1,009 research outputs found
Fast integral equation methods for the modified Helmholtz equation
We present a collection of integral equation methods for the solution to the
two-dimensional, modified Helmholtz equation, u(\x) - \alpha^2 \Delta u(\x) =
0, in bounded or unbounded multiply-connected domains. We consider both
Dirichlet and Neumann problems. We derive well-conditioned Fredholm integral
equations of the second kind, which are discretized using high-order, hybrid
Gauss-trapezoid rules. Our fast multipole-based iterative solution procedure
requires only O(N) or operations, where N is the number of nodes
in the discretization of the boundary. We demonstrate the performance of the
methods on several numerical examples.Comment: Published in Computers & Mathematics with Application
Reformulation of the Stochastic Potential Switching Algorithm and a Generalized Fourtuin-Kasteleyn Representation
A new formulation of the stochastic potential switching algorithm is
presented. This reformulation naturally leads us to a generalized
Fourtuin-Kasteleyn representation of the partition function Z. A formula for
internal energy E and that of heat capacity C are derived from derivatives of
the partition function. We also derive a formula for the exchange probability
in the replica exchange Monte Carlo method. By combining the formulae with the
Stochastic Cutoff method, we can greatly reduce the computational time to
perform internal energy and heat capacity measurements and the replica exchange
Monte Carlo method in long-range interacting systems. Numerical simulations in
three dimensional magnetic dipolar systems show the validity and efficiency of
the method.Comment: 11 pages, 6 figures, to appear in PR
Persistence in systems with algebraic interaction
Persistence in coarsening 1D spin systems with a power law interaction
is considered. Numerical studies indicate that for sufficiently
large values of the interaction exponent ( in our
simulations), persistence decays as an algebraic function of the length scale
, . The Persistence exponent is found to be
independent on the force exponent and close to its value for the
extremal () model, . For smaller
values of the force exponent (), finite size effects prevent the
system from reaching the asymptotic regime. Scaling arguments suggest that in
order to avoid significant boundary effects for small , the system size
should grow as .Comment: 4 pages 4 figure
How can a 22-pole ion trap exhibit 10 local minima in the effective potential?
The column density distribution of trapped OH ions in a 22-pole ion trap
is measured for different trap parameters. The density is obtained from
position-dependent photodetachment rate measurements. Overall, agreement is
found with the effective potential of an ideal 22-pole. However, in addition we
observe 10 distinct minima in the trapping potential, which indicate a breaking
of the 22-fold symmetry. Numerical simulations show that a displacement of a
subset of the radiofrequency electrodes can serve as an explanation for this
symmetry breaking
Fast multipole networks
Two prerequisites for robotic multiagent systems are mobility and
communication. Fast multipole networks (FMNs) enable both ends within a unified
framework. FMNs can be organized very efficiently in a distributed way from
local information and are ideally suited for motion planning using artificial
potentials. We compare FMNs to conventional communication topologies, and find
that FMNs offer competitive communication performance (including higher network
efficiency per edge at marginal energy cost) in addition to advantages for
mobility
Coulomb Interactions via Local Dynamics: A Molecular--Dynamics Algorithm
We derive and describe in detail a recently proposed method for obtaining
Coulomb interactions as the potential of mean force between charges which are
dynamically coupled to a local electromagnetic field. We focus on the Molecular
Dynamics version of the method and show that it is intimately related to the
Car--Parrinello approach, while being equivalent to solving Maxwell's equations
with freely adjustable speed of light. Unphysical self--energies arise as a
result of the lattice interpolation of charges, and are corrected by a
subtraction scheme based on the exact lattice Green's function. The method can
be straightforwardly parallelized using standard domain decomposition. Some
preliminary benchmark results are presented.Comment: 8 figure
Immunocytochemical localization of the neuron-specific form of the c-src gene product, pp60c-src(+), in rat brain
Neurons express high levels of a variant form of the c-src gene product, denoted pp60c-src(+), which contains a 6 amino acid insert in the amino-terminal half of the c-src protein. We have determined the localization of pp60c-src(+) in neurons using an affinity-purified anti-peptide antibody, referred to as affi-SB12, that exclusively recognizes this neuron-specific form of the c-src gene product. Using affi-SB12, we examined the distribution of pp60c-src(+) by immunoperoxidase staining of sections through adult rat brains, pp60c-src(+) was widely distributed in rat brain and appeared to be differentially expressed in subpopulations of neurons. The majority of immunoreactive neurons was found in the mesencephalon, cerebellum, pons, and medulla. Telencephalic structures that contained substantial populations of pp60c-src(+)-immunoreactive neurons included layer V of the cerebral cortex and the ventral pallidum. Within individual neurons, pp60c-src(+) immunoreactivity was localized to the cell soma and dendritic processes, while labeling of axons and nerve terminals (puncta) was not as readily detected. Dense accumulations of immunoreactive axons were rare, being most prominent in portions of the inferior and superior olive, and in the spinal trigeminal nucleus. While the regional distribution of pp60c-src(+) immunoreactivity does not correlate with any specific neuronal cell type or first messenger system, this unique pattern of expression of pp60c-src(+) suggests the existence of a previously uncharacterized functional organization within the brain. Furthermore, the localization of this neuron-specific tyrosine kinase in functionally important areas of the nerve cell, namely, dendritic processes, axons, and nerve terminals, suggests that pp60c-src(+) may regulate pleiotropic functions in specific classes of neurons in the adult central nervous system
Local Simulation Algorithms for Coulomb Interaction
Long ranged electrostatic interactions are time consuming to calculate in
molecular dynamics and Monte-Carlo simulations. We introduce an algorithmic
framework for simulating charged particles which modifies the dynamics so as to
allow equilibration using a local Hamiltonian. The method introduces an
auxiliary field with constrained dynamics so that the equilibrium distribution
is determined by the Coulomb interaction. We demonstrate the efficiency of the
method by simulating a simple, charged lattice gas.Comment: Last figure changed to improve demonstration of numerical efficienc
Colloquium: Trapped ions as quantum bits -- essential numerical tools
Trapped, laser-cooled atoms and ions are quantum systems which can be
experimentally controlled with an as yet unmatched degree of precision. Due to
the control of the motion and the internal degrees of freedom, these quantum
systems can be adequately described by a well known Hamiltonian. In this
colloquium, we present powerful numerical tools for the optimization of the
external control of the motional and internal states of trapped neutral atoms,
explicitly applied to the case of trapped laser-cooled ions in a segmented
ion-trap. We then delve into solving inverse problems, when optimizing trapping
potentials for ions. Our presentation is complemented by a quantum mechanical
treatment of the wavepacket dynamics of a trapped ion. Efficient numerical
solvers for both time-independent and time-dependent problems are provided.
Shaping the motional wavefunctions and optimizing a quantum gate is realized by
the application of quantum optimal control techniques. The numerical methods
presented can also be used to gain an intuitive understanding of quantum
experiments with trapped ions by performing virtual simulated experiments on a
personal computer. Code and executables are supplied as supplementary online
material (http://kilian-singer.de/ent).Comment: accepted for publication in Review of Modern Physics 201
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