Isospin relaxation time in heavy-ion collisions at intermediate energies

Using an isospin-dependent transport model, we have studied the isospin and momentum relaxation times in the heavy residues formed in heavy-ion collisions at intermediate energies. It is found that only at incident energies below the Fermi energy, chemical or thermal equilibrium can be reached before dynamical instability is developed in the heavy residues. Also, the isospin relaxation time is shorter (longer) than that for momentum at beam energies lower (higher) than the Fermi energy.Comment: 8 pages Latex + 2 ps Figs.; Phys. Rev. C in pres

Presymplectic current and the inverse problem of the calculus of variations

The inverse problem of the calculus of variations asks whether a given system of partial differential equations (PDEs) admits a variational formulation. We show that the existence of a presymplectic form in the variational bicomplex, when horizontally closed on solutions, allows us to construct a variational formulation for a subsystem of the given PDE. No constraints on the differential order or number of dependent or independent variables are assumed. The proof follows a recent observation of Bridges, Hydon and Lawson and generalizes an older result of Henneaux from ordinary differential equations (ODEs) to PDEs. Uniqueness of the variational formulation is also discussed.Comment: v2: 17 pages, no figures, BibTeX; minor corrections, close to published versio

Local Anisotropy of Fluids using Minkowski Tensors

Statistics of the free volume available to individual particles have previously been studied for simple and complex fluids, granular matter, amorphous solids, and structural glasses. Minkowski tensors provide a set of shape measures that are based on strong mathematical theorems and easily computed for polygonal and polyhedral bodies such as free volume cells (Voronoi cells). They characterize the local structure beyond the two-point correlation function and are suitable to define indices $0\leq \beta_\nu^{a,b}\leq 1$ of local anisotropy. Here, we analyze the statistics of Minkowski tensors for configurations of simple liquid models, including the ideal gas (Poisson point process), the hard disks and hard spheres ensemble, and the Lennard-Jones fluid. We show that Minkowski tensors provide a robust characterization of local anisotropy, which ranges from $\beta_\nu^{a,b}\approx 0.3$ for vapor phases to $\beta_\nu^{a,b}\to 1$ for ordered solids. We find that for fluids, local anisotropy decreases monotonously with increasing free volume and randomness of particle positions. Furthermore, the local anisotropy indices $\beta_\nu^{a,b}$ are sensitive to structural transitions in these simple fluids, as has been previously shown in granular systems for the transition from loose to jammed bead packs

On the Microscopic Origin of Cholesteric Pitch

We present a microscopic analysis of the instability of the nematic phase to chirality when molecular chirality is introduced perturbatively. We show that previously neglected short-range biaxial correlations play a crucial role in determining the cholesteric pitch. We propose an order parameter which quantifies the chirality of a molecule.Comment: RevTeX 3.0, 4 pages, one included eps figure. Published versio

The infrared behaviour of the static potential in perturbative QCD

The definition of the quark-antiquark static potential is given within an effective field theory framework. The leading infrared divergences of the static singlet potential in perturbation theory are explicitly calculated.Comment: 4 pages, 2 postscript figures, uses revtex.st

Minkowski Tensors of Anisotropic Spatial Structure

This article describes the theoretical foundation of and explicit algorithms for a novel approach to morphology and anisotropy analysis of complex spatial structure using tensor-valued Minkowski functionals, the so-called Minkowski tensors. Minkowski tensors are generalisations of the well-known scalar Minkowski functionals and are explicitly sensitive to anisotropic aspects of morphology, relevant for example for elastic moduli or permeability of microstructured materials. Here we derive explicit linear-time algorithms to compute these tensorial measures for three-dimensional shapes. These apply to representations of any object that can be represented by a triangulation of its bounding surface; their application is illustrated for the polyhedral Voronoi cellular complexes of jammed sphere configurations, and for triangulations of a biopolymer fibre network obtained by confocal microscopy. The article further bridges the substantial notational and conceptual gap between the different but equivalent approaches to scalar or tensorial Minkowski functionals in mathematics and in physics, hence making the mathematical measure theoretic method more readily accessible for future application in the physical sciences

A dynamical model of surrogate reactions

A new dynamical model is developed to describe the whole process of surrogate reactions; transfer of several nucleons at an initial stage, thermal equilibration of residues leading to washing out of shell effects and decay of populated compound nuclei are treated in a unified framework. Multi-dimensional Langevin equations are employed to describe time-evolution of collective coordinates with a time-dependent potential energy surface corresponding to different stages of surrogate reactions. The new model is capable of calculating spin distributions of the compound nuclei, one of the most important quantity in the surrogate technique. Furthermore, various observables of surrogate reactions can be calculated, e.g., energy and angular distribution of ejectile, and mass distributions of fission fragments. These features are important to assess validity of the proposed model itself, to understand mechanisms of the surrogate reactions and to determine unknown parameters of the model. It is found that spin distributions of compound nuclei produced in $^{18}$O+$^{238}$U $\rightarrow ^{16}$O+$^{240*}$U and $^{18}$O+$^{236}$U $\rightarrow ^{16}$O+$^{238*}$U reactions are equivalent and much less than 10$\hbar$, therefore satisfy conditions proposed by Chiba and Iwamoto (PRC 81, 044604(2010)) if they are used as a pair in the surrogate ratio method.Comment: 17 pages, 5 figure

Turbulence in a free surface

We report an experimental and numerical study of turbulent fluid motion in a free surface. The flow is realized experimentally on the surface of a tank filled with water stirred by a vertically oscillating grid positioned well below the surface. Particles floating on the surface are used to visualize the flow. The effect of surface waves appears to be negligible. The flow is unconventional in that it is confined to two dimensions but does not have squared vorticity as a conservation law, that it is not divergence free and that it inherits scaling features of the mean square velocity differences S_2(R) and the vorticity fluctuations Omega(R) from the bulk 3-d turbulence.Comment: 4 pages, 4 Postscript figure