Spectral functions of half-filled one-dimensional Hubbard rings with varying boundary conditions

We study the effect of varying the boundary condition on: the spectral function of a finite one-dimensional Hubbard chain, which we compute using direct (Lanczos) diagonalization of the Hamiltonian. By direct comparison with the two-body response functions and with the exact solution of the Bethe ansatz equations, we can identify both spinon and holon features in the spectra. At half-filling the spectra have the well-known structure of a low-energy holon band and its shadow-which spans the whole Brillouin zone-and a spinon band present for momenta less than the Fermi momentum. Features related to the twisted boundary condition are cusps in the spinon band. We show that the spectral building principle, adapted to account for both the finite system size and the twisted boundary condition, describes the spectra well in terms of single spinon and holon excitations. We argue that these finite-size effects are a signature of spin-charge separation and that their study should help establish the existence and nature of spin-charge separation in finite-size systems.

Rapidly varying boundaries in equations with nonlinear boundary conditions. The case of a Lipschitz deformation

We analyze the behavior of solutions of nonlinear elliptic equations with nonlinear boundary conditions of type partial derivative u/partial derivative n + g( x, u) = 0 when the boundary of the domain varies very rapidly. We show that the limit boundary condition is given by partial derivative u/partial derivative n+gamma(x) g(x, u) = 0, where gamma(x) is a factor related to the oscillations of the boundary at point x. For the case where we have a Lipschitz deformation of the boundary,. is a bounded function and we show the convergence of the solutions in H-1 and C-alpha norms and the convergence of the eigenvalues and eigenfunctions of the linearization around the solutions. If, moreover, a solution of the limit problem is hyperbolic, then we show that the perturbed equation has one and only one solution nearby.

VERY RAPIDLY VARYING BOUNDARIES IN EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS. THE CASE of A NON UNIFORMLY LIPSCHITZ DEFORMATION

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

The direct boundary element method: 2D site effects assessment on laterally varying layered media (methodology)

The Direct Boundary Element Method (DBEM) is presented to solve the elastodynamic field equations in 2D, and a complete comprehensive implementation is given. The DBEM is a useful approach to obtain reliable numerical estimates of site effects on seismic ground motion due to irregular geological configurations, both of layering and topography. The method is based on the discretization of the classical Somigliana's elastodynamic representation equation which stems from the reciprocity theorem. This equation is given in terms of the Green's function which is the full-space harmonic steady-state fundamental solution. The formulation permits the treatment of viscoelastic media, therefore site models with intrinsic attenuation can be examined. By means of this approach, the calculation of 2D scattering of seismic waves, due to the incidence of P and SV waves on irregular topographical profiles is performed. Sites such as, canyons, mountains and valleys in irregular multilayered media are computed to test the technique. The obtained transfer functions show excellent agreement with already published results.

The Lake Tekapo experiment (LTEX): An investigation of atmospheric boundary layer processes in complex terrain

A research program on atmospheric boundary layer processes and local wind regimes in complex terrain was conducted in the vicinity of Lake Tekapo in the southern Alps of New Zealand, during two 1-month field campaigns in 1997 and 1999. The effects of the interaction of thermal and dynamic forcing were of specific interest, with a particular focus on the interaction of thermal forcing of differing scales. The rationale and objectives of the field and modeling program are described, along with the methodology used to achieve them. Specific research aims include improved knowledge of the role of surface forcing associated with varying energy balances across heterogeneous terrain, thermal influences on boundary layer and local wind development, and dynamic influences of the terrain through channeling effects. Data were collected using a network of surface meteorological and energy balance stations, radiosonde and pilot balloon soundings, tethered balloon and kite-based systems, sodar, and an instrumented light aircraft. These data are being used to investigate the energetics of surface heat fluxes, the effects of localized heating/cooling and advective processes on atmospheric boundary layer development, and dynamic channeling. A complementary program of numerical modeling includes application of the Regional Atmospheric Modeling System (RAMS) to case studies characterizing typical boundary layer structures and airflow patterns observed around Lake Tekapo. Some initial results derived from the special observation periods are used to illustrate progress made to date. In spite of the difficulties involved in obtaining good data and undertaking modeling experiments in such complex terrain, initial results show that surface thermal heterogeneity has a significant influence on local atmospheric structure and wind fields in the vicinity of the lake. This influence occurs particularly in the morning. However, dynamic channeling effects and the larger-scale thermal effect of the mountain region frequently override these more local features later in the day.

Variations of surface boundary layer parameters associated with Cyclone Gonu over the Arabian Sea using QuikSCAT data

This study attempted to quantify the variations of the surface marine atmospheric boundary layer (MABL) parameters associated with the tropical Cyclone Gonu formed over the Arabian Sea during 30 May–7 June 2007 (just after the monsoon onset). These characteristics were evaluated in terms of surface wind, drag coefficient, wind stress, horizontal divergence, and frictional velocity using 0.5◦ × 0.5◦ resolution Quick Scatterometer (QuikSCAT) wind products. The variation of these different surface boundary layer parameters was studied for three defined cyclone life stages: prior to the formation, during, and after the cyclone passage. Drastic variations of the MABL parameters during the passage of the cyclone were observed. The wind strength increased from 12 to 22 m s−1 in association with different stages of Gonu. Frictional velocity increased from a value of 0.1–0.6 m s−1 during the formative stage of the system to a high value of 0.3–1.4 m s−1 during the mature stage. Drag coefficient varied from 1.5 × 10−3 to 2.5 × 10−3 during the occurrence of Gonu. Wind stress values varied from 0.4 to 1.1 N m−2. Wind stress curl values varied from 10 × 10−7 to 45 × 10−7 N m−3. Generally, convergent winds prevailed with the numerical value of divergence varying from 0 to –4 × 10−5 s−1. Maximum variations of the wind parameters were found in the wall cloud region of the cyclone. The parameters returned to normally observed values in 1–3 days after the cyclone passage

Consistent Dirichlet Boundary Conditions for Numerical Solution of Moving Boundary Problems

We consider the imposition of Dirichlet boundary conditions in the finite element modelling of moving boundary problems in one and two dimensions for which the total mass is prescribed. A modification of the standard linear finite element test space allows the boundary conditions to be imposed strongly whilst simultaneously conserving a discrete mass. The validity of the technique is assessed for a specific moving mesh finite element method, although the approach is more general. Numerical comparisons are carried out for mass-conserving solutions of the porous medium equation with Dirichlet boundary conditions and for a moving boundary problem with a source term and time-varying mass.

Boundary layer structure and decoupling from synoptic scale flow during NAMBLEX

This paper presents an overview of the meteorology and planetary boundary layer structure observed during the NAMBLEX field campaign to aid interpretation of the chemical and aerosol measurements. The campaign has been separated into five periods corresponding to the prevailing synoptic condition. Comparisons between meteorological measurements ( UHF wind profiler, Doppler sodar, sonic aneometers mounted on a tower at varying heights and a standard anemometer) and the ECMWF analysis at 10 m and 1100 m identified days when the internal boundary layer was decoupled from the synoptic flow aloft. Generally the agreement was remarkably good apart from during period one and on a few days during period four when the diurnal swing in wind direction implies a sea/land breeze circulation near the surface. During these periods the origin of air sampled at Mace Head would not be accurately represented by back trajectories following the winds resolved in ECMWF analyses. The wind profiler observations give a detailed record of boundary layer structure including an indication of its depth, average wind speed and direction. Turbulence statistics have been used to assess the height to which the developing internal boundary layer, caused by the increased surface drag at the coast, reaches the sampling location under a wide range of marine conditions. Sampling conducted below 10 m will be impacted by emission sources at the shoreline in all wind directions and tidal conditions, whereas sampling above 15 m is unlikely to be affected in any of the wind directions and tidal heights sampled during the experiment.

Numerical modeling of the propagation environment in the atmospheric boundary layer over the Persian Gulf

Strong vertical gradients at the top of the atmospheric boundary layer affect the propagation of electromagnetic waves and can produce radar ducts. A three-dimensional, time-dependent, nonhydrostatic numerical model was used to simulate the propagation environment in the atmosphere over the Persian Gulf when aircraft observations of ducting had been made. A division of the observations into high- and low-wind cases was used as a framework for the simulations. Three sets of simulations were conducted with initial conditions of varying degrees of idealization and were compared with the observations taken in the Ship Antisubmarine Warfare Readiness/Effectiveness Measuring (SHAREM-115) program. The best results occurred with the initialization based on a sounding taken over the coast modified by the inclusion of data on low-level atmospheric conditions over the Gulf waters. The development of moist, cool, stable marine internal boundary layers (MIBL) in air flowing from land over the waters of the Gulf was simulated. The MIBLs were capped by temperature inversions and associated lapses of humidity and refractivity. The low-wind MIBL was shallower and the gradients at its top were sharper than in the high-wind case, in agreement with the observations. Because it is also forced by land–sea contrasts, a sea-breeze circulation frequently occurs in association with the MIBL. The size, location, and internal structure of the sea-breeze circulation were realistically simulated. The gradients of temperature and humidity that bound the MIBL cause perturbations in the refractivity distribution that, in turn, lead to trapping layers and ducts. The existence, location, and surface character of the ducts were well captured. Horizontal variations in duct characteristics due to the sea-breeze circulation were also evident. The simulations successfully distinguished between high- and low-wind occasions, a notable feature of the SHAREM-115 observations. The modeled magnitudes of duct depth and strength, although leaving scope for improvement, were most encouraging.

The importance of wind and buoyancy forcing for the boundary density variations and the geostrophic component of the AMOC at 26°N

It is widely thought that changes in both the surface buoyancy fluxes and wind stress drive variability in the Atlantic meridional overturning circulation (AMOC), but that they drive variability on different time scales. For example, wind forcing dominates short-term variability through its effects on Ekman currents and coastal upwelling, whereas buoyancy forcing is important for longer time scales (multiannual and decadal). However, the role of the wind forcing on multiannual to decadal time scales is less clear. Here the authors present an analysis of simulations with the Nucleus for European Modelling of the Ocean (NEMO) ocean model with the aim of explaining the important drivers of the zonal density gradient at 26°N, which is directly related to the AMOC. In the experiments, only one of either the wind stress or the buoyancy forcing is allowed to vary in time, whereas the other remains at its seasonally varying climatology. On subannual time scales, variations in the density gradient, and in the AMOC minus Ekman, are driven largely by local wind-forced coastal upwelling at both the western and eastern boundaries. On decadal time scales, buoyancy forcing related to the North Atlantic Oscillation dominates variability in the AMOC. Interestingly, however, it is found that wind forcing also plays a role at longer time scales, primarily impacting the interannual variability through the excitation of Rossby waves in the central Atlantic, which propagate westward to interact with the western boundary, but also by modulating the decadal time-scale response to buoyancy forcing.

A numerical model of the ionospheric signatures of time-varying magnetic reconnection: III. Quasi-instantaneous convection responses in the Cowley-Lockwood paradigm

Using a numerical implementation of the Cowley and Lockwood (1992) model of flow excitation in the magnetosphere–ionosphere (MI) system, we show that both an expanding (on a _12-min timescale) and a quasiinstantaneous response in ionospheric convection to the onset of magnetopause reconnection can be accommodated by the Cowley–Lockwood conceptual framework. This model has a key feature of time dependence, necessarily considering the history of the coupled MI system. We show that a residual flow, driven by prior magnetopause reconnection, can produce a quasi-instantaneous global ionospheric convection response; perturbations from an equilibrium state may also be present from tail reconnection, which will superpose constructively to give a similar effect. On the other hand, when the MI system is relatively free of pre-existing flow, we can most clearly see the expanding nature of the response. As the open-closed field line boundary will frequently be in motion from such prior reconnection (both at the dayside magnetopause and in the cross-tail current sheet), it is expected that there will usually be some level of combined response to dayside reconnection.

Clouds, aerosols, and precipitation in the marine boundary layer: an ARM Mobile Facility Deployment

The Clouds, Aerosol, and Precipitation in the Marine Boundary Layer (CAP-MBL) deployment at Graciosa Island in the Azores generated a 21-month (April 2009–December 2010) comprehensive dataset documenting clouds, aerosols, and precipitation using the Atmospheric Radiation Measurement Program (ARM) Mobile Facility (AMF). The scientific aim of the deployment is to gain improved understanding of the interactions of clouds, aerosols, and precipitation in the marine boundary layer. Graciosa Island straddles the boundary between the subtropics and midlatitudes in the northeast Atlantic Ocean and consequently experiences a great diversity of meteorological and cloudiness conditions. Low clouds are the dominant cloud type, with stratocumulus and cumulus occurring regularly. Approximately half of all clouds contained precipitation detectable as radar echoes below the cloud base. Radar and satellite observations show that clouds with tops from 1 to 11 km contribute more or less equally to surface-measured precipitation at Graciosa. A wide range of aerosol conditions was sampled during the deployment consistent with the diversity of sources as indicated by back-trajectory analysis. Preliminary findings suggest important two-way interactions between aerosols and clouds at Graciosa, with aerosols affecting light precipitation and cloud radiative properties while being controlled in part by precipitation scavenging. The data from Graciosa are being compared with short-range forecasts made with a variety of models. A pilot analysis with two climate and two weather forecast models shows that they reproduce the observed time-varying vertical structure of lower-tropospheric cloud fairly well but the cloud-nucleating aerosol concentrations less well. The Graciosa site has been chosen to be a permanent fixed ARM site that became operational in October 2013.

Recurrence of particles in static and time varying oval billiards

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Effects of varying curvature and width on the electronic states of GaAs quantum rings

Stationary states of an electron in thin GaAs elliptical quantum rings are calculated within the effective-mass approximation. The width of the ring varies smoothly along the centerline, which is an ellipse. The solutions of the Schrödinger equation with Dirichlet boundary conditions are approximated by a product of longitudinal and transversal wave functions. The ground-state probability density shows peaks: (i) where the curvature is larger in a constant-with ring, and (ii) in thicker parts of a circular ring. For rings of typical dimensions, it is shown that the effects of a varying width may be stronger than those of the varying curvature. Also, a width profile which compensates the main localization effects of the varying curvature is obtained.

A geometric approach to cosmological boundary conditions

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)