology., Comment: 9 pages, 8 figures

We present numerical results for a chemical reaction of colloidal particles which are transported by a laminar fluid and are focused by periodic obstacles in such a way that the two components are well mixed and consequently the chemical reaction is speeded up. The roles of the various system parameters (diffusion coefficients, reaction rate, obstacles sizes) are studied. We show that focusing speeds up the reaction from the diffusion limited rate (t to the power -1/2) to very close to the perfect mixing rate, (t to the power -1)., Comment: 19 pages, 8 figures

We study the convective instability of the melt during the initial transient in a directional solidification experiment in a vertical configuration. We obtain analytically the dispersion relation, and perform an additional asymptotic expansion for large Rayleigh number that permits a simpler analytical analysis and a better numerical behavior. We find a transient instability, i.e. a regime in which the system destabilizes during the transient whereas the final unperturbed steady state is stable. This could be relevant to growth mode predictions in solidification., Comment: 28 pages, 5 figures. The following article has been accepted for publication in Physics of Fluids. After it is published, it will be found at http://pof.aip.org

We present results of simulations of transitions in planar arrays of superheated superconducting granules (PASS) immersed in an external magnetic field parallel to the system. Analysis of the behaviour of the system when the external field is slowly increased from zero shows the existence of an interval of external fields for which no transitions are produced. This gap is found to be a consequence of ordering induced by transitions. However, this ordering is different for diluted and for concentrated systems. Avalanches of different sizes with distributions depending on concentration are observed., Comment: 19 pages, 12 figures, to appear in Nuclear Instruments and Methods in Physics Research A

The dynamics of a small Prandtl number binary mixture in a laterally heated cavity is studied numerically. By combining temporal integration, steady state solving and linear stability analysis of the full PDE equations, we have been able to locate and characterize a codimension-three degenerate Takens-Bogdanov point whose unfolding describes the dynamics of the system for a certain range of Rayleigh numbers and separation ratios near S=-1., Comment: 8 pages, 5 figures

We present a derivation of the sharp-interface limit of a generic fluctuating phase-field model for solidification. As a main result, we obtain a sharp-interface projection which presents noise terms in both the diffusion equation and in the moving boundary conditions. The presented procedure does not rely on the fluctuation-dissipation theorem, and can therefore be applied to account for both internal and external fluctuations in either variational or non-variational phase-field formulations. In particular, it can be used to introduce thermodynamical fluctuations in non-variational formulations of the phase-field model, which permit to reach better computational efficiency and provide more flexibility for describing some features of specific physical situations. This opens the possibility of performing quantitative phase-field simulations in crystal growth while accounting for the proper fluctuations of the system., Comment: 21 pages, 1 figure, submitted to Phys. Rev. E

We study initial transient stages in directional solidification by means of a non-variational phase field model with fluctuations. This model applies for the symmetric solidification of dilute binary solutions and does not invoke fluctuation-dissipation theorem to account for the fluctuation statistics. We devote our attention to the transient regime during which concentration gradients are building up and fluctuations act to destabilize the interface. To this end, we calculate both the temporally dependent growth rate of each mode and the power spectrum of the interface evolving under the effect of fluctuations. Quantitative agreement is found when comparing the phase-field simulations with theoretical predictions., Comment: 6 pages, 3 figures, accepted for publication in Fluctuations and Noise Letters

We present a numerical study of sidebranching of a solidifying dendrite by means of a phase--field model. Special attention is paid to the regions far from the tip of the dendrite, where linear theories are no longer valid. Two regions have been distinguished outside the linear region: a first one in which sidebranching is in a competition process and a second one further down where branches behave as independent of each other. The shape of the dendrite and integral parameters characterizing the whole dendrite (contour length and area of the dendrite) have been computed and related to the characteristic tip radius for both surface tension and kinetic dominated dendrites. Conclusions about the different behaviors observed and comparison with available experiments and theoretical predictions are presented., Comment: 10 pages, 7 figures, Accepted for publication in Phys. Rev. E

A global bifurcation of the blue sky catastrophe type has been found in a small Prandtl number binary mixture contained in a laterally heated cavity. The system has been studied numerically applying the tools of bifurcation theory. The catastrophe corresponds to the destruction of an orbit which, for a large range of Rayleigh numbers, is the only stable solution. This orbit is born in a global saddle-loop bifurcation and becomes chaotic in a period doubling cascade just before its disappearance at the blue sky catastrophe., Comment: 4 pages, 6 figures, REVTeX, To be published in Physical Review Letters

We perform simulations of planar arrays of superheated superconducting granules (PASS) under an external magnetic field, analyzing transitions undergone by the system when the external field is slowly increased from zero. We observe, for high concentrations, the existence of an interval of external fields for which no transitions are induced. This effect is analogous to a "hot border zone" identified in the response of Superheated Superconducting Granule detectors. We explain such behaviour as produced by a geometrical ordering dynamically induced in the system by transitions in preferential sites due to diamagnetic interactions., Comment: 12 pages, 6 figures, accepted for publication in Solid State Communications

The phase-field method is reviewed from the general perspective of converting a free boundary problem into a set of coupled partial differential equations. Its main advantage is that it avoids front tracking by using phase fields to locate the fronts. These fields interpolate between different constant values in each bulk phase through diffuse interfaces of finite thickness. In solidification, the phase fields can be understood as order parameters, and the model is often derived to dynamically minimise a free energy functional. However, this is not a necessary requirement, and both derivations involving a free energy (basic solidification model) and not (first viscous fingering model) are worked out. In any case, the model is required to reproduce the original free boundary problem in the limit of vanishing interface thickness. This limit and its higher order corrections, important to make quantitative contact between simulations and experiments, are discussed for both examples. Applications to fluctuations in solidification, the growth of liquid crystal mesophases, and viscous fingering in Hele-Shaw cells are presented., Comment: 44 pp., 14 figs., review article to appear in Advances in Condensed Matter and Statistical Mechanics, ed. by E. Korucheva and R. Cuerno, Nova Science Publishers

The simulation of the transition sequence of superheated Type I superconducting granules (SSG) in disordered suspensions when an external magnetic field is slowly increased from zero has been studied. Simulation takes into account diamagnetic interactions and the presence of surface defects. Results have been obtained for the transition sequence and surface fields distribution covering a wide range of densities. These results are compared with previous analytical perturbative theory, which provides qualitative information on transitions and surface magnetic fields during transitions, but with a range of validity apparently limited to extremely dilute samples. Simulations taking into account the complete diamagnetic interactions between spheres appear to be a promising tool in interpreting SSG experiments, in applications such as particle detectors, and in some fundamental calculations of Solid State Physics., Comment: 25 pages, 11 figures, accepted for publication in European Physics Journal B

We study the dynamics of generic reaction-diffusion fronts, including pulses and chemical waves, in the presence of multiplicative noise. We discuss the connection between the reaction-diffusion Langevin-like field equations and the kinematic (eikonal) description in terms of a stochastic moving-boundary or sharp-interface approximation. We find that the effective noise is additive and we relate its strength to the noise parameters in the original field equations, to first order in noise strength, but including a partial resummation to all orders which captures the singular dependence on the microscopic cutoff associated to the spatial correlation of the noise. This dependence is essential for a quantitative and qualitative understanding of fluctuating fronts, affecting both scaling properties and nonuniversal quantities. Our results predict phenomena such as the shift of the transition point between the pushed and pulled regimes of front propagation, in terms of the noise parameters, and the corresponding transition to a non-KPZ universality class. We assess the quantitative validity of the results in several examples including equilibrium fluctuations, kinetic roughening, and the noise-induced pushed-pulled transition, which is predicted and observed for the first time. The analytical predictions are successfully tested against rigorous results and show excellent agreement with numerical simulations of reaction-diffusion field equations with multiplicative noise., Comment: 17 pages, 6 figures