1,385 research outputs found
Solving the radial Dirac equations: a numerical odyssey
We discuss, in a pedagogical way, how to solve for relativistic wave
functions from the radial Dirac equations. After an brief introduction, in
Section II we solve the equations for a linear Lorentz scalar potential,
V_s(r), that provides for confinement of a quark. The case of massless u and d
quarks is treated first, as these are necessarily quite relativistic. We use an
iterative procedure to find the eigenenergies and the upper and lower component
wave functions for the ground state and then, later, some excited states.
Solutions for the massive quarks (s, c, and b) are also presented. In Section
III we solve for the case of a Coulomb potential, which is a time-like
component of a Lorentz vector potential, V_v(r). We re-derive, numerically, the
(analytically well-known) relativistic hydrogen atom eigenenergies and wave
functions, and later extend that to the cases of heavier one-electron atoms and
muonic atoms. Finally, Section IV finds solutions for a combination of the V_s
and V_v potentials. We treat two cases. The first is one in which V_s is the
linear potential used in Sec. II and V_v is Coulombic, as in Sec. III. The
other is when both V_s and V_v are linearly confining, and we establish when
these potentials give a vanishing spin-orbit interaction (as has been shown to
be the case in quark models of the hadronic spectrum).Comment: 39 pages (total), 23 figures, 2 table
A unified approach for the solution of the Fokker-Planck equation
This paper explores the use of a discrete singular convolution algorithm as a
unified approach for numerical integration of the Fokker-Planck equation. The
unified features of the discrete singular convolution algorithm are discussed.
It is demonstrated that different implementations of the present algorithm,
such as global, local, Galerkin, collocation, and finite difference, can be
deduced from a single starting point. Three benchmark stochastic systems, the
repulsive Wong process, the Black-Scholes equation and a genuine nonlinear
model, are employed to illustrate the robustness and to test accuracy of the
present approach for the solution of the Fokker-Planck equation via a
time-dependent method. An additional example, the incompressible Euler
equation, is used to further validate the present approach for more difficult
problems. Numerical results indicate that the present unified approach is
robust and accurate for solving the Fokker-Planck equation.Comment: 19 page
Network Topology of an Experimental Futures Exchange
Many systems of different nature exhibit scale free behaviors. Economic
systems with power law distribution in the wealth is one of the examples. To
better understand the working behind the complexity, we undertook an empirical
study measuring the interactions between market participants. A Web server was
setup to administer the exchange of futures contracts whose liquidation prices
were coupled to event outcomes. After free registration, participants started
trading to compete for the money prizes upon maturity of the futures contracts
at the end of the experiment. The evolving `cash' flow network was
reconstructed from the transactions between players. We show that the network
topology is hierarchical, disassortative and scale-free with a power law
exponent of 1.02+-0.09 in the degree distribution. The small-world property
emerged early in the experiment while the number of participants was still
small. We also show power law distributions of the net incomes and
inter-transaction time intervals. Big winners and losers are associated with
high degree, high betweenness centrality, low clustering coefficient and low
degree-correlation. We identify communities in the network as groups of the
like-minded. The distribution of the community sizes is shown to be power-law
distributed with an exponent of 1.19+-0.16.Comment: 6 pages, 12 figure
Molecular dynamics simulation of the fragile glass former ortho-terphenyl: a flexible molecule model
We present a realistic model of the fragile glass former orthoterphenyl and
the results of extensive molecular dynamics simulations in which we
investigated its basic static and dynamic properties. In this model the
internal molecular interactions between the three rigid phenyl rings are
described by a set of force constants, including harmonic and anharmonic terms;
the interactions among different molecules are described by Lennard-Jones
site-site potentials. Self-diffusion properties are discussed in detail
together with the temperature and momentum dependencies of the
self-intermediate scattering function. The simulation data are compared with
existing experimental results and with the main predictions of the Mode
Coupling Theory.Comment: 20 pages and 28 postscript figure
Algorithm for normal random numbers
We propose a simple algorithm for generating normally distributed pseudo
random numbers. The algorithm simulates N molecules that exchange energy among
themselves following a simple stochastic rule. We prove that the system is
ergodic, and that a Maxwell like distribution that may be used as a source of
normally distributed random deviates follows when N tends to infinity. The
algorithm passes various performance tests, including Monte Carlo simulation of
a finite 2D Ising model using Wolff's algorithm. It only requires four simple
lines of computer code, and is approximately ten times faster than the
Box-Muller algorithm.Comment: 5 pages, 3 encapsulated Postscript Figures. Submitted to
Phys.Rev.Letters. For related work, see http://pipe.unizar.es/~jf
Phase diffusion as a model for coherent suppression of tunneling in the presence of noise
We study the stabilization of coherent suppression of tunneling in a driven
double-well system subject to random periodic function ``kicks''. We
model dissipation due to this stochastic process as a phase diffusion process
for an effective two-level system and derive a corresponding set of Bloch
equations with phase damping terms that agree with the periodically kicked
system at discrete times. We demonstrate that the ability of noise to localize
the system on either side of the double-well potenital arises from overdamping
of the phase of oscillation and not from any cooperative effect between the
noise and the driving field. The model is investigated with a square wave
drive, which has qualitatively similar features to the widely studied
cosinusoidal drive, but has the additional advantage of allowing one to derive
exact analytic expressions.Comment: 17 pages, 4 figures, submitted to Phys. Rev.
'Reclaiming the criminal' : the role and training of prison officers in England, 1877-1914
This article examines the role and training of prison officers in England, between 1877 and 1914. It is concerned with the changing penal philosophies and practices of this period and how these were implemented in local prisons, and the duties of the prison officer. More broadly, this article argues that the role of the prison officer and their training (from 1896) reflect wider ambiguities in prison policy and practice during this period
Social preferences, accountability, and wage bargaining
We assess the extent of preferences for employment in a collective wage bargaining situation with heterogeneous workers. We vary the size of the union and introduce a treatment mechanism transforming the voting game into an individual allocation task. Our results show that highly productive workers do not take employment of low productive workers into account when making wage proposals, regardless of whether insiders determine the wage or all workers. The level of pro-social preferences is small in the voting game, while it increases as the game is transformed into an individual allocation task. We interpret this as an accountability effect
Theory of Circle Maps and the Problem of One-Dimensional Optical Resonator with a Periodically Moving Wall
We consider the electromagnetic field in a cavity with a periodically
oscillating perfectly reflecting boundary and show that the mathematical theory
of circle maps leads to several physical predictions. Notably, well-known
results in the theory of circle maps (which we review briefly) imply that there
are intervals of parameters where the waves in the cavity get concentrated in
wave packets whose energy grows exponentially. Even if these intervals are
dense for typical motions of the reflecting boundary, in the complement there
is a positive measure set of parameters where the energy remains bounded.Comment: 34 pages LaTeX (revtex) with eps figures, PACS: 02.30.Jr, 42.15.-i,
42.60.Da, 42.65.Y
Dark-in-Bright Solitons in Bose-Einstein Condensates with Attractive Interactions
We demonstrate a possibility to generate localized states in effectively
one-dimensional Bose-Einstein condensates with a negative scattering length in
the form of a dark soliton in the presence of an optical lattice (OL) and/or a
parabolic magnetic trap. We connect such structures with twisted localized
modes (TLMs) that were previously found in the discrete nonlinear
Schr{\"o}dinger equation. Families of these structures are found as functions
of the OL strength, tightness of the magnetic trap, and chemical potential, and
their stability regions are identified. Stable bound states of two TLMs are
also found. In the case when the TLMs are unstable, their evolution is
investigated by means of direct simulations, demonstrating that they transform
into large-amplitude fundamental solitons. An analytical approach is also
developed, showing that two or several fundamental solitons, with the phase
shift between adjacent ones, may form stable bound states, with
parameters quite close to those of the TLMs revealed by simulations. TLM
structures are found numerically and explained analytically also in the case
when the OL is absent, the condensate being confined only by the magnetic trap.Comment: 13 pages, 7 figures, New Journal of Physics (in press
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