We consider a cell growth model involving a nonlinear system of partial differential equations which describes the growth of two types of cell populations with contact inhibition. Numerical experiments show that there is a parameter regime where, for a large class of initial data, the large time behaviour of the solutions is described by a segregated travelling wave solution with positive wave speed c.

We consider an initial-boundary value problem for a degenerate pseudoparabolic regularization of a nonlinear forward-backward-forward parabolic equation, with a bounded nonlinearity which is increasing at infinity. We prove existence of suitably defined nonnegative solutions of the problem in a space of Radon measures. Solutions satisfy several monotonicity and regularization properties; in particular, their singular part is nonincreasing and may disappear in finite time.

Graphics processing units (GPU) are currently used as a cost-effective platform forcomputer simulations and big-data processing. Large scale applications require thatmultiple GPUs work together but the efficiency obtained with cluster of GPUs is, at times,sub-optimal because the GPU features are not exploited at their best. We describe how itis possible to achieve an excellent efficiency for applications in statistical mechanics,particle dynamics and networks analysis by using suitable memory access patterns andmechanisms like CUDA streams, profiling tools, etc.

We correct an error in the proof of Theorem 4.1 of the paper "Boundedness of solutions to anisotropic variational problems" [Comm. Part. Diff. Eq. 36 (2011); 470-486].

Spatial and velocity statistics of heavy point-like particles in incompressible, homogeneous, and isotropic three-dimensional turbulence is studied by means of direct numerical simulations at two values of the Taylor-scale Reynolds number Re-lambda similar to 200 and Re-lambda similar to 400, corresponding to resolutions of 512(3) and 2048(3) grid points, respectively. Particles Stokes number values range from St approximate to 0.2 to 70.

In [Comm. Appl. Math. Comput. Sci., 4 (2009), pp. 153-175], Barenblatt presents a model for partial laminarization and acceleration of shear flows by the presence of suspended particles of different sizes, and provides a formal asymptotic analysis of the resulting velocity equation. In the present paper we revisit the model. In particular we allow for a continuum of particle sizes, rewrite the velocity equation in a form which involves the Laplace transform of a given function or measure, and provide several rigorous asymptotic expansions for the velocity.

We present a highly optimized implementation of a Monte Carlo (MC) simulator for the three-dimensional Ising spin-glass model with bimodal disorder, i.e.; the 3D Edwards-Anderson model running on CUDA enabled GPUs. Multi-GPU systems exchange data by means of the Message Passing Interface (MPI). The chosen MC dynamics is the classic Metropolis one, which is purely dissipative, since the aim was the study of the critical off-equilibrium relaxation of the system.

Magnetoencephalopgraphy (MEG) is a non-invasive functional imaging modality for mapping cerebral electromagnetic activity from measurements of the weak magnetic field that it generates. It is well known that the MEG inverse problem, i.e. the problem of identifying electric currents from the induced magnetic fields, is a severely underdetermined problem and, without complementary prior information, no unique solution can be found.

We examine spatially explicit models described by reaction-diffusion partial differential equations for the study of predator-prey population dynamics. The numerical methods we propose are based on the coupling of a finite difference/element spatial discretization and a suitable partitioned Runge-Kutta scheme for the approximation in time. The RK scheme here implemented uses an implicit scheme for the stiff diffusive term and a partitioned RK symplectic scheme for the reaction term (IMSP schemes).

A sharp integrability condition on the right-hand side of the p-Laplace system for all its solutions to be continuous is exhibited. Their uniform continuity is also analyzed and estimates for their modulus of continuity are provided. The relevant estimates are shown to be optimal as the right-hand side ranges in classes of rearrangement-invariant spaces, such as Lebesgue, Lorentz, Lorentz-Zygmund, and Marcinkiewicz spaces, as well as some customary Orlicz spaces.