11,026 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
The detection of extragalactic N: Consequences for nitrogen nucleosynthesis and chemical evolution
Detections of extragalactic N are reported from observations of the
rare hydrogen cyanide isotope HCN toward the Large Magellanic Cloud
(LMC) and the core of the (post-) starburst galaxy NGC 4945. Accounting for
optical depth effects, the LMC data from the massive star-forming region N113
infer a N ratio of 111 17, about twice the C
value. For the LMC star-forming region N159HW and for the central region of NGC
4945, N ratios are also 100. The N ratios
are smaller than all interstellar nitrogen isotope ratios measured in the disk
and center of the Milky Way, strongly supporting the idea that N is
predominantly of `primary' nature, with massive stars being its dominant
source. Although this appears to be in contradiction with standard stellar
evolution and nucleosynthesis calculations, it supports recent findings of
abundant N production due to rotationally induced mixing of protons into
the helium-burning shells of massive stars.Comment: 15 pages including one postscript figure, accepted for publication by
ApJ Letter, further comments: please contact Yi-nan Chi
Higher-order splitting algorithms for solving the nonlinear Schr\"odinger equation and their instabilities
Since the kinetic and the potential energy term of the real time nonlinear
Schr\"odinger equation can each be solved exactly, the entire equation can be
solved to any order via splitting algorithms. We verified the fourth-order
convergence of some well known algorithms by solving the Gross-Pitaevskii
equation numerically. All such splitting algorithms suffer from a latent
numerical instability even when the total energy is very well conserved. A
detail error analysis reveals that the noise, or elementary excitations of the
nonlinear Schr\"odinger, obeys the Bogoliubov spectrum and the instability is
due to the exponential growth of high wave number noises caused by the
splitting process. For a continuum wave function, this instability is
unavoidable no matter how small the time step. For a discrete wave function,
the instability can be avoided only for \dt k_{max}^2{<\atop\sim}2 \pi, where
.Comment: 10 pages, 8 figures, submitted to Phys. Rev.
Fractional-Period Excitations in Continuum Periodic Systems
We investigate the generation of fractional-period states in continuum
periodic systems. As an example, we consider a Bose-Einstein condensate
confined in an optical-lattice potential. We show that when the potential is
turned on non-adiabatically, the system explores a number of transient states
whose periodicity is a fraction of that of the lattice. We illustrate the
origin of fractional-period states analytically by treating them as resonant
states of a parametrically forced Duffing oscillator and discuss their
transient nature and potential observability.Comment: 10 pages, 6 figures (some with multiple parts); revised version:
minor clarifications of a couple points, to appear in Physical Review
How long does treatment with fixed orthodontic appliances last? A systematic review
INTRODUCTION
There is little agreement on the expected duration of a course of orthodontic treatment; however, a consensus appears to have emerged that fixed appliance treatment is overly lengthy. This has spawned numerous novel approaches directed at reducing the duration of treatment, occasionally with an acceptance that occlusal outcomes may be compromised. The aim of this study was to determine the mean duration and the number of visits required for comprehensive orthodontic treatment involving fixed appliances.
METHODS
Multiple electronic databases were searched with no language restrictions, authors were contacted as required, and reference lists of potentially relevant studies were screened. Randomized controlled trials and nonrandomized prospective studies concerning fixed appliance treatment with treatment duration as an outcome measure were included. Data extraction and quality assessment were performed independently and in duplicate.
RESULTS
Twenty-five studies were included after screening: 20 randomized controlled trials and 5 controlled clinical trials. Twenty-two studies were eligible for meta-analysis after quality assessment. The mean treatment duration derived from the 22 included studies involving 1089 participants was 19.9Â months (95% confidence interval, 19.58, 20.22Â months). Sensitivity analyses were carried out including 3 additional studies, resulting in average duration of treatment of 20.02Â months (95% confidence interval, 19.71, 20.32Â months) based on data from 1211 participants. The mean number of required visits derived from 5 studies was 17.81 (95% confidence interval, 15.47, 20.15 visits).
CONCLUSIONS
Based on prospective studies carried out in university settings, comprehensive orthodontic treatment on average requires less than 2Â years to complete
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