428 research outputs found
Stationary solutions of linear stochastic delay differential equations - Applications to biological systems
Recently, Küchler and Mensch [Stochastics Stochastics Rep. 40, 23 (1992)] derived exact stationary probability densities for linear stochastic delay differential equations. This paper presents an alternative derivation of these solutions by means of the Fokker-Planck approach introduced by Guillouzic [Phys. Rev. E 59, 3970 (1999); 61, 4906 (2000)]. Applications of this approach, which is argued to have greater generality, are discussed in the context of stochastic models for population growth and tracking movements
Multivariate Ornstein-Uhlenbeck processes with mean-field dependent coefficients: Application to postural sway
We study the transient and stationary behavior of many-particle systems in terms of multivariate OrnsteinUhlenbeck processes with friction and diffusion coefficients that depend nonlinearly on process mean fields. Mean-field approximations of this kind of system are derived in terms of Fokker-Planck equations. In such systems, multiple stationary solutions as well as bifurcations of stationary solutions may occur. In addition, strictly monotonically decreasing steady-state autocorrelation functions that decay faster than exponential functions are found, which are used to describe the erratic motion of the center of pressure during quiet standing
The complete amino acid sequence of the antenna polypeptide B806-866-β from the cytoplasmic membrane of the green bacterium Chloroflexus auranliacus
AbstractThe bacteriochlorophyll a-binding polypeptide B806–866-β was extracted from membranes of the green thermophilic bacterium Chloroflexus aurantiacus with chloroform/methanol/ammonium acetate. Purification of the antenna polypeptide (6.3 kDa) was achieved by chromatography on Sephadex LH-60, Whatman DE-32 and by FPLC. The complete amino acid sequence (53 amino acid residues) was determined. The B806–866-β polypeptide is sequence homologous to the antenna β-polypeptides of purple bacteria (27–40%) and exhibits the characteristic three domain structure of the B870, B800–850 and B800–820 antenna complexes. The two typical His residues, conserved in all antenna β-polypeptides of purple bacteria, were found: His-24 lies within the N-terminal hydrophilic domain and His-42 within the central hydrophobic domain. This polypeptide together with the previously described α-polypeptide form the basic structural unit of the B806–866 antenna complex from C. aurantiacus
Canonical-dissipative limit cycle oscillators with a short-range interaction in phase space
We consider limit cycle oscillators in terms of canonical-dissipative systems that exhibit a short-range interaction in velocity and position space as described by the Dirac delta function. We derive analytical expressions for stationary distribution functions in phase space and energy space and propose a numerical simulation scheme for the simulation of the many body system as well. We show that the short-range interaction squeezes or stretches energy distribution functions depending on whether the interaction can be regarded as attractive or repulsive. In addition to the interaction effect, we show that energy distribution functions become narrower when limit cycle attractors become stronger. Finally, energy distributions become broader when the pumping energy is increased. The latter effect however disappears in the high energy domain.Розглянуто граничні циклічні осцилятори в термінах канонічно-дисипативних систем, які демонструють короткосяжну взаємодію у швидкісному та позиційному просторі, що описаний дельта-функцією Дірака. Виведено аналітичні вирази для стаціонарних функцій розподілу у фазовому просторі та енергетичному просторі та запропоновано числову симуляційну схему для моделювання багаточастинкової системи. Показано, що короткосяжна взаємодія стискає чи розтягує енергетичні функції розподілу залежно від того, чи взаємодію можна вважати притягальною, чи відштовхувальною. Крім впливу взаємодії, показано, що енергетичні функції розподілу стають вужчими, якщо межа циклічних атракторів стає сильнішою. Накінець, енергетичні розподіли стають ширшими з ростом енергії накачки. Цей ефект, проте, зникає у високоенергетичній області
The antiferromagnetic phi4 Model, II. The one-loop renormalization
It is shown that the four dimensional antiferromagnetic lattice phi4 model
has the usual non-asymptotically free scaling law in the UV regime around the
chiral symmetrical critical point. The theory describes a scalar and a
pseudoscalar particle. A continuum effective theory is derived for low
energies. A possibility of constructing a model with a single chiral boson is
mentioned.Comment: To appear in Phys. Rev.
Meson-Baryon-Baryon Vertex Function and the Ward-Takahashi Identity
Ohta proposed a solution for the well-known difficulty of satisfying the
Ward-Takahashi identity for a photo-meson-baryon-baryon amplitude (MBB)
when a dressed meson-baryon-baryon (MBB) vertex function is present. He
obtained a form for the MBB amplitude which contained, in addition to
the usual pole terms, longitudinal seagull terms which were determined entirely
by the MBB vertex function. He arrived at his result by using a Lagrangian
which yields the MBB vertex function at tree level. We show that such a
Lagrangian can be neither hermitian nor charge conjugation invariant. We have
been able to reproduce Ohta's result for the MBB amplitude using the
Ward-Takahashi identity and no other assumption, dynamical or otherwise, and
the most general form for the MBB and MBB vertices. However, contrary
to Ohta's finding, we find that the seagull terms are not robust. The seagull
terms extracted from the MBB vertex occur unchanged in tree graphs,
such as in an exchange current amplitude. But the seagull terms which appear in
a loop graph, as in the calculation of an electromagnetic form factor, are, in
general, different. The whole procedure says nothing about the transverse part
of the (MBB) vertex and its contributions to the amplitudes in
question.Comment: A 20 pages Latex file and 16 Postscript figures in an uuencoded
format. Use epsf.sty to include the figures into the Latex fil
Towards nonlinear quantum Fokker-Planck equations
It is demonstrated how the equilibrium semiclassical approach of Coffey et
al. can be improved to describe more correctly the evolution. As a result a new
semiclassical Klein-Kramers equation for the Wigner function is derived, which
remains quantum for a free quantum Brownian particle as well. It is transformed
to a semiclassical Smoluchowski equation, which leads to our semiclassical
generalization of the classical Einstein law of Brownian motion derived before.
A possibility is discussed how to extend these semiclassical equations to
nonlinear quantum Fokker-Planck equations based on the Fisher information
Dynamical model and nonextensive statistical mechanics of a market index on large time windows
The shape and tails of partial distribution functions (PDF) for a financial
signal, i.e. the S&P500 and the turbulent nature of the markets are linked
through a model encompassing Tsallis nonextensive statistics and leading to
evolution equations of the Langevin and Fokker-Planck type. A model originally
proposed to describe the intermittent behavior of turbulent flows describes the
behavior of normalized log-returns for such a financial market index, for small
and large time windows, both for small and large log-returns. These turbulent
market volatility (of normalized log-returns) distributions can be sufficiently
well fitted with a -distribution. The transition between the small time
scale model of nonextensive, intermittent process and the large scale Gaussian
extensive homogeneous fluctuation picture is found to be at a 200 day
time lag. The intermittency exponent () in the framework of the
Kolmogorov log-normal model is found to be related to the scaling exponent of
the PDF moments, -thereby giving weight to the model. The large value of
points to a large number of cascades in the turbulent process. The
first Kramers-Moyal coefficient in the Fokker-Planck equation is almost equal
to zero, indicating ''no restoring force''. A comparison is made between
normalized log-returns and mere price increments.Comment: 40 pages, 14 figures; accepted for publication in Phys Rev
Nonlinear Realization of Chiral Symmetry on the Lattice
We formulate lattice theories in which chiral symmetry is realized
nonlinearly on the fermion fields. In this framework the fermion mass term does
not break chiral symmetry. This property allows us to use the Wilson term to
remove the doubler fermions while maintaining exact chiral symmetry on the
lattice. Our lattice formulation enables us to address non-perturbative
questions in effective field theories of baryons interacting with pions and in
models involving constituent quarks interacting with pions and gluons. We show
that a system containing a non-zero density of static baryons interacting with
pions can be studied on the lattice without encountering complex action
problems. In our formulation one can also decide non-perturbatively if the
chiral quark model of Georgi and Manohar provides an appropriate low-energy
description of QCD. If so, one could understand why the non-relativistic quark
model works.Comment: 34 pages, 2 figures, revised version to be published in J. High
Energy Phys. (changes in the 1st paragraph, additional descriptions on the
nature of the coordinate singularities in Sec.2, references added
Solution of generalized fractional reaction-diffusion equations
This paper deals with the investigation of a closed form solution of a
generalized fractional reaction-diffusion equation. The solution of the
proposed problem is developed in a compact form in terms of the H-function by
the application of direct and inverse Laplace and Fourier transforms.
Fractional order moments and the asymptotic expansion of the solution are also
obtained.Comment: LaTeX, 18 pages, corrected typo
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