10,760 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
Analytical and experimental study of stratification and liquid-ullage coupling, 1 June 1964 - 31 May 1965
Closed-form solution for stratification of subcooled fluids in containers subjected to heating, and for liquid-ullage vapor couplin
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
Higher Order Force Gradient Symplectic Algorithms
We show that a recently discovered fourth order symplectic algorithm, which
requires one evaluation of force gradient in addition to three evaluations of
the force, when iterated to higher order, yielded algorithms that are far
superior to similarly iterated higher order algorithms based on the standard
Forest-Ruth algorithm. We gauge the accuracy of each algorithm by comparing the
step-size independent error functions associated with energy conservation and
the rotation of the Laplace-Runge-Lenz vector when solving a highly eccentric
Kepler problem. For orders 6, 8, 10 and 12, the new algorithms are
approximately a factor of , , and better.Comment: 23 pages, 10 figure
The Complete Characterization of Fourth-Order Symplectic Integrators with Extended-Linear Coefficients
The structure of symplectic integrators up to fourth-order can be completely
and analytical understood when the factorization (split) coefficents are
related linearly but with a uniform nonlinear proportional factor. The analytic
form of these {\it extended-linear} symplectic integrators greatly simplified
proofs of their general properties and allowed easy construction of both
forward and non-forward fourth-order algorithms with arbitrary number of
operators. Most fourth-order forward integrators can now be derived
analytically from this extended-linear formulation without the use of symbolic
algebra.Comment: 12 pages, 2 figures, submitted to Phys. Rev. E, corrected typo
Phase diagram and universality of the Lennard-Jones gas-liquid system
The gas-liquid phase transition of the three-dimensional Lennard-Jones
particles system is studied by molecular dynamics simulations. The gas and
liquid densities in the coexisting state are determined with high accuracy. The
critical point is determined by the block density analysis of the Binder
parameter with the aid of the law of rectilinear diameter. From the critical
behavior of the gas-liquid coexsisting density, the critical exponent of the
order parameter is estimated to be . Surface tension is
estimated from interface broadening behavior due to capillary waves. From the
critical behavior of the surface tension, the critical exponent of the
correlation length is estimated to be . The obtained values of
and are consistent with those of the Ising universality class.Comment: 8 pages, 8 figures, new results are adde
Mapping functions and critical behavior of percolation on rectangular domains
The existence probability and the percolation probability of the
bond percolation on rectangular domains with different aspect ratios are
studied via the mapping functions between systems with different aspect ratios.
The superscaling behavior of and for such systems with exponents
and , respectively, found by Watanabe, Yukawa, Ito, and Hu in [Phys. Rev.
Lett. \textbf{93}, 190601 (2004)] can be understood from the lower order
approximation of the mapping functions and for and ,
respectively; the exponents and can be obtained from numerically
determined mapping functions and , respectively.Comment: 17 pages with 6 figure
Vibrational energy relaxation in proteins
An overview of theories related to vibrational energy relaxation (VER) in
proteins is presented. VER of a selected mode in cytochrome c is studied using
two theoretical approaches. One is the equilibrium simulation approach with
quantum correction factors, and the other is the reduced model approach which
describes the protein as an ensemble of normal modes interacting through
nonlinear coupling elements. Both methods result in estimates of the VER time
(sub ps) for a CD stretching mode in the protein at room temperature. The
theoretical predictions are in accord with the experimental data of Romesberg's
group. A perspective on future directions for the detailed study of time scales
and mechanisms for VER in proteins is presented.Comment: 12 pages, 4 figures, accepted for publication in PNA
Geometric and impurity effects on quantum rings in magnetic fields
We investigate the effects of impurities and changing ring geometry on the
energetics of quantum rings under different magnetic field strengths. We show
that as the magnetic field and/or the electron number are/is increased, both
the quasiperiodic Aharonov-Bohm oscillations and various magnetic phases become
insensitive to whether the ring is circular or square in shape. This is in
qualitative agreement with experiments. However, we also find that the
Aharonov-Bohm oscillation can be greatly phase-shifted by only a few impurities
and can be completely obliterated by a high level of impurity density. In the
many-electron calculations we use a recently developed fourth-order imaginary
time projection algorithm that can exactly compute the density matrix of a
free-electron in a uniform magnetic field.Comment: 8 pages, 7 figures, to appear in PR
`St\"uckelberg interferometry' with ultracold molecules
We report on the realization of a time-domain `St\"uckelberg interferometer',
which is based on the internal state structure of ultracold Feshbach molecules.
Two subsequent passages through a weak avoided crossing between two different
orbital angular momentum states in combination with a variable hold time lead
to high-contrast population oscillations. This allows for a precise
determination of the energy difference between the two molecular states. We
demonstrate a high degree of control over the interferometer dynamics. The
interferometric scheme provides new possibilities for precision measurements
with ultracold molecules.Comment: 4 pages, 5 figure
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