Transport in a Levy ratchet: Group velocity and distribution spread

We consider the motion of an overdamped particle in a periodic potential lacking spatial symmetry under the influence of symmetric L\'evy noise, being a minimal setup for a ``L\'evy ratchet.'' Due to the non-thermal character of the L\'evy noise, the particle exhibits a motion with a preferred direction even in the absence of whatever additional time-dependent forces. The examination of the L\'evy ratchet has to be based on the characteristics of directionality which are different from typically used measures like mean current and the dispersion of particles' positions, since these get inappropriate when the moments of the noise diverge. To overcome this problem, we discuss robust measures of directionality of transport like the position of the median of the particles displacements' distribution characterizing the group velocity, and the interquantile distance giving the measure of the distributions' width. Moreover, we analyze the behavior of splitting probabilities for leaving an interval of a given length unveiling qualitative differences between the noises with L\'evy indices below and above unity. Finally, we inspect the problem of the first escape from an interval of given length revealing independence of exit times on the structure of the potential.Comment: 9 pages, 12 figure

Onsagers fluctuation theory and new developments including non-equilibrium Lévy fluctuations

he first part of the paper briefly reviews and explains basic ideas of the theory of Gaussian fluctuations and their relaxation developed in 1931 by Lars Onsager in the context of a general theory of irreversible processes. Motivated by Onsager’s approach, we extend the theory to fluctuations including Lévy processes. We assume that deviations from Gaussian distributions, which are often observed in non-equilibrium systems, may be described by convoluted Gauss–Lévy distributions and their relation to stationary states by generalized Smoluchowski equations. The central part of the distributions we study here is determined by the Gaussian core with the wings decaying according to a power law characteristic for a Lévy-type contribution to statistics. Furthermore, we develop a generalization of Onsager’s theory of linear relaxation processes to those which include statistically independent Gaussian fluctuations and (non-equilibrium) Lévy noises. We apply the generalized version of the fluctuation-dissipation theorem (FDT) to analyze regime of the linear response of the non-equilibrium system driven by Lévy (Cauchy) white noise and subject to thermal (Gaussian) fluctuations. In the last part, applications to non-Maxwellian velocity fluctuations and their relaxations are investigated

Anomalous diffusion and generalized Sparre-Andersen scaling

We are discussing long-time, scaling limit for the anomalous diffusion composed of the subordinated L\'evy-Wiener process. The limiting anomalous diffusion is in general non-Markov, even in the regime, where ensemble averages of a mean-square displacement or quantiles representing the group spread of the distribution follow the scaling characteristic for an ordinary stochastic diffusion. To discriminate between truly memory-less process and the non-Markov one, we are analyzing deviation of the survival probability from the (standard) Sparre-Andersen scaling.Comment: 5 pages, 3 figure

Stationary states in Langevin dynamics under asymmetric L\'evy noises

Properties of systems driven by white non-Gaussian noises can be very different from these systems driven by the white Gaussian noise. We investigate stationary probability densities for systems driven by $\alpha$-stable L\'evy type noises, which provide natural extension to the Gaussian noise having however a new property mainly a possibility of being asymmetric. Stationary probability densities are examined for a particle moving in parabolic, quartic and in generic double well potential models subjected to the action of $\alpha$-stable noises. Relevant solutions are constructed by methods of stochastic dynamics. In situations where analytical results are known they are compared with numerical results. Furthermore, the problem of estimation of the parameters of stationary densities is investigated.Comment: 9 pages, 9 figures, 3 table

Spectral Theory of Sparse Non-Hermitian Random Matrices

Sparse non-Hermitian random matrices arise in the study of disordered physical systems with asymmetric local interactions, and have applications ranging from neural networks to ecosystem dynamics. The spectral characteristics of these matrices provide crucial information on system stability and susceptibility, however, their study is greatly complicated by the twin challenges of a lack of symmetry and a sparse interaction structure. In this review we provide a concise and systematic introduction to the main tools and results in this field. We show how the spectra of sparse non-Hermitian matrices can be computed via an analogy with infinite dimensional operators obeying certain recursion relations. With reference to three illustrative examples --- adjacency matrices of regular oriented graphs, adjacency matrices of oriented Erd\H{o}s-R\'{e}nyi graphs, and adjacency matrices of weighted oriented Erd\H{o}s-R\'{e}nyi graphs --- we demonstrate the use of these methods to obtain both analytic and numerical results for the spectrum, the spectral distribution, the location of outlier eigenvalues, and the statistical properties of eigenvectors.Comment: 60 pages, 10 figure

Spectrum of non-Hermitian heavy tailed random matrices

Let (X_{jk})_{j,k>=1} be i.i.d. complex random variables such that |X_{jk}| is in the domain of attraction of an alpha-stable law, with 0< alpha <2. Our main result is a heavy tailed counterpart of Girko's circular law. Namely, under some additional smoothness assumptions on the law of X_{jk}, we prove that there exists a deterministic sequence a_n ~ n^{1/alpha} and a probability measure mu_alpha on C depending only on alpha such that with probability one, the empirical distribution of the eigenvalues of the rescaled matrix a_n^{-1} (X_{jk})_{1<=j,k<=n} converges weakly to mu_alpha as n tends to infinity. Our approach combines Aldous & Steele's objective method with Girko's Hermitization using logarithmic potentials. The underlying limiting object is defined on a bipartized version of Aldous' Poisson Weighted Infinite Tree. Recursive relations on the tree provide some properties of mu_alpha. In contrast with the Hermitian case, we find that mu_alpha is not heavy tailed.Comment: Expanded version of a paper published in Communications in Mathematical Physics 307, 513-560 (2011

Study of photo-proton reactions driven by bremsstrahlung radiation of high-intensity laser generated electrons

Photo-nuclear reactions were investigated using a high power table-top laser. The laser system at the University of Jena ( I similar to 3-5 x 10(19) W cm(-2)) produced hard bremsstrahlung photons ( kT similar to 2(9 MeV) via a laser-gas interaction which served to induce ( gamma, p) and ( gamma, n) reactions in Mg, Ti, Zn and Mo isotopes. Several ( gamma, p) decay channels were identified using nuclear activation analysis to determine their integral reaction yields

Analytical expressions for stopping-power ratios relevant for accurate dosimetry in particle therapy

In particle therapy, knowledge of the stopping-power ratios (STPRs) of the ion beam for air and water is necessary for accurate ionization chamber dosimetry. Earlier work has investigated the STPRs for pristine carbon ion beams, but here we expand the calculations to a range of ions (1 <= z <= 18) as well as spread out Bragg peaks (SOBPs) and provide a theoretical in-depth study with a special focus on the parameter regime relevant for particle therapy. The Monte Carlo transport code SHIELD-HIT is used to calculate complete particle-fluence spectra which are required for determining STPRs according to the recommendations of the International Atomic Energy Agency (IAEA). We confirm that the STPR depends primarily on the current energy of the ions rather than on their charge z or absolute position in the medium. However, STPRs for different sets of stopping-power data for water and air recommended by the International Commission on Radiation Units & Measurements (ICRU) are compared, including also the recently revised data for water, yielding deviations up to 2% in the plateau region. In comparison, the influence of the secondary particle spectra on the STPR is about two orders of magnitude smaller in the whole region up till the practical range. The gained insights enable us to propose an analytic approximation for the STPR for both pristine and SOBPs as a function of penetration depth, which parametrically depend only on the initial energy and the residual range of the ion, respectively.Comment: 21 pages, 5 figures, fixed bug with figures in v

Phagocytosis of Staphylococcus aureus by Macrophages Exerts Cytoprotective Effects Manifested by the Upregulation of Antiapoptotic Factors

It is becoming increasingly apparent that Staphylococcus aureus are able to survive engulfment by macrophages, and that the intracellular environment of these host cells, which is essential to innate host defenses against invading microorganisms, may in fact provide a refuge for staphylococcal survival and dissemination. Based on this, we postulated that S. aureus might induce cytoprotective mechanisms by changing gene expression profiles inside macrophages similar to obligate intracellular pathogens, such as Mycobacterium tuberculosis. To validate our hypothesis we first ascertained whether S. aureus infection could affect programmed cell death in human (hMDMs) and mouse (RAW 264.7) macrophages and, specifically, protect these cells against apoptosis. Our findings indicate that S. aureus-infected macrophages are more resistant to staurosporine-induced cell death than control cells, an effect partly mediated via the inhibition of cytochrome c release from mitochondria. Furthermore, transcriptome analysis of human monocyte-derived macrophages during S. aureus infection revealed a significant increase in the expression of antiapoptotic genes. This was confirmed by quantitative RT-PCR analysis of selected genes involved in mitochondria-dependent cell death, clearly showing overexpression of BCL2 and MCL1. Cumulatively, the results of our experiments argue that S. aureus is able to induce a cytoprotective effect in macrophages derived from different mammal species, which can prevent host cell elimination, and thus allow intracellular bacterial survival. Ultimately, it is our contention that this process may contribute to the systemic dissemination of S. aureus infection

A Potential New Pathway for Staphylococcus aureus Dissemination: The Silent Survival of S. aureus Phagocytosed by Human Monocyte-Derived Macrophages

Although considered to be an extracellular pathogen, Staphylococcus aureus is able to invade a variety of mammalian, non-professional phagocytes and can also survive engulfment by professional phagocytes such as neutrophils and monocytes. In both of these cell types S. aureus promptly escapes from the endosomes/phagosomes and proliferates within the cytoplasm, which quickly leads to host cell death. In this report we show that S. aureus interacted with human monocyte-derived macrophages in a very different way to those of other mammalian cells. Upon phagocytosis by macrophages, S. aureus persisted intracellularly in vacuoles for 3–4 days before escaping into the cytoplasm and causing host cell lysis. Until the point of host cell lysis the infected macrophages showed no signs of apoptosis or necrosis and were functional. They were able to eliminate intracellular staphylococci if prestimulated with interferon-γ at concentrations equivalent to human therapeutic doses. S. aureus survival was dependent on the alternative sigma factor B as well as the global regulator agr, but not SarA. Furthermore, isogenic mutants deficient in α-toxin, the metalloprotease aureolysin, protein A, and sortase A were efficiently killed by macrophages upon phagocytosis, although with different kinetics. In particular α-toxin was a key effector molecule that was essential for S. aureus intracellular survival in macrophages. Together, our data indicate that the ability of S. aureus to survive phagocytosis by macrophages is determined by multiple virulence factors in a way that differs considerably from its interactions with other cell types. S. aureus persists inside macrophages for several days without affecting the viability of these mobile cells which may serve as vehicles for the dissemination of infection