1,182 research outputs found
Self-Similarity for Ballistic Aggregation Equation
We consider ballistic aggregation equation for gases in which each particle
is iden- ti?ed either by its mass and impulsion or by its sole impulsion. For
the constant aggregation rate we prove existence of self-similar solutions as
well as convergence to the self-similarity for generic solutions. For some
classes of mass and/or impulsion dependent rates we are also able to estimate
the large time decay of some moments of generic solutions or to build some new
classes of self-similar solutions
Diffusivities and Viscosities of Poly(ethylene oxide) Oligomers
The Publisher Version is available at: http://pubs.acs.org/doi/pdf/10.1021/je100430qDiffusivities and viscosities of poly(ethylene oxide) (PEO) oligomer melts of 1 to 12 repeat units have been obtained from equilibrium molecular dynamics simulations using the TraPPE-UA force field. The simulations generate diffusion coefficients with high accuracy for all molecular
weights studied, but statistical uncertainties for the viscosity calculations significantly increase
for longer chains. There is in good agreement of calculated viscosities and densities with available experimental data. The simulations can be used to fill in gaps in the data and for extrapolations with respect to chain length, temperature and pressure. We have explored the convergence characteristics of the Green-Kubo formulae for different chain lengths and propose
minimal production times required for convergence of the transport properties. The chain length dependence of transport properties suggests that neither Rouse nor reptation models are applicable in the short-chain regime investigated.This publication is based on work supported by Award No. KUS-CI-018-02 made by King
Abdullah University of Science and Technology (KAUST). This paper is dedicated to Sir John Rowlinson or his many contributions to experiment, theory and history of thermodynamics and for his mentorship of one of us (AZP) at a critical and formative time
Asymptotics of self-similar solutions to coagulation equations with product kernel
We consider mass-conserving self-similar solutions for Smoluchowski's
coagulation equation with kernel with
. It is known that such self-similar solutions
satisfy that is bounded above and below as . In
this paper we describe in detail via formal asymptotics the qualitative
behavior of a suitably rescaled function in the limit . It turns out that as . As becomes larger
develops peaks of height that are separated by large regions
where is small. Finally, converges to zero exponentially fast as . Our analysis is based on different approximations of a nonlocal
operator, that reduces the original equation in certain regimes to a system of
ODE
Moment bounds for the Smoluchowski equation and their consequences
We prove uniform bounds on moments X_a = \sum_{m}{m^a f_m(x,t)} of the
Smoluchowski coagulation equations with diffusion, valid in any dimension. If
the collision propensities \alpha(n,m) of mass n and mass m particles grow more
slowly than (n+m)(d(n) + d(m)), and the diffusion rate d(\cdot) is
non-increasing and satisfies m^{-b_1} \leq d(m) \leq m^{-b_2} for some b_1 and
b_2 satisfying 0 \leq b_2 < b_1 < \infty, then any weak solution satisfies X_a
\in L^{\infty}(\mathbb{R}^d \times [0,T]) \cap L^1(\mathbb{R}^d \times [0,T])
for every a \in \mathbb{N} and T \in (0,\infty), (provided that certain moments
of the initial data are finite). As a consequence, we infer that these
conditions are sufficient to ensure uniqueness of a weak solution and its
conservation of mass.Comment: 30 page
Self-similar chain conformations in polymer gels
We use molecular dynamics simulations to study the swelling of randomly
end-cross-linked polymer networks in good solvent conditions. We find that the
equilibrium degree of swelling saturates at Q_eq = N_e**(3/5) for mean strand
lengths N_s exceeding the melt entanglement length N_e. The internal structure
of the network strands in the swollen state is characterized by a new exponent
nu=0.72. Our findings are in contradiction to de Gennes' c*-theorem, which
predicts Q_eq proportional N_s**(4/5) and nu=0.588. We present a simple Flory
argument for a self-similar structure of mutually interpenetrating network
strands, which yields nu=7/10 and otherwise recovers the classical Flory-Rehner
theory. In particular, Q_eq = N_e**(3/5), if N_e is used as effective strand
length.Comment: 4 pages, RevTex, 3 Figure
ABJ(M) Chiral Primary Three-Point Function at Two-loops
This article is distributed under the terms of the Creative Commons
Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.archiveprefix: arXiv primaryclass: hep-th reportnumber: QMUL-PH-14-10 slaccitation: %%CITATION = ARXIV:1404.1117;%%archiveprefix: arXiv primaryclass: hep-th reportnumber: QMUL-PH-14-10 slaccitation: %%CITATION = ARXIV:1404.1117;%%archiveprefix: arXiv primaryclass: hep-th reportnumber: QMUL-PH-14-10 slaccitation: %%CITATION = ARXIV:1404.1117;%%Article funded by SCOAP
Partial domain wall partition functions
We consider six-vertex model configurations on an n-by-N lattice, n =< N,
that satisfy a variation on domain wall boundary conditions that we define and
call "partial domain wall boundary conditions". We obtain two expressions for
the corresponding "partial domain wall partition function", as an
(N-by-N)-determinant and as an (n-by-n)-determinant. The latter was first
obtained by I Kostov. We show that the two determinants are equal, as expected
from the fact that they are partition functions of the same object, that each
is a discrete KP tau-function, and, recalling that these determinants represent
tree-level structure constants in N=4 SYM, we show that introducing 1-loop
corrections, as proposed by N Gromov and P Vieira, preserves the determinant
structure.Comment: 30 pages, LaTeX. This version, which appeared in JHEP, has an
abbreviated abstract and some minor stylistic change
Heavy quarkonium moving in a quark-gluon plasma
By means of effective field theory techniques, we study the modifications of some properties of weakly coupled heavy quarkonium states propagating through a quark-gluon plasma at temperatures much smaller than the heavy quark mass, mQ. Two different cases are considered, corresponding to two different hierarchies between the typical size of the bound state, r, the binding energy, E, the temperature, T, and the screening mass, mD. The first case corresponds to the hierarchy mQâ«1/râ«Tâ«Eâ«mD, relevant for moderate temperatures, and the second one to the hierarchy mQâ«Tâ«1/r, mDâ«E, relevant for studying the dissociation mechanism. In the first case we determine the perturbative correction to the binding energy and to the decay width of states with arbitrary angular momentum, finding that the width is a decreasing function of the velocity. A different behavior characterizes the second kinematical case, where the width of s-wave states becomes a nonmonotonic function of the velocity, increasing at moderate velocities and decreasing in the ultrarelativistic limit. We obtain a simple analytical expression of the decay width for Tâ«1/râ«mDâ«E at moderate velocities, and we derive the s-wave spectral function for the more general case Tâ«1/r, mDâ«E. A brief discussion of the possible experimental signatures as well as a comparison with the relevant lattice data are also presented
Axisymmetric pulse recycling and motion in bulk semiconductors
The Kroemer model for the Gunn effect in a circular geometry (Corbino disks)
has been numerically solved. The results have been interpreted by means of
asymptotic calculations. Above a certain onset dc voltage bias, axisymmetric
pulses of the electric field are periodically shed by an inner circular
cathode. These pulses decay as they move towards the outer anode, which they
may not reach. As a pulse advances, the external current increases continuously
until a new pulse is generated. Then the current abruptly decreases, in
agreement with existing experimental results. Depending on the bias, more
complex patterns with multiple pulse shedding are possible.Comment: 8 pages, 15 figure
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