scholarly journals Wave Asymptotics for Waveguides and Manifolds with Infinite Cylindrical Ends

2021 ◽  
Author(s):  
T J Christiansen ◽  
K Datchev
Keyword(s):  
Wave Equation ◽  
Scattering Theory ◽  
Additional Assumption ◽  
Black Box ◽  
Decay Rates ◽  
Compact Sets ◽  
New Approach ◽  
High Energies ◽  
Wave Decay ◽  
Generalized Eigenfunctions

Abstract We describe wave decay rates associated to embedded resonances and spectral thresholds for waveguides and manifolds with infinite cylindrical ends. We show that if the cut-off resolvent is polynomially bounded at high energies, as is the case in certain favorable geometries, then there is an associated asymptotic expansion, up to a $O(t^{-k_0})$ remainder, of solutions of the wave equation on compact sets as $t \to \infty $. In the most general such case we have $k_0=1$, and under an additional assumption on the infinite ends we have $k_0 = \infty $. If we localize the solutions to the wave equation in frequency as well as in space, then our results hold for quite general waveguides and manifolds with infinite cylindrical ends. To treat problems with and without boundary in a unified way, we introduce a black box framework analogous to the Euclidean one of Sjöstrand and Zworski. We study the resolvent, generalized eigenfunctions, spectral measure, and spectral thresholds in this framework, providing a new approach to some mostly well-known results in the scattering theory of manifolds with cylindrical ends.

The principles of duality in the light of the system economic theory

2019 ◽  
pp. 127-149
Author(s):  
George B. Kleiner
Keyword(s):  
Economic Theory ◽  
Economic System ◽  
External Environment ◽  
Black Box ◽  
Space Time ◽  
Production Cycle ◽  
Economic Systems ◽  
New Approach ◽  
Reproduction Cycle ◽  
Basic Concepts

This paper shows the diversity and significance of relations of duality among different economic systems. The composition of the principles underlying the system economic theory used for the analysis of duality in the economy is investigated. The concept of the economic system is clarified and the equivalence of three basic concepts of the economic system is shown: a) as a space-time volume (“black box”); b) as a complex of elements and connections among them; c) as a tetrad, including object, project, process and environment components. In a new way, the concept of the tetrad is revealed. The actual interpretation of the interrelationships of its components, based on the mechanisms of intersystem circulation of spatial and temporal resources and the transmission of abilities from one economic system to another, is proposed. On the basis of the obtained results, the most essential aspects of duality in the theory of economic systems are considered. It is shown that the interaction of internal content and the nearest external environment of economic systems lies in the nature of the relations of duality. A new approach to modeling the structure and to functioning of the economic system, based on the description of its activities in the form of two interconnected tetrads (the first tetrad reflects the intrasystem production cycle and the second one — the external realization-reproduction cycle) is put forward. It is shown that the concept of duality in a system economy creates prerequisites for adapting the functioning of local economic systems (objects, projects, etc.) in a market, administrative and functional environments and, as a result, harmonizing the economy as a whole.

Stabilization of the wave equation with a nonlinear delay term in the boundary conditions

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Wassila Ghecham ◽  
Salah-Eddine Rebiai ◽  
Fatima Zohra Sidiali
Keyword(s):  
Wave Equation ◽  
Original Problem ◽  
Existence Of Solutions ◽  
Semigroup Theory ◽  
Decay Rates ◽  
Uniform Decay ◽  
Delay Term ◽  
Nonlinear Semigroup Theory ◽  
Nonlinear Boundary Feedback ◽  
Nonlinear Delay

Abstract A wave equation in a bounded and smooth domain of ℝ n {\mathbb{R}^{n}} with a delay term in the nonlinear boundary feedback is considered. Under suitable assumptions, global existence and uniform decay rates for the solutions are established. The proof of existence of solutions relies on a construction of suitable approximating problems for which the existence of the unique solution will be established using nonlinear semigroup theory and then passage to the limit gives the existence of solutions to the original problem. The uniform decay rates for the solutions are obtained by proving certain integral inequalities for the energy function and by establishing a comparison theorem which relates the asymptotic behavior of the energy and of the solutions to an appropriate dissipative ordinary differential equation.

A New Approach to Elastodynamic Response of Cylindrical Shell Based on Generalized Solution Structure Theorem for Wave Equation

2010 ◽  
Author(s):  
Shugen Xu ◽  
Weiqiang Wang ◽  
Yan Liu
Keyword(s):  
Wave Equation ◽  
Solution Structure ◽  
Structure Theorem ◽  
Dynamic Pressure ◽  
Structural Response ◽  
Generalized Solution ◽  
New Approach ◽  
Response Data ◽  
Elastodynamic Response ◽  
Detailed Derivation

In this paper, a generalized solution structure theorem has been provided. It can be use to solve the wave equation about the structural response of cylinder under the dynamic pressure. This new approach also can be used to solve a batch of partial differential equations with the similar form. A detailed derivation process has been given to show how the solution is obtained. Finally, a practical example is presented, and all the elastodynamic response data at any point during dynamic pressure can be acquired conveniently.

scholarly journals Wave Propagation on Microstate Geometries

2019 ◽  
Vol 21 (3) ◽  
pp. 705-760 ◽  
Author(s):  
Joe Keir
Keyword(s):  
Wave Equation ◽  
Decay Rates ◽  
Mathematical Treatment ◽  
Linear Wave ◽  
Local Energy ◽  
Linear Wave Equation ◽  
Uniform Decay ◽  
Uniformly Bounded ◽  
Kaluza Klein ◽  
Made In

AbstractSupersymmetric microstate geometries were recently conjectured (Eperon et al. in JHEP 10:031, 2016. 10.1007/JHEP10(2016)031) to be nonlinearly unstable due to numerical and heuristic evidence, based on the existence of very slowly decaying solutions to the linear wave equation on these backgrounds. In this paper, we give a thorough mathematical treatment of the linear wave equation on both two- and three-charge supersymmetric microstate geometries, finding a number of surprising results. In both cases, we prove that solutions to the wave equation have uniformly bounded local energy, despite the fact that three-charge microstates possess an ergoregion; these geometries therefore avoid Friedman’s “ergosphere instability” (Friedman in Commun Math Phys 63(3):243–255, 1978). In fact, in the three-charge case we are able to construct solutions to the wave equation with local energy that neither grows nor decays, although these data must have non-trivial dependence on the Kaluza–Klein coordinate. In the two-charge case, we construct quasimodes and use these to bound the uniform decay rate, showing that the only possible uniform decay statements on these backgrounds have very slow decay rates. We find that these decay rates are sublogarithmic, verifying the numerical results of Eperon et al. (2016). The same construction can be made in the three-charge case, and in both cases the data for the quasimodes can be chosen to have trivial dependence on the Kaluza–Klein coordinates.

scholarly journals Excitation of ion wakefields by electromagnetic pulses in dense plasmas

2009 ◽  
Vol 75 (1) ◽  
pp. 15-18 ◽  
Author(s):  
P. K. SHUKLA
Keyword(s):  
Wave Equation ◽  
Electromagnetic Wave ◽  
Electromagnetic Waves ◽  
Electromagnetic Pulse ◽  
Dense Plasma ◽  
Ponderomotive Force ◽  
Electromagnetic Pulses ◽  
Dense Plasmas ◽  
High Energies

AbstractThe excitation of electrostatic ion wakefields by electromagnetic pulses in a very dense plasma is considered. For this purpose, a wave equation for the ion wakefield in the presence of the ponderomotive force of the electromagnetic waves is obtained. Choosing a typical profile for the electromagnetic pulse, the form of the ion wakefields is deduced. The electromagnetic wave-generated ion wakefields can trap protons and accelerate them to high energies in dense plasmas.

scholarly journals Λ-Doublet Population Inversion in Collisions of OH, OD, CH, CD and NH+

1980 ◽  
Vol 87 ◽  
pp. 583-587 ◽  
Author(s):  
R. N. Dixon ◽  
D. Field
Keyword(s):  
Qualitative Agreement ◽  
Scattering Theory ◽  
Population Inversion ◽  
Closed Shell ◽  
Inelastic Collisions ◽  
The Other ◽  
New Approach ◽  
Maser Action

The results of a new approach to the problem of the collisional step in the pumping cycle for OH and CH masers are reported. Rotationally inelastic collisions of OH and CH with both open and closed shell collision partners are considered using an expression derived from scattering theory. It is shown how Λ-doublet population inversion may arise in OH and CH. H-atoms and H2 may show opposite behaviour with CH, one partner cooling where collisions with the other lead to inversion. Implications for maser action are discussed and reveal excellent qualitative agreement with observation. Λ-doublet population inversion in OD, CD and NH+ is also considered.

ANTIDEUTERON PRODUCTION AND THE PHYSICS OF COALESCENCE: IMPLICATIONS OF A NEW APPROACH

2002 ◽  
Vol 11 (05) ◽  
pp. 387-401
Author(s):  
BHASKAR DE ◽  
S. BHATTACHARYYA ◽  
P. GUPTAROY
Keyword(s):  
High Energy ◽  
Measured Data ◽  
New Combination ◽  
Coalescence Model ◽  
New Approach ◽  
Nuclear Collisions ◽  
High Energies ◽  
Text Production ◽  
Theoretical Results

Within the framework of coalescence model, the problem of antideuteron [Formula: see text] production in some high energy nuclear collisions has here been studied with the help of a new combination of models (NCM) outlined in some detail in the text. The totality of the approach, including one useful parametrization, adopted here leads us to obtain finally some theoretical results which are modestly in agreement with the measured data on various aspects of antideuteron production in both Pb + Pb and Au + Au collisions at moderately high energies. The implications of all this are discussed at the end of the paper.

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