How to estimate the number of self-avoiding walks over 10^100? Use random walks

Counting the number of N-step self-avoiding walks (SAWs) on a lattice is one of the most difficult problems of enumerative combinatorics. Once we give up calculating the exact number of them, however, we have a chance to apply powerful computational methods of statistical mechanics to this problem. In this paper, we develop a statistical enumeration method for SAWs using the multicanonical Monte Carlo method. A key part of this method is to expand the configuration space of SAWs to random walks, the exact number of which is known. Using this method, we estimate a number of N-step SAWs on a square lattice, c_N, up to N=256. The value of c_256 is 5.6(1)*10^108 (the number in the parentheses is the statistical error of the last digit) and this is larger than one googol (10^100).Comment: 5 pages, 3 figures, 1 table, to appear in proceedings of YSMSPIP in Senda

Transport coefficients of a mesoscopic fluid dynamics model

We investigate the properties of stochastic rotation dynamics (Malevanets-Kapral method), a mesoscopic model used for simulating fluctuating hydrodynamics. Analytical results are given for the transport coefficients. We discuss the most efficient way of measuring the transport properties and obtain excellent agreement between the theoretical and numerical calculations.Comment: 12 pages, 9 figures, submitted to J. Chem. Phy

Niobium hyperfine structure in crystal calcium tungstate

A study of the niobium hyperfine structure in single crystal calcium tungstate was made by the combination of the technique of electron paramagnetic resonance and electron nuclear double resonance (EPR/ENDOR). The microwave frequency was about 9.4 GHz and the radio frequency from 20MHz to 70 MHz. The rare earth ions Nd(3+), U(3+), or Tm(3+) were added as the charge compensator for Nb(5+). To create niobium paramagnetic centers, the sample was irradiated at 77 deg K with a 10 thousand curie Co-60 gamma source for 1 to 2 hours at a dose rate of 200 K rads per hour and then transferred quickly into the cavity. In a general direction of magnetic field, the spectra showed 4 sets of 10 main lines corresponding to 4 nonequivalent sites of niobium with I = 9/2. These 4 sets of lines coalesced into 2 sets of 10 in the ab-plane and into a single set of 10 along the c-axis. This symmetry suggested that the tungsten ions are substituted by the niobium ions in the crystal

An MO theory of the cubic field splitting of 3d5 6S ions in II-IV compounds of Td symmetry

Molecular orbital techniques used to find cubic field splitting 3a of certain ions in periodic group II-VI compounds of T sub d symmetr

On Phase Transition of NH4H2PO4NH_{4}H_{2}PO_{4}-Type Crystals by Cluster Variation Method

The Cluster Variation Method (CVM) is applied to the Ishibashi model for ammonium dihydrogen phosphate ($\rm NH_{4}H_{2}PO_{4}$) of a typical hydrogen bonded anti-ferroelectric crystal. The staggered and the uniform susceptibility without hysteresis are calculated at equilibrium. On the other hand, by making use of the natural iteration method (NIM) for the CVM, hysteresis phenomena of uniform susceptibility versus temperature observed in experiments is well explained on the basis of local minimum in Landau type variational free energy. The polarization $P$ curves against the uniform field is also calculated.Comment: 14 pages, 10 figure

Constraints on unparticle long range forces from big bang nucleosynthesis bounds on the variation of the gravitational coupling

We use big bang nucleosynthesis bounds on the variation of the gravitational coupling to derive constraints on the strength of the deviation from the gravitational inverse-square law due to tensor and vector unparticle exchange.Comment: 4 pages, 3 figures, change in the title and other minor changes to match version published in Physical Review

Cryogenic Calibration Setup for Broadband Complex Impedance Measurements

Reflection measurements give access to the complex impedance of a material on a wide frequency range. This is of interest to study the dynamical properties of various materials, for instance disordered superconductors. However reflection measurements made at cryogenic temperature suffer from the difficulty to reliably subtract the circuit contribution. Here we report on the design and first tests of a setup able to precisely calibrate in situ the sample reflection, at 4.2 K and up to 2 GHz, by switching and measuring, during the same cool down, the sample and three calibration standards.Comment: (6 pages, 6 figures