Search results for "PD"
showing 10 items of 1971 documents
Anomalous localized resonance using a folded geometry in three dimensions
2013
If a body of dielectric material is coated by a plasmonic structure of negative dielectric material with nonzero loss parameter, then cloaking by anomalous localized resonance (CALR) may occur as the loss parameter tends to zero. It was proved in other papers by authors that if the coated structure is circular (2D) and dielectric constant of the shell is a negative constant (with loss parameter), then CALR occurs, and if the coated structure is spherical (3D), then CALR does not occur. The aim of this paper is to show that the CALR takes place if the spherical coated structure has a specially designed anisotropic dielectric tensor. The anisotropic dielectric tensor is designed by unfolding …
(Ag)Pd-Fe3O4 Nanocomposites as Novel Catalysts for Methane Partial Oxidation at Low Temperature
2020
Nanostructured composite materials based on noble mono-(Pd) or bi-metallic (Ag/Pd) particles supported on mixed iron oxides (II/III) with bulk magnetite structure (Fe3O4) have been developed in order to assess their potential for heterogeneous catalysis applications in methane partial oxidation. Advancing the direct transformation of methane into value-added chemicals is consensually accepted as the key to ensuring sustainable development in the forthcoming future. On the one hand, nanosized Fe3O4 particles with spherical morphology were synthesized by an aqueous-based reflux method employing different Fe (II)/Fe (III) molar ratios (2 or 4) and reflux temperatures (80, 95 or 110 °
Explicit polynomial solutions of fourth order linear elliptic Partial Differential Equations for boundary based smooth surface generation
2011
We present an explicit polynomial solution method for surface generation. In this case the surface in question is characterized by some boundary configuration whereby the resulting surface conforms to a fourth order linear elliptic Partial Differential Equation, the Euler–Lagrange equation of a quadratic functional defined by a norm. In particular, the paper deals with surfaces generated as explicit Bézier polynomial solutions for the chosen Partial Differential Equation. To present the explicit solution methodologies adopted here we divide the Partial Differential Equations into two groups namely the orthogonal and the non-orthogonal cases. In order to demonstrate our methodology we discus…
Numerical study of blow-up and dispersive shocks in solutions to generalized Korteweg–de Vries equations
2015
Abstract We present a detailed numerical study of solutions to general Korteweg–de Vries equations with critical and supercritical nonlinearity, both in the context of dispersive shocks and blow-up. We study the stability of solitons and show that they are unstable against being radiated away and blow-up. In the L 2 critical case, the blow-up mechanism by Martel, Merle and Raphael can be numerically identified. In the limit of small dispersion, it is shown that a dispersive shock always appears before an eventual blow-up. In the latter case, always the first soliton to appear will blow up. It is shown that the same type of blow-up as for the perturbations of the soliton can be observed whic…
A numerical approach to Blow-up issues for dispersive perturbations of Burgers' equation
2014
We provide a detailed numerical study of various issues pertaining to the dynamics of the Burgers equation perturbed by a weak dispersive term: blow-up in finite time versus global existence, nature of the blow-up, existence for "long" times, and the decomposition of the initial data into solitary waves plus radiation. We numerically construct solitons for fractionary Korteweg-de Vries equations.
Representation of capacity drop at a road merge via point constraints in a first order traffic model
2018
We reproduce the capacity drop phenomenon at a road merge by implementing a non-local point constraint at the junction in a first order traffic model. We call capacity drop the situation in which the outflow through the junction is lower than the receiving capacity of the outgoing road, as too many vehicles trying to access the junction from the incoming roads hinder each other. In this paper, we first construct an enhanced version of the locally constrained model introduced by Haut et al. (Proceedings 16th IFAC World Congress. Prague, Czech Republic 229 (2005) TuM01TP/3), then we propose its counterpart featuring a non-local constraint and finally we compare numerically the two models by c…
Quantitative Properties on the Steady States to A Schr\"odinger-Poisson-Slater System
2014
A relatively complete picture on the steady states of the following Schr$\ddot{o}$dinger-Poisson-Slater (SPS) system \[ \begin{cases} -\Delta Q+Q=VQ-C_{S}Q^{2}, & Q>0\text{ in }\mathbb{R}^{3}\\ Q(x)\to0, & \mbox{as }x\to\infty,\\ -\Delta V=Q^{2}, & \text{in }\mathbb{R}^{3}\\ V(x)\to0 & \mbox{as }x\to\infty. \end{cases} \] is given in this paper: existence, uniqueness, regularity and asymptotic behavior at infinity, where $C_{S}>0$ is a constant. To the author's knowledge, this is the first uniqueness result on SPS system.
On some partial data Calder\'on type problems with mixed boundary conditions
2020
In this article we consider the simultaneous recovery of bulk and boundary potentials in (degenerate) elliptic equations modelling (degenerate) conducting media with inaccessible boundaries. This connects local and nonlocal Calder\'on type problems. We prove two main results on these type of problems: On the one hand, we derive simultaneous bulk and boundary Runge approximation results. Building on these, we deduce uniqueness for localized bulk and boundary potentials. On the other hand, we construct a family of CGO solutions associated with the corresponding equations. These allow us to deduce uniqueness results for arbitrary bounded, not necessarily localized bulk and boundary potentials.…
The fractional Calder\'on problem
2017
We review recent progress in the fractional Calder\'on problem, where one tries to determine an unknown coefficient in a fractional Schr\"odinger equation from exterior measurements of solutions. This equation enjoys remarkable uniqueness and approximation properties, which turn out to yield strong results in related inverse problems.
Existence and uniqueness of global classical solutions to a two species cancer invasion haptotaxis model
2017
We consider a haptotaxis cancer invasion model that includes two families of cancer cells. Both families, migrate on the extracellular matrix and proliferate. Moreover the model describes an epithelial-to-mesenchymal-like transition between the two families, as well as a degradation and a self-reconstruction process of the extracellular matrix. We prove positivity and conditional global existence and uniqueness of the classical solutions of the problem for large initial data.