A method for estimating the orientation of a directional sound source from source directivity and multi-microphone recordings: principles and application

Taking into account directivity of real sound sources makes it possible to try solving an interesting and biologically relevant problem: estimating the orientation in three-dimensional space of a directional sound source. The source, of known directivity, produces a broadband signal (in the ultrasonic range, in this application) that is recorded by microphones whose position with respect to source is known. An analytical method to process the recorded signals and estimate source orientation is developed in this paper. Experiments testing method performance in estimating source orientation were performed both in a laboratory environment with a Polaroid transducer as source and in a flight room with a Myotis daubentonii bat. In the first case, results showed the estimation method to be accurate and pointed out its limitations. The latter case is significant as an example biological application of the method for extracting behavioral features from bats; results are compared with alternative calculations based on microphone root-mean-square (rms)-pressure values.     

Continuous dependence estimates for viscosity solutions of integro-PDEs

We present a general framework for deriving continuous dependence estimates for, possibly polynomially growing, viscosity solutions of fully nonlinear degenerate parabolic integro-PDEs. We use this framework to provide explicit estimates for the continuous dependence on the coefficients and the “Lévy measure” in the Bellman/Isaacs integro-PDEs arising in stochastic control/differential games. Moreover, these explicit estimates are used to prove regularity results and rates of convergence for some singular perturbation problems. Finally, we illustrate our results on some integro-PDEs arising when attempting to price European/American options in an incomplete stock market driven by a geometric Lévy process. Many of the results obtained herein are new even in the convex case where stochastic control theory provides an alternative to our pure PDE methods.     

Least-squares spectral method for solving advective population balance problems

The combined CFD-PBE (population balance models) are computationally intensive requiring efficient numerical methods for solving practical problems. In this paper, a high order method is presented based on the least-squares method (LSM) for the solution of a spatial-dependent population balance equation which includes advective processes. Numerical experiments are performed in order to study the behavior of the proposed method for one-dimensional cases using model problems with analytical solutions.     

Secondary-ion mass spectrometry as a quantitative microanalytical technique

Recent progress in ion microscopy and ion-microprobe analysis is reviewed with special emphasis on the potential of the method for the determination of impurities in locally restricted areas of the sample. Emphasis is placed on the calibration of the depth scale and on the potential of the method for three-dimensional analysis.     

On distributional solutions of local and nonlocal problems of porous medium type

We present a theory of well-posedness and a priori estimates for bounded distributional (or very weak) solutions of

(0.1)${?}_{t}u?{\mathfrak{L}}^{\sigma ,\mu }[\phi (u)]=g(x,t)\text{in}{\mathbb{R}}^N\times (0,T),$

where φ is merely continuous and nondecreasing, and ${\mathfrak{L}}^{\sigma ,\mu }$ is the generator of a general symmetric Lévy process. This means that ${\mathfrak{L}}^{\sigma ,\mu }$ can have both local and nonlocal parts like, e.g., ${\mathfrak{L}}^{\sigma ,\mu }=\mathrm{\Delta }?{(?\mathrm{\Delta })}^{\frac{1}{2}}$. New uniqueness results for bounded distributional solutions to this problem and the corresponding elliptic equation are presented and proven. A key role is played by a new Liouville type result for ${\mathfrak{L}}^{\sigma ,\mu }$. Existence and a priori estimates are deduced from a numerical approximation, and energy-type estimates are also obtained.     

Monitoring of tropospheric ozone in the ambient air with passive samplers

Two sampling campaigns in suburban places in the north zone of Santa Clara city, Cuba, have been carried out on a weekly base with the use of Radiello passive diffusion tubes in order to monitor the tropospheric ozone (O₃) levels in 2010. The first campaign was scheduled from February to April (cold season) and the second one in August and October (warm season), both of them at two sampling sites, i.e., Farm and School of Art Instructors. After aqueous extraction, the samples were analyzed by UV–VIS spectrophotometry.A seasonal trend was observed with the maximum O₃ concentrations in the cold season and the minimum levels in the warm season. Samples collected during the cold season showed the highest O₃ levels. Higher levels were reached at the Farm site with average values of about 58 ± 12 μg/m³, which exceeded the limit of the Cuban Standard 99:1999. In the warm season, the O₃ concentrations were similar for both sites, but lower than those observed in the cold season. The overall, seasonal average value was found to be 24 μg/m³. Despite the higher weekly average temperatures in August, the O₃ concentrations during this month showed the lowest values of the whole sampling period, which finding is in agreement with that reported by the Meteorological Institute of Cuba.Mathematical models, based on the Cochrane-Orcutt algorithm, were fitted to the acquired data set to explain the change in the tropospheric ozone concentrations under various meteorological conditions during the two campaigns. The correlation coefficients for both the cold and the warm seasons demonstrated a strong correlation, i.e., 0.779 and 0.951, respectively. The high correlation of wind speed in the model from the first sampling campaign explains the sharp decrease in O₃ concentrations at the SAI sampling site from the sixth week of sampling.     

The discontinuous Galerkin method for fractional degenerate convection-diffusion equations

We propose and study discontinuous Galerkin methods for strongly degenerate convection-diffusion equations perturbed by a fractional diffusion (Lévy) operator. We prove various stability estimates along with convergence results toward properly defined (entropy) solutions of linear and nonlinear equations. Finally, the qualitative behavior of solutions of such equations are illustrated through numerical experiments.     

A Connection between Singular Stochastic Control and Optimal Stopping

We show that the value function of a singular stochastic control problem is equal to the integral of the value function of an associated optimal stopping problem. The connection is proved for a general class of diffusions using the method of viscosity solutions.