16,200 research outputs found
Four Points Linearizable Lattice Schemes
We provide conditions for a lattice scheme defined on a four points lattice
to be linearizable by a point transformation. We apply the obtained conditions
to a symmetry preserving difference scheme for the potential Burgers introduced
by Dorodnitsyn \cite{db} and show that it is not linearizable
Next-to-leading order gravitational spin1-spin2 coupling with Kaluza-Klein reduction
We use the recently proposed Kaluza-Klein (KK) reduction over the time
dimension, within an effective field theory (EFT) approach, to calculate the
next to leading order (NLO) gravitational spin1-spin2 interaction between two
spinning compact objects. It is shown here that to NLO in the spin1-spin2
interaction, the reduced KK action within the stationary approximation is
sufficient to describe the gravitational interaction, and that it simplifies
calculation substantially. We also find here that the gravito-magnetic vector
field defined within the KK decomposition of the metric mostly dominates the
mediation of the interaction. Our results coincide with those calculated in the
ADM Hamiltonian formalism, and we provide another explanation for the
discrepancy with the result previously derived within the EFT approach, thus
demonstrating clearly the equivalence of the ADM Hamiltonian formalism and the
EFT action approach.Comment: 12 pages, revtex4-1, 3 figures; v2: reference added; v3: edited,
section 3 elaborated; v4: publishe
Linearizability and fake Lax pair for a consistent around the cube nonlinear non-autonomous quad-graph equation
We discuss the linearization of a non-autonomous nonlinear partial difference
equation belonging to the Boll classification of quad-graph equations
consistent around the cube. We show that its Lax pair is fake. We present its
generalized symmetries which turn out to be non-autonomous and depending on an
arbitrary function of the dependent variables defined in two lattice points.
These generalized symmetries are differential difference equations which, in
some case, admit peculiar B\"acklund transformations.Comment: arXiv admin note: text overlap with arXiv:1311.2406 by other author
A discrete linearizability test based on multiscale analysis
In this paper we consider the classification of dispersive linearizable
partial difference equations defined on a quad-graph by the multiple scale
reduction around their harmonic solution. We show that the A_1, A_2 and A_3
linearizability conditions restrain the number of the parameters which enter
into the equation. A subclass of the equations which pass the A_3
C-integrability conditions can be linearized by a Mobius transformation
A discrete integrability test based on multiscale analysis
In this article we present the results obtained applying the multiple scale
expansion up to the order \epsilon^6 to a dispersive multilinear class of
equations on a square lattice depending on 13 parameters. We show that the
integrability conditions given by the multiple scale expansion give rise to 4
nonlinear equations, 3 of which are new, depending at most on 2 parameters and
containing integrable sub cases. Moreover at least one sub case provides an
example of a new integrable system
Approximately Counting Triangles in Sublinear Time
We consider the problem of estimating the number of triangles in a graph.
This problem has been extensively studied in both theory and practice, but all
existing algorithms read the entire graph. In this work we design a {\em
sublinear-time\/} algorithm for approximating the number of triangles in a
graph, where the algorithm is given query access to the graph. The allowed
queries are degree queries, vertex-pair queries and neighbor queries.
We show that for any given approximation parameter , the
algorithm provides an estimate such that with high constant
probability, , where
is the number of triangles in the graph . The expected query complexity of
the algorithm is , where
is the number of vertices in the graph and is the number of edges, and
the expected running time is . We also prove
that queries are necessary, thus establishing that
the query complexity of this algorithm is optimal up to polylogarithmic factors
in (and the dependence on ).Comment: To appear in the 56th Annual IEEE Symposium on Foundations of
Computer Science (FOCS 2015
QCDF90: Lattice QCD with Fortran 90
We have used Fortran 90 to implement lattice QCD. We have designed a set of
machine independent modules that define fields (gauge, fermions, scalars,
etc...) and overloaded operators for all possible operations between fields,
matrices and numbers. With these modules it is very simple to write high-level
efficient programs for QCD simulations. To increase performances our modules
also implements assignments that do not require temporaries, and a machine
independent precision definition. We have also created a useful compression
procedure for storing the lattice configurations, and a parallel implementation
of the random generators. We have widely tested our program and modules on
several parallel and single processor supercomputers obtaining excellent
performances.Comment: LaTeX file, 8 pages, no figures. More information available at:
http://hep.bu.edu/~leviar/qcdf90.htm
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