Stacking Entropy of Hard Sphere Crystals

Classical hard spheres crystallize at equilibrium at high enough density. Crystals made up of stackings of 2-dimensional hexagonal close-packed layers (e.g. fcc, hcp, etc.) differ in entropy by only about $10^{-3}k_B$ per sphere (all configurations are degenerate in energy). To readily resolve and study these small entropy differences, we have implemented two different multicanonical Monte Carlo algorithms that allow direct equilibration between crystals with different stacking sequences. Recent work had demonstrated that the fcc stacking has higher entropy than the hcp stacking. We have studied other stackings to demonstrate that the fcc stacking does indeed have the highest entropy of ALL possible stackings. The entropic interactions we could detect involve three, four and (although with less statistical certainty) five consecutive layers of spheres. These interlayer entropic interactions fall off in strength with increasing distance, as expected; this fall-off appears to be much slower near the melting density than at the maximum (close-packing) density. At maximum density the entropy difference between fcc and hcp stackings is $0.00115 +/- 0.00004 k_B$ per sphere, which is roughly 30% higher than the same quantity measured near the melting transition.Comment: 15 page

Stanford Aerospace Research Laboratory research overview

Over the last ten years, the Stanford Aerospace Robotics Laboratory (ARL) has developed a hardware facility in which a number of space robotics issues have been, and continue to be, addressed. This paper reviews two of the current ARL research areas: navigation and control of free flying space robots, and modelling and control of extremely flexible space structures. The ARL has designed and built several semi-autonomous free-flying robots that perform numerous tasks in a zero-gravity, drag-free, two-dimensional environment. It is envisioned that future generations of these robots will be part of a human-robot team, in which the robots will operate under the task-level commands of astronauts. To make this possible, the ARL has developed a graphical user interface (GUI) with an intuitive object-level motion-direction capability. Using this interface, the ARL has demonstrated autonomous navigation, intercept and capture of moving and spinning objects, object transport, multiple-robot cooperative manipulation, and simple assemblies from both free-flying and fixed bases. The ARL has also built a number of experimental test beds on which the modelling and control of flexible manipulators has been studied. Early ARL experiments in this arena demonstrated for the first time the capability to control the end-point position of both single-link and multi-link flexible manipulators using end-point sensing. Building on these accomplishments, the ARL has been able to control payloads with unknown dynamics at the end of a flexible manipulator, and to achieve high-performance control of a multi-link flexible manipulator

Free energies of crystalline solids: a lattice-switch Monte Carlo method

We present a method for the direct evaluation of the difference between the free energies of two crystalline structures, of different symmetry. The method rests on a Monte Carlo procedure which allows one to sample along a path, through atomic-displacement-space, leading from one structure to the other by way of an intervening transformation that switches one set of lattice vectors for another. The configurations of both structures can thus be sampled within a single Monte Carlo process, and the difference between their free energies evaluated directly from the ratio of the measured probabilities of each. The method is used to determine the difference between the free energies of the fcc and hcp crystalline phases of a system of hard spheres.Comment: 5 pages Revtex, 3 figure

Parameter-free expression for superconducting Tc in cuprates

A parameter-free expression for the superconducting critical temperature of layered cuprates is derived which allows us to express Tc in terms of experimentally measured parameters. It yields Tc values observed in about 30 lanthanum, yttrium and mercury-based samples for different levels of doping. This remarkable agreement with the experiment as well as the unusual critical behaviour and the normal-state gap indicate that many cuprates are close to the Bose-Einstein condensation regime.Comment: 5 pages, 2 figures. Will be published in Physical Review

Quantum calculations of Coulomb reorientation for sub-barrier fusion

Classical mechanics and Time Dependent Hartree-Fock (TDHF) calculations of heavy ions collisions are performed to study the rotation of a deformed nucleus in the Coulomb field of its partner. This reorientation is shown to be independent on charges and relative energy of the partners. It only depends upon the deformations and inertias. TDHF calculations predict an increase by 30% of the induced rotation due to quantum effects while the nuclear contribution seems negligible. This reorientation modifies strongly the fusion cross-section around the barrier for light deformed nuclei on heavy collision partners. For such nuclei a hindrance of the sub-barrier fusion is predicted.Comment: accepted for publication in Physical Review Lette

Accuracy of B(E2; 0+ -> 2+) transition rates from intermediate-energy Coulomb excitation experiments

The method of intermediate-energy Coulomb excitation has been widely used to determine absolute B(E2; 0+ -> 2+) quadrupole excitation strengths in exotic nuclei with even numbers of protons and neutrons. Transition rates measured with intermediate-energy Coulomb excitation are compared to their respective adopted values and for the example of 26Mg to the B(E2; 0+ -> 2+) values obtained with a variety of standard methods. Intermediate-energy Coulomb excitation is found to have an accuracy comparable to those of long-established experimental techniques.Comment: to be published in Phys. Rev.

Magneto-Transport in the Two-Dimensional Lorentz Gas

We consider the two-dimensional Lorentz gas with Poisson distributed hard disk scatterers and a constant magnetic field perpendicular to the plane of motion. The velocity autocorrelation is computed numerically over the full range of densities and magnetic fields with particular attention to the percolation threshold between hopping transport and pure edge currents. The Ohmic and Hall conductance are compared with mode-coupling theory and a recent generalized kinetic equation valid for low densities and small fields. We argue that the long time tail as $t^{-2}$ persists for non-zero magnetic field.Comment: 7 pages, 14 figures. Uses RevTeX and epsfig.sty. Submitted to Physical Review

Role of the Nuclear and Electromagnetic Interactions in the Coherent Dissociation of the Relativistic 7^7Li Nucleus into the 3^3H + 4^4He Channel

The differential cross section in the transverse momentum $Q$ and a total cross section of $(31\pm4)$ mb for the coherent dissociation of a 3-A-GeV/$c$ $^7$Li nucleus through the $^3$H$+^4$He channel have been measured on emulsion nuclei. The observed $Q$ dependence of the cross section is explained by the predominant supposition of the nuclear diffraction patterns on light (C, N, O) and heavy (Br, Ag) emulsion nuclei. The contributions to the cross section from nuclear diffraction ($Q\le400$ MeV/$c$) and Coulomb $(Q\le50$ MeV/$c$) dissociations are calculated to be 40.7 and 4 mb, respectively.Comment: ISSN 0021-3640, Pleiades Publishing, Ltd., 200

Double Giant Dipole Resonance in ^{208}Pb

Double-dipole excitations in ^{208}Pb are analyzed within a microscopic model explicitly treating 2p2h-excitations. Collective states built from such 2p2h-excitations are shown to appear at about twice the energy of the isovector giant dipole resonance, in agreement with the experimental findings. The calculated cross section for Coulomb excitation at relativistic energies cannot explain simultaneously the measured single-dipole and double-dipole cross sections, however.Comment: 7 pages, Latex, 5 postscript figure

Variation with mass of \boldmath{B(E3; 0_1^+ \to 3_1^-)} transition rates in A=124−134A=124-134 even-mass xenon nuclei

$B(E3; 0_1^+ \to 3_1^-)$ transition matrix elements have been measured for even-mass $^{124-134}$Xe nuclei using sub-barrier Coulomb excitation in inverse kinematics. The trends in energy $E(3^-)$ and $B(E3; 0_1^+ \to 3_1^-)$ excitation strengths are well reproduced using phenomenological models based on a strong coupling picture with a soft quadrupole mode and an increasing occupation of the intruder $h_{11/2}$ orbital.Comment: 5 pages, 4 figures, PRC in pres