2,696 research outputs found
Relations for zeros of special polynomials associated to the Painleve equations
A method for finding relations for the roots of polynomials is presented. Our
approach allows us to get a number of relations for the zeros of the classical
polynomials and for the roots of special polynomials associated with rational
solutions of the Painleve equations. We apply the method to obtain the
relations for the zeros of several polynomials. They are: the Laguerre
polynomials, the Yablonskii - Vorob'ev polynomials, the Umemura polynomials,
the Ohyama polynomials, the generalized Okamoto polynomials, and the
generalized Hermite polynomials. All the relations found can be considered as
analogues of generalized Stieltjes relations.Comment: 17 pages, 5 figure
A tree of linearisable second-order evolution equations by generalised hodograph transformations
We present a list of (1+1)-dimensional second-order evolution equations all
connected via a proposed generalised hodograph transformation, resulting in a
tree of equations transformable to the linear second-order autonomous evolution
equation. The list includes autonomous and nonautonomous equations.Comment: arXiv version is already officia
Subsonic high-angle-of-attack aerodynamic characteristics of a cone and cylinder with triangular cross sections and a cone with a square cross section
Experiments were conducted in the 12-Foot Pressure Wind Tunnel at Ames Research Center on three models with noncircular cross sections: a cone having a square cross section with rounded corners and a cone and cylinder with triangular cross sections and rounded vertices. The cones were tested with both sharp and blunt noses. Surface pressures and force and moment measurements were obtained over an angle of attack range from 30 deg to 90 deg and selected oil-flow experiments were conducted to visualize surface flow patterns. Unit Reynolds numbers ranged from 0.8x1,000,000/m to 13.0x1,000,000/m at a Mach number of 0.25, except for a few low-Reynolds-number runs at a Mach number of 0.17. Pressure data, as well as force data and oil-flow photographs, reveal that the three dimensional flow structure at angles of attack up to 75 deg is very complex and is highly dependent on nose bluntness and Reynolds number. For angles of attack from 75 deg to 90 deg the sectional aerodynamic characteristics are similar to those of a two dimensional cylinder with the same cross section
Galaxy correlations and the BAO in a void universe: structure formation as a test of the Copernican Principle
A suggested solution to the dark energy problem is the void model, where
accelerated expansion is replaced by Hubble-scale inhomogeneity. In these
models, density perturbations grow on a radially inhomogeneous background. This
large scale inhomogeneity distorts the spherical Baryon Acoustic Oscillation
feature into an ellipsoid which implies that the bump in the galaxy correlation
function occurs at different scales in the radial and transverse correlation
functions. We compute these for the first time, under the approximation that
curvature gradients do not couple the scalar modes to vector and tensor modes.
The radial and transverse correlation functions are very different from those
of the concordance model, even when the models have the same average BAO scale.
This implies that if void models are fine-tuned to satisfy average BAO data,
there is enough extra information in the correlation functions to distinguish a
void model from the concordance model. We expect these new features to remain
when the full perturbation equations are solved, which means that the radial
and transverse galaxy correlation functions can be used as a powerful test of
the Copernican Principle.Comment: 12 pages, 8 figures, matches published versio
Differential constraints and exact solutions of nonlinear diffusion equations
The differential constraints are applied to obtain explicit solutions of
nonlinear diffusion equations. Certain linear determining equations with
parameters are used to find such differential constraints. They generalize the
determining equations used in the search for classical Lie symmetries
On Scaling Solutions with a Dissipative Fluid
We study the asymptotic behaviour of scaling solutions with a dissipative
fluid and we show that, contrary to recent claims, the existence of stable
accelerating attractor solution which solves the `energy' coincidence problem
depends crucially on the chosen equations of state for the thermodynamical
variables. We discuss two types of equations of state, one which contradicts
this claim, and one which supports it.Comment: 8 pages and 5 figures; to appear in Class. Quantum Gra
Integrable discretizations of derivative nonlinear Schroedinger equations
We propose integrable discretizations of derivative nonlinear Schroedinger
(DNLS) equations such as the Kaup-Newell equation, the Chen-Lee-Liu equation
and the Gerdjikov-Ivanov equation by constructing Lax pairs. The discrete DNLS
systems admit the reduction of complex conjugation between two dependent
variables and possess bi-Hamiltonian structure. Through transformations of
variables and reductions, we obtain novel integrable discretizations of the
nonlinear Schroedinger (NLS), modified KdV (mKdV), mixed NLS, matrix NLS,
matrix KdV, matrix mKdV, coupled NLS, coupled Hirota, coupled Sasa-Satsuma and
Burgers equations. We also discuss integrable discretizations of the
sine-Gordon equation, the massive Thirring model and their generalizations.Comment: 24 pages, LaTeX2e (IOP style), final versio
The Hamiltonian Structure of the Second Painleve Hierarchy
In this paper we study the Hamiltonian structure of the second Painleve
hierarchy, an infinite sequence of nonlinear ordinary differential equations
containing PII as its simplest equation. The n-th element of the hierarchy is a
non linear ODE of order 2n in the independent variable depending on n
parameters denoted by and . We introduce new
canonical coordinates and obtain Hamiltonians for the and
evolutions. We give explicit formulae for these Hamiltonians showing that they
are polynomials in our canonical coordinates
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