scholarly journals The Diffraction of Transient Electro-Magnetic Waves by a Wedge

1958 ◽  
Vol 11 (2) ◽  
pp. 95-103 ◽  
Author(s):  
A. C. Butcher ◽  
J. S. Lowndes
Keyword(s):  
Wave Equation ◽  
Time Dependence ◽  
Half Plane ◽  
Line Source ◽  
Time Dependent ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Electro Magnetic ◽  
Infinite Wedge ◽  
Magnetic Waves

Much of the work on the theory of diffraction by an infinite wedge has been for cases of harmonic time-dependence. Oberhettinger (1) obtained an expression for the Green's function of the wave equation in the two dimensional case of a line source of oscillating current parallel to the edge of a wedge with perfectly conducting walls. Solutions of the time-dependent wave equation have been obtained by Keller and Blank (2), Kay (3) and more recently by Turner (4) who considered the diffraction of a cylindrical pulse by a half plane.

Diffraction of a pulse by a resistive half-plane. I. Normal incidence

1960 ◽  
Vol 255 (1283) ◽  
pp. 538-549 ◽  
Keyword(s):  
Time Dependence ◽  
Half Plane ◽  
Wave Diffraction ◽  
Diffraction Problem ◽  
Normal Incidence ◽  
Step Function ◽  
Two Dimensional ◽  
Dynamic Similarity ◽  
Function Time ◽  
Dimensional Wave

The two-dimensional wave diffraction problem, acoustic or electromagnetic, in which a pulse of step-function time dependence is diffracted by a resistive half-plane is solved by assuming dynamic similarity in the solution.

Diffraction by a half plane perpendicular to the distinguished axis of a gyrotropic medium (oblique incidence)

1981 ◽  
Vol 59 (3) ◽  
pp. 403-424 ◽  
Author(s):  
S. Przeździecki ◽  
R. A. Hurd
Keyword(s):  
Half Plane ◽  
Fourier Transforms ◽  
Boundary Value ◽  
Diffraction Problem ◽  
Closed Form Solution ◽  
Second Order ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Dimensional Solution ◽  
Electromagnetic Plane Wave

An exact, closed form solution is found for the following half plane diffraction problem. (I) The medium surrounding the half plane is gyrotropic. (II) The scattering half plane is perfectly conducting and oriented perpendicular to the distinguished axis of the medium. (III) The direction of propagation of the incident electromagnetic plane wave is arbitrary (skew) with respect to the edge of the half plane. The result presented is a generalization of a solution for the same problem with incidence normal to the edge of the half plane (two-dimensional case).The fundamental, distinctive feature of the problem is that it constitutes a boundary value problem for a system of two coupled second order partial differential equations. All previously solved electromagnetic diffraction problems reduced to boundary value problems for either one or two uncoupled second order equations. (Exception: the two-dimensional case of the present problem.) The problem is formulated in terms of the (generalized) scalar Hertz potentials and leads to a set of two coupled Wiener–Hopf equations. This set, previously thought insoluble by quadratures, yields to the Wiener–Hopf–Hilbert method.The three-dimensional solution is synthesized from appropriate solutions to two-dimensional problems. Peculiar waves of ghost potentials, which correspond to zero electromagnetic fields play an essential role in this synthesis. The problem is two-moded: that is, superpositions of both ordinary and extraordinary waves are necessary for the spectral representation of the solution. An important simplifying feature of the problem is that the coupling of the modes is purely due to edge diffraction, there being no reflection coupling. The solution is simple in that the Fourier transforms of the potentials are just algebraic functions. Basic properties of the solution are briefly discussed.

The half-plane diffraction problem for harmonic time dependence

1959 ◽  
Vol 252 (1270) ◽  
pp. 411-417 ◽  
Keyword(s):  
Electromagnetic Field ◽  
Time Dependence ◽  
Boundary Value Problems ◽  
Half Plane ◽  
Mixed Type ◽  
Boundary Value ◽  
Diffraction Problem ◽  
Two Dimensional ◽  
Conducting Screen ◽  
Plane Diffraction

Green’s functions are obtained for the boundary-value problems of mixed type describing the general two-dimensional diffraction problems at a screen in the form of a half-plane (Sommerfeld’s problem), applicable to acoustically rigid or soft screens, and to the full electromagnetic field at a perfectly conducting screen.

scholarly journals Time-dependent quantum correlations in two-dimensional expanding spacetime

2021 ◽  
Vol 81 (6) ◽  
Author(s):  
Chanyong Park
Keyword(s):  
Time Dependence ◽  
Entanglement Entropy ◽  
Critical Time ◽  
Quantum Correlations ◽  
Time Dependent ◽  
Thermal System ◽  
Two Dimensional ◽  
Eternal Inflation ◽  
Braneworld Model ◽  
Boundary Model

AbstractIn expanding universes, the entanglement entropy must be time-dependent because the background geometry changes with time. For understanding time evolution of quantum correlations, we take into account two distinct holographic models, the dS boundary model and the braneworld model. In this work, we focus on two-dimensional expanding universes for analytic calculation and comparison. Although two holographic models realize expanding universes in totally different ways, we show that they result in the qualitatively same time-dependence for eternal inflation. We further investigate the time-dependent correlations in the radiation-dominated era of the braneworld model. Intriguingly, the holographic result reveals that a thermal system in the expanding universe is dethermalized after a critical time characterized by the subsystem size.

scholarly journals Time-dependent metric for the two-dimensional, non-Hermitian coupled oscillator

2019 ◽  
Vol 35 (08) ◽  
pp. 2050041 ◽  
Author(s):  
Andreas Fring ◽  
Thomas Frith
Keyword(s):  
Harmonic Oscillator ◽  
Time Dependence ◽  
Time Dependent ◽  
Two Dimensional ◽  
Coupling Term ◽  
Coupled Oscillator ◽  
Explicit Time Dependence ◽  
Independent Model

We provide a time-dependent Dyson map and metric for the two-dimensional harmonic oscillator with a non-Hermitian ixy coupling term. This particular time-independent model exhibits spontaneously broken [Formula: see text]-symmetry and becomes unphysical in the broken regime, with the spectrum becoming partially complex. By introducing an explicit time dependence into the Dyson map, we provide a time-dependent metric that renders the model consistent across the unbroken and broken regimes.

Time-dependence and holography in the c=1 matrix model This paper was presented at the Theory CANADA 4 conference, held at Centre de recherches mathématiques, Montréal, Québec, Canada on 4–7 June 2008.

2009 ◽  
Vol 87 (3) ◽  
pp. 263-266
Author(s):  
Joanna L. Karczmarek
Keyword(s):  
String Theory ◽  
Time Dependence ◽  
Matrix Model ◽  
Time Dependent ◽  
Quantum Mechanical ◽  
Two Dimensional ◽  
The Matrix ◽  
Background Material ◽  
The Relationship ◽  
Time Dependent Solution

Ideas related to the study of time-dependence in two dimensional Liouville string theory using the c=1 matrix model are reviewed. Following an introduction to Liouville string theory, the matrix model and the relationship between the two, an example of an exact quantum mechanical time-dependent solution is given. There is a brief discussion of the holographic issues complicating the construction of the exact spacetime interpretation of such solutions. An attempt is made to include sufficient background material to make the presentation self-contained and accessible to a non-expert.

scholarly journals ON A BOUNDARY VALUE PROBLEM FOR ONE OVERDETERMINED SYSTEM IN A HALF-PLANE

2021 ◽  
Vol 4 (1) ◽  
pp. 226-231
Author(s):  
Mikhail V. Urev ◽  
Kholmatzhon Kh. Imomnazarov ◽  
Ilham K. Iskandarov
Keyword(s):  
Boundary Value Problem ◽  
Half Plane ◽  
Boundary Value ◽  
Generalized Solution ◽  
Stationary System ◽  
Dimensional Case ◽  
Mass Force ◽  
Two Dimensional ◽  
Overdetermined System ◽  
Significant Difference

This paper considers a boundary value problem for an overdetermined system of equations in a half-plane. This problem arises in particular when solving a stationary system of the two-velocity hydrodynamics with one pressure and homogeneous divergent conditions and the Dirichlet boundary conditions for two phase velocities, as well as in problems of electrodynamics. The generalized solution to a stationary system of the two-velocity hydrodynamics in the case of two-dimensional unbounded domains, for instance, in a half-plane, has a significant difference from the three-dimensional case. Namely, in the two-dimensional case for the velocities it is impossible to satisfy the pre-set conditions at infinity and the condition of boundedness at infinity is imposed. In this case, the medium is considered to be homogeneous, and the energy dissipation occurs due to the shear viscosities of the phases of the subsystems, and other effects are not discussed in this paper. The mass transfer occurs due to the mass force. With an appropriate choice of functional spaces, the existence and uniqueness of a generalized solution with an appropriate stability estimate has been proved.

The transition from two-dimensional to three-dimensional planforms in infinite-Prandtl-number thermal convection

1990 ◽  
Vol 216 ◽  
pp. 71-91 ◽  
Author(s):  
Bryan Travis ◽  
Peter Olson ◽  
Gerald Schubert
Keyword(s):  
Aspect Ratio ◽  
Prandtl Number ◽  
Time Dependence ◽  
Thermal Convection ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Time Dependent ◽  
Two Dimensional ◽  
Random Initial Conditions ◽  
The Stability

The stability of two-dimensional thermal convection in an infinite-Prandtl-number fluid layer with zero-stress boundaries is investigated using numerical calculations in three-dimensional rectangles. At low Rayleigh numbers (Ra < 20000) calculations of the stability of two-dimensional rolls to cross-roll disturbances are in agreement with the predictions of Bolton & Busse for a fluid with a large but finite Prandtl number. Within the range 2 × 104 < Ra [les ] 5 × 105, steady rolls with basic wavenumber α > 2.22 (aspect ratio < 1.41) are stable solutions. Two-dimensional rolls with basic wavenumber α < 1.96 (aspect ratio > 1.6) are time dependent for Ra > 4 × 104. For every case in which the initial condition was a time-dependent large-aspect-ratio roll, two-dimensional convection was found to be unstable to three-dimensional convection. Time-dependent rolls are replaced by either bimodal or knot convection in cases where the horizontal dimensions of the rectangular box are less than twice the depth. The bimodal planforms are steady states for Ra [les ] 105, but one case at Ra = 5 × 105 exhibits time dependence in the form of pulsating knots. Calculations at Ra = 105 in larger domains resulted in fully three-dimensional cellular planforms. A steady-state square planform was obtained in a 2.4 × 2.4 × 1 rectangular box. started from random initial conditions. Calculations in a 3 × 3 × 1 box produced steady hexagonal cells when started from random initial conditions, and a rectangular planform when started from a two-dimensional roll. An hexagonal planform started in a 3.5 × 3.5 × 1 box at Ra = 105 exhibited oscillatory time dependence, including boundary-layer instabilities and pulsating plumes. Thus, the stable planform in three-dimensional convection is sensitive to the size of the rectangular domain and the initial conditions. The sensitivity of heat transfer to planform variations is less than 10%.

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