141 research outputs found
Space-time velocity correlation function for random walks
Space-time correlation functions constitute a useful instrument from the
research toolkit of continuous-media and many-body physics. We adopt here this
concept for single-particle random walks and demonstrate that the corresponding
space-time velocity auto-correlation functions reveal correlations which extend
in time much longer than estimated with the commonly employed temporal
correlation functions. A generic feature of considered random-walk processes is
an effect of velocity echo identified by the existence of time-dependent
regions where most of the walkers are moving in the direction opposite to their
initial motion. We discuss the relevance of the space-time velocity correlation
functions for the experimental studies of cold atom dynamics in an optical
potential and charge transport on micro- and nano-scales.Comment: Phys. Rev. Lett., in pres
Levy walks with velocity fluctuations
The standard Levy walk is performed by a particle that moves ballistically
between randomly occurring collisions, when the intercollision time is a random
variable governed by a power-law distribution. During instantaneous collision
events the particle randomly changes the direction of motion but maintains the
same constant speed. We generalize the standard model to incorporate velocity
fluctuations into the process. Two types of models are considered, namely, (i)
with a walker changing the direction and absolute value of its velocity during
collisions only, and (ii) with a walker whose velocity continuously fluctuates.
We present full analytic evaluation of both models and emphasize the importance
of initial conditions. We show that the type of the underlying Levy walk
process can be identified by looking at the ballistic regions of the diffusion
profiles. Our analytical results are corroborated by numerical simulations
L\'evy walks
Random walk is a fundamental concept with applications ranging from quantum
physics to econometrics. Remarkably, one specific model of random walks appears
to be ubiquitous across many fields as a tool to analyze transport phenomena in
which the dispersal process is faster than dictated by Brownian diffusion. The
L\'{e}vy walk model combines two key features, the ability to generate
anomalously fast diffusion and a finite velocity of a random walker. Recent
results in optics, Hamiltonian chaos, cold atom dynamics, bio-physics, and
behavioral science demonstrate that this particular type of random walks
provides significant insight into complex transport phenomena. This review
provides a self-consistent introduction to L\'{e}vy walks, surveys their
existing applications, including latest advances, and outlines further
perspectives.Comment: 50 page
Chaoticity of the Wet Granular Gas
In this work we derive an analytic expression for the Kolmogorov-Sinai
entropy of dilute wet granular matter, valid for any spatial dimension. The
grains are modelled as hard spheres and the influence of the wetting liquid is
described according to the Capillary Model, in which dissipation is due to the
hysteretic cohesion force of capillary bridges. The Kolmogorov-Sinai entropy is
expanded in a series with respect to density. We find a rapid increase of the
leading term when liquid is added. This demonstrates the sensitivity of the
granular dynamics to humidity, and shows that the liquid significantly
increases the chaoticity of the granular gas.Comment: 13 pages, 10 figures, Physical Review
Unbiased retrieval of frequency-dependent mechanical properties from noisy time-dependent signals
The mechanical response of materials to dynamic loading is often quantified by the frequency-dependent complex modulus. Probing materials directly in the frequency domain faces technical challenges such as a limited range of frequencies, long measurement times, or small sample sizes. Furthermore, many biological samples, such as cells or tissues, can change their properties upon repetitive probing at different frequencies. Therefore, it is common practice to extract the material properties by fitting predefined mechanical models to measurements performed in the time domain. This practice, however, precludes the probing of unique and yet unexplored material properties. In this report, we demonstrate that the frequency-dependent complex modulus can be robustly retrieved in a model-independent manner directly from time-dependent stress-strain measurements. While applying a rolling average eliminates random noise and leads to a reliable complex modulus in the lower frequency range, a Fourier transform with a complex frequency helps to recover the material properties at high frequencies. Finally, by properly designing the probing procedure, the recovery of reliable mechanical properties can be extended to an even wider frequency range. Our approach can be used with many state-of-the-art experimental methods to interrogate the mechanical properties of biological and other complex materials
Nucleosomal arrangement affects single-molecule transcription dynamics.
In eukaryotes, gene expression depends on chromatin organization. However, how chromatin affects the transcription dynamics of individual RNA polymerases has remained elusive. Here, we use dual trap optical tweezers to study single yeast RNA polymerase II (Pol II) molecules transcribing along a DNA template with two nucleosomes. The slowdown and the changes in pausing behavior within the nucleosomal region allow us to determine a drift coefficient, χ, which characterizes the ability of the enzyme to recover from a nucleosomal backtrack. Notably, χ can be used to predict the probability to pass the first nucleosome. Importantly, the presence of a second nucleosome changes χ in a manner that depends on the spacing between the two nucleosomes, as well as on their rotational arrangement on the helical DNA molecule. Our results indicate that the ability of Pol II to pass the first nucleosome is increased when the next nucleosome is turned away from the first one to face the opposite side of the DNA template. These findings help to rationalize how chromatin arrangement affects Pol II transcription dynamics
A Riemann hypothesis analogue for invariant rings
AbstractA Riemann hypothesis analogue for coding theory was introduced by I.M. Duursma [A Riemann hypothesis analogue for self-dual codes, in: A. Barg, S. Litsyn (Eds.), Codes and Association Schemes (Piscataway, NJ, 1999), American Mathematical Society, Providence, RI, 2001, pp. 115–124]. In this paper, we extend zeta polynomials for linear codes to ones for invariant rings, and we investigate whether a Riemann hypothesis analogue holds for some concrete invariant rings. Also we shall show that there is some subring of an invariant ring such that the subring is not an invariant ring but extremal polynomials all satisfy the Riemann hypothesis analogue
Periodic ethanol supply as a path toward unlimited lifespan of Caenorhabditis elegans dauer larvae
The dauer larva is a specialized stage of worm development optimized for survival under harsh conditions that have been used as a model for stress resistance, metabolic adaptations, and longevity. Recent findings suggest that the dauer larva of Caenorhabditis elegans may utilize external ethanol as an energy source to extend their lifespan. It was shown that while ethanol may serve as an effectively infinite source of energy, some toxic compounds accumulating as byproducts of its metabolism may lead to the damage of mitochondria and thus limit the lifespan of larvae. A minimal mathematical model was proposed to explain the connection between the lifespan of a dauer larva and its ethanol metabolism. To explore theoretically if it is possible to extend even further the lifespan of dauer larvae, we incorporated two natural mechanisms describing the recovery of damaged mitochondria and elimination of toxic compounds, which were previously omitted in the model. Numerical simulations of the revised model suggested that while the ethanol concentration is constant, the lifespan still stays limited. However, if ethanol is supplied periodically, with a suitable frequency and amplitude, the dauer could survive as long as we observe the system. Analytical methods further help to explain how feeding frequency and amplitude affect lifespan extension. Based on the comparison of the model with experimental data for fixed ethanol concentration, we proposed the range of feeding protocols that could lead to even longer dauer survival and it can be tested experimentally
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