scholarly journals Classifying pole-skipping points

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Yong jun Ahn ◽  
Viktor Jahnke ◽  
Hyun-Sik Jeong ◽  
Kyung-Sun Lee ◽  
Mitsuhiro Nishida ◽  
...  
Keyword(s):  
Boundary Condition ◽  
Physical Properties ◽  
Green’S Function ◽  
Green's Function ◽  
Vector Fields ◽  
Type I ◽  
Type Ii ◽  
Limiting Behavior ◽  
Scalar And Vector Fields ◽  
Analytical Expressions

Abstract We clarify general mathematical and physical properties of pole-skipping points. For this purpose, we analyse scalar and vector fields in hyperbolic space. This setup is chosen because it is simple enough to allow us to obtain analytical expressions for the Green’s function and check everything explicitly, while it contains all the essential features of pole-skipping points. We classify pole-skipping points in three types (type-I, II, III). Type-I and Type-II are distinguished by the (limiting) behavior of the Green’s function near the pole-skipping points. Type-III can arise at non-integer iω values, which is due to a specific UV condition, contrary to the types I and II, which are related to a non-unique near horizon boundary condition. We also clarify the relation between the pole-skipping structure of the Green’s function and the near horizon analysis. We point out that there are subtle cases where the near horizon analysis alone may not be able to capture the existence and properties of the pole-skipping points.

scholarly journals Pole-skipping and hydrodynamic analysis in Lifshitz, AdS2 and Rindler geometries

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Haiming Yuan ◽  
Xian-Hui Ge
Keyword(s):  
Boundary Condition ◽  
Green’S Function ◽  
Green's Function ◽  
Equations Of Motion ◽  
Equation Of Motion ◽  
Boundary Theory ◽  
Hydrodynamic Analysis ◽  
Dimensionless Variables ◽  
Pass Through ◽  
Special Points

Abstract The “pole-skipping” phenomenon reflects that the retarded Green’s function is not unique at a pole-skipping point in momentum space (ω, k). We explore the universality of pole-skipping in different geometries. In holography, near horizon analysis of the bulk equation of motion is a more straightforward way to derive a pole-skipping point. We use this method in Lifshitz, AdS2 and Rindler geometries. We also study the complex hydrodynamic analyses and find that the dispersion relations in terms of dimensionless variables $$ \frac{\omega }{2\pi T} $$ ω 2 πT and $$ \frac{\left|k\right|}{2\pi T} $$ k 2 πT pass through pole-skipping points $$ \left(\frac{\omega_n}{2\pi T},\frac{\left|{k}_n\right|}{2\pi T}\right) $$ ω n 2 πT k n 2 πT at small ω and k in the Lifshitz background. We verify that the position of the pole-skipping points does not depend on the standard quantization or alternative quantization of the boundary theory in AdS2× ℝd−1 geometry. In the Rindler geometry, we cannot find the corresponding Green’s function to calculate pole-skipping points because it is difficult to impose the boundary condition. However, we can still obtain “special points” near the horizon where bulk equations of motion have two incoming solutions. These “special points” correspond to the nonuniqueness of the Green’s function in physical meaning from the perspective of holography.

scholarly journals Dirac System with Discontinuities at Two Points

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Fatma Hıra ◽  
Nihat Altınışık
Keyword(s):  
Boundary Condition ◽  
Asymptotic Behaviour ◽  
Green’S Function ◽  
Green's Function ◽  
Transmission Conditions ◽  
Dirac System

We deal with a regular Dirac system which has discontinuities at two points and contains eigenparameter in a boundary condition and two transmission conditions. We investigate asymptotic behaviour of eigenvalues and corresponding eigenfunctions of this Dirac system and construct Green’s function.

scholarly journals Penyelesaian Persamaan Telegraph Dan Simulasinya

2013 ◽  
Vol 2 (1) ◽  
pp. 33
Author(s):  
Agus Miftakus Surur ◽  
Yudi Ari Adi ◽  
Sugiyanto Sugiyanto
Keyword(s):  
Boundary Condition ◽  
Wave Equation ◽  
Green’S Function ◽  
Green's Function ◽  
Mathematical Formula ◽  
Equation Solving ◽  
Condition Problem

Equation Telegraph is one of type from wave equation. Solving of the wave equation obtainable by using Green's function with the method of boundary condition problem. This research aim to to show the process obtain;get the mathematical formula from wave equation and also know the form of solution of wave equation by using Green's function. Result of analysis indicate that the process get the mathematical formula from wave equation from applicable Green's function in equation which deal with the wave equation, that is applied in equation Telegraph.  Solution started with searching public form from Green's function, hereinafter look for the solving of wave equation in Green's function. Application from the wave equation used to look for the solving of equation Telegraph.  Result from equation Telegraph which have been obtained will be shown in the form of picture (knowable to simulasi) so that form of the the equation Telegraph.

scholarly journals Impact assessment of interlayers on geological storage of carbon dioxide in Songliao Basin

2019 ◽  
Vol 74 ◽  
pp. 85 ◽  
Author(s):  
Deping Zhang ◽  
Chengkai Fan ◽  
Dongqin Kuang
Keyword(s):  
Physical Properties ◽  
Songliao Basin ◽  
Type I ◽  
Type Ii ◽  
Geological Storage ◽  
Storage Efficiency ◽  
Reservoir Prediction ◽  
Injection Volume ◽  
Sand Body ◽  
Cap Rock

Reservoirs in the Songliao Basin are characterized by strong heterogeneity, which increases the difficulty of exact reservoir prediction. The clay interlayer developed in the reservoir is an important factor affecting the heterogeneity of the reservoir. Using the reservoir numerical simulation technology, an attempt has been made to investigate the storage efficiency during CO2 sequestration in Songliao Basin considering different types of interlayer in underground formations. Results indicate that type I interlayer, with a large thickness embedded between the two sand bodies has function of shunting and blocking to alleviate the impacts on cap rock. The type II interlayer has a small thickness and locates inside a single sand body, with poor physical properties and continuity, which has the same blocking effect on CO2 distribution and moderating influence on the cap rock. The physical properties of type III interlayer are same as the type II interlayer, but it has uneven distribution and poor continuity. In addition, three schemes of perforated zone were designed and their effects on CO2 storage efficiency and stability were studied. For a single reservoir, the scheme I is to perforate a whole reservoir, which is more conducive to maintain the reservoir’s stability. For multiple sets of “single-reservoir”, the scheme II can be preferentially selected to perforate the reservoir section below the interlayer when the injection volume is small. However, the scheme III can be used to perforate the interlayer and the reservoir below that when the injection volume is large. The study is beneficial to provide guidance and advice for selecting a suitable CO2 geological storage and reduce the risk of CO2 leakage.

Composite boundary‐valued solution of the 2.5-D Green’s function for arbitrary acoustic media

Geophysics ◽  
1998 ◽  
Vol 63 (5) ◽  
pp. 1813-1823 ◽  
Author(s):  
Bing Zhou ◽  
Stewart A. Greenhalgh
Keyword(s):  
Boundary Condition ◽  
Green’S Function ◽  
Frequency Domain ◽  
Green's Function ◽  
Mixed Boundary ◽  
Waveform Inversion ◽  
Acoustic Medium ◽  
Model Parameters ◽  
Low Velocity ◽  
Acoustic Media

Theoretically, the Green’s function can be used to calculate the wavefield response of a specified source and the Fréchet derivative with respect to the model parameters for crosshole seismic full‐waveform inversion. In this paper, we apply the finite‐element method to numerically compute the 2.5-D Green’s function for an arbitrary acoustic medium by solving a composite boundary‐valued problem in the wavenumber‐frequency domain. The composite boundary condition consists of a 2.5-D absorbing boundary condition for the propagating wave field and a mixed boundary condition for the evanescent field in inhomogeneous media modeling. A numerical experiment performed for a uniform earth (having a known exact solution) shows the accuracy of the computation in the frequency and time domain. An inhomogeneous medium test, involving an embedded low‐velocity layer, demonstrates that the permissible range of [Formula: see text] at each frequency can be determined rationally from the critical wavenumber value of the medium around the source. Furthermore, it shows that the frequency‐domain solution is not improved continuously by increasing the number of [Formula: see text] samples because of the complicated nature of the wavefield. Both experiments show that the proposed method is effective and flexible for computing the 2.5-D Green’s function for arbitrary acoustic media.

Propagation of a Radar Modulated Ocean Wave Field

2014 ◽  
Author(s):  
M. S. M. Paalvast ◽  
P. Naaijen ◽  
H. R. M. Huijsmans
Keyword(s):  
Boundary Condition ◽  
Free Surface ◽  
Green’S Function ◽  
Wave Field ◽  
Frequency Domain ◽  
Green's Function ◽  
Propagation Model ◽  
Surface Boundary ◽  
Surface Source ◽  
Wave Elevation

In this article a study has been carried out to explore the feasibility of a wave propagation model that is able to predict the wave field in a deterministic sense, based on remote observations of the sea surface. The surface is modulated in order to simulate images created by a marine radar operating at grazing incidence. The developed model uses an integral equation method, utilizing the frequency domain Green’s function which fulfills the linear free surface boundary condition. Synthesized observations of either the wave elevation or surface tilt at the source points are used to initialize the wave model. At each of the locations of the added remote free surface panels, time traces of the observed wave elevation or surface tilt can be recorded. A Fourier Transform (FFT) of these time traces yields the frequency domain description of the boundary condition that has to be satisfied by the wave potential. The derived Green’s function for the free surface source panels is then used to solve the source of strength at these panels. Once values have been found for the sources, the potential, and thus the surface elevation, may be calculated at the ship’s location.

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