Activation process driven by strongly non-Gaussian noises

The constructive role of non-Gaussian random fluctuations is studied in the context of the passage over the dichotomously switching potential barrier. Our attention focuses on the interplay of the effects of independent sources of fluctuations: an additive stable noise representing non-equilibrium external random force acting on the system and a fluctuating barrier. In particular, the influence of the structure of stable noises on the mean escape time and on the phenomenon of resonant activation (RA) is investigated. By use of the numerical Monte Carlo method it is documented that the suitable choice of the barrier switching rate and random external fields may produce resonant phenomenon leading to the enhancement of the kinetics and the shortest, most efficient reaction time.Comment: 11 pages, 8 figure

Resonant activation driven by strongly non-Gaussian noises

The constructive role of non-Gaussian random fluctuations is studied in the context of the passage over the dichotomously switching potential barrier. Our attention focuses on the interplay of the effects of independent sources of fluctuations: an additive stable noise representing non-equilibrium external random force acting on the system and a fluctuating barrier. In particular, the influence of the structure of stable noises on the mean escape time and on the phenomenon of resonant activation (RA) is investigated. By use of the numerical Monte Carlo method it is documented that the suitable choice of the barrier switching rate and random external fields may produce resonant phenomenon leading to the enhancement of the kinetics and the shortest, most efficient reaction time.Comment: 9 pages, 7 figures, RevTeX

Subordinated diffusion and CTRW asymptotics

Anomalous transport is usually described either by models of continuous time random walks (CTRW) or, otherwise by fractional Fokker-Planck equations (FFPE). The asymptotic relation between properly scaled CTRW and fractional diffusion process has been worked out via various approaches widely discussed in literature. Here, we focus on a correspondence between CTRWs and time and space fractional diffusion equation stemming from two different methods aimed to accurately approximate anomalous diffusion processes. One of them is the Monte Carlo simulation of uncoupled CTRW with a L\'evy $\alpha$-stable distribution of jumps in space and a one-parameter Mittag-Leffler distribution of waiting times. The other is based on a discretized form of a subordinated Langevin equation in which the physical time defined via the number of subsequent steps of motion is itself a random variable. Both approaches are tested for their numerical performance and verified with known analytical solutions for the Green function of a space-time fractional diffusion equation. The comparison demonstrates trade off between precision of constructed solutions and computational costs. The method based on the subordinated Langevin equation leads to a higher accuracy of results, while the CTRW framework with a Mittag-Leffler distribution of waiting times provides efficiently an approximate fundamental solution to the FFPE and converges to the probability density function of the subordinated process in a long-time limit.Comment: 10 pages, 7 figure

Resonant effects in a voltage-activated channel gating

The non-selective voltage activated cation channel from the human red cells, which is activated at depolarizing potentials, has been shown to exhibit counter-clockwise gating hysteresis. We have analyzed the phenomenon with the simplest possible phenomenological models by assuming $2\times 2$ discrete states, i.e. two normal open/closed states with two different states of ``gate tension.'' Rates of transitions between the two branches of the hysteresis curve have been modeled with single-barrier kinetics by introducing a real-valued ``reaction coordinate'' parameterizing the protein's conformational change. When described in terms of the effective potential with cyclic variations of the control parameter (an activating voltage), this model exhibits typical ``resonant effects'': synchronization, resonant activation and stochastic resonance. Occurrence of the phenomena is investigated by running the stochastic dynamics of the model and analyzing statistical properties of gating trajectories.Comment: 12 pages, 9 figure

Implication of Barrier Fluctuations on the Rate of Weakly Adiabatic Electron Transfer

The problem of escape of a Brownian particle in a cusp-shaped metastable potential is of special importance in nonadiabatic and weakly-adiabatic rate theory for electron transfer (ET) reactions. Especially, for the weakly-adiabatic reactions, the reaction follows an adiabaticity criterion in the presence of a sharp barrier. In contrast to the non-adiabatic case, the ET kinetics can be, however considerably influenced by the medium dynamics. In this paper, the problem of the escape time over a dichotomously fluctuating cusp barrier is discussed with its relevance to the high temperature ET reactions in condensed media.Comment: RevTeX 4, 14 pages, 3 figures. To be printed in IJMP C. References corrected and update

Underdamped stochastic harmonic oscillator

We investigate stationary states of the linear damped stochastic oscillator driven by L\'evy noises. In the long time limit kinetic and potential energies of the oscillator do not fulfill the equipartition theorem and their distributions follow the power-law asymptotics. At the same time, partition of the mechanical energy is controlled by the damping coefficient. We show that in the limit of vanishing damping a stochastic analogue of the equipartition theorem can be proposed, namely the statistical properties of potential and kinetic energies attain distributions characterized by the same width. Finally, we demonstrate that the ratio of instantaneous kinetic and potential energies which signifies departure from the mechanical energy equipartition, follows universal power-law asymptotics.Comment: 8 pages. 3 figure

L\'evy flights versus L\'evy walks in bounded domains

L\'evy flights and L\'evy walks serve as two paradigms of random walks resembling common features but also bearing fundamental differences. One of the main dissimilarities are discontinuity versus continuity of their trajectories and infinite versus finite propagation velocity. In consequence, well developed theory of L\'evy flights is associated with their pathological physical properties, which in turn are resolved by the concept of L\'evy walks. Here, we explore L\'evy flights and L\'evy walks models on bounded domains examining their differences and analogies. We investigate analytically and numerically whether and under which conditions both approaches yield similar results in terms of selected statistical observables characterizing the motion: the survival probability, mean first passage time and stationary PDFs. It is demonstrated that similarity of models is affected by the type of boundary conditions and value of the stability index defining asymptotics of the jump length distribution.Comment: 15 pages, 13 figure

Challenges of Liberalization. The Case of Polish Electricity and Gas Sector

This paper applies the general insights of liberalization of the electricity and gas market to the market conditions of a particularly important new Member State in the EU, Poland. To this end the aim of this paper is to explain the Polish experience of liberalizing its energy market by reviewing those developments that produced its current shape. In fact there are two possible scenarios Polish policy makers can follow in liberalizing its energy sector. One would involve the UK approach that encompasses: ownership unbundling, less market concentration, less public ownership and more private capital in the industry. The second scenario follows the continental model: more concentration and vertical integration and more State or public ownership in the energy field (for instance, the French model). These two widely diverging approaches reflect different energy consumption patterns, energy mixes, sources of supply and natural resources of various countries. Having these differences in mind this research reviews developments that have produced the current state of liberalization of the electricity and gas sectors in Poland and discusses the prospects for further progress towards an integrated, competitive and liberalized European electricity and gas market in the light of the challenges that remain. These challenges include uneven unbundling, discriminatory third party access, insufficient independency of national regulator, consolidation and anti-competitive behaviour of incumbents or abuse of one’s dominant position on the market

Challenges of Liberalization. The Case of Polish Electricity and Gas Sector

This paper applies the general insights of liberalization of the electricity and gas market to the market conditions of a particularly important new Member State in the EU, Poland. To this end the aim of this paper is to explain the Polish experience of liberalizing its energy market by reviewing those developments that produced its current shape. In fact there are two possible scenarios Polish policy makers can follow in liberalizing its energy sector. One would involve the UK approach that encompasses: ownership unbundling, less market concentration, less public ownership and more private capital in the industry. The second scenario follows the continental model: more concentration and vertical integration and more State or public ownership in the energy field (for instance, the French model). These two widely diverging approaches reflect different energy consumption patterns, energy mixes, sources of supply and natural resources of various countries. Having these differences in mind this research reviews developments that have produced the current state of liberalization of the electricity and gas sectors in Poland and discusses the prospects for further progress towards an integrated, competitive and liberalized European electricity and gas market in the light of the challenges that remain. These challenges include uneven unbundling, discriminatory third party access, insufficient independency of national regulator, consolidation and anti-competitive behaviour of incumbents or abuse of one’s dominant position on the market