Variational analysis of the Gross-Neveu model in an S^1 space

The Gross-Neveu model in an S^1 space is analyzed by means of a variational technique: the Gaussian effective potential. By making the proper connection with previous exact results at finite temperature, we show that this technique is able to describe the phase transition occurring in this model. We also make some remarks about the appropriate treatment of Grassmann variables in variational approaches.

Variational analysis of ablation for variable properties

"Work was performed as part of a Cornell Aeronautical Laboratory Internal Research Project."

A Variational Calculation of TE and TM Cutoff Wavenumbers in Circular Eccentric Guides by Conformal Mapping

The cutoff wavenumbers of higher order modes in circular eccentric guides are computed with the variational analysis combined with a conformal mapping. A conformal mapping is applied to the variational formulation, and the variational equation is solved by the finite-element method. Numerical results for TE and TM cutoff wavenumbers are presented for different distances between the centers and ratio of the radii. Comparisons with numerical results found in the literature validate the presented method

VARIATIONAL SPIKED OSCILLATOR

A variational analysis of the spiked harmonic oscillator Hamiltonian -d2/dr2 + r2 + lambda/r5/2, lambda > 0, is reported. A trial function automatically satisfying both the Dirichlet boundary condition at the origin and the boundary condition at infinity is introduced. The results are excellent for a very large range of values of the coupling parameter lambda, suggesting that the present variational function is appropriate for the treatment of the spiked oscillator in all its regimes (strong, moderate, and weak interactions).

Variational and perturbative schemes for a spiked harmonic oscillator

A variational analysis of the spiked harmonic oscillator Hamiltonian operator - d2/dx2 + x2 + l(l + 1)/x2 + λ|x| -α, where α is a real positive parameter, is reported in this work. The formalism makes use of the functional space spanned by the solutions of the Schrödinger equation for the linear harmonic oscillator Hamiltonian supplemented by a Dirichlet boundary condition, and a standard procedure for diagonalizing symmetric matrices. The eigenvalues obtained by increasing the dimension of the basis set provide accurate approximations for the ground state energy of the model system, valid for positive and relatively large values of the coupling parameter λ. Additionally, a large coupling perturbative expansion is carried out and the contributions up to fourth-order to the ground state energy are explicitly evaluated. Numerical results are compared for the special case α = 5/2. © 1989 American Institute of Physics.

Continuity of set-valued maps revisited in the light of tame geometry

Continuity of set-valued maps is hereby revisited: after recalling some basic concepts of variational analysis and a short description of the State-of-the-Art, we obtain as by-product two Sard type results concerning local minima of scalar and vector valued functions. Our main result though, is inscribed in the framework of tame geometry, stating that a closed-valued semialgebraic set-valued map is almost everywhere continuous (in both topological and measure-theoretic sense). The result –depending on stratification techniques– holds true in a more general setting of o-minimal (or tame) set-valued maps. Some applications are briefly discussed at the end.

Assessing levels of uncertainty in recent temperature time series

We examine to what degree we can expect to obtain accurate temperature trends for the last two decades near the surface and in the lower troposphere. We compare temperatures obtained from surface observations and radiosondes as well as satellite-based measurements from the Microwave Soundings Units (MSU), which have been adjusted for orbital decay and non-linear instrument-body effects, and reanalyses from the European Centre for Medium-Range Weather Forecasts (ERA) and the National Centre for Environmental Prediction (NCEP). In regions with abundant conventional data coverage, where the MSU has no major influence on the reanalysis, temperature anomalies obtained from microwave sounders, radiosondes and from both reanalyses agree reasonably. Where coverage is insufficient, in particular over the tropical oceans, large differences are found between the MSU and either reanalysis. These differences apparently relate to changes in the satellite data availability and to differing satellite retrieval methodologies, to which both reanalyses are quite sensitive over the oceans. For NCEP, this results from the use of raw radiances directly incorporated into the analysis, which make the reanalysis sensitive to changes in the underlying algorithms, e.g. those introduced in August 1992. For ERA, the bias-correction of the one-dimensional variational analysis may introduce an error when the satellite relative to which the correction is calculated is biased itself or when radiances change on a time scale longer than a couple of months, e.g. due to orbit decay. ERA inhomogeneities are apparent in April 1985, October/November 1986 and April 1989. These dates can be identified with the replacements of satellites. It is possible that a negative bias in the sea surface temperatures (SSTs) used in the reanalyses may have been introduced over the period of the satellite record. This could have resulted from a decrease in the number of ship measurements, a concomitant increase in the importance of satellite-derived SSTs, and a likely cold bias in the latter. Alternately, a warm bias in SSTs could have been caused by an increase in the percentage of buoy measurements (relative to deeper ship intake measurements) in the tropical Pacific. No indications for uncorrected inhomogeneities of land surface temperatures could be found. Near-surface temperatures have biases in the boundary layer in both reanalyses, presumably due to the incorrect treatment of snow cover. The increase of near-surface compared to lower tropospheric temperatures in the last two decades may be due to a combination of several factors, including high-latitude near-surface winter warming due to an enhanced NAO and upper-tropospheric cooling due to stratospheric ozone decrease.

A Weak Maximum Principle for Optimal Control Problems with Nonsmooth Mixed Constraints

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Dynamical collapse in a degenerate binary fermion mixture using a hydrodynamic model

We use a time-dependent dynamical hydrodynamic model to study a collapse in a degenerate fermion-fermion mixture ( DFFM) of different atoms. Due to a strong Pauli-blocking repulsion among identical spin-polarized fermions at short distances, there cannot be a collapse for repulsive interspecies fermion fermion interaction. However, there can be a collapse for a sufficiently attractive interspecies fermion-fermion interaction in a DFFM of different atoms. Using a variational analysis and numerical solution of the hydrodynamic model, we study different aspects of collapse in such a DFFM initiated by a jump in the interspecies fermion-fermion interaction ( scattering length) to a large negative ( attractive) value using a Feshbach resonance. Suggestion for experiments of collapse in a DFFM of distinct atoms is made.

Spatially-antisymmetric localization of matter wave in a bichromatic optical lattice

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

Dynamics of quasi-one-dimensional bright and vortex solitons of a dipolar Bose-Einstein condensate with repulsive atomic interaction

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

Localization of a dipolar Bose-Einstein condensate in a bichromatic optical lattice

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

Symmetry breaking in a localized interacting binary Bose-Einstein condensate in a bichromatic optical lattice

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

Matter-wave localization in a random potential

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

The tangential variation of a localized flux-type eigenvalue problem

In this work the differentiability of the principal eigenvalue lambda = lambda(1)(Gamma) to the localized Steklov problem -Delta u + qu = 0 in Omega, partial derivative u/partial derivative nu = lambda chi(Gamma)(x)u on partial derivative Omega, where Gamma subset of partial derivative Omega is a smooth subdomain of partial derivative Omega and chi(Gamma) is its characteristic function relative to partial derivative Omega, is shown. As a key point, the flux subdomain Gamma is regarded here as the variable with respect to which such differentiation is performed. An explicit formula for the derivative of lambda(1) (Gamma) with respect to Gamma is obtained. The lack of regularity up to the boundary of the first derivative of the principal eigenfunctions is a further intrinsic feature of the problem. Therefore, the whole analysis must be done in the weak sense of H(1)(Omega). The study is of interest in mathematical models in morphogenesis. (C) 2011 Elsevier Inc. All rights reserved.