58,082 research outputs found
A New Numerical Approach for the Solutions of Partial Differential Equations in Three-Dimensional Space
This paper deals with the numerical computation of the solutions of nonlinear partial differential equations in threedimensional space subjected to boundary and initial conditions. Specifically, the modified cubic B-spline differential quadrature method is proposed where the cubic B-splines are employed as a set of basis functions in the differential quadrature method. The method transforms the three-dimensional nonlinear partial differential equation into a system of ordinary differential equations which is solved by considering an optimal five stage and fourth-order strong stability preserving Runge-Kutta scheme. The stability region of the numerical method is investigated and the accuracy and efficiency of the method are shown by means of three test problems: the threedimensional space telegraph equation, the Van der Pol nonlinear wave equation and the dissipative wave equation. The results show that the numerical solution is in good agreement with the exact solution. Finally the comparison with the numerical solution obtained with some numerical methods proposed in the pertinent literature is performed
Simplified normal forms near a degenerate elliptic fixed point in two-parametric families of area-preserving maps
We derive simplified normal forms for an area-preserving map in a
neighbourhood of a degenerate resonant elliptic fixed point. Such fixed points
appear in generic two-parameter families of area-preserving maps. We also
derive a simplified normal form for a generic two-parametric unfolding. The
normal forms are used to analyse bifurcations of -periodic orbits. In
particular, for we find regions of parameters where the normal form has
"meandering'' invariant curves
Left-invariant evolutions of wavelet transforms on the Similitude Group
Enhancement of multiple-scale elongated structures in noisy image data is
relevant for many biomedical applications but commonly used PDE-based
enhancement techniques often fail at crossings in an image. To get an overview
of how an image is composed of local multiple-scale elongated structures we
construct a multiple scale orientation score, which is a continuous wavelet
transform on the similitude group, SIM(2). Our unitary transform maps the space
of images onto a reproducing kernel space defined on SIM(2), allowing us to
robustly relate Euclidean (and scaling) invariant operators on images to
left-invariant operators on the corresponding continuous wavelet transform.
Rather than often used wavelet (soft-)thresholding techniques, we employ the
group structure in the wavelet domain to arrive at left-invariant evolutions
and flows (diffusion), for contextual crossing preserving enhancement of
multiple scale elongated structures in noisy images. We present experiments
that display benefits of our work compared to recent PDE techniques acting
directly on the images and to our previous work on left-invariant diffusions on
orientation scores defined on Euclidean motion group.Comment: 40 page
Hamiltonian Analysis of Non-Relativistic Covariant RFDiff Horava-Lifshitz Gravity
We perform the Hamiltonian analysis of non-relativistic covariant
Horava-Lifshitz gravity in the formulation presented recently in
arXiv:1009.4885. We argue that the resulting Hamiltonian structure is in
agreement with the original construction of non-relativistic covariant
Ho\v{r}ava-Lifshitz gravity presented in arXiv:1007.2410. Then we extend this
construction to the case of RFDiff invariant Ho\v{r}ava-Lifshitz theory. We
find well behaved Hamiltonian system with the number of the first and the
second class constraints that ensure the correct number of physical degrees of
freedom of gravity.Comment: 15 pages, v2. Title changed, major corrections in section 3.
performed, corrected typos and references added,v3: additional typos
corrected, references added,v4.additional comments added, version published
in PR
Metastable Vacua in Perturbed Seiberg-Witten Theories, Part 2: Fayet-Iliopoulos Terms and K\"ahler Normal Coordinates
We show that the perturbation of an N=2 supersymmetric gauge theory by a
superpotential linear in the Kahler normal coordinates of the Coulomb branch,
discussed in arXiv:0704.3613, is equivalent to the perturbation by
Fayet-Iliopoulos terms. It follows that the would-be meta-stable vacuum at the
origin of the normal coordinates in fact preserves N=1 supersymmetry unless the
superpotential is truncated to a finite-degree polynomial of the adjoint scalar
fields. We examine the criteria for supersymmetry breaking under a perturbation
by Fayet-Iliopoulos terms and present a general classification of
non-supersymmetric critical points. In some explicit examples, we are also able
to study local stability of these points and demonstrate that, if the
perturbation is chosen appropriately, they indeed correspond to
supersymmetry-breaking vacua. Relations of these constructions to flux
compactifications and geometric meta-stability are also discussed.Comment: 25 page
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