ICE Second Halley radial: TDA mission support and DSN operations

The article documents the operations encompassing the International Cometary Explorer (ICE) second Halley radial experiment centered around March 28, 1986. The support was provided by the Deep Space Network (DSN) 64-meter subnetwork. Near continuous support was provided the last two weeks of March and the first two weeks of April to insure the collection of adequate background data for the Halley radial experiment. During the last week of March, plasma wave measurements indicate that ICE was within the Halley heavy ion pick-up region

Diffusion in a crowded environment

We analyze a pair of diffusion equations which are derived in the infinite system--size limit from a microscopic, individual--based, stochastic model. Deviations from the conventional Fickian picture are found which ultimately relate to the depletion of resources on which the particles rely. The macroscopic equations are studied both analytically and numerically, and are shown to yield anomalous diffusion which does not follow a power law with time, as is frequently assumed when fitting data for such phenomena. These anomalies are here understood within a consistent dynamical picture which applies to a wide range of physical and biological systems, underlining the need for clearly defined mechanisms which are systematically analyzed to give definite predictions.Comment: 4 pages, 3 figures, minor change

Intrinsic noise and discrete-time processes

A general formalism is developed to construct a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are therefore internal to the system and not externally specified. For finite populations an approximate Gaussian scheme is devised to describe the stochastic fluctuations in the non-chaotic regime. More generally, the stochastic dynamics can be captured using a stochastic difference equation, derived through an approximation to the Markov chain. The scheme is demonstrated using the logistic map as a case study.Comment: Modified version accepted for publication in Phys. Rev. E Rapid Communications. New figures adde

Dynamical description of vesicle growth and shape change

We systematize and extend the description of vesicle growth and shape change using linear nonequilibrium thermodynamics. By restricting the study to shape changes from spheres to axisymmetric ellipsoids, we are able to give a consistent formulation which includes the lateral tension of the vesicle membrane. This allows us to generalize and correct a previous calculation. Our present calculations suggest that, for small growing vesicles, a prolate ellipsoidal shape should be favored over oblate ellipsoids, whereas for large growing vesicles oblates should be favored over prolates. The validity of this prediction is examined in the light of the various assumptions made in its derivation.Comment: 6 page

Kondo behavior, ferromagnetic correlations, and crystal fields in the heavy Fermion compounds Ce3X (X=In, Sn)

We report measurements of inelastic neutron scattering, magnetic susceptibility, magnetization, and the magnetic field dependence of the specific heat for the heavy Fermion compounds Ce$_3$In and Ce$_3$Sn. The neutron scattering results show that the excited crystal field levels have energies $E_1$ = 13.2 meV, $E_2$ = 44.8 meV for Ce$_3$In and $E_1$ = 18.5 meV, $E_2$ = 36.1 meV for Ce$_3$Sn. The Kondo temperature deduced from the quasielastic linewidth is 17 K for Ce$_3$In and 40 K for Ce$_3$Sn. The low temperature behavior of the specific heat, magnetization, and susceptibility can not be well-described by J=1/2 Kondo physics alone, but require calculations that include contributions from the Kondo effect, broadened crystal fields, and ferromagnetic correlations, all of which are known to be important in these compounds. We find that in Ce$_3$In the ferromagnetic fluctuation makes a 10-15 % contribution to the ground state doublet entropy and magnetization. The large specific heat coefficient $\gamma$ in this heavy fermion system thus arises more from the ferromagnetic correlations than from the Kondo behavior.Comment: 8 pages, 6 figure

Nonexistence of extremals for the adjoint restriction inequality on the hyperboloid

We study the problem of existence of extremizers for the $L^2$ to $L^p$ adjoint Fourier restriction inequalities on the hyperboloid in dimensions 3 and 4, in which cases $p$ is an even integer. We will use the method developed by Foschi to show that extremizers do not exist.Comment: 32 pages. Correction for Theorem 1.2 and Proposition 7.5 and addition of Remark 1.

Quantum Hamilton-Jacobi equation

The nontrivial transformation of the phase space path integral measure under certain discretized analogues of canonical transformations is computed. This Jacobian is used to derive a quantum analogue of the Hamilton-Jacobi equation for the generating function of a canonical transformation that maps any quantum system to a system with a vanishing Hamiltonian. A formal perturbative solution of the quantum Hamilton-Jacobi equation is given.Comment: 4 pages, RevTe

Canonical Transformations and Path Integral Measures

This paper is a generalization of previous work on the use of classical canonical transformations to evaluate Hamiltonian path integrals for quantum mechanical systems. Relevant aspects of the Hamiltonian path integral and its measure are discussed and used to show that the quantum mechanical version of the classical transformation does not leave the measure of the path integral invariant, instead inducing an anomaly. The relation to operator techniques and ordering problems is discussed, and special attention is paid to incorporation of the initial and final states of the transition element into the boundary conditions of the problem. Classical canonical transformations are developed to render an arbitrary power potential cyclic. The resulting Hamiltonian is analyzed as a quantum system to show its relation to known quantum mechanical results. A perturbative argument is used to suppress ordering related terms in the transformed Hamiltonian in the event that the classical canonical transformation leads to a nonquadratic cyclic Hamiltonian. The associated anomalies are analyzed to yield general methods to evaluate the path integral's prefactor for such systems. The methods are applied to several systems, including linear and quadratic potentials, the velocity-dependent potential, and the time-dependent harmonic oscillator.Comment: 28 pages, LaTe