1,324 research outputs found
Algebraic models for the hierarchy structure of evolution equations at small x
We explore several models of QCD evolution equations simplified by
considering only the rapidity dependence of dipole scattering amplitudes, while
provisionally neglecting their dependence on transverse coordinates. Our main
focus is on the equations that include the processes of pomeron splittings. We
examine the algebraic structures of the governing equation hierarchies, as well
as the asymptotic behavior of their solutions in the large-rapidity limit.Comment: 12 pages, 5 figures; minor changes in the revised versio
Tunneling transition to the Pomeron regime
We point out that, in some models of small-x hard processes, the transition
to the Pomeron regime occurs through a sudden tunneling effect, rather than a
slow diffusion process. We explain the basis for such a feature and we
illustrate it for the BFKL equation with running coupling by gluon rapidity
versus scale correlation plots.Comment: 17 pages, 5 figures, mpeg animations available from
http://www.lpthe.jussieu.fr/~salam/tunneling/ . v2 includes additional
reference
Monopoles and Modifications of Bundles over Elliptic Curves
Modifications of bundles over complex curves is an operation that allows one to construct a new bundle from a given one. Modifications can change a topological type of bundle. We describe the topological type in terms of the characteristic classes of the bundle. Being applied to the Higgs bundles modifications establish an equivalence between different classical integrable systems. Following Kapustin and Witten we define the modifications in terms of monopole solutions of the Bogomolny equation. We find the Dirac monopole solution in the case R × (elliptic curve). This solution is a three-dimensional generalization of the Kronecker series. We give two representations for this solution and derive a functional equation for it generalizing the Kronecker results. We use it to define Abelian modifications for bundles of arbitrary rank. We also describe non-Abelian modifications in terms of theta-functions with characteristic
Identification of Boundary Conditions Using Natural Frequencies
The present investigation concerns a disc of varying thickness of whose
flexural stiffness varies with the radius according to the law , where and are constants. The problem of finding boundary
conditions for fastening this disc, which are inaccessible to direct
observation, from the natural frequencies of its axisymmetric flexural
oscillations is considered. The problem in question belongs to the class of
inverse problems and is a completely natural problem of identification of
boundary conditions. The search for the unknown conditions for fastening the
disc is equivalent to finding the span of the vectors of unknown conditions
coefficients. It is shown that this inverse problem is well posed. Two theorems
on the uniqueness and a theorem on stability of the solution of this problem
are proved, and a method for establishing the unknown conditions for fastening
the disc to the walls is indicated. An approximate formula for determining the
unknown conditions is obtained using first three natural frequencies. The
method of approximate calculation of unknown boundary conditions is explained
with the help of three examples of different cases for the fastening the disc
(rigid clamping, free support, elastic fixing).
Keywords: Boundary conditions, a disc of varying thickness,inverse problem,
Plucker condition.Comment: 19 page
Polymyxin-Resistant Acinetobacter spp. Isolates: What is Next?
Univ Fed Sao Paulo, Div Infect Dis, Lab Especial Microbiol Clin, BR-04025010 Sao Paulo, SP, BrazilUniv Fed Sao Paulo, Div Infect Dis, Lab Especial Microbiol Clin, BR-04025010 Sao Paulo, SP, BrazilWeb of Scienc
Traveling wave fronts and the transition to saturation
We propose a general method to study the solutions to nonlinear QCD evolution
equations, based on a deep analogy with the physics of traveling waves. In
particular, we show that the transition to the saturation regime of high energy
QCD is identical to the formation of the front of a traveling wave. Within this
physical picture, we provide the expressions for the saturation scale and the
gluon density profile as a function of the total rapidity and the transverse
momentum. The application to the Balitsky-Kovchegov equation for both fixed and
running coupling constants confirms the effectiveness of this method.Comment: 9 pages, 3 figures, references adde
Hecke Transformations of Conformal Blocks in WZW Theory. I. KZB Equations for Non-Trivial Bundles
We describe new families of the Knizhnik-Zamolodchikov-Bernard (KZB) equations related to the WZW-theory corresponding to the adjoint G-bundles of different topological types over complex curves Σg,n of genus g with n marked points. The bundles are defined by their characteristic classes - elements of H²(Σg,n,Z(G)), where Z(G) is a center of the simple complex Lie group G. The KZB equations are the horizontality condition for the projectively flat connection (the KZB connection) defined on the bundle of conformal blocks over the moduli space of curves. The space of conformal blocks has been known to be decomposed into a few sectors corresponding to the characteristic classes of the underlying bundles. The KZB connection preserves these sectors. In this paper we construct the connection explicitly for elliptic curves with marked points and prove its flatness
Quantum interference in nanofractals and its optical manifestation
We consider quantum interferences of ballistic electrons propagating inside
fractal structures with nanometric size of their arms. We use a scaling
argument to calculate the density of states of free electrons confined in a
simple model fractal. We show how the fractal dimension governs the density of
states and optical properties of fractal structures in the RF-IR region. We
discuss the effect of disorder on the density of states along with the
possibility of experimental observation.Comment: 19 pages, 6 figure
Patchiness and Demographic Noise in Three Ecological Examples
Understanding the causes and effects of spatial aggregation is one of the
most fundamental problems in ecology. Aggregation is an emergent phenomenon
arising from the interactions between the individuals of the population, able
to sense only -at most- local densities of their cohorts. Thus, taking into
account the individual-level interactions and fluctuations is essential to
reach a correct description of the population. Classic deterministic equations
are suitable to describe some aspects of the population, but leave out features
related to the stochasticity inherent to the discreteness of the individuals.
Stochastic equations for the population do account for these
fluctuation-generated effects by means of demographic noise terms but, owing to
their complexity, they can be difficult (or, at times, impossible) to deal
with. Even when they can be written in a simple form, they are still difficult
to numerically integrate due to the presence of the "square-root" intrinsic
noise. In this paper, we discuss a simple way to add the effect of demographic
stochasticity to three classic, deterministic ecological examples where
aggregation plays an important role. We study the resulting equations using a
recently-introduced integration scheme especially devised to integrate
numerically stochastic equations with demographic noise. Aimed at scrutinizing
the ability of these stochastic examples to show aggregation, we find that the
three systems not only show patchy configurations, but also undergo a phase
transition belonging to the directed percolation universality class.Comment: 20 pages, 5 figures. To appear in J. Stat. Phy
Deep inelastic scattering and "elastic" diffraction
We examine the total cross section of virtual photons on protons,
, at low and its
connection with ``elastic'' diffractive production in the two-gluon exchange dynamics for the virtual forward
Compton scattering amplitude. Solely based on the generic structure of
two-gluon exchange, we establish that the cross section is described by the
(imaginary part of the) amplitude for forward scattering of vector
states, . The
generalized vector dominance/color dipole picture (GVD/CDP) is accordingly
established to only rest on the two-gluon-exchange generic structure. This is
explicitly seen by the sum rules that allow one to directly relate the total
cross section to the cross section for elastic diffractive forward production,
, of vector states.Comment: 24 pages, latex file with three eps figures. BI-TP 2002/2
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