Large amplitude oscillations for a class of symmetric polynomial differential systems in R³

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Aharonov-Bohm oscillations in a quantum ring: Eccentricity and electric-field effects

The effects of an in-plane electric field and eccentricity on the electronic spectrum of a GaAs quantum ring in a perpendicular magnetic field are studied. The effective-mass equation is solved by two different methods: an adiabatic approximation and a diagonalization procedure after a conformal mapping. It is shown that the electric field and the eccentricity may suppress the Aharonov-Bohm oscillations of the lower energy levels. Simple expressions for the threshold energy and the number of flat energy bands are found. In the case of a thin and eccentric ring, the intensity of a critical field which compensates the main effects of eccentricity is determined. The energy spectra are found in qualitative agreement with previous experimental and theoretical works on anisotropic rings.

A fully adaptive multiresolution scheme for shock computations

The scheme is based on Ami Harten's ideas (Harten, 1994), the main tools coming from wavelet theory, in the framework of multiresolution analysis for cell averages. But instead of evolving cell averages on the finest uniform level, we propose to evolve just the cell averages on the grid determined by the significant wavelet coefficients. Typically, there are few cells in each time step, big cells on smooth regions, and smaller ones close to irregularities of the solution. For the numerical flux, we use a simple uniform central finite difference scheme, adapted to the size of each cell. If any of the required neighboring cell averages is not present, it is interpolated from coarser scales. But we switch to ENO scheme in the finest part of the grids. To show the feasibility and efficiency of the method, it is applied to a system arising in polymer-flooding of an oil reservoir. In terms of CPU time and memory requirements, it outperforms Harten's multiresolution algorithm.The proposed method applies to systems of conservation laws in 1Dpartial derivative(t)u(x, t) + partial derivative(x)f(u(x, t)) = 0, u(x, t) is an element of R-m. (1)In the spirit of finite volume methods, we shall consider the explicit schemeupsilon(mu)(n+1) = upsilon(mu)(n) - Deltat/hmu ((f) over bar (mu) - (f) over bar (mu)-) = [Dupsilon(n)](mu), (2)where mu is a point of an irregular grid Gamma, mu(-) is the left neighbor of A in Gamma, upsilon(mu)(n) approximate to 1/mu-mu(-) integral(mu-)(mu) u(x, t(n))dx are approximated cell averages of the solution, (f) over bar (mu) = (f) over bar (mu)(upsilon(n)) are the numerical fluxes, and D is the numerical evolution operator of the scheme.According to the definition of (f) over bar (mu), several schemes of this type have been proposed and successfully applied (LeVeque, 1990). Godunov, Lax-Wendroff, and ENO are some of the popular names. Godunov scheme resolves well the shocks, but accuracy (of first order) is poor in smooth regions. Lax-Wendroff is of second order, but produces dangerous oscillations close to shocks. ENO schemes are good alternatives, with high order and without serious oscillations. But the price is high computational cost.Ami Harten proposed in (Harten, 1994) a simple strategy to save expensive ENO flux calculations. The basic tools come from multiresolution analysis for cell averages on uniform grids, and the principle is that wavelet coefficients can be used for the characterization of local smoothness.. Typically, only few wavelet coefficients are significant. At the finest level, they indicate discontinuity points, where ENO numerical fluxes are computed exactly. Elsewhere, cheaper fluxes can be safely used, or just interpolated from coarser scales. Different applications of this principle have been explored by several authors, see for example (G-Muller and Muller, 1998).Our scheme also uses Ami Harten's ideas. But instead of evolving the cell averages on the finest uniform level, we propose to evolve the cell averages on sparse grids associated with the significant wavelet coefficients. This means that the total number of cells is small, with big cells in smooth regions and smaller ones close to irregularities. This task requires improved new tools, which are described next.

Coherent properties and Rabi oscillations in two-level donor systems

Coherent properties and Rabi oscillations in two-level donor systems, under terahertz excitation, are theoretically investigated. Here we are concerned with donor states in bulk GaAs and GaAs-(Ga,Al)As quantum dots. We study confinement effects, in the presence of an applied magnetic field, on the electronic and on-center donor states in GaAs- (Ga,Al)As dots, as compared to the situation in bulk GaAs, and estimate some of the associated decay rate parameters. Using the optical Bloch equations with damping, we study the time evolution of the Is and 2p(+) states in the presence of an applied magnetic field and of a terahertz laser. We also discuss the role played by the distinct dephasing rates on the photocurrent and calculate the electric dipole transition moment. Results indicate that the Rabi oscillations are more robust as the total dephasing rate diminishes, corresponding to a favorable coherence time.

Probing neutrino oscillations in supersymmetric models at the Large Hadron Collider

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A branch-and-price approach to p-median location problems

This paper describes a branch-and-price algorithm for the p-median location problem. The objective is to locate p facilities (medians) such as the sum of the distances from each demand point to its nearest facility is minimized. The traditional column generation process is compared with a stabilized approach that combines the column generation and Lagrangean/surrogate relaxation. The Lagrangean/surrogate multiplier modifies; the reduced cost criterion, providing the selection of new productive columns at the search tree. Computational experiments are conducted considering especially difficult instances to the traditional column generation and also with some large-scale instances. (C) 2004 Elsevier Ltd. All rights reserved.

Spatio-temporal dynamics and transition from asymptotic equilibrium to bounded oscillations in Chrysomya albiceps (Diptera, Calliphoridae)

The sensitivity of parameters that govern the stability of population size in Chrysomya albiceps and describe its spatial dynamics was evaluated in this study. The dynamics was modeled using a density-dependent model of population growth. Our simulations show that variation in fecundity and mainly in survival has marked effect on the dynamics and indicates the possibility of transitions from one-point equilibrium to bounded oscillations. C. albiceps exhibits a two-point limit cycle, but the introduction of diffusive dispersal induces an evident qualitative shift from two-point limit cycle to a one fixed-point dynamics. Population dynamics of C. albiceps is here compared to dynamics of Cochliomyia macellaria, C. megacephala and C. putoria.

Dynamics of experimental populations of native and introduced blowflies (Diptera: Calliphoridae): mathematical modelling and the transition from asymptotic equilibrium to bounded oscillations

The equilibrium dynamics of native and introduced blowflies is modelled using a density-dependent model of population growth that takes into account important features of the life-history in these flies. A theoretical analysis indicates that the product of maximum fecundity and survival is the primary determinant of the dynamics. Cochliomyia macellaria, a blowfly native to the Americas and the introduced Chrysomya megacephala and Chrysomya putoria, differ in their dynamics in that the first species shows a damping oscillatory behavior leading to a one-point equilibrium, whereas in the last two species population numbers show a two-point limit cycle. Simulations showed that variation in fecundity has a marked effect on the dynamics and indicates the possibility of transitions from one-point equilibrium to bounded oscillations and aperiodic behavior. Variation in survival has much less influence on the dynamics.

Hormonal Oscillations During the Estrous Cycle Influence the Morphophysiology of the Gerbil (Meriones unguiculatus) Female Prostate (Skene Paraurethral Glands)

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

CP trajectory diagram - a tool for a pictorial representation of CP and matter effects in neutrino oscillations

We introduce a CP trajectory diagram in bi-probability space as a powerful tool for a pictorial representation of the genuine CP and the matter effects in neutrino oscillations. The existence of correlated ambiguity in the B is uncovered. The principles of tuning the beam energy for a determination of CP-violating phase delta and the sign of Deltam(13)(2) given baseline distance are proposed to resolve the ambiguity and to maximize the CP-odd effect. We finally point out, quite contrary to what is usually believed, that the ambiguity may be resolved with similar to 50% chance in the super-JHF experiment despite its relatively short baseline of 300 km. (C) 2003 Elsevier B.V. B.V. All rights reserved.

Loss of superfluidity in a Bose-Einstein condensate via forced resonant oscillations

We predict the loss of superfluidity in a Bose-Einstein condensate in an axially symmetric harmonic trap alone during resonant collective oscillations via a classical dynamical transition. The forced resonant oscillation can be initiated by (a) periodic modulation of the atomic scattering length with a frequency that equals twice the radial trapping frequency or multiples thereof, or by (b) periodic modulation of the radial trapping potential with a frequency that equals the radial trapping frequency or multiples thereof. Suggestion for future experiment is made. (C) 2003 Elsevier B.V. B.V. All rights reserved.

Probing supernova physics with neutrino oscillations

We point out that solar neutrino oscillations with large mixing angle as evidenced in current solar neutrino data have a strong impact on strategies for diagnosing collapse-driven supernova (SN) through neutrino observations. Such oscillations induce a significant deformation of the energy spectra of neutrinos, thereby allowing us to obtain otherwise inaccessible features of SN neutrino spectra. We demonstrate that one can determine temperatures and luminosities of non-electron flavor neutrinos by observing (υ) over bar (e) from galactic SN in massive water Cherenkov detectors by the charged current reactions on protons. (C) 2002 Elsevier B.V. B.V. All rights reserved.

CP and T violation in neutrino oscillations

In this short lecture, I discuss some basic phenomenological aspects of CP and T violation in neutrino oscillation. Using CP/T trajectory diagrams in the bi-probability space, I try to sketch out some essential features of the interplay between the effect of CP/T violating phase and that of the matter in neutrino oscillation.

First quantized approaches to neutrino oscillations and second quantization

Neutrino oscillations are treated from the point of view of relativistic first quantized theories and compared to second quantized treatments. Within first quantized theories, general oscillation probabilities can be found for Dirac fermions and charged spin 0 bosons. A clear modification in the oscillation formulas can be obtained and its origin is elucidated and confirmed to be inevitable from completeness and causality requirements. The left-handed nature of created and detected neutrinos can also be implemented in the first quantized Dirac theory in the presence of mixing; the probability loss due to the changing of initially left-handed neutrinos to the undetected right-handed neutrinos can be obtained in analytic form. Concerning second quantized approaches, it is shown in a calculation using virtual neutrino propagation that both neutrinos and antineutrinos may also contribute as intermediate particles. The sign of the contributing neutrino energy may have to be chosen explicitly without being automatic in the formalism. At last, a simple second quantized description of the flavor oscillation phenomenon is devised. In this description there is no interference terms between positive and negative components, but it still gives simple normalized oscillation probabilities. A new effect appearing in this context is an inevitable but tiny violation of the initial flavor of neutrinos. The probability loss due to the conversion of left-handed neutrinos to right-handed neutrinos is also presented.

CP and T trajectory diagrams for a unified graphical representation of neutrino oscillations

Recently the CP trajectory diagram was introduced to demonstrate the difference between the intrinsic CP violating effects to those induced by matter for neutrino oscillation. In this Letter we introduce the T trajectory diagram. In these diagrams the probability for a given oscillation process is plotted versus the probability for the CP- or the T-conjugate processes, which forms an ellipse as the CP- or T-violating phase is varied. Since the CP- and the T-conjugate processes are related by CPT symmetry, even in the presence of matter, these two trajectory diagrams are closely related with each other and form a unified description of neutrino oscillations in matter. (C) 2002 Published by Elsevier B.V. B.V.