Model for Dissipative Highly Nonlinear Waves in Dry Granular Systems

A model is presented for the characterization of dissipative effects on highly nonlinear waves in one-dimensional dry granular media. The model includes three terms: Hertzian, viscoelastic, and a term proportional to the square of the relative velocity of particles. The model outcomes are confronted with different experiments where the granular system is subject to several constraints for different materials. Excellent qualitative and quantitative agreement between theory and experiments is found.Comment: Link to the Journal: http://prl.aps.org/abstract/PRL/v104/i11/e11800

Ionisation by quantised electromagnetic fields: The photoelectric effect

In this paper we explain the photoelectric effect in a variant of the standard model of non relativistic quantum electrodynamics, which is in some aspects more closely related to the physical picture, than the one studied in [BKZ]: Now we can apply our results to an electron with more than one bound state and to a larger class of electron-photon interactions. We will specify a situation, where ionisation probability in second order is a weighted sum of single photon terms. Furthermore we will see, that Einstein's equality $$E_{kin}=h\nu-\bigtriangleup E>0$$ for the maximal kinetic energy $E_{kin}$ of the electron, energy $h\nu$ of the photon and ionisation gap $\bigtriangleup E$ is the crucial condition for these single photon terms to be nonzero.Comment: 59 pages, LATEX2

NVU dynamics. III. Simulating molecules at constant potential energy

This is the final paper in a series that introduces geodesic molecular dynamics at constant potential energy. This dynamics is entitled NVU dynamics in analogy to standard energy-conserving Newtonian NVE dynamics. In the first two papers [Ingebrigtsen et al., J. Chem. Phys. 135, 104101 (2011); ibid, 104102 (2011)], a numerical algorithm for simulating geodesic motion of atomic systems was developed and tested against standard algorithms. The conclusion was that the NVU algorithm has the same desirable properties as the Verlet algorithm for Newtonian NVE dynamics, i.e., it is time-reversible and symplectic. Additionally, it was concluded that NVU dynamics becomes equivalent to NVE dynamics in the thermodynamic limit. In this paper, the NVU algorithm for atomic systems is extended to be able to simulate geodesic motion of molecules at constant potential energy. We derive an algorithm for simulating rigid bonds and test this algorithm on three different systems: an asymmetric dumbbell model, Lewis-Wahnstrom OTP, and rigid SPC/E water. The rigid bonds introduce additional constraints beyond that of constant potential energy for atomic systems. The rigid-bond NVU algorithm conserves potential energy, bond lengths, and step length for indefinitely long runs. The quantities probed in simulations give results identical to those of Nose-Hoover NVT dynamics. Since Nose-Hoover NVT dynamics is known to give results equivalent to those of NVE dynamics, the latter results show that NVU dynamics becomes equivalent to NVE dynamics in the thermodynamic limit also for molecular systems.Comment: 14 pages, 12 figure

Effects of Diversity on Multi-agent Systems: Minority Games

We consider a version of large population games whose agents compete for resources using strategies with adaptable preferences. The games can be used to model economic markets, ecosystems or distributed control. Diversity of initial preferences of strategies is introduced by randomly assigning biases to the strategies of different agents. We find that diversity among the agents reduces their maladaptive behavior. We find interesting scaling relations with diversity for the variance and other parameters such as the convergence time, the fraction of fickle agents, and the variance of wealth, illustrating their dynamical origin. When diversity increases, the scaling dynamics is modified by kinetic sampling and waiting effects. Analyses yield excellent agreement with simulations.Comment: 41 pages, 16 figures; minor improvements in content, added references; to be published in Physical Review