10,186 research outputs found
General solution for Hamiltonians with extended cubic and quartic potentials
We integrate with hyperelliptic functions a two-particle Hamiltonian with
quartic potential and additionnal linear and nonpolynomial terms in the
Liouville integrable cases 1:6:1 and 1:6:8.Comment: LaTex 2e. To appear, Theoretical and Mathematical Physics 200
On the exact solutions of the Bianchi IX cosmological model in the proper time
It has recently been argued that there might exist a four-parameter analytic
solution to the Bianchi IX cosmological model, which would extend the
three-parameter solution of Belinskii et al. to one more arbitrary constant. We
perform the perturbative Painlev\'e test in the proper time variable, and
confirm the possible existence of such an extension.Comment: 8 pages, no figure, standard Latex, to appear in Regular and chaotic
dynamics (1998
Sub-10 nm colloidal lithography for integrated spin-photo-electronic devices
Colloidal lithography [1] is how patterns are reproduced in a variety of
natural systems and is used more and more as an efficient fabrication tool in
bio-, opto-, and nano-technology. Nanoparticles in the colloid are made to form
a mask on a given material surface, which can then be transferred via etching
into nano-structures of various sizes, shapes, and patterns [2,3]. Such
nanostructures can be used in biology for detecting proteins [4] and DNA [5,6],
for producing artificial crystals in photonics [7,8] and GHz oscillators in
spin-electronics [9-14]. Scaling of colloidal patterning down to 10-nm and
below, dimensions comparable or smaller than the main relaxation lengths in the
relevant materials, including metals, is expected to enable a variety of new
ballistic transport and photonic devices, such as spin-flip THz lasers [15]. In
this work we extend the practice of colloidal lithography to producing
large-area, near-ballistic-injection, sub-10 nm point-contact arrays and
demonstrate their integration in to spin-photo-electronic devices.Comment: 15 pages, 5 figure
Integration of a generalized H\'enon-Heiles Hamiltonian
The generalized H\'enon-Heiles Hamiltonian
with an additional
nonpolynomial term is known to be Liouville integrable for three
sets of values of . It has been previously integrated by genus
two theta functions only in one of these cases. Defining the separating
variables of the Hamilton-Jacobi equations, we succeed here, in the two other
cases, to integrate the equations of motion with hyperelliptic functions.Comment: LaTex 2e. To appear, Journal of Mathematical Physic
Detection and construction of an elliptic solution to the complex cubic-quintic Ginzburg-Landau equation
In evolution equations for a complex amplitude, the phase obeys a much more
intricate equation than the amplitude. Nevertheless, general methods should be
applicable to both variables. On the example of the traveling wave reduction of
the complex cubic-quintic Ginzburg-Landau equation (CGL5), we explain how to
overcome the difficulties arising in two such methods: (i) the criterium that
the sum of residues of an elliptic solution should be zero, (ii) the
construction of a first order differential equation admitting the given
equation as a differential consequence (subequation method).Comment: 12 pages, no figure, to appear, Theoretical and Mathematical Physic
Meromorphic traveling wave solutions of the complex cubic-quintic Ginzburg-Landau equation
We look for singlevalued solutions of the squared modulus M of the traveling
wave reduction of the complex cubic-quintic Ginzburg-Landau equation. Using
Clunie's lemma, we first prove that any meromorphic solution M is necessarily
elliptic or degenerate elliptic. We then give the two canonical decompositions
of the new elliptic solution recently obtained by the subequation method.Comment: 14 pages, no figure, to appear, Acta Applicandae Mathematica
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