Smoothed Particle Hydrodynamics for Relativistic Heavy Ion Collisions

The method of smoothed particle hydrodynamics (SPH) is developped appropriately for the study of relativistic heavy ion collision processes. In order to describe the flow of a high energy but low baryon number density fluid, the entropy is taken as the SPH base. We formulate the method in terms of the variational principle. Several examples show that the method is very promising for the study of hadronic flow in RHIC physics.Comment: 14 pages, 8figure

On Virtual Displacement and Virtual Work in Lagrangian Dynamics

The confusion and ambiguity encountered by students, in understanding virtual displacement and virtual work, is discussed in this article. A definition of virtual displacement is presented that allows one to express them explicitly for holonomic (velocity independent), non-holonomic (velocity dependent), scleronomous (time independent) and rheonomous (time dependent) constraints. It is observed that for holonomic, scleronomous constraints, the virtual displacements are the displacements allowed by the constraints. However, this is not so for a general class of constraints. For simple physical systems, it is shown that, the work done by the constraint forces on virtual displacements is zero. This motivates Lagrange's extension of d'Alembert's principle to system of particles in constrained motion. However a similar zero work principle does not hold for the allowed displacements. It is also demonstrated that d'Alembert's principle of zero virtual work is necessary for the solvability of a constrained mechanical problem. We identify this special class of constraints, physically realized and solvable, as {\it the ideal constraints}. The concept of virtual displacement and the principle of zero virtual work by constraint forces are central to both Lagrange's method of undetermined multipliers, and Lagrange's equations in generalized coordinates.Comment: 12 pages, 10 figures. This article is based on an earlier article physics/0410123. It includes new figures, equations and logical conten

Molecular formations in ultracold mixtures of interacting and noninteracting atomic gases

Atom-molecule equilibrium for molecular formation processes is discussed for boson-fermion, fermion-fermion, and boson-boson mixtures of ultracold atomic gases in the framework of quasichemical equilibrium theory. After presentation of the general formulation, zero-temperature phase diagrams of the atom-molecule equilibrium states are calculated analytically; molecular, mixed, and dissociated phases are shown to appear for the change of the binding energy of the molecules. The temperature dependences of the atom or molecule densities are calculated numerically, and finite-temperature phase structures are obtained of the atom-molecule equilibrium in the mixtures. The transition temperatures of the atom or molecule Bose-Einstein condensations are also evaluated from these results. Quantum-statistical deviations of the law of mass action in atom-molecule equilibrium, which should be satisfied in mixtures of classical Maxwell-Boltzmann gases, are calculated, and the difference in the different types of quantum-statistical effects is clarified. Mean-field calculations with interparticle interactions (atom-atom, atom-molecule, and molecule-molecule) are formulated, where interaction effects are found to give the linear density-dependent term in the effective molecular binding energies. This method is applied to calculations of zero-temperature phase diagrams, where new phases with coexisting local-equilibrium states are shown to appear in the case of strongly repulsive interactions.Comment: 35 pages, 14 figure

GCIP water and energy budget synthesis (WEBS)

As part of the World Climate Research Program\u27s (WCRPs) Global Energy and Water-Cycle Experiment (GEWEX) Continental-scale International Project (GCIP), a preliminary water and energy budget synthesis (WEBS) was developed for the period 1996–1999 from the “best available” observations and models. Besides this summary paper, a companion CD-ROM with more extensive discussion, figures, tables, and raw data is available to the interested researcher from the GEWEX project office, the GAPP project office, or the first author. An updated online version of the CD-ROM is also available at http://ecpc.ucsd.edu/gcip/webs.htm/. Observations cannot adequately characterize or “close” budgets since too many fundamental processes are missing. Models that properly represent the many complicated atmospheric and near-surface interactions are also required. This preliminary synthesis therefore included a representative global general circulation model, regional climate model, and a macroscale hydrologic model as well as a global reanalysis and a regional analysis. By the qualitative agreement among the models and available observations, it did appear that we now qualitatively understand water and energy budgets of the Mississippi River Basin. However, there is still much quantitative uncertainty. In that regard, there did appear to be a clear advantage to using a regional analysis over a global analysis or a regional simulation over a global simulation to describe the Mississippi River Basin water and energy budgets. There also appeared to be some advantage to using a macroscale hydrologic model for at least the surface water budgets

Differential flow in heavy-ion collisions at balance energies

A strong differential transverse collective flow is predicted for the first time to occur in heavy-ion collisions at balance energies. We also give a novel explanation for the disappearance of the total transverse collective flow at the balance energies. It is further shown that the differential flow especially at high transverse momenta is a useful microscope capable of resolving the balance energy's dual sensitivity to both the nuclear equation of state and in-medium nucleon-nucleon cross sections in the reaction dynamics.Comment: Phys. Rev. Lett. (1999) in pres

A quantum-like description of the planetary systems

The Titius-Bode law for planetary distances is reviewed. A model describing the basic features of this rule in the "quantum-like" language of a wave equation is proposed. Some considerations about the 't Hooft idea on the quantum behaviour of deterministic systems with dissipation are discussed.Comment: LaTex file, 17 pages, no figures. Version published in Foundations of Physics, August 200

Condensation of Ideal Bose Gas Confined in a Box Within a Canonical Ensemble

We set up recursion relations for the partition function and the ground-state occupancy for a fixed number of non-interacting bosons confined in a square box potential and determine the temperature dependence of the specific heat and the particle number in the ground state. A proper semiclassical treatment is set up which yields the correct small-T-behavior in contrast to an earlier theory in Feynman's textbook on Statistical Mechanics, in which the special role of the ground state was ignored. The results are compared with an exact quantum mechanical treatment. Furthermore, we derive the finite-size effect of the system.Comment: 18 pages, 8 figure

Critical Enhancement of the In-medium Nucleon-Nucleon Cross Section at low Temperatures

The in-medium nucleon-nucleon cross section is calculated starting from the thermodynamic T-matrix at finite temperatures. The corresponding Bethe-Salpeter-equation is solved using a separable representation of the Paris nucleon-nucleon-potential. The energy-dependent in-medium N-N cross section at a given density shows a strong temperature dependence. Especially at low temperatures and low total momenta, the in-medium cross section is strongly modified by in-medium effects. In particular, with decreasing temperature an enhancement near the Fermi energy is observed. This enhancement can be discussed as a precursor of the superfluid phase transition in nuclear matter.Comment: 10 pages with 4 figures (available on request from the authors), MPG-VT-UR 34/94 accepted for publication in Phys. Rev.

Prototype digital weather laboratory at Colorado State University, The

Includes bibliographical references