1,000 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
Self-similar solutions with fat tails for Smoluchowski's coagulation equation with locally bounded kernels
The existence of self-similar solutions with fat tails for Smoluchowski's
coagulation equation has so far only been established for the solvable and the
diagonal kernel. In this paper we prove the existence of such self-similar
solutions for continuous kernels that are homogeneous of degree and satisfy . More precisely,
for any we establish the existence of a continuous weak
self-similar profile with decay as
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
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
Power Steering Concept
This senior project was created in conjunction with Edwards Lifesciences. This project was created under an non-disclosure agreement and will not be submitted to any outside sources. The submitted title page will act as proof of completion
Tailoring Three-Point Functions and Integrability III. Classical Tunneling
We compute three-point functions between one large classical operator and two
large BPS operators at weak coupling. We consider operators made out of the
scalars of N=4 SYM, dual to strings moving in the sphere. The three-point
function exponentiates and can be thought of as a classical tunneling process
in which the classical string-like operator decays into two classical BPS
states. From an Integrability/Condensed Matter point of view, we simplified
inner products of spin chain Bethe states in a classical limit corresponding to
long wavelength excitations above the ferromagnetic vacuum. As a by-product we
solved a new long-range Ising model in the thermodynamic limit.Comment: 37 pages, 10 figure
Thermal width and gluo-dissociation of quarkonium in pNRQCD
The thermal width of heavy-quarkonium bound states in a quark-gluon plasma
has been recently derived in an effective field theory approach. Two phenomena
contribute to the width: the Landau damping phenomenon and the break-up of a
colour-singlet bound state into a colour-octet heavy quark-antiquark pair by
absorption of a thermal gluon. In the paper, we investigate the relation
between the singlet-to-octet thermal break-up and the so-called
gluo-dissociation, a mechanism for quarkonium dissociation widely used in
phenomenological approaches. The gluo-dissociation thermal width is obtained by
convoluting the gluon thermal distribution with the cross section of a gluon
and a 1S quarkonium state to a colour octet quark-antiquark state in vacuum, a
cross section that at leading order, but neglecting colour-octet effects, was
computed long ago by Bhanot and Peskin. We will, first, show that the effective
field theory framework provides a natural derivation of the gluo-dissociation
factorization formula at leading order, which is, indeed, the singlet-to-octet
thermal break-up expression. Second, the singlet-to-octet thermal break-up
expression will allow us to improve the Bhanot--Peskin cross section by
including the contribution of the octet potential, which amounts to include
final-state interactions between the heavy quark and antiquark. Finally, we
will quantify the effects due to final-state interactions on the
gluo-dissociation cross section and on the quarkonium thermal width.Comment: 17 pages, 6 figure
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
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