The inelastic hard dimer gas: a non-spherical model for granular matter

We study a two-dimensional gas of inelastic smooth hard dimers. Since the collisions between dimers are dissipative, being characterized by a coefficient of restitution $\alpha<1$, and no external driving force is present, the energy of the system decreases in time and no stationary state is achieved. However, the resulting non equilibrium state of the system displays several interesting properties in close analogy with systems of inelastic hard spheres, whose relaxational dynamics has been thoroughly explored. We generalise to inelastic systems a recently method introduced [G.Ciccotti and G.Kalibaeva, J. Stat. Phys. {\bf 115}, 701 (2004)] to study the dynamics of rigid elastic bodies made up of different spheres hold together by rigid bonds. Each dimer consists of two hard disks of diameter $d$, whose centers are separated by a fixed distance $a$. By describing the rigid bonds by means of holonomic constraints and deriving the appropriate collision rules between dimers, we reduce the dynamics to a set of equations which can be solved by means of event driven simulation. After deriving the algorithm we study the decay of the total kinetic energy, and of the ratio between the rotational and the translational kinetic energy of inelastic dimers. We show numerically that the celebrated Haff's homogeneous cooling law $t^{-2}$, describing how the kinetic energy of an inelastic hard sphere system with constant coefficient of restitution decreases in time, holds even in the case of these non spherical particles. We fully characterize this homogeneous decay process in terms of appropriate decay constants and confirm numerically the scaling behavior of the velocity distributions.Comment: 21 pages, 6 figures and 2 tables, submitted to JC

Microstructure of metal - metalloid and metal - metal alloys on data of molecular-dynamic experiment

The microstructure establishment of amorphous alloys with various concentrations of components is the aim of the paper as well as the establishment of the influence character of the second component type, the atomic environment of microclasters and single disturbances on the microstructure. As a result the microstructure of metal - metalloid and metal - metal amorphous alloys with various concentrations of components has been investigated. Some features of the microstructure in dependence on the second component type have been discovered. The influence of single disturbances on the microstructure has been investigated. The complex of molecular dynamics programs and programs, applied for the structure analysis has been improvedAvailable from VNTIC / VNTIC - Scientific & Technical Information Centre of RussiaSIGLERURussian Federatio

Deterministic and stochastic algorithms for mechanical systems under constraints

We discuss the general philosophy underlying the statistical behaviour, the dynamical evolution and the integration of the equations of motion for systems subject to constraints. We also show how all this is related to the treatment of general non-Hamiltonian systems. Then we introduce a family of algorithms derivable from approximations of the evolution operator obtained via the Trotter formula. Generalizing the treatment to time-dependent force fields we also show how one can adapt those algorithms to ordinary stochastic differential equations

Simulation of a diatomic liquid using hard spheres model

In this work we demonstrate the possibility of including constraints in hard systems, using the simple case of a dimer of hard spheres, where the analytical solution exists. We make a detailed description of the model and show that the system's dynamics can be solved in a rigorous way. We also illustrate our theoretical results with some numerical calculations on a simple diatomic liquid

Molecular dynamics of complex systems: non-Hamiltonian, constrained, quantum-classical

Lecture notes in physic

Fast simulation of polymer chains

We propose an algorithm for the fast and efficient simulation of polymers represented by chains of hard spheres. The particles are linked by holonomic bond constraints. While the motion of the polymers is free (i.e., no collisions occur) the equations of motion can be easily integrated using a collocation-based partitioned Gauss-Runge-Kutta method. The method is reversible, symplectic, and preserves energy. Moreover the numerical scheme allows the integration using much longer time steps than any explicit integrator such as the popular Verlet method. If polymers collide the point of impact can be determined to arbitrary precision by simple nested intervals. Once the collision point is known the impulsive contribution can be computed analytically. We illustrate our approach by means of a suitable numerical example