Derivation of an integral of Boros and Moll via convolution of Student t-densities

We show that the evaluation of an integral considered by Boros and Moll is a special case of a convolution result about Student t-densities obtained by the authors in 2008

A Massive Neutron Star in the Globular Cluster M5

We report the results of 19 years of Arecibo timing for two pulsars in the globular cluster NGC 5904 (M5), PSR B1516+02A (M5A) and PSR B1516+02B (M5B). This has resulted in the measurement of the proper motions of these pulsars and, by extension, that of the cluster itself. M5B is a 7.95-ms pulsar in a binary system with a > 0.13 solar mass companion and an orbital period of 6.86 days. In deep HST images, no optical counterpart is detected within ~2.5 sigma of the position of the pulsar, implying that the companion is either a white dwarf or a low-mass main-sequence star. The eccentricity of the orbit (e = 0.14) has allowed a measurement of the rate of advance of periastron: (0.0142 +/-0.0007) degrees per year. We argue that it is very likely that this periastron advance is due to the effects of general relativity, the total mass of the binary system then being 2.29 +/-0.17 solar masses. The small measured mass function implies, in a statistical sense, that a very large fraction of this total mass is contained in the pulsar: 2.08 +/- 0.19 solar masses (1 sigma); there is a 5% probability that the mass of this object is < 1.72 solar masses and a 0.77% probability that is is between 1.2 and 1.44 solar masses. Confirmation of the median mass for this neutron star would exclude most ``soft'' equations of state for dense neutron matter. Millisecond pulsars (MSPs) appear to have a much wider mass distribution than is found in double neutron star systems; about half of these objects are significantly more massive than 1.44 solar masses. A possible cause is the much longer episode of mass accretion necessary to recycle a MSP, which in some cases corresponds to a much larger mass transfer.Comment: 10 pages in ApJ emulate format, 2 tables, 6 figures. Added February 2008 data, slightly revised mass limits. Accepted for publication in Ap

The smallest eigenvalue of Hankel matrices

Let H_N=(s_{n+m}),n,m\le N denote the Hankel matrix of moments of a positive measure with moments of any order. We study the large N behaviour of the smallest eigenvalue lambda_N of H_N. It is proved that lambda_N has exponential decay to zero for any measure with compact support. For general determinate moment problems the decay to 0 of lambda_N can be arbitrarily slow or arbitrarily fast. In the indeterminate case, where lambda_N is known to be bounded below by a positive constant, we prove that the limit of the n'th smallest eigenvalue of H_N for N tending to infinity tends rapidly to infinity with n. The special case of the Stieltjes-Wigert polynomials is discussed

Large deviations for ideal quantum systems

We consider a general d-dimensional quantum system of non-interacting particles, with suitable statistics, in a very large (formally infinite) container. We prove that, in equilibrium, the fluctuations in the density of particles in a subdomain of the container are described by a large deviation function related to the pressure of the system. That is, untypical densities occur with a probability exponentially small in the volume of the subdomain, with the coefficient in the exponent given by the appropriate thermodynamic potential. Furthermore, small fluctuations satisfy the central limit theorem.Comment: 28 pages, LaTeX 2

Kinematics of the swimming of Spiroplasma

\emph{Spiroplasma} swimming is studied with a simple model based on resistive-force theory. Specifically, we consider a bacterium shaped in the form of a helix that propagates traveling-wave distortions which flip the handedness of the helical cell body. We treat cell length, pitch angle, kink velocity, and distance between kinks as parameters and calculate the swimming velocity that arises due to the distortions. We find that, for a fixed pitch angle, scaling collapses the swimming velocity (and the swimming efficiency) to a universal curve that depends only on the ratio of the distance between kinks to the cell length. Simultaneously optimizing the swimming efficiency with respect to inter-kink length and pitch angle, we find that the optimal pitch angle is 35.5$^\circ$ and the optimal inter-kink length ratio is 0.338, values in good agreement with experimental observations.Comment: 4 pages, 5 figure

Levy Flights in Inhomogeneous Media

We investigate the impact of external periodic potentials on superdiffusive random walks known as Levy flights and show that even strongly superdiffusive transport is substantially affected by the external field. Unlike ordinary random walks, Levy flights are surprisingly sensitive to the shape of the potential while their asymptotic behavior ceases to depend on the Levy index $\mu$. Our analysis is based on a novel generalization of the Fokker-Planck equation suitable for systems in thermal equilibrium. Thus, the results presented are applicable to the large class of situations in which superdiffusion is caused by topological complexity, such as diffusion on folded polymers and scale-free networks.Comment: 4 pages, 4 figure

Superfluidity and dimerization in a multilayered system of fermionic polar molecules

We consider a layered system of fermionic molecules with permanent dipole moments aligned by an external field. The dipole interactions between fermions in adjacent layers are attractive and induce inter-layer pairing. Due to competition for pairing among adjacent layers, the mean-field ground state of the layered system is a dimerized superfluid, with pairing only between every-other layer. We construct an effective Ising-XY lattice model that describes the interplay between dimerization and superfluid phase fluctuations. In addition to the dimerized superfluid ground state, and high temperature normal state, at intermediate temperature, we find an unusual dimerized "pseudogap" state with only short-range phase coherence. We propose light scattering experiments to detect dimerization.Comment: 4 pages main text + 3 pages supplemental Appendices, 4 figure

Dynamic Wettability Properties of Single Wood Pulp Fibers and Their Relationship to Absorbency

The Wilhelmy technique is used to measure dynamic wetting properties of single wood pulp fibers. Several different fiber types are examined, differing both in species and processing conditions. It is found that there are significant differences in water wettability of these fibers because of varying fiber surface chemistry. The compilation of a "dynamic wettability profile" for complex materials such as pulp fibers is advocated in order to characterize more fully the behavior of these materials in wetting situations. The bulk absorbency performance of three-dimensionally random pads of these fibers is found to be directly related to the initial advancing contact angles of single fibers. The measurement of single fiber wetting properties allows the separation of structural factors from surface chemical factors in considering the absorbency of a random network

FFLO oscillations and magnetic domains in the Hubbard model with off-diagonal Coulomb repulsion

We observe the effect of non-zero magnetization m onto the superconducting ground state of the one dimensional repulsive Hubbard model with correlated hopping X. For t/2 < X < 2t/3, the system first manifests Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) oscillations in the pair-pair correlations. For m = m1 a kinetic energy driven macroscopic phase separation into low-density superconducting domains and high-density polarized walls takes place. For m > m2 the domains fully localize, and the system eventually becomes a ferrimagnetic insulator.Comment: IOP RevTeX class, 18 pages, 13 composite *.eps figure