14,461 research outputs found
Fourth Order Algorithms for Solving the Multivariable Langevin Equation and the Kramers Equation
We develop a fourth order simulation algorithm for solving the stochastic
Langevin equation. The method consists of identifying solvable operators in the
Fokker-Planck equation, factorizing the evolution operator for small time steps
to fourth order and implementing the factorization process numerically. A key
contribution of this work is to show how certain double commutators in the
factorization process can be simulated in practice. The method is general,
applicable to the multivariable case, and systematic, with known procedures for
doing fourth order factorizations. The fourth order convergence of the
resulting algorithm allowed very large time steps to be used. In simulating the
Brownian dynamics of 121 Yukawa particles in two dimensions, the converged
result of a first order algorithm can be obtained by using time steps 50 times
as large. To further demostrate the versatility of our method, we derive two
new classes of fourth order algorithms for solving the simpler Kramers equation
without requiring the derivative of the force. The convergence of many fourth
order algorithms for solving this equation are compared.Comment: 19 pages, 2 figure
Dynamical Effects from Asteroid Belts for Planetary Systems
The orbital evolution and stability of planetary systems with interaction
from the belts is studied using the standard phase-plane analysis. In addition
to the fixed point which corresponds to the Keplerian orbit, there are other
fixed points around the inner and outer edges of the belt. Our results show
that for the planets, the probability to move stably around the inner edge is
larger than the one to move around the outer edge. It is also interesting that
there is a limit cycle of semi-attractor for a particular case. Applying our
results to the Solar System, we find that our results could provide a natural
mechanism to do the orbit rearrangement for the larger Kuiper Belt Objects and
thus successfully explain the absence of these objects beyond 50 AU.Comment: accepted by International Journal of Bifurcation and Chaos in Aug.
2003, AAS Latex, 27 pages with 6 color figure
The Gamow-Teller States in Relativistic Nuclear Models
The Gamow-Teller(GT) states are investigated in relativistic models. The
Landau-Migdal(LM) parameter is introduced in the Lagrangian as a contact term
with the pseudo-vector coupling. In the relativistic model the total GT
strength in the nucleon space is quenched by about 12% in nuclear matter and by
about 6% in finite nuclei, compared with the one of the Ikeda-Fujii-Fujita sum
rule. The quenched amount is taken by nucleon-antinucleon excitations in the
time-like region. Because of the quenching, the relativistic model requires a
larger value of the LM parameter than non-relativistic models in describing the
excitation energy of the GT state. The Pauli blocking terms are not important
for the description of the GT states.Comment: REVTeX4, no figure
Non-Markovian dynamics of a nanomechanical resonator measured by a quantum point contact
We study the dynamics of a nanomechanical resonator (NMR) subject to a
measurement by a low transparency quantum point contact (QPC) or tunnel
junction in the non-Markovian domain. We derive the non-Markovian
number-resolved (conditional) and unconditional master equations valid to
second order in the tunneling Hamiltonian without making the rotating-wave
approximation and the Markovian approximation, generally made for systems in
quantum optics. Our non-Markovian master equation reduces, in appropriate
limits, to various Markovian versions of master equations in the literature. We
find considerable difference in dynamics between the non-Markovian cases and
its Markovian counterparts. We also calculate the time-dependent transport
current through the QPC which contains information about the measured NMR
system. We find an extra transient current term proportional to the expectation
value of the symmetrized product of the position and momentum operators of the
NMR. This extra current term, with a coefficient coming from the combination of
the imaginary parts of the QPC reservoir correlation functions, has a
substantial contribution to the total transient current in the non-Markovian
case, but was generally ignored in the studies of the same problem in the
literature. Considering the contribution of this extra term, we show that a
significantly qualitative and quantitative difference in the total transient
current between the non-Markovian and the Markovian wide-band-limit cases can
be observed. Thus, it may serve as a witness or signature of the non-Markovian
features in the coupled NMR-QPC system.Comment: Accepted for publication in Physical Review B (20 pages, 13 figures
A new broken U(1)-symmetry in extreme type-II superconductors
A phase transition within the molten phase of the Abrikosov vortex system
without disorder in extreme type-II superconductors is found via large-scale
Monte-Carlo simulations. It involves breaking a U(1)-symmetry, and has a
zero-field counterpart, unlike vortex lattice melting. Its hallmark is the loss
of number-conservation of connected vortex paths threading the entire system
{\it in any direction}, driving the vortex line tension to zero. This tension
plays the role of a generalized ``stiffness'' of the vortex liquid, and serves
as a probe of the loss of order at the transition, where a weak specific heat
anomaly is found.Comment: 5 pages, 3 figure
Differentiation of Lactobacillus-probiotic strains by visual comparison of random amplified polymorphic DNA (RAPD) profiles
In the present study, distinctive RAPD fingerprints were generated for 12Â Lactobacillus-probiotic strains from 5 Lactobacillus species (L. brevis, L. reuteri, L. gallinarium, L. salivarius and L. panis) after optimization of the RAPD parameters such as MgCl2, Taq polymerase, primer concentration and type of primer. The strains were differentiated under the same PCR protocol but different concentration of primer OPM-05 (50 pmole to differentiate the 5 L. brevis strains and 75 pmole to differentiate 2 strains of L. gallinarium, 3 strains of L. reuteri, a strain of L. panis and L. salivarius). The RAPD fingerprints generated could be differentiated by visual comparison of the profiles, without being analysed by relevant software. This allows specific, rapid, immediate and convenient identification of the Lactobacillus strains
On the Analytic Structure of the Quark Self-Energy in Nambu-Jona- Lasinio Models
The self-energy of quarks is investigated for various models which are
inspired by the Nambu--Jona-Lasinio (NJL) model. Including, beyond the
Hartree-Fock approximation, terms up to second-order in the quark interaction,
the real and imaginary parts of scalar and vector components of the self-energy
are discussed. The second-order contributions depend on the energy and momentum
of the quark under consideration. This leads to solutions of the Dirac equation
which are significantly different from those of a free quark or a quark with
constant effective mass, as obtained in the Hartree-Fock approximation.Comment: 15 pages LaTeX, 6 figures can be obtained from author
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