15,798 research outputs found
Spectral characteristics for a spherically confined -1/r + br^2 potential
We consider the analytical properties of the eigenspectrum generated by a
class of central potentials given by V(r) = -a/r + br^2, b>0. In particular,
scaling, monotonicity, and energy bounds are discussed. The potential is
considered both in all space, and under the condition of spherical confinement
inside an impenetrable spherical boundary of radius R. With the aid of the
asymptotic iteration method, several exact analytic results are obtained which
exhibit the parametric dependence of energy on a, b, and R, under certain
constraints. More general spectral characteristics are identified by use of a
combination of analytical properties and accurate numerical calculations of the
energies, obtained by both the generalized pseudo-spectral method, and the
asymptotic iteration method. The experimental significance of the results for
both the free and confined potential V(r) cases are discussed.Comment: 16 pages, 4 figure
Perturbation expansions for a class of singular potentials
Harrell's modified perturbation theory [Ann. Phys. 105, 379-406 (1977)] is
applied and extended to obtain non-power perturbation expansions for a class of
singular Hamiltonians H = -D^2 + x^2 + A/x^2 + lambda/x^alpha, (A\geq 0, alpha
> 2), known as generalized spiked harmonic oscillators. The perturbation
expansions developed here are valid for small values of the coupling lambda >
0, and they extend the results which Harrell obtained for the spiked harmonic
oscillator A = 0. Formulas for the the excited-states are also developed.Comment: 23 page
Discontinuous Molecular Dynamics for Rigid Bodies: Applications
Event-driven molecular dynamics simulations are carried out on two rigid body
systems which differ in the symmetry of their molecular mass distributions.
First, simulations of methane in which the molecules interact via discontinuous
potentials are compared with simulations in which the molecules interact
through standard continuous Lennard-Jones potentials. It is shown that under
similar conditions of temperature and pressure, the rigid discontinuous
molecular dynamics method reproduces the essential dynamical and structural
features found in continuous-potential simulations at both gas and liquid
densities. Moreover, the discontinuous molecular dynamics approach is
demonstrated to be between 2 to 100 times more efficient than the standard
molecular dynamics method depending on the specific conditions of the
simulation. The rigid discontinuous molecular dynamics method is also applied
to a discontinuous-potential model of a liquid composed of rigid benzene
molecules, and equilibrium and dynamical properties are shown to be in
qualitative agreement with more detailed continuous-potential models of
benzene. Qualitative differences in the dynamics of the two models are related
to the relatively crude treatment of variations in the repulsive interactions
as one benzene molecule rotates by another.Comment: 14 pages, double column revte
The use of prevalence as a measure of lice burden: a case study of Lepeophtheirus salmonis on Scottish Atlantic salmon, Salmo salar L., farms
This study investigates the benefits of using prevalence as a summary measure of sea lice infestation on farmed Atlantic salmon, Salmo salar L. Aspects such as sampling effort, the relationship between abundance and prevalence arising from the negative binomial distribution, and how this relationship can be used to indicate the degree of aggregation of lice on a site at a given time point are discussed. As a case study, data were drawn from over 50 commercial Atlantic salmon farms on the west coast of Scotland between 2002 and 2006. Descriptive statistics and formal analysis using a linear modelling technique identified significant variations in sea lice prevalence across year class, region and season. Supporting evidence of a functional relationship between prevalence and abundance of sea lice is provided, which is explained through the negative binomial distribution
Evaluating the Applicability of the Fokker-Planck Equation in Polymer Translocation: A Brownian Dynamics Study
Brownian dynamics (BD) simulations are used to study the translocation
dynamics of a coarse-grained polymer through a cylindrical nanopore. We
consider the case of short polymers, with a polymer length, N, in the range
N=21-61. The rate of translocation is controlled by a tunable friction
coefficient, gamma_{0p}, for monomers inside the nanopore. In the case of
unforced translocation, the mean translocation time scales with polymer length
N as ~ (N-N_p)^alpha, where N_p is the average number of monomers in the
nanopore. The exponent approaches the value alpha=2 when the pore friction is
sufficiently high, in accord with the prediction for the case of the
quasi-static regime where pore friction dominates. In the case of forced
translocation, the polymer chain is stretched and compressed on the cis and
trans sides, respectively, for low gamma_{0p}. However, the chain approaches
conformational quasi-equilibrium for sufficiently large gamma_{0p}. In this
limit the observed scaling of with driving force and chain length
supports the FP prediction that is proportional to N/f_d for sufficiently
strong driving force. Monte Carlo simulations are used to calculate
translocation free energy functions for the system. The free energies are used
with the Fokker-Planck equation to calculate translocation time distributions.
At sufficiently high gamma_{0p}, the predicted distributions are in excellent
agreement with those calculated from the BD simulations. Thus, the FP equation
provides a valid description of translocation dynamics for sufficiently high
pore friction for the range of polymer lengths considered here. Increasing N
will require a corresponding increase in pore friction to maintain the validity
of the FP approach. Outside the regime of low N and high pore friction, the
polymer is out of equilibrium, and the FP approach is not valid.Comment: 13 pages, 11 figure
Sextic anharmonic oscillators and orthogonal polynomials
Under certain constraints on the parameters a, b and c, it is known that
Schroedinger's equation
-y"(x)+(ax^6+bx^4+cx^2)y(x) = E y(x), a > 0, with the sextic anharmonic
oscillator potential is exactly solvable. In this article we show that the
exact wave function y is the generating function for a set of orthogonal
polynomials P_n^{(t)}(x) in the energy variable E. Some of the properties of
these polynomials are discussed in detail and our analysis reveals scaling and
factorization properties that are central to quasi-exact solvability. We also
prove that this set of orthogonal polynomials can be reduced,by means of a
simple scaling transformation, to a remarkable class of orthogonal polynomials,
P_n(E)=P_n^{(0)}(E) recently discovered by Bender and Dunne.Comment: 11 page
Transmission of Renormalized Benzene Circuits
The renormalization equations emerge from a Greenian-matrix solution of the
discretized Schrodinger equation. A by-product of these equations is the
decimation process, which enables substituted-benzenes to be mapped onto
corresponding dimers, that are used to construct the series and parallel
circuits of single-, double- and triple-dimers. The transmittivities of these
circuits are calculated by the Lippmann-Schwinger theory, which yields the
transmission-energy function T(E). The average value of T(E) provides a measure
of the electron transport in the circuit in question. The undulating nature of
the T(E) profiles give rise to resonances (T=1) and anti-resonances (T=0)
across the energy spectrum. Analysis of the structure of the T(E) graphs
highlights the distinguishing features associated with the homo- and
hetero-geneous series and parallel circuits. Noteworthy results include the
preponderance of p-dimers in circuits with high T(E) values, and the fact that
parallel circuits tend to be better transmitters than their series
counterparts.Comment: 32 pages, 14 figures, 1 tabl
Polymer Translocation Dynamics in the Quasi-Static Limit
Monte Carlo (MC) simulations are used to study the dynamics of polymer
translocation through a nanopore in the limit where the translocation rate is
sufficiently slow that the polymer maintains a state of conformational
quasi-equilibrium. The system is modeled as a flexible hard-sphere chain that
translocates through a cylindrical hole in a hard flat wall. In some
calculations, the nanopore is connected at one end to a spherical cavity.
Translocation times are measured directly using MC dynamics simulations. For
sufficiently narrow pores, translocation is sufficiently slow that the mean
translocation time scales with polymer length N according to \propto
(N-N_p)^2, where N_p is the average number of monomers in the nanopore; this
scaling is an indication of a quasi-static regime in which polymer-nanopore
friction dominates. We use a multiple-histogram method to calculate the
variation of the free energy with Q, a coordinate used to quantify the degree
of translocation. The free energy functions are used with the Fokker-Planck
formalism to calculate translocation time distributions in the quasi-static
regime. These calculations also require a friction coefficient, characterized
by a quantity N_{eff}, the effective number of monomers whose dynamics are
affected by the confinement of the nanopore. This was determined by fixing the
mean of the theoretical distribution to that of the distribution obtained from
MC dynamics simulations. The theoretical distributions are in excellent
quantitative agreement with the distributions obtained directly by the MC
dynamics simulations for physically meaningful values of N_{eff}. The free
energy functions for narrow-pore systems exhibit oscillations with an amplitude
that is sensitive to the nanopore length. Generally, larger oscillation
amplitudes correspond to longer translocation times.Comment: 13 pages, 13 figure
Construction of exact solutions to eigenvalue problems by the asymptotic iteration method
We apply the asymptotic iteration method (AIM) [J. Phys. A: Math. Gen. 36,
11807 (2003)] to solve new classes of second-order homogeneous linear
differential equation. In particular, solutions are found for a general class
of eigenvalue problems which includes Schroedinger problems with Coulomb,
harmonic oscillator, or Poeschl-Teller potentials, as well as the special
eigenproblems studied recently by Bender et al [J. Phys. A: Math. Gen. 34 9835
(2001)] and generalized in the present paper to higher dimensions.Comment: 10 page
Wave equation and dispersion relations for a compressible rotating fluid
A fundamental non-classical fourth-order partial differential equation to
describe small amplitude linear oscillations in a rotating compressible fluid,
is obtained. The dispersion relations for such a fluid, and the different
regions of the group and phase velocity are analyzed.Comment: 9 page
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