Approximation and support theorem for a wave equation in two space dimensions

We prove a characterization of the support of the law of the solution for a stochastic wave equation with two-dimensional space variable, driven by a noise white in time and correlated in space. The result is a consequence of an approximation theorem, in the convergence of probability, for equations obtained by smoothing the random noise. For some particular classes of coefficients, approximation in the Lp-norm for p¿1 is also proved.

Photonic characteristics of Langmuir-Blodgett self-assembled monolayers of colloidal silica particles

Monodispersed colloidal crystals based on silica sub-micrometric particles were synthesized using the Stöber-Fink-Bohn process. The control of nucleation and coalescence result in improved characteristics such as high sphericity and very low size dispersion. The resulting silica particles show characteristics suitable for self-assembling across large areas of closely-packed 2D crystal monolayers by an accurate Langmuir-Blodgett deposition process on glass, fused silica and silicon substrates. Due to their special optical properties, colloidal films have potential applications in fields including photonics, electronics, electro-optics, medicine (detectors and sensors), membrane filters and surface devices. The deposited monolayers of silica particles were characterized by means of FESEM, AFM and optical transmittance measurements in order to analyze their specific properties and characteristics. We propose a theoretical calculation for the photonic band gaps in 2D systems using an extrapolation of the photonic behavior of the crystal from 3D to 2D. In this work we show that the methodology used and the conditions in self-assembly processes are decisive for producing high-quality two-dimensional colloidal crystals by the Langmuir-Blodgett technique.

Dilaton quantum cosmology in two dimensions

We consider a renormalizable two-dimensional model of dilaton gravity coupled to a set of conformal fields as a toy model for quantum cosmology. We discuss the cosmological solutions of the model and study the effect of including the back reaction due to quantum corrections. As a result, when the matter density is below some threshold new singularities form in a weak-coupling region, which suggests that they will not be removed in the full quantum theory. We also solve the Wheeler-DeWitt equation. Depending on the quantum state of the Universe, the singularities may appear in a quantum region where the wave function is not oscillatory, i.e., when there is not a well-defined notion of classical spacetime.

Supergravity models of (3+1)-dimensional QCD

The most general black M5-brane solution of eleven-dimensional supergravity (with a flat R4 spacetime in the brane and a regular horizon) is characterized by charge, mass and two angular momenta. We use this metric to construct general dual models of large-N QCD (at strong coupling) that depend on two free parameters. The mass spectrum of scalar particles is determined analytically (in the WKB approximation) and numerically in the whole two-dimensional parameter space. We compare the mass spectrum with analogous results from lattice calculations, and find that the supergravity predictions are close to the lattice results everywhere on the two dimensional parameter space except along a special line. We also examine the mass spectrum of the supergravity Kaluza-Klein (KK) modes and find that the KK modes along the compact D-brane coordinate decouple from the spectrum for large angular momenta. There are however KK modes charged under a U(1)×U(1) global symmetry which do not decouple anywhere on the parameter space. General formulas for the string tension and action are also given.

Energy-momentum tensor for scalar fields coupled to the dilaton in two dimensions

We clarify some issues related to the evaluation of the mean value of the energy-momentum tensor for quantum scalar fields coupled to the dilaton field in two-dimensional gravity. Because of this coupling, the energy-momentum tensor for matter is not conserved and therefore it is not determined by the trace anomaly. We discuss different approximations for the calculation of the energy-momentum tensor and show how to obtain the correct amount of Hawking radiation. We also compute cosmological particle creation and quantum corrections to the Newtonian potential.

Horizontal Grid Size Selection and its Influence on Mesoscale Model Simulations

The use of two-dimensional spectral analysis applied to terrain heights in order to determine characteristic terrain spatial scales and its subsequent use for the objective definition of an adequate grid size required to resolve terrain forcing are presented in this paper. In order to illustrate the influence of grid size, atmospheric flow in a complex terrain area of the Spanish east coast is simulated by the Regional Atmospheric Modeling System (RAMS) mesoscale numerical model using different horizontal grid resolutions. In this area, a grid size of 2 km is required to account for 95% of terrain variance. Comparison among results of the different simulations shows that, although the main wind behavior does not change dramatically, some small-scale features appear when using a resolution of 2 km or finer. Horizontal flow pattern differences are significant both in the nighttime, when terrain forcing is more relevant, and in the daytime, when thermal forcing is dominant. Vertical structures also are investigated, and results show that vertical advection is influenced highly by the horizontal grid size during the daytime period. The turbulent kinetic energy and potential temperature vertical cross sections show substantial differences in the structure of the planetary boundary layer for each model configuration

Cardiac disease in systemic lupus erythematosus: prospective study of 70 patients.

A prospective two dimensional and Doppler echocardiographic study of 70 consecutive patients with systemic lupus erythematosus (SLE) and 40 controls was carried out. Forty patients (57%) were found to have echocardiographic disturbance. Valvular abnormalities were detected in 31 patients (44%) and in only two controls (5%). Mitral valve abnormalities were the most common findings (23/70 (33%)) with mild or moderate regurgitation the most frequent lesion (16% and 9% respectively). Three patients (4%) had a morphological echocardiographic pattern suggestive of non-infective verrucous vegetations affecting the mitral valve. No patient had haemodynamically significant clinical valve disease. Pericardial effusion was identified in 19 patients (27%), of whom 14 had mild and clinically silent disease. Myocardial abnormalities were found in 14 patients (20%), but clinical features of myocardial dysfunction were present in only one. Patients with antiphospholipid antibodies were found to have an increased prevalence of endocardial lesions, mainly valvular regurgitation. It is concluded that the inclusion of echocardiography in a study protocol of patients with SLE can identify an important subset of patients with cardiac abnormalities, many of which are clinically silent. In addition, the association of antiphospholipid antibodies with endocardial lesions suggests that these antibodies may have a prominent role in the pathogenetic mechanisms of heart valve disease in SLE.

Cardiac disease in systemic lupus erythematosus. Prospective study of 70 patients.

A prospective two dimensional and Doppler echocardiographic study of 70 consecutive patients with systemic lupus erythematosus (SLE) and 40 controls was carried out. Forty patients (57%) were found to have echocardiographic disturbance. Valvular abnormalities were detected in 31 patients (44%) and in only two controls (5%). Mitral valve abnormalities were the most common findings (23/70 (33%)) with mild or moderate regurgitation the most frequent lesion (16% and 9% respectively). Three patients (4%) had a morphological echocardiographic pattern suggestive of non-infective verrucous vegetations affecting the mitral valve. No patient had haemodynamically significant clinical valve disease. Pericardial effusion was identified in 19 patients (27%), of whom 14 had mild and clinically silent disease. Myocardial abnormalities were found in 14 patients (20%), but clinical features of myocardial dysfunction were present in only one. Patients with antiphospholipid antibodies were found to have an increased prevalence of endocardial lesions, mainly valvular regurgitation. It is concluded that the inclusion of echocardiography in a study protocol of patients with SLE can identify an important subset of patients with cardiac abnormalities, many of which are clinically silent. In addition, the association of antiphospholipid antibodies with endocardial lesions suggests that these antibodies may have a prominent role in the pathogenetic mechanisms of heart valve disease in SLE.