Delay nonlinear boundary conditions as limit of reactions concentrating in the boundary

In this work, we are interested in the dynamic behavior of a parabolic problem with nonlinear boundary conditions and delay in the boundary. We construct a reaction-diffusion problem with delay in the interior, where the reaction term is concentrated in a neighborhood of the boundary and this neighborhood shrinks to boundary, as a parameter epsilon goes to zero. We analyze the limit of the solutions of this concentrated problem and prove that these solutions converge in certain continuous function spaces to the unique solution of the parabolic problem with delay in the boundary. This convergence result allows us to approximate the solution of equations with delay acting on the boundary by solutions of equations with delay acting in the interior and it may contribute to analyze the dynamic behavior of delay equations when the delay is at the boundary. (C) 2012 Elsevier Inc. All rights reserved.

Exact field-driven interface dynamics in the two-dimensional stochastic Ising model with helicoidal boundary conditions

We investigate the interface dynamics of the two-dimensional stochastic Ising model in an external field under helicoidal boundary conditions. At sufficiently low temperatures and fields, the dynamics of the interface is described by an exactly solvable high-spin asymmetric quantum Hamiltonian that is the infinitesimal generator of the zero range process. Generally, the critical dynamics of the interface fluctuations is in the Kardar-Parisi-Zhang universality class of critical behavior. We remark that a whole family of RSOS interface models similar to the Ising interface model investigated here can be described by exactly solvable restricted high-spin quantum XXZ-type Hamiltonians. (C) 2012 Elsevier B.V. All rights reserved.

One-dimensional point interaction with Griffiths' boundary conditions

Griffiths proposed a pair of boundary conditions that define a point interaction in one dimensional quantum mechanics. The conditions involve the nth derivative of the wave function where n is a non-negative integer. We re-examine the interaction so defined and explicitly confirm that it is self-adjoint for any even value of n and for n = 1. The interaction is not self-adjoint for odd n > 1. We then propose a similar but different pair of boundary conditions with the nth derivative of the wave function such that the ensuing point interaction is self-adjoint for any value of n.

Error Upper Bounds for a Computational Method for Nonlinear Boundary and Initial-Value Problems

This work develops a computational approach for boundary and initial-value problems by using operational matrices, in order to run an evolutive process in a Hilbert space. Besides, upper bounds for errors in the solutions and in their derivatives can be estimated providing accuracy measures.

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.

A nonlinear elliptic problem with terms concentrating in the boundary

In this paper, we investigate the behavior of a family of steady-state solutions of a nonlinear reaction diffusion equation when some reaction and potential terms are concentrated in a e-neighborhood of a portion G of the boundary. We assume that this e-neighborhood shrinks to G as the small parameter e goes to zero. Also, we suppose the upper boundary of this e-strip presents a highly oscillatory behavior. Our main goal here was to show that this family of solutions converges to the solutions of a limit problem, a nonlinear elliptic equation that captures the oscillatory behavior. Indeed, the reaction term and concentrating potential are transformed into a flux condition and a potential on G, which depends on the oscillating neighborhood. Copyright (C) 2012 John Wiley & Sons, Ltd.

BRAZILIAN OFFSHORE WAVE CLIMATE BASED ON NWW3 REANALYSIS

This paper provides a description of the wave climate off the Brazilian coast based on an eleven-year time series (Jan/1997-Dec/2007) obtained from the NWW3 operational model hindcast reanalysis. Information about wave climate in Brazilian waters is very scarce and mainly based on occasional short-term observations, the present analysis being the first covering such temporal and spatial scales. To define the wave climate, six sectors were defined and analyzed along the Brazilian shelf-break: South (W1), Southeast (W2), Central (W3), East (W4), Northeast (W5) and North (W6). W1, W2 and W3 wave regimes are determined by the South Atlantic High (SAH) and the passage of synoptic cold fronts; W4, W5 and W6 are controlled by the Intertropical Convergence Zone (ITCZ) and its meridional oscillation. The most energetic waves are from the S, generated by the strong winds associated to the passage of cold fronts, which mainly affect the southern region. Wave power presents a decrease in energy levels from south to north, with its annual variation showing that the winter months are the most energetic in W1 to W4, while in W5 and W6 the most energetic conditions occur during the austral summer. The information presented here provides boundary conditions for studies related to coastal processes, fundamental for a better understanding of the Brazilian coastal zone.

Impacts of interruption of the Agulhas leakage on the tropical Atlantic in coupled ocean-atmosphere simulations

In this paper we use a coupled ocean-atmosphere model to investigate the impact of the interruption of Agulhas leakage of Indian ocean water on the tropical Atlantic, a region where strong coupled ocean-atmosphere interactions occur. The effect of a shut down of leakage of Indian ocean water is isolated from the effect of a collapse of the MOC. In our experiments, the ocean model is forced with boundary conditions in the southeastern corner of the domain that correspond to no interocean exchange of Indian ocean water into the Atlantic. The southern boundary condition is taken from the Levitus data and ensures an MOC in the Atlantic. Within this configuration, instead of warm and salty Indian ocean water temperature (cold) and salinity (fresh) anomalies of southern ocean origin propagate into the South Atlantic and eventually reach the equatorial region, mainly in the thermocline. This set up mimics the closure of the ""warm water path"" in favor of the ""cold water path"". As part of the atmospheric response, there is a northward shift of the intertropical convergence zone (ITCZ). The changes in trade winds lead to reduced Ekman pumping in the equatorial region. This leads to a freshening and warming of the surface waters along the equator. Especially in the Cold Tongue region, the cold and fresh subsurface anomalies do not reach the surface due to the reduced upwelling. The anomaly signals are transported by the equatorial undercurrent and spread away from the equator within the thermocline. Part of the anomaly eventually reaches the Tropical North Atlantic, where it affects the Guinea Dome. Surprisingly, the main effect at the surface is small on the equator and relatively large at the Guinea Dome. In the atmosphere, the northward shift of the ITCZ is associated with a band of negative precipitation anomalies and higher salinities over the Tropical South Atlantic. An important implication of these results is that the modified water characteristics due to a shut down of the Agulhas leakage remain largely unaffected when crossing the equatorial Atlantic and therefore can affect the deepwater formation in the North Atlantic. This supports the hypothesis that the Agulhas leakage is an important source region for climate change and decadal variability of the Atlantic.

Influence of the meridional overturning circulation on tropical Atlantic climate and variability

The influence of the meridional overturning circulation on tropical Atlantic climate and variability has been investigated using the atmosphere-ocean coupled model Speedy-MICOM (Miami Isopycnic Coordinate Ocean Model). In the ocean model MICOM the strength of the meridional overturning cell can be regulated by specifying the lateral boundary conditions. In case of a collapse of the basinwide meridional overturning cell the SST response in the Atlantic is characterized by a dipole with a cooling in the North Atlantic and a warming in the tropical and South Atlantic. The cooling in the North Atlantic is due to the decrease in the strength of the western boundary currents, which reduces the northward advection of heat. The warming in the tropical Atlantic is caused by a reduced ventilation of water originating from the South Atlantic. This effect is most prominent in the eastern tropical Atlantic during boreal summer when the mixed layer attains its minimum depth. As a consequence the seasonal cycle as well as the interannual variability in SST is reduced. The characteristics of the cold tongue mode are changed: the variability in the eastern equatorial region is strongly reduced and the largest variability is now in the Benguela, Angola region. Because of the deepening of the equatorial thermocline, variations in the thermocline depth in the eastern tropical Atlantic no longer significantly affect the mixed layer temperature. The gradient mode remains unaltered. The warming of the tropical Atlantic enhances and shifts the Hadley circulation. Together with the cooling in the North Atlantic, this increases the strength of the subtropical jet and the baroclinicity over the North Atlantic.