On integrability of the differential constraints arising from the singularity analysis

Integrability of the differential constraints arising from the singularity analysis of two (1+1)-dimensional second-order evolution equations is studied. Two nonlinear ordinary differential equations are obtained in this way, which are integrable by quadratures in spite of very complicated branching of their solutions.Comment: arxiv version is already offcia

Backlund transformation and special solutions for Drinfeld-Sokolov-Satsuma-Hirota system of coupled equations

Using the Weiss method of truncated singular expansions, we construct an explicit Backlund transformation of the Drinfeld-Sokolov-Satsuma-Hirota system into itself. Then we find all the special solutions generated by this transformation from the trivial zero solution of this system.Comment: LaTeX, 5 page

Further explorations of Skyrme-Hartree-Fock-Bogoliubov mass formulas. XI: Stabilizing neutron stars against a ferromagnetic collapse

We construct a new Hartree-Fock-Bogoliubov (HFB) mass model, labeled HFB-18, with a generalized Skyrme force. The additional terms that we have introduced into the force are density-dependent generalizations of the usual $t_1$ and $t_2$ terms, and are chosen in such a way as to avoid the high-density ferromagnetic instability of neutron stars that is a general feature of conventional Skyrme forces, and in particular of the Skyrme forces underlying all the HFB mass models that we have developed in the past. The remaining parameters of the model are then fitted to essentially all the available mass data, an rms deviation $\sigma$ of 0.585 MeV being obtained. The new model thus gives almost as good a mass fit as our best-fit model HFB-17 ($\sigma$ = 0.581 MeV), and has the advantage of avoiding the ferromagnetic collapse of neutron stars.Comment: accepted for publication in Physical Review

Measurement of the lunar neutron density profile

An in situ measurement of the lunar neutron density from 20 to 400 g/sq cm depth between the lunar surface was made by the Apollo 17 Lunar Neutron Probe Experiment using particle tracks produced by the B10(n, alpha)Li7 reaction. Both the absolute magnitude and depth profile of the neutron density are in good agreement with past theoretical calculations. The effect of cadmium absorption on the neutron density and in the relative Sm149 to Gd157 capture rates obtained experimentally implies that the true lunar Gd157 capture rate is about one half of that calculated theoretically

Voltage-flux-characteristics of asymmetric dc SQUIDs

We present a detailed analysis of voltage-flux V(Phi)-characteristics for asymmetric dc SQUIDs with various kinds of asymmetries. For finite asymmetry alpha_I in the critical currents of the two Josephson junctions, the minima in the V(Phi)-characteristics for bias currents of opposite polarity are shifted along the flux axis by Delta_Phi = (alpha_I)*(beta_L) relative to each other; beta_L is the screening parameter. This simple relation allows the determination of alpha_I in our experiments on YBa_2Cu_3O_(7-x} dc SQUIDs and comparison with theory. Extensive numerical simulations within a wide range of beta_L and noise parameter Gamma reveal a systematic dependence of the transfer function V_Phi on alpha_I and alpha_R (junction resistance asymmetry). As for the symmetric dc SQUID, V_Phi factorizes into g(Gamma*beta_L)*f(alpha_I,beta_L), where now f also depends on alpha_I. For \beta_L below five we find mostly a decrease of V_Phi with increasing alpha_I, which however can only partially account for the frequently observed discrepancy in V_Phi between theory and experiment for high-T_c dc SQUIDs.Comment: 4 pages, 7 figures, Applied Superconductivity Conference 2000, to be published in IEEE Trans. Appl. Supercon

Winning quick and dirty: the greedy random walk

As a strategy to complete games quickly, we investigate one-dimensional random walks where the step length increases deterministically upon each return to the origin. When the step length after the kth return equals k, the displacement of the walk x grows linearly in time. Asymptotically, the probability distribution of displacements is a purely exponentially decaying function of |x|/t. The probability E(t,L) for the walk to escape a bounded domain of size L at time t decays algebraically in the long time limit, E(t,L) ~ L/t^2. Consequently, the mean escape time ~ L ln L, while ~ L^{2n-1} for n>1. Corresponding results are derived when the step length after the kth return scales as k^alpha$ for alpha>0.Comment: 7 pages, 6 figures, 2-column revtext4 forma