39,233 research outputs found
On a Classical, Geometric Origin of Magnetic Moments, Spin-Angular Momentum and the Dirac Gyromagnetic Ratio
By treating the real Maxwell Field and real linearized Einstein equations as
being imbedded in complex Minkowski space, one can interpret magnetic moments
and spin-angular momentum as arising from a charge and mass monopole source
moving along a complex world line in the complex Minkowski space. In the
circumstances where the complex center of mass world-line coincides with the
complex center of charge world-line, the gyromagnetic ratio is that of the
Dirac electron.Comment: 17 page
The Real Meaning of Complex Minkowski-Space World-Lines
In connection with the study of shear-free null geodesics in Minkowski space,
we investigate the real geometric effects in real Minkowski space that are
induced by and associated with complex world-lines in complex Minkowski space.
It was already known, in a formal manner, that complex analytic curves in
complex Minkowski space induce shear-free null geodesic congruences. Here we
look at the direct geometric connections of the complex line and the real
structures. Among other items, we show, in particular, how a complex world-line
projects into the real Minkowski space in the form of a real shear-free null
geodesic congruence.Comment: 16 page
Electromagnetic Dipole Radiation Fields, Shear-Free Congruences and Complex Center of Charge World Lines
We show that for asymptotically vanishing Maxwell fields in Minkowski space
with non-vanishing total charge, one can find a unique geometric structure, a
null direction field, at null infinity. From this structure a unique complex
analytic world-line in complex Minkowski space that can be found and then
identified as the complex center of charge. By ''sitting'' - in an imaginary
sense, on this world-line both the (intrinsic) electric and magnetic dipole
moments vanish. The (intrinsic) magnetic dipole moment is (in some sense)
obtained from the `distance' the complex the world line is from the real space
(times the charge). This point of view unifies the asymptotic treatment of the
dipole moments For electromagnetic fields with vanishing magnetic dipole
moments the world line is real and defines the real (ordinary center of
charge). We illustrate these ideas with the Lienard-Wiechert Maxwell field. In
the conclusion we discuss its generalization to general relativity where the
complex center of charge world-line has its analogue in a complex center of
mass allowing a definition of the spin and orbital angular momentum - the
analogues of the magnetic and electric dipole moments.Comment: 17 page
The Large Footprints of H-Space on Asymptotically Flat Space-Times
We show that certain structures defined on the complex four dimensional space
known as H-Space have considerable relevance for its closely associated
asymptotically flat real physical space-time. More specifically for every
complex analytic curve on the H-space there is an asymptotically shear-free
null geodesic congruence in the physical space-time. There are specific
geometric structures that allow this world-line to be chosen in a unique
canonical fashion giving it physical meaning and significance.Comment: 7 page
Twisting Null Geodesic Congruences, Scri, H-Space and Spin-Angular Momentum
The purpose of this work is to return, with a new observation and rather
unconventional point of view, to the study of asymptotically flat solutions of
Einstein equations. The essential observation is that from a given
asymptotically flat space-time with a given Bondi shear, one can find (by
integrating a partial differential equation) a class of asymptotically
shear-free (but, in general, twistiing) null geodesic congruences. The class is
uniquely given up to the arbitrary choice of a complex analytic world-line in a
four-parameter complex space. Surprisingly this parameter space turns out to be
the H-space that is associated with the real physical space-time under
consideration. The main development in this work is the demonstration of how
this complex world-line can be made both unique and also given a physical
meaning. More specifically by forcing or requiring a certain term in the
asymptotic Weyl tensor to vanish, the world-line is uniquely determined and
becomes (by several arguments) identified as the `complex center-of-mass'.
Roughly, its imaginary part becomes identified with the intrinsic spin-angular
momentum while the real part yields the orbital angular momentum.Comment: 26 pages, authors were relisted alphabeticall
Modeling multi-cellular systems using sub-cellular elements
We introduce a model for describing the dynamics of large numbers of
interacting cells. The fundamental dynamical variables in the model are
sub-cellular elements, which interact with each other through phenomenological
intra- and inter-cellular potentials. Advantages of the model include i)
adaptive cell-shape dynamics, ii) flexible accommodation of additional
intra-cellular biology, and iii) the absence of an underlying grid. We present
here a detailed description of the model, and use successive mean-field
approximations to connect it to more coarse-grained approaches, such as
discrete cell-based algorithms and coupled partial differential equations. We
also discuss efficient algorithms for encoding the model, and give an example
of a simulation of an epithelial sheet. Given the biological flexibility of the
model, we propose that it can be used effectively for modeling a range of
multi-cellular processes, such as tumor dynamics and embryogenesis.Comment: 20 pages, 4 figure
The Universal Cut Function and Type II Metrics
In analogy with classical electromagnetic theory, where one determines the
total charge and both electric and magnetic multipole moments of a source from
certain surface integrals of the asymptotic (or far) fields, it has been known
for many years - from the work of Hermann Bondi - that energy and momentum of
gravitational sources could be determined by similar integrals of the
asymptotic Weyl tensor. Recently we observed that there were certain overlooked
structures, {defined at future null infinity,} that allowed one to determine
(or define) further properties of both electromagnetic and gravitating sources.
These structures, families of {complex} `slices' or `cuts' of Penrose's null
infinity, are referred to as Universal Cut Functions, (UCF). In particular, one
can define from these structures a (complex) center of mass (and center of
charge) and its equations of motion - with rather surprising consequences. It
appears as if these asymptotic structures contain in their imaginary part, a
well defined total spin-angular momentum of the source. We apply these ideas to
the type II algebraically special metrics, both twisting and twist-free.Comment: 32 page
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