A modified lattice Boltzmann model with a stochastic relaxation mechanism mimicking "virtual" collisions between free-streaming particles and solid walls is introduced. This modified scheme permits to compute plane channel flows in satisfactory agreement with analytical results over a broad spectrum of Knudsen numbers, ranging from the hydrodynamic regime, all the way to quasi-free flow regimes up to Kn \sim 30.

This paper describes a physical-based methodology for the retrieval of geophysical parameters (temperature, water vapor and ozone) from highly resolved infrared radiance, and presents the algorithm which implements the procedure. The algorithm we have implemented is mostly intended for the Infrared Atmospheric Sounding Interferometer which is planned to be flown on the first European Meteorological Operational Satellite (Metop/1) in 2006. Nevertheless, with minor modifications, the code is well suited for any nadir viewing satellite and airborne infrared sensor with a sampling rate in the range of 0.1–2 cm^(-1). Basically, the implementation of the inverse scheme follows Rodgers’ Statistical Regularization method. However, an additional regularization parameter is introduced in the inverse scheme which gains to the algorithm the capability of improving the retrieval accuracy and to constraint the step size of Newton updates in such a way to lead iterates toward the feasible region of the inverse solution. Although, the paper mostly focuses on documenting and discussing the mathematical details of the inverse method, retrieval exercises have been provided, which exemplify the use and potential performance of the method. These retrieval exercises have been performed for the Infrared Atmospheric Sounding Interferometer. In addition, examples of application to real observations have been discussed based on the Interferometric Monitoring Greenhouse (IMG) gases Fourier Transform Spectrometer which has flown on the Japanese Advanced Earth Observation Satellite.

The Ra and Pr number scaling of the Nusselt number Nu, the Reynolds number Re, the temperature fluctuations, and the kinetic and thermal dissipation rates is studied for (numerical) homogeneous Rayleigh–Bénard turbulence, i.e., Rayleigh–Bénard turbulence with periodic boundary conditions in all directions and a volume forcing of the temperature field by a mean gradient. This system serves as model system for the bulk of Rayleigh–Bénard flow and therefore as model for the so-called "ultimate regime of thermal convection." With respect to the Ra dependence of Nu and Re we confirm our earlier results [D. Lohse and F. Toschi, "The ultimate state of thermal convection," Phys. Rev. Lett. 90, 034502 (2003)] which are consistent with the Kraichnan theory [R. H. Kraichnan, "Turbulent thermal convection at arbitrary Prandtl number," Phys. Fluids 5, 1374 (1962)] and the Grossmann–Lohse (GL) theory [S. Grossmann and D. Lohse, "Scaling in thermal convection: A unifying view," J. Fluid Mech. 407, 27 (2000); "Thermal convection for large Prandtl number," Phys. Rev. Lett. 86, 3316 (2001); "Prandtl and Rayleigh number dependence of the Reynolds number in turbulent thermal convection," Phys. Rev. E 66, 016305 (2002); "Fluctuations in turbulent Rayleigh–Bénard convection: The role of plumes," Phys. Fluids 16, 4462 (2004)], which both predict Nu~Ra1/2 and Re~Ra1/2. However the Pr dependence within these two theories is different. Here we show that the numerical data are consistent with the GL theory Nu~Pr1/2, Re~Pr–1/2. For the thermal and kinetic dissipation rates we find epsilontheta/(kappaDelta2L–2)~(Re Pr)0.87 and epsilonu/(nu3L–4)~Re2.77, both near (but not fully consistent) the bulk dominated behavior, whereas the temperature fluctuations do not depend on Ra and Pr. Finally, the dynamics of the heat transport is studied and put into the context of a recent theoretical finding by Doering et al. ["Comment on ultimate state of thermal convection" (private communication)].

The achievement of Bose-Einstein condensation in ultracold vapors of alkali atoms has accelerated the study of dilute atomic gases in condensed quantum states. This review introduces some key issues in the area.

The statistical geometry of dispersing Lagrangian clusters of four particles (tetrahedra) is studied by means of high-resolution direct numerical simulations of three-dimensional homogeneous isotropic turbulence. We give evidence of a self-similar regime of shape dynamics characterized by almost two-dimensional, strongly elongated geometries. The analysis of four-point velocity-difference statistics and orientation shows that inertial-range eddies typically generate a straining field with a strong extensional component aligned with the elongation direction and weak extensional/compressional components in the orthogonal plane.

We prove global existence and uniqueness of smooth solutions to a nonlinear system of parabolic equations, which arises to describe the evolution of the chemical aggression due to the action of sulphur dioxide on calcium carbonate stones. This system is not strongly parabolic and only some energy estimates are available. Nevertheless, global (in time) results are proven using a weak continuation principle for the local solutions.

We consider a hybrid control system and general optimal control problems for this system. We suppose that the switching strategy imposes restrictions on control sets and we provide necessary conditions for an optimal hybrid trajectory, stating a Hybrid Necessary Principle (HNP). Our result generalizes various necessary principles available in the literature.

Starting from the classical fluidodynamic models for traffic flow, we extend the theory to general networks. The problem at junction is underdetermined and is solved by two rules: (A) Incoming traffic distributes to outgoing roads according to fixed coefficients; (B) Drivers optimize the trough flow. Existence of solutions is provided by a wave front tracking algorithm.

Using a recent model for traffic flow on networks, we address a specific traffic regulation problem. Given a crossing with some expected traffic, is it preferable to construct a traffic circle or a light? We study the two solutions in terms of flow control and compare the performances.

We set a control model to study the biomechanical problem of swing pumping. After describing the sytem, we provide the solution to some optimal control problems.

We consider the problem of two bodies rolling one on each other. A quantization in introduced by means of the selection of base points and paths on one of the body. The reachability and path planning problem is considered.

In this paper we are concerned with the pointwise behaviour of functions in certain classes of weakly differentiable functions. We focus on first order Orlicz-Sobolev spaces and we establish optimal theorems of Rademacher type and of approximate differentiability type in this setting.

To produce grids conforming to the boundary of a physical domain with boundary orthogonality features, algebraic methods like transfinite interpolating schemes can be profitably used. Moreover, the coupling of Hermite-type (also interpolating prescribed boundary direction) schemes with elliptic methods turns out to be effective to overcome the drawback of both algebraic and elliptic strategies. Thus, in this paper, we present an algorithm for the generation of boundaryorthogonal grids which couples a mixed Hermite algebraic method with a boundaryorthogonalelliptic scheme. Numerical tests on domains with classical geometries show satisfactory performances of the algorithm and coupling effectiveness in achieving grid boundary orthogonality and smoothness.

We study the inverse problem of determining the position of the moving C-terminal domain in a metalloprotein from measurements of its mean paramagnetic tensor $\bar\chi$. The latter can be represented as a finite sum involving the corresponding magnetic susceptibility tensor $\chi$ and a finite number of rotations. We obtain an optimal estimate for the maximum probability that the C-terminal domain can assume a given orientation, and we show that only three rotations are required in the representation of $\bar\chi$, and that in general two are not enough.

The paper gives a contribution of wavelet aspects to classical algebraic polynomial approximation theory. Algebraic polynomial interpolating scaling functions and wavelets are constructed by using the interpolating properties of de la Vallée Poussin kernels w.r.t. the four kinds of Chebyshev weights. For the decomposition and reconstruction of a given function the structure of the involved matrices is studied in order to reduce the computational effort by means of fast cosine and sine transforms.