126 research outputs found
Multiple positive solutions for boundary value problems of second-order differential equations system on the half-line
In this paper, we study the existence of positive solutions for boundary value problems of second-order differential equations system with integral boundary condition on the half-line. By using a three functionals fixed point theorem in a cone and a fixed point theorem in a cone due to Avery-Peterson, we show the existence of at least two and three monotone increasing positive solutions with suitable growth conditions imposed on the nonlinear terms
Existence and Monotone Iteration of Positive Pseudosymmetric Solutions for a Third-Order Four-Point BVP with -Laplacian
We study the existence and monotone iteration of solutions for a third-order four-point boundary value problem with -Laplacian. An existence result of positive, concave, and pseudosymmetric solutions and its monotone iterative scheme are established by using the monotone iterative technique. Meanwhile, as an application of our result, an example is given
Double Trace Interfaces
We introduce and study renormalization group interfaces between two
holographic conformal theories which are related by deformation by a scalar
double trace operator. At leading order in the 1/N expansion, we derive
expressions for the two point correlation functions of the scalar, as well as
the spectrum of operators living on the interface. We also compute the
interface contribution to the sphere partition function, which in two
dimensions gives the boundary g factor. Checks of our proposal include
reproducing the g factor and some defect overlap coefficients of Gaiotto's RG
interfaces at large N, and the two-point correlation function whenever
conformal perturbation theory is valid.Comment: 59 pages, 2 figure
Weak solvability of the unconditionally stable difference scheme for the coupled sine-Gordon system
In this paper, we study the existence and uniqueness of weak solution for the system of finite difference schemes for coupled sine-Gordon equations. A novel first order of accuracy unconditionally stable difference scheme is considered. The variational method also known as the energy method is applied to prove unique weak solvability.We also present a new unified numerical method for the approximate solution of this problem by combining the difference scheme and the fixed point iteration. A test problem is considered, and results of numerical experiments are presented with error analysis to verify the accuracy of the proposed numerical method
Four dimensional Abelian duality and SL(2,Z) action in three dimensional conformal field theory
Recently, Witten showed that there is a natural action of the group SL(2,Z)
on the space of 3 dimensional conformal field theories with U(1) global
symmetry and a chosen coupling of the symmetry current to a background gauge
field on a 3-fold N. He further argued that, for a class of conformal field
theories, in the nearly Gaussian limit, this SL(2,Z) action may be viewed as a
holographic image of the well-known SL(2,Z) Abelian duality of a pure U(1)
gauge theory on AdS-like 4-folds M bounded by N, as dictated by the AdS/CFT
correspondence. However, he showed that explicitly only for the generator T;
for the generator S, instead, his analysis remained conjectural. In this paper,
we propose a solution of this problem. We derive a general holographic formula
for the nearly Gaussian generating functional of the correlators of the
symmetry current and, using this, we show that Witten's conjecture is indeed
correct when N=S^3. We further identify a class of homology 3-spheres N for
which Witten's conjecture takes a particular simple form.Comment: analysis of sect. 5 generalized; 43 pages, Plain TeX, no figures,
requires AMS font files amssym.def and amssym.te
Genus Two Partition Functions and Renyi Entropies of Large c CFTs
We compute genus two partition functions in two dimensional conformal field
theories at large central charge, focusing on surfaces that give the third
Renyi entropy of two intervals. We compute this for generalized free theories
and for symmetric orbifolds, and compare it to the result in pure gravity. We
find a new phase transition if the theory contains a light operator of
dimension . This means in particular that unlike the second
Renyi entropy, the third one is no longer universal.Comment: 28 pages + Appendice
Particles and fields in fluid turbulence
The understanding of fluid turbulence has considerably progressed in recent
years. The application of the methods of statistical mechanics to the
description of the motion of fluid particles, i.e. to the Lagrangian dynamics,
has led to a new quantitative theory of intermittency in turbulent transport.
The first analytical description of anomalous scaling laws in turbulence has
been obtained. The underlying physical mechanism reveals the role of
statistical integrals of motion in non-equilibrium systems. For turbulent
transport, the statistical conservation laws are hidden in the evolution of
groups of fluid particles and arise from the competition between the expansion
of a group and the change of its geometry. By breaking the scale-invariance
symmetry, the statistically conserved quantities lead to the observed anomalous
scaling of transported fields. Lagrangian methods also shed new light on some
practical issues, such as mixing and turbulent magnetic dynamo.Comment: 165 pages, review article for Rev. Mod. Phy
2D growth processes: SLE and Loewner chains
This review provides an introduction to two dimensional growth processes.
Although it covers a variety processes such as diffusion limited aggregation,
it is mostly devoted to a detailed presentation of stochastic Schramm-Loewner
evolutions (SLE) which are Markov processes describing interfaces in 2D
critical systems. It starts with an informal discussion, using numerical
simulations, of various examples of 2D growth processes and their connections
with statistical mechanics. SLE is then introduced and Schramm's argument
mapping conformally invariant interfaces to SLE is explained. A substantial
part of the review is devoted to reveal the deep connections between
statistical mechanics and processes, and more specifically to the present
context, between 2D critical systems and SLE. Some of the SLE remarkable
properties are explained, as well as the tools for computing with SLE. This
review has been written with the aim of filling the gap between the
mathematical and the physical literatures on the subject.Comment: A review on Stochastic Loewner evolutions for Physics Reports, 172
pages, low quality figures, better quality figures upon request to the
authors, comments welcom
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