An approximation procedure for solutions to Mayer problems with cost functional not of classC

1982 ◽  
Vol 36 (3) ◽  
pp. 433-449 ◽  
Author(s):  
R. F. Baum
Keyword(s):  
Approximation Procedure ◽  
Cost Functional ◽  
Mayer Problems

Enforcing Local Power Conservation for Metasurface Design Using Electromagnetic Inversion

2020 ◽  
Author(s):  
Trevor Brown ◽  
Yousef Vahabzadeh ◽  
Christophe Caloz ◽  
Puyan Mojabi
Keyword(s):  
Optimization Procedure ◽  
Incident Field ◽  
Additional Constraint ◽  
Two Dimensional ◽  
Local Power ◽  
Power Conservation ◽  
Cost Functional ◽  
Field Transformation

<pre>A method based on electromagnetic inversion is extended to facilitate the design of passive, lossless, and reciprocal metasurfaces. More specifically, the inversion step is modified to ensure that the field transformation satisfies local power conservation, using available knowledge of the incident field. This paper formulates a novel cost functional to apply this additional constraint, and describes the optimization procedure used to find a solution that satisfies both the user-defined field specifications and local power conservation. Lastly, the method is demonstrated with a two-dimensional (2D) example.</pre>

scholarly journals Non-negative Martingale Solutions to the Stochastic Thin-Film Equation with Nonlinear Gradient Noise

2021 ◽  
Author(s):  
Konstantinos Dareiotis ◽  
Benjamin Gess ◽  
Manuel V. Gnann ◽  
Günther Grün
Keyword(s):  
Thin Film ◽  
Energy Estimates ◽  
Approximation Procedure ◽  
Thin Film Flow ◽  
Thin Film Equations ◽  
Scalar Conservation Law ◽  
Thin Film Equation ◽  
Degenerate Parabolic ◽  
Scalar Conservation ◽  
Martingale Solutions

AbstractWe prove the existence of non-negative martingale solutions to a class of stochastic degenerate-parabolic fourth-order PDEs arising in surface-tension driven thin-film flow influenced by thermal noise. The construction applies to a range of mobilites including the cubic one which occurs under the assumption of a no-slip condition at the liquid-solid interface. Since their introduction more than 15 years ago, by Davidovitch, Moro, and Stone and by Grün, Mecke, and Rauscher, the existence of solutions to stochastic thin-film equations for cubic mobilities has been an open problem, even in the case of sufficiently regular noise. Our proof of global-in-time solutions relies on a careful combination of entropy and energy estimates in conjunction with a tailor-made approximation procedure to control the formation of shocks caused by the nonlinear stochastic scalar conservation law structure of the noise.

Essentially non-oscillatory and weighted essentially non-oscillatory schemes

Acta Numerica ◽  
2020 ◽  
Vol 29 ◽  
pp. 701-762
Author(s):  
Chi-Wang Shu
Keyword(s):  
Main Idea ◽  
High Order Accuracy ◽  
Finite Difference Schemes ◽  
Approximation Procedure ◽  
Discontinuous Solutions ◽  
Weno Schemes ◽  
Convection Diffusion ◽  
Different Types ◽  
Basic Ideas ◽  
Weighted Eno

Essentially non-oscillatory (ENO) and weighted ENO (WENO) schemes were designed for solving hyperbolic and convection–diffusion equations with possibly discontinuous solutions or solutions with sharp gradient regions. The main idea of ENO and WENO schemes is actually an approximation procedure, aimed at achieving arbitrarily high-order accuracy in smooth regions and resolving shocks or other discontinuities sharply and in an essentially non-oscillatory fashion. Both finite volume and finite difference schemes have been designed using the ENO or WENO procedure, and these schemes are very popular in applications, most noticeably in computational fluid dynamics but also in other areas of computational physics and engineering. Since the main idea of the ENO and WENO schemes is an approximation procedure not directly related to partial differential equations (PDEs), ENO and WENO schemes also have non-PDE applications. In this paper we will survey the basic ideas behind ENO and WENO schemes, discuss their properties, and present examples of their applications to different types of PDEs as well as to non-PDE problems.

scholarly journals An Analytic and Numerical Investigation of a Differential Game

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 66
Author(s):  
Aviv Gibali ◽  
Oleg Kelis
Keyword(s):  
Differential Game ◽  
Equation Approach ◽  
Linear Quadratic ◽  
Control Cost ◽  
Dual Representation ◽  
Cost Functional ◽  
Variational Derivatives ◽  
Zero Sum ◽  
The Cost ◽  
Derivatives Of

In this paper we present an appropriate singular, zero-sum, linear-quadratic differential game. One of the main features of this game is that the weight matrix of the minimizer’s control cost in the cost functional is singular. Due to this singularity, the game cannot be solved either by applying the Isaacs MinMax principle, or the Bellman–Isaacs equation approach. As an application, we introduced an interception differential game with an appropriate regularized cost functional and developed an appropriate dual representation. By developing the variational derivatives of this regularized cost functional, we apply Popov’s approximation method and show how the numerical results coincide with the dual representation.

scholarly journals Computing the Sound of the Sea in a Seashell

2021 ◽  
Author(s):  
Jonathan Ben-Artzi ◽  
Marco Marletta ◽  
Frank Rösler
Keyword(s):  
Characteristic Function ◽  
Helmholtz Resonator ◽  
Positive Answer ◽  
Approximation Procedure ◽  
Universal Algorithm

AbstractThe question of whether there exists an approximation procedure to compute the resonances of any Helmholtz resonator, regardless of its particular shape, is addressed. A positive answer is given, and it is shown that all that one has to assume is that the resonator chamber is bounded and that its boundary is $${{\mathcal {C}}}^2$$ C 2 . The proof is constructive, providing a universal algorithm which only needs to access the values of the characteristic function of the chamber at any requested point.

scholarly journals Photoconductivity of Low-Bandgap Polymer and Polymer: Fullerene Bulk Heterojunction Studied by Constant Photocurrent Method

2015 ◽  
Vol 3 (1) ◽  
Author(s):  
V. V. Malov ◽  
A. R. Tameev ◽  
S. V. Novikov ◽  
M. V. Khenkin ◽  
A. G. Kazanskii ◽  
...  
Keyword(s):  
Molecular Orbital ◽  
Bulk Heterojunction ◽  
Inorganic Materials ◽  
Fullerene Derivative ◽  
Approximation Procedure ◽  
Photoelectric Properties ◽  
Highest Occupied Molecular Orbital ◽  
Donor Acceptor ◽  
Lowest Unoccupied Molecular Orbital ◽  
Doped Polymers

AbstractOptical and photoelectric properties of modern photosensitive polymers are of great interest due to their prospects for photovoltaic applications. In particular, an investigation of absorption and photoconductivity edge of these materials could provide valuable information. For these purpose we applied the constant photocurrent method which has proved its efficiency for inorganic materials. PCDTBT and PTB7 polymers were used as objects for the study as well as their blends with a fullerene derivative PC71BM. The measurements by constant photocurrent method (CPM) show that formation of bulk heterojunction (BHJ) in the blends increases photoconductivity and results in a redshift of the photocurrent edge in the doped polymers compared with that in the neat polymers. Obtained from CPM data, spectral dependences of absorption coefficient were approximated using Gaussian distribution of density-of-states within HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital) bands. The approximation procedure allowed us to evaluate rather optical than electrical bandgaps for the studied materials. Moreover, spectra of polymer:PC71BM blends were fitted well by the sum of two Gaussian peaks which reveal both the transitions within the polymer and the transitions involving charge transfer states at the donor-acceptor interface in the BHJ.

Sign in / Sign up

Export Citation Format

Share Document