We present a numerical study of mixing and reaction efficiency in closed domains. In particular, we focus our attention on laminar flows. In the case of inert transport the mixing properties of the flows strongly depend on the details of the Lagrangian transport. We also study the reaction efficiency. Starting with a little spot of product, we compute the time needed to complete the reaction in the container. We find that the reaction efficiency is not strictly related to the mixing properties of the flow. In particular, reaction acts as a "dynamical regulator."

We introduce a new class of models for aggregate or clustered point patterns, which encompasses and extends most of the classical models. We derive summary statistics and simulation procedures.

The inverse problem of constructing a symmetric Toeplitz matrix with prescribed eigenvalues has been a challenge both theoretically and computationally in the literature. It is now known in theory that symmetric Toeplitz matrices can have arbitrary real spectra. This paper addresses a similar problem--can the three largest eigenvalues of symmetric pentadiagonal Toeplitz matrices be arbitrary? Given three real numbers ? ? ?, this paper finds that the ratio ? = ?-? ?-? , including infinity if ? = ?, determines whether there is a symmetric pentadiagonal Toeplitz matrix with ?, ? and ? as its three largest eigenvalues. It is shown that such a matrix of size n × n does not exist if n is even and ? is too large or if n is odd and ? is too close to 1. When such a matrix does exist, a numerical method is proposed for the construction.

The effect of a small gravitomagnetic monopole on (accelerated) circular orbits in the equatorial plane of the Taub-NUT spacetime is compared to the corresponding (accelerated) orbits pushed slightly off the equatorial plane in the absense of the monopole (Schwarzschild spacetime).

The long standing difficulty in General Relativity of classifying the dynamics of cosmological models, e.g.\ as chaotic, is directly related to the gauge freedom intrinsic to relativistic spacetime theories: in general the invariance under diffeomorphisms makes any analysis of dynamical evolution dependent from the particular choice of time slicing one uses. We show here that the speciality index, a scalar dimensionless curvature invariant that has been mainly used in numerical relativity as an indicator of the special or non-special Petrov type character of a spacetime, is a time-independent quantity (a pure number) at each Kasner step of the Belinski-Khalatnikov-Lifshitz (BKL) map approximating the Mixmaster cosmology. Thus the BKL dynamics can be characterized in terms of the speciality index, i.e. in terms of curvature invariants directly related to observables. Possible applications for the associated Mixmaster dynamics are discussed.

The motion of spinning test particles along circular orbits in static vacuum spacetimes belonging to the Weyl class is discussed. Spin alignment and coupling with background parameters in the case of superimposed Weyl fields, corresponding to a single Schwarzschild black hole and single Chazy-Curzon particle as well as to two Schwarzschild black holes and two Chazy-Curzon particles, are studied in detail for standard choices of supplementary conditions. Applications to the gravitomagnetic "clock effect'' are also discussed.

The construction of a radar coordinate system about the world line of an observer is discussed. Radar coordinates for a hyperbolic observer as well as a uniformly rotating observer are described in detail. The utility of the notion of radar distance and the admissibility of radar coordinates are investigated. Our results provide a critical assessment of the physical significance of radar coordinates.

The periastron position advance for geodesic motion in axially symmetric solutions of the Einstein field equations belonging to the Weyl class of vacuum solutions is investigated. Explicit examples corresponding to either static solutions (single Chazy-Curzon, Schwarzschild and a pair of them), or stationary solution (single rotating Chazy-Curzon and Kerr black hole) are discussed. The results are then applied to the case of S2-SgrA$^*$ binary system of which the periastron position advance will be soon measured with a great accuracy.

The motion of a spinning test particle given by the Mathisson-Papapetrou equations is studied on an exterior vacuum C metric background spacetime describing the accelerated motion of a spherically symmetric gravitational source. We consider circular orbits of the particle around the direction of acceleration of the source. The symmetries of this configuration lead to the reduction of the differential equations of motion to algebraic relations. The spin supplementary conditions as well as the coupling between the spin of the particle and the acceleration of the source are discussed.

The behavior of charged spinning test particles moving along circular orbits in the equatorial plane of the Reissner{Nordstrom space{time is studied in the framework of the Dixon Souriau model completed with standard choices of supplementary conditions. The gravitomagnetic "clock effect," i.e. the delay in the arrival times of two oppositely circulating particles as measured by a static observer, is derived and discussed in the cases in which the particles have equal/opposite charge and spin, the latter being directed along the z-axis.

We study the behavior of nonzero rest mass spinning test particles moving along circular orbits in the Schwarzschild spacetime in the case in which the components of the spin tensor are allowed to vary along the orbit, generalizing some previous work.

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.