Search results for "equation"
showing 10 items of 4219 documents
New construction of algebro-geometric solutions to the Camassa-Holm equation and their numerical evaluation
2011
An independent derivation of solutions to the Camassa-Holm equation in terms of multi-dimensional theta functions is presented using an approach based on Fay's identities. Reality and smoothness conditions are studied for these solutions from the point of view of the topology of the underlying real hyperelliptic surface. The solutions are studied numerically for concrete examples, also in the limit where the surface degenerates to the Riemann sphere, and where solitons and cuspons appear.
Deducing a Drain Spacing Formula by Applying Dimensional Analysis and Self-Similarity Theory
2016
For designing a steady state drainage system a drain flow formula coupled with the Dupuit-Forcheimer form of the differential equation of groundwater flow is used. At first, in this paper the most applied drain flow formulas in steady-state conditions are reviewed and compared using as dependent variable the ratio between the maximum water table height and the distance between two lines of parallel drains. These equation are also tested using experimental field data measured in three plot drained by surface pipe drains having different value of drain spacing. Then, applying the dimensional analysis and the self-similarity theory, a new drain spacing formula is theoretically deduced and comp…
INITIAL PARAMETRIC REPRESENTATION OF BLOBS
2009
Blobs, developed by J.F. Blinn in 1982, are the implicit surfaces obtained by composition of a real numerical function and a distance function. Since, many authors (C. Murakami, H. Nishimura, G. Wyvill…) defined their own function of density, from these implicit surfaces are interesting from several points of view. In particular, their fusion makes it possible to easily obtain an implicit equation of resulting surface. However, these surfaces do not admit a parametric equation yet. In this article, we will establish the parametric equation of two blobs in fusion, defined by the function of density of C. Murakami, by using an algebraic method. Then, we will develop another method, based on …
New Quadratic Self-Assembly of Double-Decker Phthalocyanine on Gold(111) Surface : From Macroscopic to Microscopic Scale
2018
Unveiling the self-organization mechanism of semiconducting organic molecules onto metallic surfaces is the first step to design hybrid devices in which the self-assembling is exploited to tailor magnetic properties. In this study, double-decker rare-earth phthalocyanines, namely, lutetium phthalocyanine (LuPc2), are deposited on Au(111) gold surface forming large-scale self-assemblies. Global and local experimental techniques, namely, grazing incidence X-ray diffraction and scanning tunneling microscopy, supplemented by density functional theory calculations with van der Waals corrections, give insight into the molecular structural arrangement of the thin film and the self organization at …
Wavelet-like efficient analysis of two-dimensional arbitrarily shaped radomes using a surface formulation
2007
[1] Radomes are usually made of lossy dielectric materials, and their accurate analysis is often cumbersome because of their typical large electrical size and geometrical complexity. In real reflector antenna structures, there are always complex interactions between the radome, the reflector surfaces and the directional feeds, which are typically neglected for the sake of simplicity. In this paper we will consider all such interactions in a very accurate way, thus requiring a high number of unknowns for the numerical solution of the problem. To overcome such drawback, an integral equation formulation based on the Equivalence Principle in combination with the wavelet transform has been emplo…
Approximation von extremalflächenstücken (hyperbolischen typs) durch charakteristische räumliche vierecke
1982
We consider solutions z of the Cauchy-problem for hyperbolic Euler-Lagrange equations derived from a general Lagrangian f(x, y, z; zx, zy) in two independent variables x, y. z is supposed to be an extremal of the corresponding variational problem. Visualizing z as a surface in R3 we give a geometric interpretation of Lewy's well-known characteristic approximation scheme for the numerical solution of second order hyperbolic equations by approximating z via a polyhedral construction built up from subunits which consist of two characteristic triangles having one side in common but lying on different planes in R3. Utilizing ideas from Cartan-geometry one can (in an appropriate sense) introduce …
A general 4th-order PDE method to generate Bézier surfaces from the boundary
2006
In this paper we present a method for generating Bezier surfaces from the boundary information based on a general 4th-order PDE. This is a generalisation of our previous work on harmonic and biharmonic Bezier surfaces whereby we studied the Bezier solutions for Laplace and the standard biharmonic equation, respectively. Here we study the Bezier solutions of the Euler-Lagrange equation associated with the most general quadratic functional. We show that there is a large class of fourth-order operators for which Bezier solutions exist and hence we show that such operators can be utilised to generate Bezier surfaces from the boundary information. As part of this work we present a general method…
Monotony Based Imaging in EIT
2010
We consider the problem of determining conductivity anomalies inside a body from voltage‐current measurements on its surface. By combining the monotonicity method of Tamburrino and Rubinacci with the concept of localized potentials, we derive a new imaging method that is capable of reconstructing the exact (outer) shape of the anomalies. We furthermore show that the method can be implemented without solving any non‐homogeneous forward problems and show a first numerical result.
Stefan-Boltzmann Radiation on Non-convex Surfaces
1997
We consider the stationary heat equation for a non-convex body with Stefan–Boltzmann radiation condition on the surface. The main virtue of the resulting problem is non-locality of the boundary condition. Moreover, the problem is non-linear and in the general case also non-coercive and non-monotone. We show that the boundary value problem has a maximum principle. Hence, we can prove the existence of a weak solution assuming the existence of upper and lower solutions. In the two dimensional case or when a part of the radiation can escape the system we obtain coercivity and stronger existence result. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.
Phase-bistable patterns and cavity solitons induced by spatially periodic injection into vertical-cavity surface-emitting lasers
2014
Spatial rocking is a kind of resonant forcing able to convert a self-oscillatory system into a phase-bistable, pattern forming system, whereby the phase of the spatially averaged oscillation field locks to one of two values differing by $\ensuremath{\pi}$. We propose the spatial rocking in an experimentally relevant system---the vertical-cavity surface-emitting laser (VCSEL)---and demonstrate its feasibility through analytical and numerical tools applied to a VCSEL model. We show phase bistability, spatial patterns, such as roll patterns, domain walls, and phase (dark-ring) solitons, which could be useful for optical information storage and processing purposes.