17,394 research outputs found
Thermodynamics of a Higher Order Phase Transition: Scaling Exponents and Scaling Laws
The well known scaling laws relating critical exponents in a second order
phase transition have been generalized to the case of an arbitrarily higher
order phase transition. In a higher order transition, such as one suggested for
the superconducting transition in BaKBiO and in
BiSrCaCuO, there are singularities in higher order derivatives
of the free energy. A relation between exponents of different observables has
been found, regardless of whether the exponents are classical (mean-field
theory, no fluctuations, integer order of a transition) or not (fluctuation
effects included). We also comment on the phase transition in a thin film.Comment: 10 pages, no figure
An Alternative Method for Solving a Certain Class of Fractional Kinetic Equations
An alternative method for solving the fractional kinetic equations solved
earlier by Haubold and Mathai (2000) and Saxena et al. (2002, 2004a, 2004b) is
recently given by Saxena and Kalla (2007). This method can also be applied in
solving more general fractional kinetic equations than the ones solved by the
aforesaid authors. In view of the usefulness and importance of the kinetic
equation in certain physical problems governing reaction-diffusion in complex
systems and anomalous diffusion, the authors present an alternative simple
method for deriving the solution of the generalized forms of the fractional
kinetic equations solved by the aforesaid authors and Nonnenmacher and Metzler
(1995). The method depends on the use of the Riemann-Liouville fractional
calculus operators. It has been shown by the application of Riemann-Liouville
fractional integral operator and its interesting properties, that the solution
of the given fractional kinetic equation can be obtained in a straight-forward
manner. This method does not make use of the Laplace transform.Comment: 7 pages, LaTe
Stationary axisymmetric solutions of five dimensional gravity
We consider stationary axisymmetric solutions of general relativity that
asymptote to five dimensional Minkowski space. It is known that this system has
a hidden SL(3,R) symmetry. We identify an SO(2,1) subgroup of this symmetry
group that preserves the asymptotic boundary conditions. We show that the
action of this subgroup on a static solution generates a one-parameter family
of stationary solutions carrying angular momentum. We conjecture that by
repeated applications of this procedure one can generate all stationary
axisymmetric solutions starting from static ones. As an example, we derive the
Myers-Perry black hole starting from the Schwarzschild solution in five
dimensions.Comment: 31 pages, LaTeX; references adde
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