48 research outputs found
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 -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
-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