The dynamic behaviour of rigid blocks subjected to support excitation is represented by discontinuous differential equations with state jumps, which are not known in advance. In the numerical simulation of these systems, the jump times corresponding to the numerical trajectory do not coincide with the ones of the given problem. When multiple state jumps occur, this approximation may affect the accuracy of the solution and even cause an order reduction in the method. Focus here is on the stability and convergence properties of the numerical dynamic.

We present a new numerical model to simulate settling trajectories of discretized individual or a mixture of particles of different geometrical shapes in a quiescent fluid and their flow trajectories in a flowing fluid. Simulations unveiled diverse particle settling trajectories as a function of their geometrical shape and density. The effects of the surface concavity of a boomerang particle and aspect ratio of a rectangular particle on the periodicity and amplitude of oscillations in their settling trajectories were numerically captured.

We simulate the two-dimensional fluid flow around National Advisory Committee for Aeronautics (NACA) 0012 airfoil using a hybrid lattice Boltzmann method (HLBM), which combines the standard lattice Boltzmann method with an unstructured finite-volume formulation. The aim of the study is to assess the numerical performances and the robustness of the computational method. To this purpose, after providing a convergence study to estimate the overall accuracy of the method, we analyze the numerical solution for different values of the angle of attack at a Reynolds number equal to 10(3).

We present the most recent release of our parallel implementation of the BFS and BC algorithms for the study of large scale graphs. Although our reference platform is a high-end cluster of new generation NVIDIA GPUs and some of our optimizations are CUDA specific, most of our ideas can be applied to other platforms offering multiple levels of parallelism.

The paper concerns the uniform polynomial approximation of a function f, continuous on the unit Euclidean sphere of $R^3$ and known only at a finite number of points that are somehow uniformly distributed on the sphere. First, we focus on least squares polynomial approximation and prove that the related Lebesgue constants w.r.t. the uniform norm grow at the optimal rate. Then, we consider delayed arithmetic means of least squares polynomials whose degrees vary from n - m up to n + m, being m = ?n for any fixed parameter 0 < ? < 1.

The paper traces the early stages of Berni Alder's scientific accomplishments, focusing on his contributions to the development of Computational Methods for the study of Statistical Mechanics. Following attempts in the early 50s to implement Monte Carlo methods to study equilibrium properties of many-body systems, Alder developed in collaboration with Tom Wainwright the Molecular Dynamics approach as an alternative tool to Monte Carlo, allowing to extend simulation techniques to non-equilibrium properties.

Trajectory-based approaches to excited-state, nonadiabatic dynamics are promising simulation techniques to describe the response of complex molecular systems upon photo-excitation. They provide an approximate description of the coupled quantum dynamics of electrons and nuclei trying to access systems of growing complexity. The central question in the design of those approximations is a proper accounting of the coupling electron-nuclei and of the quantum features of the problem.

The time reversal invariance of classical dynamics is reconsidered in this paper with specific focus on its consequences for time correlation functions and associated properties such as transport coefficients. We show that, under fairly common assumptions on the interparticle potential, an isolated Hamiltonian system obeys more than one time reversal symmetry and that this entails non trivial consequences. Under an isotropic and homogeneous potential, in particular, eight valid time reversal operations exist.

A dynamical system submitted to holonomic constraints is Hamiltonian only if considered in the reduced phase space of its generalized coordinates and momenta, which need to be defined ad hoc in each particular case. However, specially in molecular simulations, where the number of degrees of freedom is exceedingly high, the representation in generalized coordinates is completely unsuitable, although conceptually unavoidable, to provide a rigorous description of its evolution and statistical properties.