Motivated by regulartiry questions for harmonic map flow, blow up phenomena for solutions of a singular parabolic pde is studied.

A method is proposed to identify solutions of the thin-film equations with non-zero contact angle

We prove existence of solutions of a new free boundary problem described by a system of degenerate parabolic equations. The problem arises in petroleum engineering and concerns fluid flows in diatomite rocks. The unknown functions represent the pressure of the fluid and a damage parameter of the porous rock. These quantities are not necessarily continuous on the free boundary, which considerably complicates the mathematical analysis.

We construct a model of traffic flow with sources and destinations on a road s network. The model is based on a conservation law for the density of traffic and on semilinearequations for traffic-type functions, i. e. functions describing paths for cars.

In the application of Pad\'{e} methods to signal processing a basic problem is to take into account the effect of measurement noise on the computed approximants. Qualitative deterministic noise models have been proposed which are consistent with experimental results. In this paper the Pad\'{e} approximants to the $Z$-transform of a complex Gaussian discrete white noise process are considered. Properties of the condensed density of the Pad\'{e} poles such as circular symmetry, asymptotic concentration on the unit circle and independence on the noise variance are proved. An analytic model of the condensed density of the Pad\'{e} poles for all orders of the approximants is also computed. Some Montecarlo simulations are provided.

We provide sample path large deviation principles for Poisson shot noise processes, and applicatons in queueing theory

We consider risk processes with delay in a Markovian environment and study the asymptotic behavior of finite and infinite horizon ruin probabilities

We propose a stochastic algorithm for solving NP-hard combinatorial optimization problems and study its convergence

In this article an accurate and efficient technique for tissue typing is presented. The proposed technique is based on Canonical Correlation Analysis, a statistical method able to simultaneously exploit the spectral and spatial information characterizing the Magnetic Resonance Spectroscopic Imaging (MRSI) data. Recently, Canonical Correlation Analysis has been successfully applied to other types of biomedical data, such as functional MRI data. Here, Canonical Correlation Analysis is adapted for MRSI data processing in order to retrieve in an accurate and efficient way the possible tissue types that characterize the organ under investigation. The potential and limitations of the new technique have been investigated by using simulated as well as in vivo prostate MRSI data, and extensive studies demonstrate a high accuracy, robustness, and efficiency. Moreover, the performance of Canonical Correlation Analysis has been compared to that of ordinary correlation analysis. The test results show that Canonical Correlation Analysis performs best in terms of accuracy and robustness

There is a growing need for statistical methods that generate an ensemble of plausible realizations of a hierarchical process from a single run or experiment. The main challenge is how to construct such an ensemble in a manner that preserves the internal dynamics (e.g. intermittency) and temporal persistency of the hierarchical process. A popular hierarchical process often used as a case study in such problems is atmospheric turbulent flow. Analogies to turbulence are often called upon when information flow from large to small scales, non Gaussian statistics, and intermittency are inherent attributes of the process under consideration. These attributes are key defining syndromes of the turbulent cascade thereby making turbulence time series ideal for testing such ensemble generation schemes. In this study, we propose a wavelet based resampling scheme (WB) and compare it to the traditional Fourier based phase randomization bootstrap (FB) approach within the context of the turbulence energy cascade. The comparison between the two resampling methods and observed ensemble statistics constructed by clustering similar meteorological conditions demonstrate that the WB reproduces several features related to intermittency of the ensemble series when compared to $FB$. In particular, the WB exhibited an increase in wavelet energy activity and an increase in the wavelet flatness factor with increasing frequency consistent with the cluster of ensemble statistics. On the other hand, the $FB$ yielded no increase in such energy activity with scale and resulted in near Gaussian wavelet coefficients at all frequencies within the inertial subrange. The extension of WB to the multivariate case is also demonstrated via the conservation of co-spectra between longitudinal and vertical velocity time series. Because the resampling strategy proposed here is conducted in the wavelet domain, gap-infected and uneven sampled time series can be readily accommodated within the WB. Finally, recommendations about the filter and block sizes are discussed.

The statistical properties of fluid particles transported by a three-dimensional fully developed turbulent flow are investigated by means of high resolution direct numerical simulations. Single trajectory statistics are investigated in a time range spanning more than three decades, from less than a tenth of the Kolmogorov time scale, taueta, up to one large-eddy turnover time. Our analysis reveals the existence of relatively rare trapping events in vortex filaments which give rise to enhanced intermittency on Lagrangian observables up to 10taueta. Lagrangian velocity structure function attain scaling properties in agreement with the multifractal prediction only for time lags larger than those affected by trapping.

We introduce a mesoscopic three-dimensional lattice Boltzmann model which attempts to mimic the physical features associated with cage effects in dynamically heterogeneous fluids. To this purpose, we extend the standard lattice Boltzmann dynamics with self-consistent constraints based on the nonlocal density of the surrounding fluid. The resulting dynamics exhibits typical features of dynamic heterogeneous fluids, such as non-Gaussian density distributions and long-time relaxation. Because of its intrinsically parallel dynamics, and absence of statistical noise, the method is expected to compute significantly faster than molecular dynamics, Monte Carlo, and lattice glass models.

We report recent results from a high-resolution numerical study of fluid particles transported by a fully developed turbulent flow. Single-particle trajectories were followed for a time range spanning more than three decades, from less than a tenth of the Kolmogorov timescale up to one large-eddy turnover time. We present some results concerning acceleration statistics and the statistics of trapping by vortex filaments.

Estimating the solvent content in protein crystals is one of the first steps in a macromolecular structure determination. We apply a new statistical technique, the independent component analysis (ICA), to determine the volume fraction of the asymmetric unit of proteins occupied by the solvent. The results for several crystal forms are in good agreement with available ones and allow to validate the method. Its main advantage with respect to existing techniques is that it requires only the knowledge of crystallographic data of structure factors and no a priori information about protein.

We present a detailed investigation of the particle pair separation process in homogeneous isotropic turbulence. We use data from direct numerical simulations up to Taylor's Reynolds number 280 following the evolution of about two million passive tracers advected by the flow over a time span of about three decades. We present data for both the separation distance and the relative velocity statistics. Statistics are measured along the particle pair trajectories both as a function of time and as a function of their separation, i.e. at fixed scales. We compare and contrast both sets of statistics in order to gain an insight into the mechanisms governing the separation process. We find very high levels of intermittency in the early stages, that is, for travel times up to order ten Kolmogorov time scales. The fixed scale statistics allow us to quantify anomalous corrections to Richardson diffusion in the inertial range of scales for those pairs that separate rapidly. It also allows a quantitative analysis of intermittency corrections for the relative velocity statistics.

Grazie alle simulazioni con i supercalcolatori, si cominciano a scoprire i meccanismi microscopici che governano il moto collettivo dei fluidi