694 research outputs found
Maximum Path Information and Fokker-Planck Equation
We present in this paper a rigorous method to derive the nonlinear
Fokker-Planck (FP) equation of anomalous diffusion directly from a
generalization of the principle of least action of Maupertuis proposed by Wang
for smooth or quasi-smooth irregular dynamics evolving in Markovian process.
The FP equation obtained may take two different but equivalent forms. It was
also found that the diffusion constant may depend on both q (the index of
Tsallis entropy) and the time t.Comment: 7 page
Specificity of the ribosomal A site for aminoacyl-tRNAs
Although some experiments suggest that the ribosome displays specificity for the identity of the esterified amino acid of its aminoacyl-tRNA substrate, a study measuring dissociation rates of several misacylated tRNAs containing the GAC anticodon from the A site showed little indication for such specificity. In this article, an expanded set of misacylated tRNAs and two 2′-deoxynucleotide-substituted mRNAs are used to demonstrate the presence of a lower threshold in koff values for aa-tRNA binding to the A site. When a tRNA binds sufficiently well to reach this threshold, additional stabilizing effects due to the esterified amino acid or changes in tRNA sequence are not observed. However, specificity for different amino acid side chains and the tRNA body is observed when tRNA binding is sufficiently weaker than this threshold. We propose that uniform aa-tRNA binding to the A site may be a consequence of a conformational change in the ribosome, induced by the presence of the appropriate combination of contributions from the anticodon, amino acid and tRNA body
Reduced dynamics of Ward solitons
The moduli space of static finite energy solutions to Ward's integrable
chiral model is the space of based rational maps from \CP^1 to itself
with degree . The Lagrangian of Ward's model gives rise to a K\"ahler metric
and a magnetic vector potential on this space. However, the magnetic field
strength vanishes, and the approximate non--relativistic solutions to Ward's
model correspond to a geodesic motion on . These solutions can be compared
with exact solutions which describe non--scattering or scattering solitons.Comment: Final version, to appear in Nonlinearit
The linear Fokker-Planck equation for the Ornstein-Uhlenbeck process as an (almost) nonlinear kinetic equation for an isolated N-particle system
It is long known that the Fokker-Planck equation with prescribed constant
coefficients of diffusion and linear friction describes the ensemble average of
the stochastic evolutions in velocity space of a Brownian test particle
immersed in a heat bath of fixed temperature. Apparently, it is not so well
known that the same partial differential equation, but now with constant
coefficients which are functionals of the solution itself rather than being
prescribed, describes the kinetic evolution (in the infinite particle limit) of
an isolated N-particle system with certain stochastic interactions. Here we
discuss in detail this recently discovered interpretation.Comment: Minor revisions and corrections (including the title
A Continuum Description of Rarefied Gas Dynamics (I)--- Derivation From Kinetic Theory
We describe an asymptotic procedure for deriving continuum equations from the
kinetic theory of a simple gas. As in the works of Hilbert, of Chapman and of
Enskog, we expand in the mean flight time of the constituent particles of the
gas, but we do not adopt the Chapman-Enskog device of simplifying the formulae
at each order by using results from previous orders. In this way, we are able
to derive a new set of fluid dynamical equations from kinetic theory, as we
illustrate here for the relaxation model for monatomic gases. We obtain a
stress tensor that contains a dynamical pressure term (or bulk viscosity) that
is process-dependent and our heat current depends on the gradients of both
temperature and density. On account of these features, the equations apply to a
greater range of Knudsen number (the ratio of mean free path to macroscopic
scale) than do the Navier-Stokes equations, as we see in the accompanying
paper. In the limit of vanishing Knudsen number, our equations reduce to the
usual Navier-Stokes equations with no bulk viscosity.Comment: 16 page
Overtwisted energy-minimizing curl eigenfields
We consider energy-minimizing divergence-free eigenfields of the curl
operator in dimension three from the perspective of contact topology. We give a
negative answer to a question of Etnyre and the first author by constructing
curl eigenfields which minimize energy on their co-adjoint orbit, yet are
orthogonal to an overtwisted contact structure. We conjecture that -contact
structures on -bundles always define tight minimizers, and prove a partial
result in this direction.Comment: published versio
Lax pair and Darboux transformation of noncommutative U(N) principal chiral model
We present a noncommutative generalization of Lax formalism of U(N) principal
chiral model in terms of a one-parameter family of flat connections. The Lax
formalism is further used to derive a set of parametric noncommutative
B\"{a}cklund transformation and an infinite set of conserved quantities. From
the Lax pair, we derive a noncommutative version of the Darboux transformation
of the model.Comment: 1+20 page
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