Given any wave speed c (independently of its sign!), we construct a traveling wave solution of the harmonic heat flow with values in the unit sphere and defined in an infinitely long cylinder. The wave connects two locally stable and axially symmetric steady states at + and - infinity, and has a singular point on the cylinder axis. In view of the bistable character of the potential, the result is surprising, and it is intimately related to the nonuniqueness of the harmonic map flow itself. The result is counter-intuitive if c has the "wrong sign", i.e. if the steady state with higher energy invades the cylinder. We show that for only one wave speed the traveling wave behaves locally, near its singular point, as a symmetric harmonic map.

Many real life problems can be represented by an ordered sequence of digital images. At a given pixel a specific time course is observed which is morphologically related to the time courses at neighbor pixels. Useful information can be usually extracted from a set of such observations if we are able to classify pixels in groups, according to some features of interest for the final user. Moreover parameters with a physical meaning can be extracted from the time courses. In a continuous setting we can formalize the problem by assuming to observe a noisy version of a positive real function defined on a bounded set T ×\Omega ‚ R×R2, parameterized by a vector of unknown functions defined on R2 with discontinuities along regular curves in \Omega which separate regions with different features. Suitable regularity conditions on the parameters are also assumed in order to take into account the physical constraints. The problem consists in estimating the parameter functions, segmenting \Omega in subsets with regular boundaries and assigning to each subset a label according to the values that the parameters assume on the subset. A global model is proposed which allows to address all of the above subproblems in the same framework. A variational approach is then adopted to compute the solution and an algorithm has been developed. Some numerical results obtained by using the proposed method to solve a dynamic Magnetic Resonance imaging problem are reported.

The Mixmaster dynamics is revisited in a new light as revealing a series of transitions in the complex scale invariant scalar invariant of the Weyl curvature tensor best represented by the speciality index S, which gives a 4-dimensional measure of the evolution of the spacetime independent of all the 3-dimensional gauge-dependent variables except the time used to parametrize it. Its graph versus time with typical spikes in its real and imaginary parts corresponding to curvature wall collisions serves as a sort of electrocardiogram of the Mixmaster universe, with each such spike pair arising from a single circuit or “pulse” around the origin in the complex plane. These pulses in the speciality index seem to invariantly characterize some of the so called spike solutions in inhomogeneous cosmology and should play an important role in the current investigations of inhomogeneous Mixmaster dynamics.

Implantation of drug eluting stents following percutaneous trans- luminal angioplasty has revealed a well established technique for treating occlusions caused by the atherosclerotic plaque. However, due to the risk of vascular re-occlusion, other alternative therapeutic strategies of drug delivery are currently being investigated. Polymeric endoluminal pave stenting is an emerging technology for preventing blood erosion and for optimizing drug release. The classical and novel methodologies are compared through a mathematical model able to predict the evolution of the drug concentration in a cross-section of the wall. Though limited to an idealized configuration, the present model is shown to catch most of the relevant aspects of the drug dynamics in a delivery system. Results of numerical simulations shows that a bi-layer gel paved stenting guarantees a uniform drug elution and a prolonged perfusion of the tissues, and remains a promising and effective technique in drug delivery.

General relativity considers Dixon’s theory as the standard theory to deal with the motion of extended bodies in a given gravitational background. We discuss here the features of the “reaction” of an extended body to the passage of a weak gravitational wave. We find that the body acquires a dipolar moment induced by its quadrupole structure. Furthermore, we derive the “world function” for the weak field limit of a gravitational wave background and use it to estimate the deviation between geodesics and the world lines of structured bodies. Measuring such deviations, due to the existence of cumulative effects, should be favorite with respect to measuring the amplitude of the gravitational wave itself.

Vaccine research is a combinatorial science requiring computational analysis of vaccine components, formulations and optimization. We have developed a framework that combines computational tools for the study of immune function and vaccine development. This framework, named ImmunoGrid combines conceptual models of the immune system, models of antigen processing and presentation, system-level models of the immune system, Grid computing, and database technology to facilitate discovery, formulation and optimization of vaccines. ImmunoGrid modules share common conceptual models and ontologies. The ImmunoGrid portal offers access to educational simulators where previously defined cases can be displayed, and to research simulators that allow the development of new, or tuning of existing, computational models. The portal is accessible at http://www.w3.org.

A mesoscopic multicomponent lattice Boltzmann model with short-range repulsion between different species and short (midranged) attractive (repulsive) interactions between like molecules is introduced. The interplay between these composite interactions gives rise to a rich configurational dynamics of the density field, exhibiting many features of disordered liquid dispersions (microemulsions) and soft-glassy materials, such as long-time relaxation due to caging effects, anomalous enhanced viscosity, aging effects under moderate shear and flow above a critical shear rate.