Orthogonal separation of variables for the Hamilton-Jacobi and wave equations in three-dimensional Minkowski space

2008 ◽  
Vol 49 (2) ◽  
pp. 023501 ◽  
Author(s):  
Joshua T. Horwood ◽  
Raymond G. McLenaghan
Keyword(s):  
Minkowski Space ◽  
Wave Equations ◽  
Separation Of Variables ◽  
Three Dimensional ◽  
Dimensional Minkowski Space

scholarly journals The Algebraic Surfaces of the Enneper Family of Maximal Surfaces in Three Dimensional Minkowski Space

Axioms ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 4
Author(s):  
Erhan Güler
Keyword(s):  
Minkowski Space ◽  
Three Dimensional ◽  
Algebraic Surfaces ◽  
Cartesian Coordinates ◽  
Maximal Surfaces ◽  
Dimensional Minkowski Space ◽  
The Family

We consider the Enneper family of real maximal surfaces via Weierstrass data (1,ζm) for ζ∈C, m∈Z≥1. We obtain the irreducible surfaces of the family in the three dimensional Minkowski space E2,1. Moreover, we propose that the family has degree (2m+1)2 (resp., class 2m(2m+1)) in the cartesian coordinates x,y,z (resp., in the inhomogeneous tangential coordinates a,b,c).

Hamilton–Jacobi theory in three-dimensional Minkowski space via Cartan geometry

2009 ◽  
Vol 50 (5) ◽  
pp. 053507 ◽  
Author(s):  
Joshua T. Horwood ◽  
Raymond G. McLenaghan ◽  
Roman G. Smirnov
Keyword(s):  
Minkowski Space ◽  
Three Dimensional ◽  
Cartan Geometry ◽  
Dimensional Minkowski Space

Constructions of spacelike Bézier Surfaces in the Three-dimensional Minkowski space

2009 ◽  
Author(s):  
Georgi H. Georgiev ◽  
George Venkov ◽  
Ralitza Kovacheva ◽  
Vesela Pasheva
Keyword(s):  
Minkowski Space ◽  
Three Dimensional ◽  
Dimensional Minkowski Space

Accretive growth kinematics in Minkowski 3-space

2017 ◽  
Vol 14 (05) ◽  
pp. 1750069
Author(s):  
Gül Tuğ ◽  
Zehra Özdemi̇r ◽  
Selçuk Han Aydin ◽  
Fai̇k Nejat Ekmekci̇
Keyword(s):  
Minkowski Space ◽  
Analytical Approach ◽  
Three Dimensional ◽  
Dimensional Minkowski Space

In this study, a model of accretive growth for arbitrary surfaces in three-dimensional Minkowski space is formulated by evolving a curve. An analytical approach to surfaces is also given in terms of a few parameters which are effective in the accretive growth of surfaces. The proposed method is visualized on some test surfaces and displayed in terms of figures.

scholarly journals 3d conformal fields with manifest sl(2, ℂ)

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Dmitry Ponomarev
Keyword(s):  
Minkowski Space ◽  
Three Dimensional ◽  
Helicity Formalism ◽  
Natural Connection ◽  
Conformal Fields ◽  
Dimensional Minkowski Space ◽  
Poincaré Algebra ◽  
Massless Fields ◽  
Weight Modules

Abstract In the present paper we construct all short representation of so(3, 2) with the sl(2, ℂ) symmetry made manifest due to the use of sl(2, ℂ) spinors. This construction has a natural connection to the spinor-helicity formalism for massless fields in AdS4 suggested earlier. We then study unitarity of the resulting representations, identify them as the lowest-weight modules and as conformal fields in the three-dimensional Minkowski space. Finally, we compare these results with the existing literature and discuss the properties of these representations under contraction of so(3, 2) to the Poincare algebra.

Vertical Dynamic Response of a Concrete Filled Steel Tube due to Transient Impact Load: Analytical Solution

2016 ◽  
Vol 16 (01) ◽  
pp. 1640014 ◽  
Author(s):  
Xuanming Ding ◽  
Yuming Fan ◽  
Ping Li ◽  
Gangqiang Kong
Keyword(s):  
Analytical Solution ◽  
Dynamic Response ◽  
Wave Equations ◽  
Impact Load ◽  
Separation Of Variables ◽  
Three Dimensional ◽  
Vertical Displacement ◽  
Steel Tube ◽  
Concrete Filled Steel Tube ◽  
The Impact

This paper presents an analytical solution of vertical dynamic response of a concrete-filled steel tube (CFST) due to transient impact loading. Both the concrete and steel are modeled by linear elastic material. The impact load is simulated by a semisinusoidal impulse. Three-dimensional (3D) wave equations those considering the vertical displacement are established. By combining the initial and boundary conditions, the frequency-domain analytical solution of displacement is deduced by Laplace transformation and separation of variables methods. The time-domain dynamic response is then obtained by numerical inverse Fourier transformation (IFT). Numerical examples are presented to verify the validity of the analytical solution developed in this study. The results indicate that the analytical solution proposed in this study shows good consistence with the existing solutions.

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