7,351 research outputs found
Kinetic Regimes and Cross-Over Times in Many-Particle Reacting Systems
We study kinetics of single species reactions ("A+A -> 0") for general local
reactivity Q and dynamical exponent z (rms displacement x_t ~ t^{1/z}.) For
small molecules z=2, whilst z=4,8 for certain polymer systems. For dimensions d
above the critical value d_c=z, kinetics are always mean field (MF). Below d_c,
the density n_t initially follows MF decay, n_0 - n_t ~ n_0^2 Q t. A 2-body
diffusion-controlled regime follows for strongly reactive systems (Q>Qstar ~
n_0^{(z-d)/d}) with n_0 - n_t ~ n_0^2 x_t^d. For Q<Qstar, MF kinetics persist,
with n_t ~ 1/Qt. In all cases n_t ~ 1/x_t^d at the longest times. Our analysis
avoids decoupling approximations by instead postulating weak physically
motivated bounds on correlation functions.Comment: 10 pages, 1 figure, uses bulk2.sty, minor changes, submitted to
Europhysics Letter
Proportion of Unaffected Sites in a Reaction-Diffusion Process
We consider the probability that a given site remains unvisited by any
of a set of random walkers in dimensions undergoing the reaction
when they meet. We find that asymptotically with a
universal exponent \theta=\ffrac12-O(\epsilon) for , while, for
, is non-universal and depends on the reaction rate. The
analysis, which uses field-theoretic renormalisation group methods, is also
applied to the reaction with . In this case, a stretched
exponential behaviour is found for all , except in the case ,
, where P(t)\sim {\rm e}^{-\const (\ln t)^{3/2}}.Comment: 10 pages, (revised version with abstract included) OUTP-94-35
A non-monotonic constitutive model is not necessary to obtain shear banding phenomena in entangled polymer solutions
In 1975 Doi and Edwards predicted that entangled polymer melts and solutions
can have a constitutive instability, signified by a decreasing stress for shear
rates greater than the inverse of the reptation time. Experiments did not
support this, and more sophisticated theories incorporated Marrucci's idea
(1996) of removing constraints by advection; this produced a monotonically
increasing stress and thus stable constitutive behavior. Recent experiments
have suggested that entangled polymer solutions may possess a constitutive
instability after all, and have led some workers to question the validity of
existing constitutive models. In this Letter we use a simple modern
constitutive model for entangled polymers, the non-stretching Rolie-Poly model
with an added solvent viscosity, and show that (1) instability and shear
banding is captured within this simple class of models; (2) shear banding
phenomena is observable for weakly stable fluids in flow geometries that impose
a sufficiently inhomogeneous total shear stress; (3) transient phenomena can
possess inhomogeneities that resemble shear banding, even for weakly stable
fluids. Many of these results are model-independent.Comment: 5 figure
Cluster mean-field approximations with the coherent-anomaly-method analysis for the driven pair contact process with diffusion
The cluster mean-field approximations are performed, up to 13 cluster sizes,
to study the critical behavior of the driven pair contact process with
diffusion (DPCPD) and its precedent, the PCPD in one dimension. Critical points
are estimated by extrapolating our data to the infinite cluster size limit,
which are in good accordance with recent simulation results. Within the cluster
mean-field approximation scheme, the PCPD and the DPCPD share the same
mean-field critical behavior. The application of the coherent anomaly method,
however, shows that the two models develop different coherent anomalies, which
lead to different true critical scaling. The values of the critical exponents
for the particle density, the pair density, the correlation length, and the
relaxation time are fairly well estimated for the DPCPD. These results support
and complement our recent simulation results for the DPCPD
The A+B -> 0 annihilation reaction in a quenched random velocity field
Using field-theoretic renormalization group methods the long-time behaviour
of the A+B -> 0 annihilation reaction with equal initial densities n_A(0) =
n_B(0) = n_0 in a quenched random velocity field is studied. At every point (x,
y) of a d-dimensional system the velocity v is parallel or antiparallel to the
x-axis and depends on the coordinates perpendicular to the flow. Assuming that
v(y) have zero mean and short-range correlations in the y-direction we show
that the densities decay asymptotically as n(t) ~ A n_0^(1/2) t^(-(d+3)/8) for
d<3. The universal amplitude A is calculated at first order in \epsilon = 3-d.Comment: 19 pages, LaTeX using IOP-macros, 5 eps-figures. It is shown that the
amplitude of the density is universal, i.e. independent of the reaction rat
Effective Edwards-Wilkinson equation for single-file diffusion
In this work, we present an effective discrete Edwards-Wilkinson equation
aimed to describe the single-file diffusion process. The key physical
properties of the system are captured defining an effective elasticity, which
is proportional to the single particle diffusion coefficient and to the inverse
squared mean separation between particles. The effective equation gives a
description of single-file diffusion using the global roughness of the system
of particles, which presents three characteristic regimes, namely normal
diffusion, subdiffusion and saturation, separated by two crossover times. We
show how these regimes scale with the parameters of the original system.
Additional repulsive interaction terms are also considered and we analyze how
the crossover times depend on the intensity of the additional terms. Finally,
we show that the roughness distribution can be well characterized by the
Edwards-Wilkinson universal form for the different single-file diffusion
processes studied here.Comment: 9 pages, 9 figure
CP Violations in Lepton Number Violation Processes and Neutrino Oscillations
We examine the constraints on the MNS lepton mixing matrix from the present
and future experimental data of the neutrino oscillation and lepton number
violation processes. We introduce a graphical representation of the CP
violation phases which appear in the lepton number violation processes such as
neutrinoless double beta decay, the conversion, and the K decay,
Using this graphical representation, we derive the
constraints on the CP violation phases in the lepton sector.Comment: 21pp, REVTeX, 9 Figure
Does changing the pulling direction give better insight into biomolecules?
Single molecule manipulation techniques reveal that the mechanical resistance
of a protein depends on the direction of the applied force. Using a lattice
model of polymers, we show that changing the pulling direction leads to
different phase diagrams. The simple model proposed here indicates that in one
case the system undergoes a transition akin to the unzipping of a
sheet, while in the other case the transition is of a shearing (slippage)
nature. Our results are qualitatively similar to experimental results. This
demonstrates the importance of varying the pulling direction since this may
yield enhanced insights into the molecular interactions responsible for the
stability of biomolecules.Comment: RevTeX v4, 10 pages with 6 eps figure
- …