9,426 research outputs found
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
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
Manufacturing influences on microstructure and fracture mechanical properties of polycrystalline tungsten
Polycrystalline tungsten is a promising candidate for future fusion applications as plasma facing material due to its good thermophysical properties at high temperatures. Fracture mechanical properties of sintered and rolled, commercially available polycrystalline tungsten are characterized taking into account the strong anisotropy due to different grain shape and orientation with respect to the rolling direction. The fracture mechanics investigations are accompanied by fractographic analyses of two tungsten plate grades with varying cold working ratios of two different manufacturers (PLANSEE SE, Austria and A.L.M.T Corp., Japan). In this respect three point bending tests (3-PB) with sub sized fracture mechanical specimens in different orientations of the anisotropic microstructure are performed at three temperatures, ranging from 25 °C to 400 °C at a deflection rate of 2 µm s − 1. In addition, crack initiation and crack growth mechanisms depending on texture and cold working ratio are investigated by means of scanning electron microscopy (SEM)
Determinação de perdas na colheita de soja: copo medidor da Embrapa.
A soja e a colheita. Principais fatores relacionados às perdas de grãos na colheita da soja. Determinação das perdas de grãos na colheita de soja pelo método do copo medidor desenvolvido pela Embrapa. Sisteam de corte e de alimentação. Sistema de trilha.Sistemas de separação e de limpeza. Sistemas de transporte, armazenamento e descarga. Problemas, causas e soluções observadas na colheita mecanizada de soja.bitstream/item/97495/1/Manual-Copo-Medidor-baixa-completo.pdfCatálogo 05 publicado em dezembro de 2013
Another integrable case in the Lorenz model
A scaling invariance in the Lorenz model allows one to consider the usually
discarded case sigma=0. We integrate it with the third Painlev\'e function.Comment: 3 pages, no figure, to appear in J. Phys.
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
Solitary waves of nonlinear nonintegrable equations
Our goal is to find closed form analytic expressions for the solitary waves
of nonlinear nonintegrable partial differential equations. The suitable
methods, which can only be nonperturbative, are classified in two classes.
In the first class, which includes the well known so-called truncation
methods, one \textit{a priori} assumes a given class of expressions
(polynomials, etc) for the unknown solution; the involved work can easily be
done by hand but all solutions outside the given class are surely missed.
In the second class, instead of searching an expression for the solution, one
builds an intermediate, equivalent information, namely the \textit{first order}
autonomous ODE satisfied by the solitary wave; in principle, no solution can be
missed, but the involved work requires computer algebra.
We present the application to the cubic and quintic complex one-dimensional
Ginzburg-Landau equations, and to the Kuramoto-Sivashinsky equation.Comment: 28 pages, chapter in book "Dissipative solitons", ed. Akhmediev, to
appea
Completeness of the cubic and quartic H\'enon-Heiles Hamiltonians
The quartic H\'enon-Heiles Hamiltonian passes the Painlev\'e test for
only four sets of values of the constants. Only one of these, identical to the
traveling wave reduction of the Manakov system, has been explicitly integrated
(Wojciechowski, 1985), while the three others are not yet integrated in the
generic case . We integrate them by building
a birational transformation to two fourth order first degree equations in the
classification (Cosgrove, 2000) of such polynomial equations which possess the
Painlev\'e property. This transformation involves the stationary reduction of
various partial differential equations (PDEs). The result is the same as for
the three cubic H\'enon-Heiles Hamiltonians, namely, in all four quartic cases,
a general solution which is meromorphic and hyperelliptic with genus two. As a
consequence, no additional autonomous term can be added to either the cubic or
the quartic Hamiltonians without destroying the Painlev\'e integrability
(completeness property).Comment: 10 pages, To appear, Theor.Math.Phys. Gallipoli, 34 June--3 July 200
Construction of Special Solutions for Nonintegrable Systems
The Painleve test is very useful to construct not only the Laurent series
solutions of systems of nonlinear ordinary differential equations but also the
elliptic and trigonometric ones. The standard methods for constructing the
elliptic solutions consist of two independent steps: transformation of a
nonlinear polynomial differential equation into a nonlinear algebraic system
and a search for solutions of the obtained system. It has been demonstrated by
the example of the generalized Henon-Heiles system that the use of the Laurent
series solutions of the initial differential equation assists to solve the
obtained algebraic system. This procedure has been automatized and generalized
on some type of multivalued solutions. To find solutions of the initial
differential equation in the form of the Laurent or Puiseux series we use the
Painleve test. This test can also assist to solve the inverse problem: to find
the form of a polynomial potential, which corresponds to the required type of
solutions. We consider the five-dimensional gravitational model with a scalar
field to demonstrate this.Comment: LaTeX, 14 pages, the paper has been published in the Journal of
Nonlinear Mathematical Physics (http://www.sm.luth.se/math/JNMP/
A reduction of the resonant three-wave interaction to the generic sixth Painleve' equation
Among the reductions of the resonant three-wave interaction system to
six-dimensional differential systems, one of them has been specifically
mentioned as being linked to the generic sixth Painleve' equation P6. We derive
this link explicitly, and we establish the connection to a three-degree of
freedom Hamiltonian previously considered for P6.Comment: 13 pages, 0 figure, J. Phys. A Special issue "One hundred years of
Painleve' VI
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