260 research outputs found
Enhancement of the Benjamin-Feir instability with dissipation
It is shown that there is an overlooked mechanism whereby some kinds of
dissipation can enhance the Benjamin-Feir instability of water waves. This
observation is new, and although it is counterintuitive, it is due to the fact
that the Benjamin-Feir instability involves the collision of modes with
opposite energy sign (relative to the carrier wave), and it is the negative
energy perturbations which are enhanced.Comment: 15 pages, 2 figures To download more papers, go to
http://www.cmla.ens-cachan.fr/~dias. Physics of Fluids (2007) to appea
Network Structures from Selection Principles
We present an analysis of the topologies of a class of networks which are
optimal in terms of the requirements of having as short a route as possible
between any two nodes while yet keeping the congestion in the network as low as
possible. Strikingly, we find a variety of distinct topologies and novel phase
transitions between them on varying the number of links per node. Our results
suggest that the emergence of the topologies observed in nature may arise both
from growth mechanisms and the interplay of dynamical mechanisms with a
selection process.Comment: 4 pages, 5 figure
Ballistic matter waves with angular momentum: Exact solutions and applications
An alternative description of quantum scattering processes rests on
inhomogeneous terms amended to the Schroedinger equation. We detail the
structure of sources that give rise to multipole scattering waves of definite
angular momentum, and introduce pointlike multipole sources as their limiting
case. Partial wave theory is recovered for freely propagating particles. We
obtain novel results for ballistic scattering in an external uniform force
field, where we provide analytical solutions for both the scattering waves and
the integrated particle flux. Our theory directly applies to p-wave
photodetachment in an electric field. Furthermore, illustrating the effects of
extended sources, we predict some properties of vortex-bearing atom laser beams
outcoupled from a rotating Bose-Einstein condensate under the influence of
gravity.Comment: 42 pages, 8 figures, extended version including photodetachment and
semiclassical theor
Electron scattering from molecules and molecular aggregates of biological relevance
In this Topical Review we survey the current state of the art in the study of low energy electron collisions with biologically relevant molecules and molecular clusters. We briefly describe the methods and techniques used in the investigation of these processes and summarise the results obtained so far for DNA constituents and their model compounds, amino acids, peptides and other biomolecules. The applications of the data obtained is briefly described as well as future required developments
Multiphoton detachment of electrons from negative ions
A simple analytical solution for the problem of multiphoton detachment from
negative ions by a linearly polarized laser field is found. It is valid in the
wide range of intensities and frequencies of the field, from the perturbation
theory to the tunneling regime, and is applicable to the excess-photon as well
as near-threshold detachment. Practically, the formulae are valid when the
number of photons is greater than two. They produce the total detachment rates,
relative intensities of the excess-photon peaks, and photoelectron angular
distributions for the hydrogen and halogen negative ions, in agreement with
those obtained in other, more numerically involved calculations in both
perturbative and non-perturbative regimes. Our approach explains the extreme
sensitivity of the multiphoton detachment probability to the asymptotic
behaviour of the bound-state wave function. Rapid oscillations in the angular
dependence of the -photon detachment probability are shown to arise due to
interference of the two classical trajectories which lead to the same final
state after the electron emerges at the opposite sides of the atom when the
field is close to maximal.Comment: 27 pages, Latex, and PostScript figures fig1.ps, fig2.ps, fig3.ps,
accepted for publication in Phys. Rev.
Propagation of charged particle waves in a uniform magnetic field
This paper considers the probability density and current distributions
generated by a point-like, isotropic source of monoenergetic charges embedded
into a uniform magnetic field environment. Electron sources of this kind have
been realized in recent photodetachment microscopy experiments. Unlike the
total photocurrent cross section, which is largely understood, the spatial
profiles of charge and current emitted by the source display an unexpected
hierarchy of complex patterns, even though the distributions, apart from
scaling, depend only on a single physical parameter. We examine the electron
dynamics both by solving the quantum problem, i. e., finding the energy Green
function, and from a semiclassical perspective based on the simple cyclotron
orbits followed by the electron. Simulations suggest that the semiclassical
method, which involves here interference between an infinite set of paths,
faithfully reproduces the features observed in the quantum solution, even in
extreme circumstances, and lends itself to an interpretation of some (though
not all) of the rich structure exhibited in this simple problem.Comment: 39 pages, 16 figure
Highly optimized tolerance and power laws in dense and sparse resource regimes
Power law cumulative frequency vs. event size distributions
are frequently cited as evidence for complexity and
serve as a starting point for linking theoretical models and mechanisms with
observed data. Systems exhibiting this behavior present fundamental
mathematical challenges in probability and statistics. The broad span of length
and time scales associated with heavy tailed processes often require special
sensitivity to distinctions between discrete and continuous phenomena. A
discrete Highly Optimized Tolerance (HOT) model, referred to as the
Probability, Loss, Resource (PLR) model, gives the exponent as a
function of the dimension of the underlying substrate in the sparse
resource regime. This agrees well with data for wildfires, web file sizes, and
electric power outages. However, another HOT model, based on a continuous
(dense) distribution of resources, predicts . In this paper we
describe and analyze a third model, the cuts model, which exhibits both
behaviors but in different regimes. We use the cuts model to show all three
models agree in the dense resource limit. In the sparse resource regime, the
continuum model breaks down, but in this case, the cuts and PLR models are
described by the same exponent.Comment: 19 pages, 13 figure
Solvable Metric Growing Networks
Structure and dynamics of complex networks usually deal with degree
distributions, clustering, shortest path lengths and other graph properties.
Although these concepts have been analysed for graphs on abstract spaces, many
networks happen to be embedded in a metric arrangement, where the geographic
distance between vertices plays a crucial role. The present work proposes a
model for growing network that takes into account the geographic distance
between vertices: the probability that they are connected is higher if they are
located nearer than farther. In this framework, the mean degree of vertices,
degree distribution and shortest path length between two randomly chosen
vertices are analysed
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