33,652 research outputs found
Solving high-order partial differential equations with indirect radial basis function networks
This paper reports a new numerical method based on radial basis function networks (RBFNs) for solving high-order partial differential equations (PDEs). The variables and their derivatives in the governing equations are represented by integrated RBFNs. The use of integration in constructing neural networks allows the straightforward implementation of multiple boundary conditions and the accurate approximation of high-order derivatives. The proposed RBFN method is verified successfully through the solution of thin-plate bending and viscous flow problems which are governed by biharmonic equations. For thermally driven cavity flows, the solutions are obtained up to a high Rayleigh number
Phenomenological construction of a relativistic nucleon-nucleon interaction for the superfluid gap equation in finite density systems
We construct phenomenologically a relativistic particle-particle channel
interaction which suits the gap equation for nuclear matter. This is done by
introducing a density-independent momentum-cutoff parameter to the relativistic
mean field (Hartree and Hartree-Fock) models so as to reproduce the pairing
properties obtained by the Bonn-B potential and not to change the saturation
property. The interaction so obtained can be used for the Relativistic
Hartree-Bogoliubov calculation, but some reservation is necessary for the
Relativistic Hartree-Fock-Bogoliubov calculation.Comment: 30 pages, 18 eps figures, uses elsart. Major revision ---
Hartree-Fock calculations are added. To appear in Nuclear Physics
Constructing Elliptic Curves over with Moderate Rank
We give several new constructions for moderate rank elliptic curves over
. In particular we construct infinitely many rational elliptic
surfaces (not in Weierstrass form) of rank 6 over using
polynomials of degree two in . While our method generates linearly
independent points, we are able to show the rank is exactly 6 \emph{without}
having to verify the points are independent. The method generalizes; however,
the higher rank surfaces are not rational, and we need to check that the
constructed points are linearly independent.Comment: 11 page
An agent-based model of jaguar movement through conservation corridors
Wildlife corridors mitigate against habitat fragmentation by connecting otherwise isolated regions, bringing well established benefits to conservation both in principle and practice. Populations of large mammals in particular may depend on habitat connectivity, yet conservation managers struggle to optimise corridor designs with the rudimentary information generally available on movement behaviours. We present an agent-based model of jaguars (Panthera onca), scaled for fragmented habitat in Belize where proposals already exist for creating a jaguar corridor. We use a leastcost approach to simulate movement paths through alternative possible landscapes. Six different types of corridor and three control conditions differ substantially in their effectiveness at mixing agents across the environment despite relatively little difference in individual welfare. Our best estimates of jaguar movement behaviours suggest that a set of five narrow corridors may out-perform one wide corridor of the same overall area. We discuss the utility of ALife modelling for conservation management
Compactness and finite forcibility of graphons
Graphons are analytic objects associated with convergent sequences of graphs.
Problems from extremal combinatorics and theoretical computer science led to a
study of graphons determined by finitely many subgraph densities, which are
referred to as finitely forcible. Following the intuition that such graphons
should have finitary structure, Lovasz and Szegedy conjectured that the
topological space of typical vertices of a finitely forcible graphon is always
compact. We disprove the conjecture by constructing a finitely forcible graphon
such that the associated space is not compact. The construction method gives a
general framework for constructing finitely forcible graphons with non-trivial
properties
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