Configurational entropy of Wigner crystals

We present a theoretical study of classical Wigner crystals in two- and three-dimensional isotropic parabolic traps aiming at understanding and quantifying the configurational uncertainty due to the presence of multiple stable configurations. Strongly interacting systems of classical charged particles confined in traps are known to form regular structures. The number of distinct arrangements grows very rapidly with the number of particles, many of these arrangements have quite low occurrence probabilities and often the lowest-energy structure is not the most probable one. We perform numerical simulations on systems containing up to 100 particles interacting through Coulomb and Yukawa forces, and show that the total number of metastable configurations is not a well defined and representative quantity. Instead, we propose to rely on the configurational entropy as a robust and objective measure of uncertainty. The configurational entropy can be understood as the logarithm of the effective number of states; it is insensitive to the presence of overlooked low-probability states and can be reliably determined even within a limited time of a simulation or an experiment.Comment: 12 pages, 8 figures. This is an author-created, un-copyedited version of an article accepted for publication in J. Phys.: Condens. Matter. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The definitive publisher-authenticated version is available online at 10.1088/0953-8984/23/7/075302.

Formation energy and interaction of point defects in two-dimensional colloidal crystals

The manipulation of individual colloidal particles using optical tweezers has allowed vacancies to be created in two-dimensional (2d) colloidal crystals, with unprecedented possibility of real-time monitoring the dynamics of such defects (Nature {\bf 413}, 147 (2001)). In this Letter, we employ molecular dynamics (MD) simulations to calculate the formation energy of single defects and the binding energy between pairs of defects in a 2d colloidal crystal. In the light of our results, experimental observations of vacancies could be explained and then compared to simulation results for the interstitial defects. We see a remarkable similarity between our results for a 2d colloidal crystal and the 2d Wigner crystal (Phys. Rev. Lett. {\bf 86}, 492 (2001)). The results show that the formation energy to create a single interstitial is $12$ lower than that of the vacancy. Because the pair binding energies of the defects are strongly attractive for short distances, the ground state should correspond to bound pairs with the interstitial bound pairs being the most probable.Comment: 5 pages, 2 figure

Transverse Myelitis

Os autores apresentam três casos de mielite transversa de instalação aguda em doentes jovens, salientando a possível gravidade do quadro neurológico, a necessidade de excluir uma causa potencialmente tratável e a controvérsia da terapêutica com corticosteroides

Evolution of physical processes in models of population dynamics

Neste texto apresentamos e discutimos um breve panorama cronológico para a dinâmica de populações, observando o ponto de vista dos autores, bem como a evolução dos principais modelos matemáticos e sua importância histórica. Com foco na predição temporal e espacial da variação do número de indivíduos de uma população, analisamos como modelar matematicamente os processos físicos como crescimento, interação, difusão e fluxo de um coletivo de indivíduos. Partimos do bem conhecido modelo de Fibonacci e discutimos como modelos que o sucederam, a saber, o modelo Malthusiano, Lotka-Volterra e Fisher-Kolmogorov, foram capazes de ampliar o entendimento do comportamento de uma população. Apresentamos, nesta linha temporal sinuosa, como as interações entre uma mesma espécie e entre espécies podem ser explicadas e modeladas. Mostramos como funciona o processo de extinção de uma espécie predadora, o fenômeno de difusão de um coletivo devido as mais diversas exigências espaciais, as migrações e invasões de territórios por meio de uma dinâmica convectiva nos modelos de dinâmica de uma população e também como a não-localidade nas interações e no crescimento ampliam enormemente nosso entendimento sobre os padrões na natureza.In this paper we present and discuss a brief overview chronological for the population dynamics, observing the point of view of the authors, as well as the evolution of the main mathematical models and its historical importance. Focusing on temporal and spatial prediction of the variation in the number of individuals in a population, we analyze how to mathematically model the physical processes such as growth, interaction, dissemination and flow of a collective of individuals. We start from the well-known model of Fibonacci and discussed how models who succeeded him, namely the Malthusian model, Lotka-Volterra and Fisher-Kolmogorov were able to expand the understanding of the behavior of a population. Here, in this winding timeline as the interactions between species and between species can be explained and modeled. We show how the process of extinguishing a predatory species works, the diffusion phenomenon of a collective because the most diverse space requirements, migration and invasions of territories by means of convective momentum in dynamic models of a population as well as non-locality in interactions and growth greatly expand our understanding of the patterns in nature

Supersymmetric and Shape-Invariant Generalization for Nonresonant and Intensity-Dependent Jaynes-Cummings Systems

A class of shape-invariant bound-state problems which represent transition in a two-level system introduced earlier are generalized to include arbitrary energy splittings between the two levels as well as intensity-dependent interactions. We show that the couple-channel Hamiltonians obtained correspond to the generalizations of the nonresonant and intensity-dependent nonresonant Jaynes-Cummings Hamiltonians, widely used in quantized theories of laser. In this general context, we determine the eigenstates, eigenvalues, the time evolution matrix and the population inversion matrix factor.Comment: A combined version of quant-ph/0005045 and quant-ph/0005046. 24 pages, LATE

Generalized Ladder Operators for Shape-invariant Potentials

A general form for ladder operators is used to construct a method to solve bound-state Schr\"odinger equations. The characteristics of supersymmetry and shape invariance of the system are the start point of the approach. To show the elegance and the utility of the method we use it to obtain energy spectra and eigenfunctions for the one-dimensional harmonic oscillator and Morse potentials and for the radial harmonic oscillator and Coulomb potentials.Comment: in Revte