20 research outputs found
A Gauge field Induced by the Global Gauge Invariance of Action Integral
As a general rule, it is considered that the global gauge invariance of an
action integral does not cause the occurrence of gauge field. However, in this
paper we demonstrate that when the so-called localized assumption is excluded,
the gauge field will be induced by the global gauge invariance of the action
integral. An example is given to support this conclusion.Comment: 13 pages. Some typing errors are corrected and the format is update
Erratum to: An Entropy Functional for Riemann-Cartan Space-Times
We correct the entropy functional constructed in Int. J. Theor. Phys. 51:362
(2012). The 'on-shell' functional one obtains from this correct functional
possesses a holographic structure without imposing any constraint on the
spin-angular momentum tensor of matter, in contrast to the conclusion made in
the above paper.Comment: 15 pages. These are the preprints of the original paper and its
erratum published in Int. J. Theor. Phy
Mappings of least Dirichlet energy and their Hopf differentials
The paper is concerned with mappings between planar domains having least
Dirichlet energy. The existence and uniqueness (up to a conformal change of
variables in the domain) of the energy-minimal mappings is established within
the class of strong limits of homeomorphisms in the
Sobolev space , a result of considerable interest in the
mathematical models of Nonlinear Elasticity. The inner variation leads to the
Hopf differential and its trajectories.
For a pair of doubly connected domains, in which has finite conformal
modulus, we establish the following principle:
A mapping is energy-minimal if and only if
its Hopf-differential is analytic in and real along the boundary of .
In general, the energy-minimal mappings may not be injective, in which case
one observes the occurrence of cracks in . Nevertheless, cracks are
triggered only by the points in the boundary of where fails to be
convex. The general law of formation of cracks reads as follows:
Cracks propagate along vertical trajectories of the Hopf differential from
the boundary of toward the interior of where they eventually terminate
before making a crosscut.Comment: 51 pages, 4 figure