17,528 research outputs found
Dynamical aspects of inextensible chains
In the present work the dynamics of a continuous inextensible chain is
studied. The chain is regarded as a system of small particles subjected to
constraints on their reciprocal distances. It is proposed a treatment of
systems of this kind based on a set Langevin equations in which the noise is
characterized by a non-gaussian probability distribution. The method is
explained in the case of a freely hinged chain. In particular, the generating
functional of the correlation functions of the relevant degrees of freedom
which describe the conformations of this chain is derived. It is shown that in
the continuous limit this generating functional coincides with a model of an
inextensible chain previously discussed by one of the authors of this work.
Next, the approach developed here is applied to a inextensible chain, called
the freely jointed bar chain, in which the basic units are small extended
objects. The generating functional of the freely jointed bar chain is
constructed. It is shown that it differs profoundly from that of the freely
hinged chain. Despite the differences, it is verified that in the continuous
limit both generating functionals coincide as it is expected.Comment: 15 pages, LaTeX 2e + various packages, 3 figures. The title has been
changed and three references have been added. A large part of the manuscript
has been rewritten to improve readability. Chapter 4 has been added. It
contains the construction of the generating functional without the
shish-kebab approximation and a new derivation of the continuous limit of the
freely jointed bar chai
Large N and double scaling limits in two dimensions
Recently, the author has constructed a series of four dimensional
non-critical string theories with eight supercharges, dual to theories of light
electric and magnetic charges, for which exact formulas for the central charge
of the space-time supersymmetry algebra as a function of the world-sheet
couplings were obtained. The basic idea was to generalize the old matrix model
approach, replacing the simple matrix integrals by the four dimensional matrix
path integrals of N=2 supersymmetric Yang-Mills theory, and the Kazakov
critical points by the Argyres-Douglas critical points. In the present paper,
we study qualitatively similar toy path integrals corresponding to the two
dimensional N=2 supersymmetric non-linear sigma model with target space CP^n
and twisted mass terms. This theory has some very strong similarities with N=2
super Yang-Mills, including the presence of critical points in the vicinity of
which the large n expansion is IR divergent. The model being exactly solvable
at large n, we can study non-BPS observables and give full proofs that double
scaling limits exist and correspond to universal continuum limits. A complete
characterization of the double scaled theories is given. We find evidence for
dimensional transmutation of the string coupling in some non-critical string
theories. We also identify en passant some non-BPS particles that become
massless at the singularities in addition to the usual BPS states.Comment: 38 pages, including an introductory section that makes the paper
self-contained, two figures and one appendix; v2: typos correcte
On the critical slowing down exponents of mode coupling theory
A method is provided to compute the parameter exponent yielding the
dynamic exponents of critical slowing down in mode coupling theory. It is
independent from the dynamic approach and based on the formulation of an
effective static field theory. Expressions of in terms of third order
coefficients of the action expansion or, equivalently, in term of six point
cumulants are provided. Applications are reported to a number of mean-field
models: with hard and soft variables and both fully-connected and dilute
interactions. Comparisons with existing results for Potts glass model, ROM,
hard and soft-spin Sherrington-Kirkpatrick and p-spin models are presented.Comment: 4 pages, 1 figur
Bosonic Field Propagators on Algebraic Curves
In this paper we investigate massless scalar field theory on non-degenerate
algebraic curves. The propagator is written in terms of the parameters
appearing in the polynomial defining the curve. This provides an alternative to
the language of theta functions. The main result is a derivation of the third
kind differential normalized in such a way that its periods around the homology
cycles are purely imaginary. All the physical correlation functions of the
scalar fields can be expressed in terms of this object. This paper contains a
detailed analysis of the techniques necessary to study field theories on
algebraic curves. A simple expression of the scalar field propagator is found
in a particular case in which the algebraic curves have internal symmetry
and one of the fields is located at a branch point.Comment: 26 pages, TeX + harvma
High-order myopic coronagraphic phase diversity (COFFEE) for wave-front control in high-contrast imaging systems
The estimation and compensation of quasi-static aberrations is mandatory to
reach the ultimate performance of high-contrast imaging systems. COFFEE is a
focal plane wave-front sensing method that consists in the extension of phase
diversity to high-contrast imaging systems. Based on a Bayesian approach, it
estimates the quasi-static aberrations from two focal plane images recorded
from the scientific camera itself. In this paper, we present COFFEE's extension
which allows an estimation of low and high order aberrations with nanometric
precision for any coronagraphic device. The performance is evaluated by
realistic simulations, performed in the SPHERE instrument framework. We develop
a myopic estimation that allows us to take into account an imperfect knowledge
on the used diversity phase. Lastly, we evaluate COFFEE's performance in a
compensation process, to optimize the contrast on the detector, and show it
allows one to reach the 10^-6 contrast required by SPHERE at a few resolution
elements from the star. Notably, we present a non-linear energy minimization
method which can be used to reach very high contrast levels (better than 10^-7
in a SPHERE-like context)Comment: Accepted in Optics Expres
Efeito do volume de calda adjuvante e horário de aplicação sobre a eficiência de controle percevejos da soja.
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