An extended Fitzhugh-Nagumo model including linear viscoelasticity is derived in general and studied in detail in the one-dimensional case. The equations of the theory are numerically integrated in two situations: (i) a free insulated fiber activated by an initial Gaussian distribution of action potential, and (ii) clamped fiber stimulated by two counter phased currents, located at both ends of the space domain. The former case accounts for a description of the physiological experiments on biological samples in which a fiber contracts because of the spread of action potential, and then relaxes. The latter case, instead, is introduced to extend recent models discussing a strongly electrically stimulated fiber so that nodal structures associated on quasistanding waves are produced. Results are qualitatively in agreement with physiological behavior of cardiac fibers. Modifications induced on the action potential of a standard Fitzhugh-Nagumo model appear to be very small even when strong external electric stimulations are activated. On the other hand, elastic backreaction is evident in the model.

The coordinate transformation which maps the Kerr metric written in standard Boyer-Lindquist coordinates to its corresponding form adapted to the natural local coordinates of an observer at rest at a fixed position in the equatorial plane, i.e., Fermi coordinates for the neighborhood of a static observer world line, is derived and discussed in a way which extends to any uniformly circularly orbiting observer there.

We discuss geodesic motion in the vacuum C metric using Bondi-like spherical coordinates, with special attention to the role played by the \lq\lq equatorial plane." We show that the spatial trajectory of photons on such a hypersurface is formally the same of photons on the equatorial plane of the Schwarzschild spacetime, apart for an energy shift involving the spacetime acceleration parameter. Furthermore, we show that photons starting their motion from this hypersurface with vanishing component of the momentum along $\theta$, remain confined on it, differently from the case of massive particles. This effect is shown to have a counterpart also in the massless limit of the C metric, i.e. in Minkowski spacetime. Finally, we give the explict map between Bondi-like spherical coordinates and Fermi coordinates (up to the second order) for the world line of an observer at rest at a fixed spatial point of the equatorial plane of the C metric, a result which may be useful to estimate both the mass and the acceleration parameter of accelerated sources.

A kinetic Lattice-Boltzmann scheme for advection-diffusion is presented. The scheme is based on a matrix formulation of the lattice Boltzmann method which permits to handle non-isotropic diffusion-advection problems. In addition, by adjusting the kinetic eigenvectors defining the collision matrix to the local value of the flow velocity, the scheme is also shown to preserve isotropy under genuinely two-dimensional flow.

We present a mathematical formulation of kinetic boundary conditions for lattice Boltzmann schemes in terms of reflection, slip, and accommodation coefficients. It is analytically and numerically shown that, in the presence of a nonzero slip coefficient, the lattice Boltzmann develops a physical slip flow component at the wall. Moreover, it is shown that the slip coefficient can be tuned in such a way to recover quantitative agreement with the analytical and experimental results up to second order in the Knudsen number.

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.