3,283 research outputs found
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
On the gravitational field of static and stationary axial symmetric bodies with multi-polar structure
We give a physical interpretation to the multi-polar Erez-Rozen-Quevedo
solution of the Einstein Equations in terms of bars. We find that each
multi-pole correspond to the Newtonian potential of a bar with linear density
proportional to a Legendre Polynomial. We use this fact to find an integral
representation of the function. These integral representations are
used in the context of the inverse scattering method to find solutions
associated to one or more rotating bodies each one with their own multi-polar
structure.Comment: To be published in Classical and Quantum Gravit
Gap Probabilities for Edge Intervals in Finite Gaussian and Jacobi Unitary Matrix Ensembles
The probabilities for gaps in the eigenvalue spectrum of the finite dimension
random matrix Hermite and Jacobi unitary ensembles on some
single and disconnected double intervals are found. These are cases where a
reflection symmetry exists and the probability factors into two other related
probabilities, defined on single intervals. Our investigation uses the system
of partial differential equations arising from the Fredholm determinant
expression for the gap probability and the differential-recurrence equations
satisfied by Hermite and Jacobi orthogonal polynomials. In our study we find
second and third order nonlinear ordinary differential equations defining the
probabilities in the general case. For N=1 and N=2 the probabilities and
thus the solution of the equations are given explicitly. An asymptotic
expansion for large gap size is obtained from the equation in the Hermite case,
and also studied is the scaling at the edge of the Hermite spectrum as , and the Jacobi to Hermite limit; these last two studies make
correspondence to other cases reported here or known previously. Moreover, the
differential equation arising in the Hermite ensemble is solved in terms of an
explicit rational function of a {Painlev\'e-V} transcendent and its derivative,
and an analogous solution is provided in the two Jacobi cases but this time
involving a {Painlev\'e-VI} transcendent.Comment: 32 pages, Latex2
Factorization of Ising correlations C(M,N) for and M+N odd, , and their lambda extensions
We study the factorizations of Ising low-temperature correlations C(M,N) for
and M+N odd, , for both the cases where there are
two factors, and where there are four factors. We find that the two
factors for satisfy the same non-linear differential equation and,
similarly, for M=0 the four factors each satisfy Okamoto sigma-form of
Painlev\'e VI equations with the same Okamoto parameters. Using a Landen
transformation we show, for , that the previous non-linear
differential equation can actually be reduced to an Okamoto sigma-form of
Painlev\'e VI equation. For both the two and four factor case, we find that
there is a one parameter family of boundary conditions on the Okamoto
sigma-form of Painlev\'e VI equations which generalizes the factorization of
the correlations C(M,N) to an additive decomposition of the corresponding
sigma's solutions of the Okamoto sigma-form of Painlev\'e VI equation which we
call lambda extensions. At a special value of the parameter, the
lambda-extensions of the factors of C(M,N) reduce to homogeneous polynomials in
the complete elliptic functions of the first and second kind. We also
generalize some Tracy-Widom (Painlev\'e V) relations between the sum and
difference of sigma's to this Painlev\'e VI framework.Comment: 45 page
Late Cretaceous to Recent Deformation Related to Inherited Structures and Subsequent Compression within the Persian Gulf: A 2D Seismic Case Study
The Persian Gulf is part of an asymmetric foreland basin related to the Zagros Orogen. Few published studies of this basin and associated onshore areas include seismic reflection data. We present a seismic-stratigraphic interpretation based on marine 2D seismic data, which reveals the presence of two types of compressional structures within the basin: (1) faulted domes related to salt movement and the offshore trace of a NNE–SSW-trending dextral basement fault (the Kazerun Fault); (2) long-wavelength (16 km), low-amplitude (60 ms two-way travel time) folds relating to the advancing deformation front associated with the orogen. Thinning of age-constrained stratal units across structures related to the offshore trace of the Kazerun Fault implies a distinct pulse of uplift on this fault during the Maastrichtian. The geometry of growth strata across other intra-basin structures suggests a second, later stage of deformation, which began in the Middle Miocene. Thickening and folding of post-Middle Miocene stratal units towards the NE (i.e. towards the Zagros Orogen) is interpreted to reflect rapid loading, subsidence and compression related to southwestwards advance of the orogen. The results of this study have implications for the interaction between pre-existing structures and later compressional events both within the Persian Gulf and elsewhere
Late Cretaceous to Recent Deformation Related to Inherited Structures and Subsequent Compression within the Persian Gulf: A 2D Seismic Case Study
The Persian Gulf is part of an asymmetric foreland basin related to the Zagros Orogen. Few published studies of this basin and associated onshore areas include seismic reflection data. We present a seismic-stratigraphic interpretation based on marine 2D seismic data, which reveals the presence of two types of compressional structures within the basin: (1) faulted domes related to salt movement and the offshore trace of a NNE–SSW-trending dextral basement fault (the Kazerun Fault); (2) long-wavelength (16 km), low-amplitude (60 ms two-way travel time) folds relating to the advancing deformation front associated with the orogen. Thinning of age-constrained stratal units across structures related to the offshore trace of the Kazerun Fault implies a distinct pulse of uplift on this fault during the Maastrichtian. The geometry of growth strata across other intra-basin structures suggests a second, later stage of deformation, which began in the Middle Miocene. Thickening and folding of post-Middle Miocene stratal units towards the NE (i.e. towards the Zagros Orogen) is interpreted to reflect rapid loading, subsidence and compression related to southwestwards advance of the orogen. The results of this study have implications for the interaction between pre-existing structures and later compressional events both within the Persian Gulf and elsewhere
Numerical simulation of particle motion in an ultrasound field using the lattice Boltzmann model
Constructing Integrable Third Order Systems:The Gambier Approach
We present a systematic construction of integrable third order systems based
on the coupling of an integrable second order equation and a Riccati equation.
This approach is the extension of the Gambier method that led to the equation
that bears his name. Our study is carried through for both continuous and
discrete systems. In both cases the investigation is based on the study of the
singularities of the system (the Painlev\'e method for ODE's and the
singularity confinement method for mappings).Comment: 14 pages, TEX FIL
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