Binary interaction algorithms for the simulation of flocking and swarming dynamics

Microscopic models of flocking and swarming takes in account large numbers of interacting individ- uals. Numerical resolution of large flocks implies huge computational costs. Typically for $N$ interacting individuals we have a cost of $O(N^2)$. We tackle the problem numerically by considering approximated binary interaction dynamics described by kinetic equations and simulating such equations by suitable stochastic methods. This approach permits to compute approximate solutions as functions of a small scaling parameter $\varepsilon$ at a reduced complexity of O(N) operations. Several numerical results show the efficiency of the algorithms proposed

Scaffold searching: automated identification of similar ring systems for the design of combinatorial libraries

Rigid ring systems can be used to position receptor-binding functional groups in 3D space and they thus play an increasingly important role in the design of combinatorial libraries. This paper discusses the use of shape-similarity methods to identify ring systems that are structurally similar to, and aligned with, a user-defined target ring system. These systems can be used as alternative scaffolds for the construction of a combinatorial library

Structural properties of electrons in quantum dots in high magnetic fields: Crystalline character of cusp states and excitation spectra

The crystalline or liquid character of the downward cusp states in N-electron parabolic quantum dots (QD's) at high magnetic fields is investigated using conditional probability distributions obtained from exact diagonalization. These states are of crystalline character for fractional fillings covering both low and high values, unlike the liquid Jastrow-Laughlin wave functions, but in remarkable agreement with the rotating-Wigner-molecule ones [Phys. Rev. B 66, 115315 (2002)]. The crystalline arrangement consists of concentric polygonal rings that rotate independently of each other, with the electrons on each ring rotating coherently. We show that the rotation stabilizes the Wigner molecule relative to the static one defined by the broken-symmetry unrestricted-Hartree-Fock solution. We discuss the non-rigid behavior of the rotating Wigner molecule and pertinent features of the excitation spectrum, including the occurrence of a gap between the ground and first excited states that underlies the incompressibility of the system. This leads us to conjecture that the rotating crystal (and not the static one) remains the relevant ground state for low fractional fillings even at the thermodynamic limit.Comment: Published version. Typos corrected. REVTEX4. 10 pages with 8 postscript figures (5 in color). For related papers, see http://www.prism.gatech.edu/~ph274cy

Metropolis Methods for Quantum Monte Carlo Simulations

Since its first description fifty years ago, the Metropolis Monte Carlo method has been used in a variety of different ways for the simulation of continuum quantum many-body systems. This paper will consider some of the generalizations of the Metropolis algorithm employed in quantum Monte Carlo: Variational Monte Carlo, dynamical methods for projector monte carlo ({\it i.e.} diffusion Monte Carlo with rejection), multilevel sampling in path integral Monte Carlo, the sampling of permutations, cluster methods for lattice models, the penalty method for coupled electron-ionic systems and the Bayesian analysis of imaginary time correlation functions.Comment: Proceedings of "Monte Carlo Methods in the Physical Sciences" Celebrating the 50th Anniversary of the Metropolis Algorith