62,830 research outputs found
Negative Specific Heat in a Quasi-2D Generalized Vorticity Model
Negative specific heat is a dramatic phenomenon where processes decrease in
temperature when adding energy. It has been observed in gravo-thermal collapse
of globular clusters. We now report finding this phenomenon in bundles of
nearly parallel, periodic, single-sign generalized vortex filaments in the
electron magnetohydrodynamic (EMH) model for the unbounded plane under strong
magnetic confinement. We derive the specific heat using a steepest descent
method and a mean field property. Our derivations show that as temperature
increases, the overall size of the system increases exponentially and the
energy drops. The implication of negative specific heat is a runaway reaction,
resulting in a collapsing inner core surrounded by an expanding halo of
filaments.Comment: 12 pages, 3 figures; updated with revision
Quaternionic Mass Matrices and CP Symmetry
A viable formulation of gauge theory with extra generations in terms of
quaternionic fields is presented. For the theory to be acceptable, the number
of generations should be equal to or greater than 4. The quark-lepton mass
matrices are generalized into quaternionic matrices.It is concluded that
explicit CP violation automatically disappears in both strong- and
weak-interaction sectors.Comment: 10 pages, LaTe
Mean field theory and coherent structures for vortex dynamics on the plane
We present a new derivation of the Onsager-Joyce-Montgomery (OJM) equilibrium
statistical theory for point vortices on the plane, using the
Bogoliubov-Feynman inequality for the free energy, Gibbs entropy function and
Landau's approximation. This formulation links the heuristic OJM theory to the
modern variational mean field theories. Landau's approximation is the physical
counterpart of a large deviation result, which states that the maximum entropy
state does not only have maximal probability measure but overwhelmingly large
measure relative to other macrostates.Comment: PACS: 47.15.Ki, 67.40.Vs, 68.35.Rh 16 page
Abstract Wiener measure using abelian Yang-Mills action on
Let be the Lie algebra of a compact Lie group. For a
-valued 1-form , consider the Yang-Mills action
\begin{equation} S_{{\rm YM}}(A) = \int_{\mathbb{R}^4} \left|dA + A \wedge A
\right|^2 \nonumber \end{equation} using the standard metric on
. When we consider the Lie group , the Lie algebra
is isomorphic to , thus .
For some simple closed loop , we want to make sense of the following path
integral, \begin{equation} \frac{1}{Z}\ \int_{A \in \mathcal{A} /\mathcal{G}}
\exp \left[ \int_{C} A\right] e^{-\frac{1}{2}\int_{\mathbb{R}^4}|dA|^2}\ DA,
\nonumber \end{equation} whereby is some Lebesgue type of measure on the
space of -valued 1-forms, modulo gauge transformations,
, and is some partition function.
We will construct an Abstract Wiener space for which we can define the above
Yang-Mills path integral rigorously, using renormalization techniques found in
lattice gauge theory. We will further show that the Area Law formula do not
hold in the abelian Yang-Mills theory
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