pinecone/core-2020-05-10-deduplication huggingface dataset:
Lagrange-Galerkin methods on spherical geodesic grids: The shallow water equations

The article of record as published may be located at http://dx.doi.org/10.1006/jcph.2000.6469The weak Lagrange-Galerkin finite element method fur the 2D shallow water equations on the sphere is presented. This method offers stable and accurate solutions because the equations are integrated along thr characteristics. The equations are written in 3D Cartesian conservation form and the domains are discretized using linear triangular elements. The use of linear triangular elements permits the construction of accurate (by virtue of the second-order spatial and temporal accuracies of the scheme) and efficient (by virtue of the less stringent CFL condition of Lagrangian methods) schemes on unstructured domains. Using linear triangles in 3D Cartesian space allows for the explicit construction of area coordinate basis functions thereby simplifying the calculation of the finite element integrals. The triangular grids are constructed by a generalization of the icosahedral grids that have been typically used in recent papers. An efficient searching strategy fur the departure points is also presented for these generalized icosahedral grids which involves very few Boating point operations. In addition a high-order scheme for computing the characteristic curves in 3D Cartesian space is presented: a general family of Runge-Kutta schemes. Results for six test cases are reported in order to confirm the accuracy of the scheme
Simulated Annealing Clusterization Algorithm for Studying the
  Multifragmentation

We present the details of the numerical realization of the recently advanced
algorithm developed to identify the fragmentation in heavy ion reactions. This
new algorithm is based on the Simulated Annealing method and is dubbed as
Simulated Annealing Clusterization Algorithm [SACA]. We discuss the different
parameters used in the Simulated Annealing method and present an economical set
of the parameters which is based on the extensive analysis carried out for the
central and peripheral collisions of Au-Au, Nb-Nb and Pb-Pb. These parameters
are crucial for the success of the algorithm. Our set of optimized parameters
gives the same results as the most conservative choice, but is very fast. We
also discuss the nucleon and fragment exchange processes which are very
important for the energy minimization and finally present the analysis of the
reaction dynamics using the new algorithm. This algorithm is can be applied
whenever one wants to identify which of a given number of constituents form
bound objects.Comment: 36 pages, 15 figures, submitted to Journal of Computational Physic
Optimal Prediction for Hamiltonian partial differential equations

Optimal prediction methods compensate for a lack of resolution in the
numerical solution of time-dependent differential equations through the use of
prior statistical information. We present a new derivation of the basic
methodology, show that field-theoretical perturbation theory provides a useful
device for dealing with quasi-linear problems, and provide a nonlinear example
that illuminates the difference between a pseudo-spectral method and an optimal
prediction method with Fourier kernels. Along the way, we explain the
differences and similarities between optimal prediction, the representer method
in data assimilation, and duality methods for finding weak solutions. We also
discuss the conditions under which a simple implementation of the optimal
prediction method can be expected to perform well.Comment: 38 pages, 16 figure
A modified parallel tree code for N-body simulation of the Large Scale
  Structure of the Universe

N-body codes to perform simulations of the origin and evolution of the Large
Scale Structure of the Universe have improved significantly over the past
decade both in terms of the resolution achieved and of reduction of the CPU
time. However, state-of-the-art N-body codes hardly allow one to deal with
particle numbers larger than a few 10^7, even on the largest parallel systems.
In order to allow simulations with larger resolution, we have first
re-considered the grouping strategy as described in Barnes (1990) (hereafter
B90) and applied it with some modifications to our WDSH-PT (Work and Data
SHaring - Parallel Tree) code. In the first part of this paper we will give a
short description of the code adopting the Barnes and Hut algorithm
\cite{barh86} (hereafter BH), and in particular of the memory and work
distribution strategy applied to describe the {\it data distribution} on a
CC-NUMA machine like the CRAY-T3E system. In the second part of the paper we
describe the modification to the Barnes grouping strategy we have devised to
improve the performance of the WDSH-PT code. We will use the property that
nearby particles have similar interaction list. This idea has been checked in
B90, where an interaction list is builded which applies everywhere within a
cell C_{group} containing a little number of particles N_{crit}. B90 reuses
this interaction list for each particle $ p \in C_{group}$ in the cell in turn.
We will assume each particle p to have the same interaction list.
  Thus it has been possible to reduce the CPU time increasing the performances.
This leads us to run simulations with a large number of particles (N ~
10^7/10^9) in non-prohibitive times.Comment: 13 pages and 7 Figure
Identification of multilayered particles from scattering data by a
  clustering method

A multilayered particle is illuminated by plane acoustic or electromagnetic
waves of one or several frequencies. We consider the inverse scattering problem
for the identification of the layers and of the refraction coefficients of the
scatterer in a non-Born region of scattering. Local deterministic and global
probabilistic minimization methods are studied. A special Reduction Procedure
is introduced to reduce the dimensionality of the minimization space. Deep's
and the Multilevel
  Single-Linkage methods for global minimization are used for the solution of
the inverse problem. Their performance is analyzed for various multilayer
configurations
Multiscale Finite-Difference-Diffusion-Monte-Carlo Method for Simulating
  Dendritic Solidification

We present a novel hybrid computational method to simulate accurately
dendritic solidification in the low undercooling limit where the dendrite tip
radius is one or more orders of magnitude smaller than the characteristic
spatial scale of variation of the surrounding thermal or solutal diffusion
field. The first key feature of this method is an efficient multiscale
diffusion Monte-Carlo (DMC) algorithm which allows off-lattice random walkers
to take longer and concomitantly rarer steps with increasing distance away from
the solid-liquid interface. As a result, the computational cost of evolving the
large scale diffusion field becomes insignificant when compared to that of
calculating the interface evolution. The second key feature is that random
walks are only permitted outside of a thin liquid layer surrounding the
interface. Inside this layer and in the solid, the diffusion equation is solved
using a standard finite-difference algorithm that is interfaced with the DMC
algorithm using the local conservation law for the diffusing quantity. Here we
combine this algorithm with a previously developed phase-field formulation of
the interface dynamics and demonstrate that it can accurately simulate
three-dimensional dendritic growth in a previously unreachable range of low
undercoolings that is of direct experimental relevance.Comment: RevTeX, 16 pages, 10 eps figures, submitted to J. Comp. Phy
Mathematical Modeling of Boson-Fermion Stars in the Generalized
  Scalar-Tensor Theories of Gravity

A model of static boson-fermion star with spherical symmetry based on the
scalar-tensor theory of gravity with massive dilaton field is investigated
numerically.
  Since the radius of star is \textit{a priori} an unknown quantity, the
corresponding boundary value problem (BVP) is treated as a nonlinear spectral
problem with a free internal boundary. The Continuous Analogue of Newton Method
(CANM) for solving this problem is applied.
  Information about basic geometric functions and the functions describing the
matter fields, which build the star is obtained. In a physical point of view
the main result is that the structure and properties of the star in presence of
massive dilaton field depend essentially both of its fermionic and bosonic
components.Comment: 16 pages, amstex, 5 figures, changed conten
Loop integrals in three outstanding gauges: Feynman, Light-cone and Coulomb

We apply negative dimensional integration method (NDIM) to three outstanding gauges: Feynman, light-cone and Coulomb gauges. Our aim is to show that NDIM is a very suitable technique to deal with loop integrals, being them originated from any gauge choice. In Feynman gauge we perform scalar two-loop four-point massless integrals; in the light-cone gauge we calculate scalar two-loop integrals contributing for two-point functions without any kind of prescriptions, since NDIM can abandon such devices -- this calculation is the first test of our prescriptionless method beyond one-loop order; finally, for the Coulomb gauge we consider a four propagator massless loop integral, in the split dimensional regularization context
A new interface method for hyperbolic problems with discontinuous coefficients: one-dimensional acoustic example

International audienceA new numerical method, called the Explicit Simplified Interface Method (ESIM), is developed in the context of acoustic wave propagation in heterogeneous media. Equations of acoustics are written as a first-order linear hyperbolic system. Away from interfaces, a standard scheme (Lax-Wendroff, TVD, WENO...) is used in a classical way. Near interfaces, the same scheme is used, but it is applied on a set of modified values deduced from numerical values and from jump conditions at interfaces. It amounts to modify the scheme so that its order of accuracy is maintained at irregular points, despite the non-smoothness of the solution. This easy to implement interface method requires few additional computational resources and it can be applied to other partial differential equations
A multi-domain spectral method for scalar and vectorial Poisson
  equations with non-compact sources

We present a spectral method for solving elliptic equations which arise in
general relativity, namely three-dimensional scalar Poisson equations, as well
as generalized vectorial Poisson equations of the type $\Delta \vec{N} +
\lambda \vec{\nabla}(\vec{\nabla}\cdot \vec{N}) = \vec{S}$ with $\lambda \not=
-1$. The source can extend in all the Euclidean space ${\bf R}^3$, provided it
decays at least as $r^{-3}$. A multi-domain approach is used, along with
spherical coordinates $(r,\theta,\phi)$. In each domain, Chebyshev polynomials
(in $r$ or $1/r$) and spherical harmonics (in $\theta$ and $\phi$) expansions
are used. If the source decays as $r^{-k}$ the error of the numerical solution
is shown to decrease at least as $N^{-2(k-2)}$, where $N$ is the number of
Chebyshev coefficients. The error is even evanescent, i.e. decreases as
$\exp(-N)$, if the source does not contain any spherical harmonics of index
$l\geq k -3$ (scalar case) or $l\geq k-5$ (vectorial case).Comment: Minor revisions. 31 pages, 13 figures, accepted for publication J.
  Comp. Phy
Numerical Simulation of Grain Boundary Grooving By Level Set Method

A numerical investigation of grain-boundary grooving by means of a Level Set
method is carried out. An idealized polygranular interconnect which consists of
grains separated by parallel grain boundaries aligned normal to the average
orientation of the surface is considered. The surface diffusion is the only
physical mechanism assumed. The surface diffusion is driven by surface
curvature gradients, and a fixed surface slope and zero atomic flux are assumed
at the groove root. The corresponding mathematical system is an initial
boundary value problem for a two-dimensional Hamilton-Jacobi type equation. The
results obtained are in good agreement with both Mullins' analytical "small
slope" solution of the linearized problem (W.W. Mullins, 1957) (for the case of
an isolated grain boundary) and with solution for the periodic array of grain
boundaries (S.A. Hackney, 1988).Comment: Submitted to the Journal of Computational Physics (19 pages, 8
  Postscript figures, 3 tables, 29 references
Spectral schemes on triangular elements

The Poisson problem with homogeneous Dirichlet boundary conditions is considered on a triangle. The mapping between square and triangle is realized by mapping an edge of the square onto a corner of the triangle. Then standard Chebyshev collocation techniques can be applied. Numerical experiments demonstrate the expected high spectral accuracy. Further it is shown that finite difference preconditioning can be successfully applied in order to construct an efficient iterative solver. Then the convection-diffusion equation is considered. Here finite difference preconditioning with central differences does not overcome instability. However, applying the first order upstream scheme, we obtain a stable system. Finally a domain decomposition technique is applied to the patching of rectangular and triangular elements
Separation of variables in perturbed cylinders

We study the Laplace operator subject to Dirichlet boundary conditions in a
two-dimensional domain that is one-to-one mapped onto a cylinder (rectangle or
infinite strip). As a result of this transformation the original eigenvalue
problem is reduced to an equivalent problem for an operator with variable
coefficients. Taking advantage of the simple geometry we separate variables by
means of the Fourier decomposition method. The ODE system obtained in this way
is then solved numerically yielding the eigenvalues of the operator. The same
approach allows us to find complex resonances arising in some non-compact
domains. We discuss numerical examples related to quantum waveguide problems.Comment: LaTeX 2e, 18 pages, 6 figure
Shock capturing and front tracking methods for granular avalanches

Shock formations are observed in granular avalanches when supercritical flow
merges into a region of subcritical flow. In this paper we employ a
shock-capturing numerical scheme for the one-dimensional Savage-Hutter theory
of granular flow to describe this phenomenon. A Lagrangian moving mesh scheme
applied to the non-conservative form of the equations reproduces smooth
solutions of these free boundary problems very well, but fails when shocks are
formed. A non-oscillatory central difference (NOC) scheme with TVD limiter or
WENO cell reconstruction for the conservative equations is therefore
introduced. For the avalanche free boundary problems it must be combined with a
front-tracking method, developed here, to properly describe the margin
evolution. It is found that this NOC scheme combined with the front-tracking
module reproduces both the shock wave and the smooth solution accurately. A
piecewise quadratic WENO reconstruction improves the smoothness of the solution
near local extrema. The schemes are checked against exact solutions for (1) an
upward moving shock wave, (2) the motion of a parabolic cap down an inclined
plane and (3) the motion of a parabolic cap down a curved slope ending in a
flat run-out region, where a shock is formed as the avalanche comes to a halt
Numerical Study of Quantum Resonances in Chaotic Scattering

This paper presents numerical evidence that for quantum systems with chaotic
classical dynamics, the number of scattering resonances near an energy $E$
scales like $\hbar^{-\frac{D(K_E)+1}{2}}$ as $\hbar\to{0}$. Here, $K_E$ denotes
the subset of the classical energy surface $\{H=E\}$ which stays bounded for
all time under the flow generated by the Hamiltonian $H$ and $D(K_E)$ denotes
its fractal dimension. Since the number of bound states in a quantum system
with $n$ degrees of freedom scales like $\hbar^{-n}$, this suggests that the
quantity $\frac{D(K_E)+1}{2}$ represents the effective number of degrees of
freedom in scattering problems.Comment: 24 pages, including 44 figure
A Fast Semi-Implicit Finite Difference Method for the TDGL Equations

We propose a finite-difference algorithm for solving the time-dependent
Ginzburg-Landau (TDGL) equation coupled to the appropriate Maxwell equation.
The time derivatives are discretized using a second order semi-implicit scheme
which, for intermediate values of the Ginzburg-Landau parameter $\kappa$,
allows time-steps two orders of magnitude larger than commonly used in explicit
schemes. We demonstrate the use of the method by solving a fully
three-dimensional problem of a current-carrying wire with longitudinal and
transverse magnetic fields.Comment: 4 figure
DNA electrophoresis studied with the cage model

The cage model for polymer reptation, proposed by Evans and Edwards, and its
recent extension to model DNA electrophoresis, are studied by numerically exact
computation of the drift velocities for polymers with a length L of up to 15
monomers. The computations show the Nernst-Einstein regime (v ~ E) followed by
a regime where the velocity decreases exponentially with the applied electric
field strength. In agreement with de Gennes' reptation arguments, we find that
asymptotically for large polymers the diffusion coefficient D decreases
quadratically with polymer length; for the cage model, the proportionality
coefficient is DL^2=0.175(2). Additionally we find that the leading correction
term for finite polymer lengths scales as N^{-1/2}, where N=L-1 is the number
of bonds.Comment: LaTeX (cjour.cls), 15 pages, 6 figures, added correctness proof of
  kink representation approac
Nodal high-order discontinuous Galerkin methods for the spherical shallow water equations

The article of record as published may be located at http://dx.doi.org/10.1006/jcph.2002.7139We present a high-order discontinuous Galerkin method for the solution of the shallow water equations on the sphere. To overcome well-known problems with polar singularities, we consider the shallow water equations in Cartesian coordinates, augmented with a Lagrange multiplier to ensure that fluid particles are constrained to the spherical surface. The global solutions are represented by a collection of curvilinear quadrilaterals from an icosahedral grid. On each of these elements the local solutions are assumed to be well approximated by a high-order nodal Lagrange polynomial, constructed from a tensor-product of the Legendre-Gauss-Lobatto points, which also Supplies a high-order quadrature. The shallow water equations are satisfied in a local discontinuous element fashion with solution continuity being enforced weakly. The numerical experiments, involving a comparison of weak and strong conservation forms and the impact of over-integration and filtering, confirm the expected high-order accuracy and the potential for using such highly parallel formulations in numerical weather prediction. (C) 2002 Elsevier Science (USA)
A Dynamic Atomistic-Continuum Method for the Simulation of Crystalline
  Materials

We present a coupled atomistic-continuum method for the modeling of defects
and interface dynamics of crystalline materials. The method uses atomistic
models such as molecular dynamics near defects and interfaces, and continuum
models away from defects and interfaces. We propose a new class of matching
conditions between the atomistic and continuum regions. These conditions ensure
the accurate passage of large scale information between the atomistic and
continuum regions and at the same time minimize the reflection of phonons at
the atomistic-continuum interface. They can be made adaptive if we choose
appropriate weight functions. We present applications to dislocation dynamics,
friction between two-dimensional crystal surfaces and fracture dynamics. We
compare results of the coupled method and the detailed atomistic model.Comment: 48 pages, 20 figure
Explicit finite-difference and direct-simulation-MonteCarlo method for
  the dynamics of mixed Bose-condensate and cold-atom clouds

We present a new numerical method for studying the dynamics of quantum fluids
composed of a Bose-Einstein condensate and a cloud of bosonic or fermionic
atoms in a mean-field approximation. It combines an explicit time-marching
algorithm, previously developed for Bose-Einstein condensates in a harmonic or
optical-lattice potential, with a particle-in-cell MonteCarlo approach to the
equation of motion for the one-body Wigner distribution function in the
cold-atom cloud. The method is tested against known analytical results on the
free expansion of a fermion cloud from a cylindrical harmonic trap and is
validated by examining how the expansion of the fermionic cloud is affected by
the simultaneous expansion of a condensate. We then present wholly original
calculations on a condensate and a thermal cloud inside a harmonic well and a
superposed optical lattice, by addressing the free expansion of the two
components and their oscillations under an applied harmonic force. These
results are discussed in the light of relevant theories and experiments.Comment: 33 pages, 13 figures, 1 tabl
Separator Based Sparsification I. Planarity Testing and Minimum Spanning Trees

AbstractWe describe algorithms and data structures for maintaining a dynamic planar graph subject to edge insertions and edge deletions that preserve planarity but that can change the embedding. We give a fully dynamic planarity testing algorithm that maintains a graph subject to edge insertions and deletions and that allows queries that test whether the graph is currently planar, or whether a potential new edge would violate planarity, inO(n1/2) amortized time per update or query. We give fully dynamic algorithms for maintaining the connected components, the best swap and the minimum spanning forest of a planar graph inO(logn) worst-case time per insertion andO(log2n) per deletion. Finally, we give fully dynamic algorithms for maintaining the 2-edge-connected components of a planar graph inO(logn) amortized time per insertion andO(log2n) per deletion. All of the data structures, except for the one that answers planarity queries, handle only insertions that keep the graph planar. All our algorithms improve previous bounds. The improvements are based upon a new type of sparsification combined with several properties of separators in planar graphs
Parameterized Pattern Matching: Algorithms and Applications

AbstractThe problem of finding sections of code that either are identical or are related by the systematic renaming of variables or constants can be modeled in terms ofparameterized strings(p-strings) andparameterized matches(p-matches). P-strings are strings over two alphabets, one of which represents parameters. Two p-strings are aparameterized match(p-match) if one p-string is obtained by renaming the parameters of the other by a one-to-one function. In this paper, we investigate parameterized pattern matching via parameterized suffix trees (p-suffix trees). We give two algorithms for constructing p-suffix trees: one (eager) that runs in linear time for fixed alphabets, and another that uses auxiliary data structures and runs inO(nlog(n)) time for variable alphabets, wherenis input length. We show that using a p-suffix tree for a pattern p-stringP, it is possible to search for all p-matches ofPwithin a text p-stringTin space linear in |P| and time linear in |T| for fixed alphabets, orO(|T|log(min(|P|, σ)) time andO(|P|) space for variable alphabets, whereσis the sum of the alphabet sizes. The simpler p-suffix tree construction algorithmeagerhas been implemented, and experiments show it to be practical. Since it runs faster than predicted by the above worst-case bound, we reanalyze the algorithm and show thateagerruns in timeO(min(t|S|+m(t,S)∣t>0)logσ)), where for an input p-stringS, m(t, S) is the number of maximal p-matches of length at leasttthat occur withinS, andσis the sum of the alphabet sizes. Experiments with the author's programdup(B. Baker,in“Comput. Sci. Statist.,” Vol. 24, 1992) for finding all maximal p-matches within a p-string have foundm(t, S) to be less than |S| in practice unlesstis small