Treatment of vector potential in a three-dimensional lattice network of spatial network method

2003 ◽  
Author(s):  
N. Yoshida ◽  
I. Fukai
Keyword(s):  
Vector Potential ◽  
Three Dimensional ◽  
Spatial Network ◽  
Dimensional Lattice ◽  
Network Method ◽  
Lattice Network

scholarly journals A note on the uniqueness of 2D elastostatic problems formulated by different types of potential functions

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 201-210
Author(s):  
José Luis Morales Guerrero ◽  
Manuel Cánovas Vidal ◽  
José Andrés Moreno Nicolás ◽  
Francisco Alhama López
Keyword(s):  
Boundary Conditions ◽  
Potential Function ◽  
Vector Potential ◽  
Numerical Scheme ◽  
Scalar Potential ◽  
Three Dimensional ◽  
Potential Functions ◽  
Network Method ◽  
Different Types ◽  
Physical Boundary

Abstract New additional conditions required for the uniqueness of the 2D elastostatic problems formulated in terms of potential functions for the derived Papkovich-Neuber representations, are studied. Two cases are considered, each of them formulated by the scalar potential function plus one of the rectangular non-zero components of the vector potential function. For these formulations, in addition to the original (physical) boundary conditions, two new additional conditions are required. In addition, for the complete Papkovich-Neuber formulation, expressed by the scalar potential plus two components of the vector potential, the additional conditions established previously for the three-dimensional case in z-convex domain can be applied. To show the usefulness of these new conditions in a numerical scheme two applications are numerically solved by the network method for the three cases of potential formulations.

scholarly journals DISCRETE AND CONTINUUM APPROACHES TO THREE-DIMENSIONAL QUANTUM GRAVITY

1991 ◽  
Vol 06 (39) ◽  
pp. 3591-3600 ◽  
Author(s):  
HIROSI OOGURI ◽  
NAOKI SASAKURA
Keyword(s):  
Gauge Theory ◽  
Moduli Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Analogue Model ◽  
Gauge Invariant ◽  
Invariant Functions ◽  
Dimensional Lattice ◽  
Chern Simons ◽  
Dimensional Surface

It is shown that, in the three-dimensional lattice gravity defined by Ponzano and Regge, the space of physical states is isomorphic to the space of gauge-invariant functions on the moduli space of flat SU(2) connections over a two-dimensional surface, which gives physical states in the ISO(3) Chern–Simons gauge theory. To prove this, we employ the q-analogue of this model defined by Turaev and Viro as a regularization to sum over states. A recent work by Turaev suggests that the q-analogue model itself may be related to an Euclidean gravity with a cosmological constant proportional to 1/k2, where q=e2πi/(k+2).

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