199 research outputs found
Aspects of the stochastic Burgers equation and their connection with turbulence
We present results for the 1 dimensional stochastically forced Burgers
equation when the spatial range of the forcing varies. As the range of forcing
moves from small scales to large scales, the system goes from a chaotic,
structureless state to a structured state dominated by shocks. This transition
takes place through an intermediate region where the system exhibits rich
multifractal behavior. This is mainly the region of interest to us. We only
mention in passing the hydrodynamic limit of forcing confined to large scales,
where much work has taken place since that of Polyakov.
In order to make the general framework clear, we give an introduction to
aspects of isotropic, homogeneous turbulence, a description of Kolmogorov
scaling, and, with the help of a simple model, an introduction to the language
of multifractality which is used to discuss intermittency corrections to
scaling.
We continue with a general discussion of the Burgers equation and forcing,
and some aspects of three dimensional turbulence where - because of the
mathematical analogy between equations derived from the Navier-Stokes and
Burgers equations - one can gain insight from the study of the simpler
stochastic Burgers equation. These aspects concern the connection of
dissipation rate intermittency exponents with those characterizing the
structure functions of the velocity field, and the dynamical behavior,
characterized by different time constants, of velocity structure functions. We
also show how the exponents characterizing the multifractal behavior of
velocity structure functions in the above mentioned transition region can
effectively be calculated in the case of the stochastic Burgers equation.Comment: 25 pages, 4 figure
Instability of rotating chiral solitons
We show that spherically symmetric chiral SU(2)×SU(2) solitons are unstable under spin-isospin rotations. Namely, the effective potential including the effects of quantizing the collective coordinate corresponding to such a rotation has no minimum in the class of functions used to describe such solitons. © 1984 The American Physical Society
Universal properties of the two-dimensional Kuramoto-Sivashinsky equation
We investigate the properties of the Kuramoto-Sivashinsky equation in two spatial dimensions. We show by an explicit, numerical, coarse-graining procedure that its long-wavelength properties are described by a stochastic, partial differential equation of the Kardar-Parisi-Zhang type. From the computed parameters in our effective, stochastic equation we argue that the length and time scales over which the correlation functions cross over from linear diffusive to those of the full nonlinear equation are very large. The behavior of the three-dimensional equation is also discussed
Stochasticity of gene products from transcriptional pulsing
Transcriptional pulsing has been observed in both prokaryotes and eukaryotes and plays a crucial role in cell-to-cell variability of protein and mRNA numbers. An important issue is how the time constants associated with episodes of transcriptional bursting and mRNA and protein degradation rates lead to different cellular mRNA and protein distributions, starting from the transient regime leading to the steady state. We address this by deriving and then investigating the exact time-dependent solution of the master equation for a transcriptional pulsing model of mRNA distributions. We find a plethora of results. We show that, among others, bimodal and long-tailed (power-law) distributions occur in the steady state as the rate constants are varied over biologically significant time scales. Since steady state may not be reached experimentally we present results for the time evolution of the distributions. Because cellular behavior is determined by proteins, we also investigate the effect of the different mRNA distributions on the corresponding protein distributions using numerical simulations
What can we learn from semi-inclusive rapidity correlations?
We study a general formulation of semi-inclusive two-particle rapidity correlations for short-range models. We use it to compare with the 205 GeV NAL Bubble Chamber data different decay distributions for independently emitted clusters. We also comment on non-independent cluster production and on semi-inclusive correlations between charged and neutral particles.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/22122/1/0000549.pd
The Non-local Kardar-Parisi-Zhang Equation With Spatially Correlated Noise
The effects of spatially correlated noise on a phenomenological equation
equivalent to a non-local version of the Kardar-Parisi-Zhang equation are
studied via the dynamic renormalization group (DRG) techniques. The correlated
noise coupled with the long ranged nature of interactions prove the existence
of different phases in different regimes, giving rise to a range of roughness
exponents defined by their corresponding critical dimensions. Finally
self-consistent mode analysis is employed to compare the non-KPZ exponents
obtained as a result of the long range -long range interactions with the DRG
results.Comment: Plain Latex, 10 pages, 2 figures in one ps fil
Clusters, correlations and transverse momenta
We discuss the short range part of two-particle correlations as it results from the phase space available in cluster decay. In such an approach, certain variables emerge which should be useful to organize the data and extract interesting information. We are in particular concerned with tests of large transverse motion of clusters.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/22256/1/0000692.pd
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