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 $n$-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 $(P)$ vs. event size $(l)$ distributions $P(\geq l)\sim l^{-\alpha}$ 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 $\alpha=1/d$ as a function of the dimension $d$ 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 $\alpha= 1+ 1/d$. 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