The Murad-Brandenburg Equation - A Wave Partial Differential Conservation Expression for the Poynting Vector/Field

2012 ◽  
Author(s):  
Paul Murad ◽  
John Brandenburg
Keyword(s):  
Vector Field ◽  
Poynting Vector ◽  
Partial Differential

scholarly journals Deformations of G2 and Spin(7) Structures

2005 ◽  
Vol 57 (5) ◽  
pp. 1012-1055 ◽  
Author(s):  
Spiro Karigiannis
Keyword(s):  
Vector Field ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Cross Product ◽  
Partial Differential ◽  
Carry Over ◽  
Unknown Vector

AbstractWe consider some deformations of G2-structures on 7-manifolds. We discover a canonical way to deform a G2-structure by a vector field in which the associated metric gets “twisted” in some way by the vector cross product. We present a system of partial differential equations for an unknown vector field w whose solution would yield a manifold with holonomy G2. Similarly we consider analogous constructions for Spin(7)-structures on 8-manifolds. Some of the results carry over directly, while others do not because of the increased complexity of the Spin(7) case.

scholarly journals Surfaces with parallel normalized mean curvature vector field in Euclidean or Minkowski 4-space

Filomat ◽  
2019 ◽  
Vol 33 (4) ◽  
pp. 1135-1145
Author(s):  
Georgi Ganchev ◽  
Velichka Milousheva
Keyword(s):  
Vector Field ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Minkowski Space ◽  
Mean Curvature ◽  
Curvature Vector ◽  
Mean Curvature Vector ◽  
Partial Differential ◽  
Invariant Functions ◽  
Systems Of Pdes

We study surfaces with parallel normalized mean curvature vector field in Euclidean or Minkowski 4-space. On any such surface we introduce special isothermal parameters (canonical parameters) and describe these surfaces in terms of three invariant functions. We prove that any surface with parallel normalized mean curvature vector field parametrized by canonical parameters is determined uniquely up to a motion in Euclidean (or Minkowski) space by the three invariant functions satisfying a system of three partial differential equations. We find examples of surfaces with parallel normalized mean curvature vector field and solutions to the corresponding systems of PDEs in Euclidean or Minkowski space in the class of the meridian surfaces.

scholarly journals Scattering detection of a solenoidal Poynting vector field

2016 ◽  
Vol 41 (15) ◽  
pp. 3615 ◽  
Author(s):  
Shima Fardad ◽  
Alessandro Salandrino ◽  
Akbar Samadi ◽  
Matthias Heinrich ◽  
Zhigang Chen ◽  
...  
Keyword(s):  
Vector Field ◽  
Poynting Vector

A Fundamental Solution for a Nonelliptic Partial Differential Operator

1979 ◽  
Vol 31 (5) ◽  
pp. 1107-1120 ◽  
Author(s):  
Peter C. Greiner
Keyword(s):  
Vector Field ◽  
Differential Operator ◽  
Fundamental Solution ◽  
Half Plane ◽  
Partial Differential Operator ◽  
Holomorphic Vector Field ◽  
Partial Differential ◽  
Upper Half Plane ◽  
Cauchy Riemann ◽  
Image Position

Let(1)and set(2)Here . Z is the “unique” (modulo multiplication by nonzero functions) holomorphic vector-field which is tangent to the boundary of the “degenerate generalized upper half-plane”(3)In our terminology t = Re z1. We note that ℒ is nowhere elliptic. To put it into context, ℒ is of the type □b, i.e. operators like ℒ occur in the study of the boundary Cauchy-Riemann complex. For more information concerning this connection the reader should consult [1] and [2].

The Poynting vector field and the energy flow within a transformer

1986 ◽  
Vol 54 (6) ◽  
pp. 528-531 ◽  
Author(s):  
F. Herrmann ◽  
G. Bruno Schmid
Keyword(s):  
Vector Field ◽  
Energy Flow ◽  
Poynting Vector
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