11,470 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
Discrete Breathers in a Nonlinear Polarizability Model of Ferroelectrics
We present a family of discrete breathers, which exists in a nonlinear
polarizability model of ferroelectric materials. The core-shell model is set up
in its non-dimensionalized Hamiltonian form and its linear spectrum is
examined. Subsequently, seeking localized solutions in the gap of the linear
spectrum, we establish that numerically exact and potentially stable discrete
breathers exist for a wide range of frequencies therein.
In addition, we present nonlinear normal mode, extended spatial profile
solutions from which the breathers bifurcate, as well as other associated
phenomena such as the formation of phantom breathers within the model.
The full bifurcation picture of the emergence and disappearance of the
breathers is complemented by direct numerical simulations of their dynamical
instability, when the latter arises.Comment: 9 pages, 7 figures, 1 tabl
Exact Solutions of the Saturable Discrete Nonlinear Schrodinger Equation
Exact solutions to a nonlinear Schr{\"o}dinger lattice with a saturable
nonlinearity are reported. For finite lattices we find two different
standing-wave-like solutions, and for an infinite lattice we find a localized
soliton-like solution. The existence requirements and stability of these
solutions are discussed, and we find that our solutions are linearly stable in
most cases. We also show that the effective Peierls-Nabarro barrier potential
is nonzero thereby indicating that this discrete model is quite likely
nonintegrable
Analytical approach to the transition to thermal hopping in the thin- and thick-wall approximations
The nature of the transition from the quantum tunneling regime at low
temperatures to the thermal hopping regime at high temperatures is investigated
analytically in scalar field theory. An analytical bounce solution is
presented, which reproduces the action in the thin-wall as well as thick-wall
limits. The transition is first order for the case of a thin wall while for the
thick wall case it is second order.Comment: Latex file, 22 pages, 4 Postscript figure
Solitary waves in a two-dimensional nonlinear Dirac equation: from discrete to continuum
In the present work, we explore a nonlinear Dirac equation motivated as the
continuum limit of a binary waveguide array model. We approach the problem both
from a near-continuum perspective as well as from a highly discrete one.
Starting from the former, we see that the continuum Dirac solitons can be
continued for all values of the discretization (coupling) parameter, down to
the uncoupled (so-called anti-continuum) limit where they result in a 9-site
configuration. We also consider configurations with 1- or 2-sites at the
anti-continuum limit and continue them to large couplings, finding that they
also persist. For all the obtained solutions, we examine not only the
existence, but also the spectral stability through a linearization analysis and
finally consider prototypical examples of the dynamics for a selected number of
cases for which the solutions are found to be unstable
Soliton Lattice and Single Soliton Solutions of the Associated Lam\'e and Lam\'e Potentials
We obtain the exact nontopological soliton lattice solutions of the
Associated Lam\'e equation in different parameter regimes and compute the
corresponding energy for each of these solutions. We show that in specific
limits these solutions give rise to nontopological (pulse-like) single
solitons, as well as to different types of topological (kink-like) single
soliton solutions of the Associated Lam\'e equation. Following Manton, we also
compute, as an illustration, the asymptotic interaction energy between these
soliton solutions in one particular case. Finally, in specific limits, we
deduce the soliton lattices, as well as the topological single soliton
solutions of the Lam\'e equation, and also the sine-Gordon soliton solution.Comment: 23 pages, 5 figures. Submitted to J. Math. Phy
Effect of levothyroxine therapy on dyslipidemia in hypothyroid patients
The aims of the present study are to observe the prevalence of hypothyroidism (both subclinical and overt hypothyroidism), its association with dyslipidemia and whether replacement therapy with thyroid hormone has an effect on plasma lipid profile of hypothyroid patients. This prospective study of one-year duration recruited 232 clinically suspected patients belonging to both sexes and age group between 20-70 years attending OPD of endocrinology department of MLN Medical College, Allahabad. Patients were screened for T3, T4 and TSH and those who were euthyroid (52 cases) were excluded from the study. Thus, the present study included only 180 newly diagnosed cases of hypothyroidism. Levothyroxine replacement therapy was administered and patients were assessed every 3-4 months for an effect on lipid profile and body mass index during the study period. In both subclinical and overt hypothyroidism associated with dyslipidemia, replacement therapy with levothyroxine resulted in reversal to normal in significant number of cases. Although majority of hypothyroid cases were overweight yet therapy with levothyroxine caused no significant changes in BMI in all grades of obesity.Keywords: Levothyroxine therapy; Dyslipidemia; Hypothyroidis
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