THE WAVE EQUATIONS FOR THE WEYL TENSOR/SPINOR AND DIMENSIONALLY DEPENDENT TENSOR IDENTITIES

1996 ◽  
Vol 05 (03) ◽  
pp. 217-225 ◽  
Author(s):  
FREDRIK ANDERSSON ◽  
S. BRIAN EDGAR
Keyword(s):  
Wave Equation ◽  
Large Class ◽  
Weyl Tensor ◽  
Wave Equations ◽  
Dimensional Case ◽  
Weyl Spinor ◽  
Four Dimensions ◽  
Identity Matching ◽  
Tensor Identity ◽  
First Time

By reconciling the wave equation for the Weyl tensor with the corresponding wave equation for the Weyl spinor, we establish a new tensor identity—involving the sum of terms each consisting of a product of the Weyl and Ricci tensors—valid in four (and only four) dimensions. This enables us to give, for the first time, the correct and simplest form of the wave equation for the Weyl tensor in four-dimensional nonvacuum spacetimes. The wave equation for the Weyl tensor in n(> 4) dimensional nonvacuum spaces is also presented for the first time; we show that there does not exist an analogous n-dimensional tensor identity matching the four-dimensional one, and so it follows that there does not exist an analogous simplification of the Weyl wave equation in the n-dimensional case. It is also shown how our new identity, and some other recently discovered identities, relate to a large class of dimensionally dependent identities found some time ago by Lovelock.

THE WAVE EQUATIONS FOR THE LANCZOS TENSOR/SPINOR, AND A NEW TENSOR IDENTITY

1994 ◽  
Vol 09 (06) ◽  
pp. 479-482 ◽  
Author(s):  
S. BRIAN EDGAR
Keyword(s):  
Wave Equations ◽  
Apparent Discrepancy ◽  
Four Dimensions ◽  
Lanczos Potential ◽  
Tensor Methods ◽  
Tensor Identity

The apparent discrepancy between the vacuum wave equations obtained for the Lanczos potential respectively by spinor and tensor methods is explained; it is shown that the additional expression in the tensor version is actually identically zero in four dimensions.

Extended F-Expansion Method for Solving the modified Korteweg-de Vries (mKdV) Equation

2020 ◽  
Vol 11 (1) ◽  
pp. 93-100
Author(s):  
Vina Apriliani ◽  
Ikhsan Maulidi ◽  
Budi Azhari
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Internal Waves ◽  
Water Waves ◽  
Wave Equations ◽  
Elliptic Functions ◽  
Expansion Method ◽  
Mkdv Equation ◽  
Innovative Methods ◽  
De Vries

One of the phenomenon in marine science that is often encountered is the phenomenon of water waves. Waves that occur below the surface of seawater are called internal waves. One of the mathematical models that can represent solitary internal waves is the modified Korteweg-de Vries (mKdV) equation. Many methods can be used to construct the solution of the mKdV wave equation, one of which is the extended F-expansion method. The purpose of this study is to determine the solution of the mKdV wave equation using the extended F-expansion method. The result of solving the mKdV wave equation is the exact solutions. The exact solutions of the mKdV wave equation are expressed in the Jacobi elliptic functions, trigonometric functions, and hyperbolic functions. From this research, it is expected to be able to add insight and knowledge about the implementation of the innovative methods for solving wave equations. 

scholarly journals Parametric instability in a free-evolving warped protoplanetary disc

2020 ◽  
Vol 500 (3) ◽  
pp. 4248-4256
Author(s):  
Hongping Deng ◽  
Gordon I Ogilvie ◽  
Lucio Mayer
Keyword(s):  
Wave Equations ◽  
Hydrodynamic Instability ◽  
Parametric Instability ◽  
Low Viscosity ◽  
Crossing Time ◽  
Particle Hydrodynamics ◽  
Smoothed Particle ◽  
First Time ◽  
Bending Wave ◽  
Grid Based

ABSTRACT Warped accretion discs of low viscosity are prone to hydrodynamic instability due to parametric resonance of inertial waves as confirmed by local simulations. Global simulations of warped discs, using either smoothed particle hydrodynamics or grid-based codes, are ubiquitous but no such instability has been seen. Here, we utilize a hybrid Godunov-type Lagrangian method to study parametric instability in global simulations of warped Keplerian discs at unprecedentedly high resolution (up to 120 million particles). In the global simulations, the propagation of the warp is well described by the linear bending-wave equations before the instability sets in. The ensuing turbulence, captured for the first time in a global simulation, damps relative orbital inclinations and leads to a decrease in the angular momentum deficit. As a result, the warp undergoes significant damping within one bending-wave crossing time. Observed protoplanetary disc warps are likely maintained by companions or aftermath of disc breaking.

scholarly journals Fractional wave equations with attenuation

2013 ◽  
Vol 16 (1) ◽  
Author(s):  
Peter Straka ◽  
Mark Meerschaert ◽  
Robert McGough ◽  
Yuzhen Zhou
Keyword(s):  
Wave Equation ◽  
Power Law ◽  
Weak Solutions ◽  
Wave Equations ◽  
Inhomogeneous Media ◽  
Medical Ultrasound ◽  
Sound Waves ◽  
Fractional Wave Equations

AbstractFractional wave equations with attenuation have been proposed by Caputo [5], Szabo [28], Chen and Holm [7], and Kelly et al. [11]. These equations capture the power-law attenuation with frequency observed in many experimental settings when sound waves travel through inhomogeneous media. In particular, these models are useful for medical ultrasound. This paper develops stochastic solutions and weak solutions to the power law wave equation of Kelly et al. [11].

On the existence of compressional MHD oscillations in an inhomogeneous magnetoplasma

1990 ◽  
Vol 44 (2) ◽  
pp. 361-375 ◽  
Author(s):  
Andrew N. Wright
Keyword(s):  
Magnetic Field ◽  
Wave Equation ◽  
Density Distribution ◽  
Cold Plasma ◽  
Wave Equations ◽  
Perturbation Field ◽  
Plasma Density Distribution ◽  
Background Magnetic Field ◽  
Transverse Fields ◽  
The Magnetic Field

In a cold plasma the wave equation for solely compressional magnetic field perturbations appears to decouple in any surface orthogonal to the background magnetic field. However, the compressional fields in any two of these surfaces are related to each other by the condition that the perturbation field b be divergence-free. Hence the wave equations in these surfaces are not truly decoupled from one another. If the two solutions happen to be ‘matched’ (i.e. V.b = 0) then the medium may execute a solely compressional oscillation. If the two solutions are unmatched then transverse fields must evolve. We consider two classes of compressional solutions and derive a set of criteria for when the medium will be able to support pure compressional field oscillations. These criteria relate to the geometry of the magnetic field and the plasma density distribution. We present the conditions in such a manner that it is easy to see if a given magnetoplasma is able to executive either of the compressional solutions we investigate.

Translation and validation of the first time fathers questionnaire into Persian

2021 ◽  
Vol 29 (10) ◽  
pp. 572-578
Author(s):  
Khadijeh Dodel ◽  
Giti Ozgoli ◽  
Aasa Premberg ◽  
Nillofar Ghasemi ◽  
Sedigheh Sedigh Mobarakabadi ◽  
...  
Keyword(s):  
Cronbach’S Alpha ◽  
Labor Support ◽  
Four Dimensions ◽  
Cronbach's Alpha ◽  
Item Questionnaire ◽  
Confirmatory Factor ◽  
First Time ◽  
Translation And Validation ◽  
Item Distribution

Background/Aims The presence of fathers during labour and birth can have favourable outcomes for the health of the mother, father and infant. However, there are few studies on fathers' experiences while being present during labour and birth, which necessitates the development of a valid questionnaire for this purpose. The aim of this study was to translate and culturally adapt the first time fathers questionnaire into Persian. Methods A total of 220 first-time fathers at private midwifery counseling centers were given a translated questionnaire to complete. Forward-backward translation of the questionnaire was conducted and content, face and construct validity were examined. After extracting factors and item distribution, confirmatory factor analysis was performed. Cronbach's alpha was used for reliability. Results A valid 19-item questionnaire with four dimensions, ‘worry’, ‘acceptance and support during labor’, ‘support during and after birth’, and ‘preparedness’ was obtained. The Cronbach's alpha was 0.78. Conclusions The Persian questionnaire is valid and reliable for examining the experiences of first-time fathers. It can be employed to evaluate fathers' experiences during labour and birth in midwifery services planning to promote quality of care during childbirth.

scholarly journals Some arguments for the wave equation in Quantum theory

2021 ◽  
Vol 5 (1) ◽  
pp. 314-336
Author(s):  
Tristram de Piro ◽  
Keyword(s):  
Electromagnetic Field ◽  
Wave Equation ◽  
Quantum Theory ◽  
Continuity Equation ◽  
Wave Equations ◽  
Maxwell's Equations ◽  
Atomic System ◽  
Balmer Series ◽  
Inertial Frames ◽  
The Stability

We clarify some arguments concerning Jefimenko’s equations, as a way of constructing solutions to Maxwell’s equations, for charge and current satisfying the continuity equation. We then isolate a condition on non-radiation in all inertial frames, which is intuitively reasonable for the stability of an atomic system, and prove that the condition is equivalent to the charge and current satisfying certain relations, including the wave equations. Finally, we prove that with these relations, the energy in the electromagnetic field is quantised and displays the properties of the Balmer series.

Strichartz Estimates for Wave Equations with Charge Transfer Hamiltonians

2021 ◽  
Vol 273 (1339) ◽  
Author(s):  
Gong Chen
Keyword(s):  
Wave Equation ◽  
Charge Transfer ◽  
Wave Equations ◽  
Linear Models ◽  
Energy Estimate ◽  
Strichartz Estimates ◽  
Content Type ◽  
Scattering States ◽  
Scattering State ◽  
A Charge

We prove Strichartz estimates (both regular and reversed) for a scattering state to the wave equation with a charge transfer Hamiltonian in R 3 \mathbb {R}^{3} : \[ ∂ t t u − Δ u + ∑ j = 1 m V j ( x − v → j t ) u = 0. \partial _{tt}u-\Delta u+\sum _{j=1}^{m}V_{j}\left (x-\vec {v}_{j}t\right )u=0. \] The energy estimate and the local energy decay of a scattering state are also established. In order to study nonlinear multisoltion systems, we will present the inhomogeneous generalizations of Strichartz estimates and local decay estimates. As an application of our results, we show that scattering states indeed scatter to solutions to the free wave equation. These estimates for this linear models are also of crucial importance for problems related to interactions of potentials and solitons, for example, in [Comm. Math. Phys. 364 (2018), no. 1, pp. 45–82].

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.

scholarly journals On the Fractional Wave Equation

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 874
Author(s):  
Francesco Iafrate ◽  
Enzo Orsingher
Keyword(s):  
Brownian Motion ◽  
Wave Equation ◽  
Wave Equations ◽  
Stable Process ◽  
Space Time ◽  
Probabilistic Interpretation ◽  
Symmetric Stable Process ◽  
Fractional Wave Equation ◽  
Fractional Wave Equations ◽  
Time Fractional Wave Equation

In this paper we study the time-fractional wave equation of order 1 < ν < 2 and give a probabilistic interpretation of its solution. In the case 0 < ν < 1 , d = 1 , the solution can be interpreted as a time-changed Brownian motion, while for 1 < ν < 2 it coincides with the density of a symmetric stable process of order 2 / ν . We give here an interpretation of the fractional wave equation for d > 1 in terms of laws of stable d−dimensional processes. We give a hint at the case of a fractional wave equation for ν > 2 and also at space-time fractional wave equations.

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