Research on unwrapping of panoramic image and spatial coordinate transformation

Abstract We construct the 4-dimensional $$ \mathcal{N}=\frac{1}{2} $$ N = 1 2 and $$ \mathcal{N} $$ N = 1 inhomogeneously mass-deformed super Yang-Mills theories from the $$ \mathcal{N} $$ N = 1* and $$ \mathcal{N} $$ N = 2* theories, respectively, and analyse their supersymmetric vacua. The inhomogeneity is attributed to the dependence of background fluxes in the type IIB supergravity on a single spatial coordinate. This gives rise to inhomogeneous mass functions in the $$ \mathcal{N} $$ N = 4 super Yang-Mills theory which describes the dynamics of D3-branes. The Killing spinor equations for those inhomogeneous theories lead to the supersymmetric vacuum equation and a boundary condition. We investigate two types of solutions in the $$ \mathcal{N}=\frac{1}{2} $$ N = 1 2 theory, corresponding to the cases of asymptotically constant mass functions and periodic mass functions. For the former case, the boundary condition gives a relation between the parameters of two possibly distinct vacua at the asymptotic boundaries. Brane interpretations for corresponding vacuum solutions in type IIB supergravity are also discussed. For the latter case, we obtain explicit forms of the periodic vacuum solutions.

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Modification to the Hawking temperature of a dynamical black hole by a flow-induced supertranslation

Journal of High Energy Physics ◽

10.1007/jhep12(2020)089 ◽

2020 ◽

Vol 2020 (12) ◽

Author(s):

Hsu-Wen Chiang ◽

Yu-Hsien Kung ◽

Pisin Chen

Keyword(s):

Black Hole ◽

Coordinate Transformation ◽

Information Loss ◽

Hawking Temperature ◽

Asymptotic Region ◽

Unruh Effect ◽

Anisotropic Flow ◽

Information Loss Paradox ◽

History Of ◽

Entire History

Abstract One interesting proposal to solve the black hole information loss paradox without modifying either general relativity or quantum field theory, is the soft hair, a diffeomorphism charge that records the anisotropic radiation in the asymptotic region. This proposal, however, has been challenged, given that away from the source the soft hair behaves as a coordinate transformation that forms an Abelian group, thus unable to store any information. To maintain the spirit of the soft hair but circumvent these obstacles, we consider Hawking radiation as a probe sensitive to the entire history of the black hole evaporation, where the soft hairs on the horizon are induced by the absorption of a null anisotropic flow, generalizing the shock wave considered in [1, 2]. To do so we introduce two different time-dependent extensions of the diffeomorphism associated with the soft hair, where one is the backreaction of the anisotropic null flow, and the other is a coordinate transformation that produces the Unruh effect and a Doppler shift to the Hawking spectrum. Together, they form an exact BMS charge generator on the entire manifold that allows the nonperturbative analysis of the black hole horizon, whose surface gravity, i.e. the Hawking temperature, is found to be modified. The modification depends on an exponential average of the anisotropy of the null flow with a decay rate of 4M, suggesting the emergence of a new 2-D degree of freedom on the horizon, which could be a way out of the information loss paradox.

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On a coordinate transformation to express an explicit duck solution in the FitzHugh-Nagumo equation

Proceedings of the seventh International Colloquium on Differential Equations ◽

10.1515/9783112319185-053 ◽

1997 ◽

pp. 405-408

Keyword(s):

Coordinate Transformation ◽

Nagumo Equation

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Correction and accuracy improvement of non-parallel shear zone model

MATEC Web of Conferences ◽

10.1051/matecconf/201820702002 ◽

2018 ◽

Vol 207 ◽

pp. 02002

Author(s):

Yaoke Wang ◽

Meng Kou ◽

Wei Ding ◽

Huan Ma ◽

Liangshan Xiong

Keyword(s):

Experimental Data ◽

Cutting Force ◽

Shear Zone ◽

Coordinate Transformation ◽

Chip Thickness ◽

Zone Model ◽

Aisi 1045 Steel ◽

Aisi 1045 ◽

Experimental Values ◽

1045 Steel

When applying the non-parallel shear zone model to predict the cutting process parameters of carbon steel workpiece, it is found that there is a big error between the prediction results and the experimental values. And also, the former approach to obtain the relevant cutting parameters of the non-parallel shear zone model by applying coordinate transformation to the parallel shear zone model has a theoretical error – it erroneously regards the determinant (|J|) of the Jacobian matrix (J) in the coordinate transformation as a constant. The shape of the shear zone obtained when |J| is not constant is drew and it is found that the two boundaries of the shear zone are two slightly curved surfaces rather than two inclined planes. Also, the error between predicted values and experimental values of cutting force and cutting thrust is slightly smaller than that of constant |J|. A corrected model where |J| is a variable is proposed. Since the specific values of inclination of the shear zone (α, β), the thickness coefficient of the shear zone (as) and the constants related to the material (f0, p) are not given in the former work, a method to obtain the above-mentioned five constants by solving multivariable constrained optimization problem based on experimental data was also proposed; based on the obtained experimental data of AISI 1045 steel workpiece cutting force, cutting thrust, chip thickness, the results of five above-mentioned model constants are obtained. It is found that, compared with prediction from uncorrected model, the cutting force and cutting thrust of AISI 1045 steel predicted by the corrected model with the obtained constants has a better agreement with the experimental values obtained by Ivester.

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