2,188 research outputs found
The first correction to the second adiabatic invariant of charged-particle motion
First correction to second adiabatic invariant of charged particle motion in magnetic fiel
Current driven rotating kink mode in a plasma column with a non-line-tied free end
First experimental measurements are presented for the kink instability in a
linear plasma column which is insulated from an axial boundary by finite sheath
resistivity. Instability threshold below the classical Kruskal-Shafranov
threshold, axially asymmetric mode structure and rotation are observed. These
are accurately reproduced by a recent kink theory, which includes axial plasma
flow and one end of the plasma column that is free to move due to a
non-line-tied boundary condition.Comment: 4 pages, 6 figure
Mappings preserving locations of movable poles: a new extension of the truncation method to ordinary differential equations
The truncation method is a collective name for techniques that arise from
truncating a Laurent series expansion (with leading term) of generic solutions
of nonlinear partial differential equations (PDEs). Despite its utility in
finding Backlund transformations and other remarkable properties of integrable
PDEs, it has not been generally extended to ordinary differential equations
(ODEs). Here we give a new general method that provides such an extension and
show how to apply it to the classical nonlinear ODEs called the Painleve
equations. Our main new idea is to consider mappings that preserve the
locations of a natural subset of the movable poles admitted by the equation. In
this way we are able to recover all known fundamental Backlund transformations
for the equations considered. We are also able to derive Backlund
transformations onto other ODEs in the Painleve classification.Comment: To appear in Nonlinearity (22 pages
Rifts in Spreading Wax Layers
We report experimental results on the rift formation between two freezing wax
plates. The plates were pulled apart with constant velocity, while floating on
the melt, in a way akin to the tectonic plates of the earth's crust. At slow
spreading rates, a rift, initially perpendicular to the spreading direction,
was found to be stable, while above a critical spreading rate a "spiky" rift
with fracture zones almost parallel to the spreading direction developed. At
yet higher spreading rates a second transition from the spiky rift to a zig-zag
pattern occurred. In this regime the rift can be characterized by a single
angle which was found to be dependent on the spreading rate. We show that the
oblique spreading angles agree with a simple geometrical model. The coarsening
of the zig-zag pattern over time and the three-dimensional structure of the
solidified crust are also discussed.Comment: 4 pages, Postscript fil
Extending the scope of microscopic solvability: Combination of the Kruskal-Segur method with Zauderer decomposition
Successful applications of the Kruskal-Segur approach to interfacial pattern
formation have remained limited due to the necessity of an integral formulation
of the problem. This excludes nonlinear bulk equations, rendering convection
intractable. Combining the method with Zauderer's asymptotic decomposition
scheme, we are able to strongly extend its scope of applicability and solve
selection problems based on free boundary formulations in terms of partial
differential equations alone. To demonstrate the technique, we give the first
analytic solution of the problem of velocity selection for dendritic growth in
a forced potential flow.Comment: Submitted to Europhys. Letters, No figures, 5 page
Lexical evolution rates by automated stability measure
Phylogenetic trees can be reconstructed from the matrix which contains the
distances between all pairs of languages in a family. Recently, we proposed a
new method which uses normalized Levenshtein distances among words with same
meaning and averages on all the items of a given list. Decisions about the
number of items in the input lists for language comparison have been debated
since the beginning of glottochronology. The point is that words associated to
some of the meanings have a rapid lexical evolution. Therefore, a large
vocabulary comparison is only apparently more accurate then a smaller one since
many of the words do not carry any useful information. In principle, one should
find the optimal length of the input lists studying the stability of the
different items. In this paper we tackle the problem with an automated
methodology only based on our normalized Levenshtein distance. With this
approach, the program of an automated reconstruction of languages relationships
is completed
A list of all integrable 2D homogeneous polynomial potentials with a polynomial integral of order at most 4 in the momenta
We searched integrable 2D homogeneous polynomial potential with a polynomial
first integral by using the so-called direct method of searching for first
integrals. We proved that there exist no polynomial first integrals which are
genuinely cubic or quartic in the momenta if the degree of homogeneous
polynomial potentials is greater than 4.Comment: 22 pages, no figures, to appear in J. Phys. A: Math. Ge
- …