23,455 research outputs found
Fractional exponential decay in the capture of ligands by randomly distributed traps in one dimension
In many biophysical and biochemical experiments one observes the decay of some ligand population by an appropriate system of traps. We analyse this decay for a one-dimensional system of radomly distributed traps, and show that one can distinguish three different regimes. The decay starts with a fractional exponential of the form exp[â (t/t0)1/2], which changes into a fractional exponential of the form exp[â (t/t1)1/3] for long times, which in its turn changes into a pure exponential time dependence, i.e. exp[ât/t2] for very long times. With these three regimes, we associate three time scales, related to the average trap density and the diffusion constant characterizing the motion of the ligands
Chaotic motion of a harmonically bound charged particle in a magnetic field, in the presence of a half-plane barrier
The motion in the plane of an harmonically bound charged particle interacting with a magnetic field and a half-plane barrier along the positive x-axis is studied. The magnetic field is perpendicular to the plane in which the particle moves. This motion is integrable in between collisions of the particle with the barrier. However, the overall motion of the particle is very complicated. Chaotic regions in phase space exist next to island structures associated with linearly stable periodic orbits. We study in detail periodic orbits of low period and in particular their bifurcation behavior. Independent sequences of period doubling bifurcations and resonant bifurcations are observed associated with independent fixed points in the Poincaré section. Due to the perpendicular magnetic field an orientation is induced on the plane and time-reversal symmetry is broken.\u
Julian Ernst Besag, 26 March 1945 -- 6 August 2010, a biographical memoir
Julian Besag was an outstanding statistical scientist, distinguished for his
pioneering work on the statistical theory and analysis of spatial processes,
especially conditional lattice systems. His work has been seminal in
statistical developments over the last several decades ranging from image
analysis to Markov chain Monte Carlo methods. He clarified the role of
auto-logistic and auto-normal models as instances of Markov random fields and
paved the way for their use in diverse applications. Later work included
investigations into the efficacy of nearest neighbour models to accommodate
spatial dependence in the analysis of data from agricultural field trials,
image restoration from noisy data, and texture generation using lattice models.Comment: 26 pages, 14 figures; minor revisions, omission of full bibliograph
Phase Diagram of a Loop on the Square Lattice
The phase diagram of the O(n) model, in particular the special case , is
studied by means of transfer-matrix calculations on the loop representation of
the O(n) model. The model is defined on the square lattice; the loops are
allowed to collide at the lattice vertices, but not to intersect. The loop
model contains three variable parameters that determine the loop density or
temperature, the energy of a bend in a loop, and the interaction energy of
colliding loop segments. A finite-size analysis of the transfer-matrix results
yields the phase diagram in a special plane of the parameter space. These
results confirm the existence of a multicritical point and an Ising-like
critical line in the low-temperature O(n) phase.Comment: LaTeX, 3 eps file
Crosslinking and gelation between linear polymers: DNA-antibody complexes in systemic lupus erythematosus
In the autoimmune disease systemic lupus erythematosus the DNA molecules of an individual are attacked by its own antibodies. As these antibodies are bivalent they can crosslink different DNA molecules which can lead to the formation of DNA-antibody complexes and gels. Statistical properties of these complexes are derived and evaluated analytically in the limit of very long DNA molecules, as well as the concentrations at which a gel is being formed. The authors also present various numerical results for DNA molecules of intermediate lengths. This work can also be considered as a theory of the crosslinking and gelation of linear polymer
First and second order transitions in dilute O(n) models
We explore the phase diagram of an O(n) model on the honeycomb lattice with
vacancies, using finite-size scaling and transfer-matrix methods. We make use
of the loop representation of the O(n) model, so that is not restricted to
positive integers. For low activities of the vacancies, we observe critical
points of the known universality class. At high activities the transition
becomes first order. For n=0 the model includes an exactly known theta point,
used to describe a collapsing polymer in two dimensions. When we vary from
0 to 1, we observe a tricritical point which interpolates between the
universality classes of the theta point and the Ising tricritical point.Comment: LaTeX, 6 eps file
Enhanced chiral logarithms in partially quenched QCD
I discuss the properties of pions in ``partially quenched'' theories, i.e.
those in which the valence and sea quark masses, and , are
different. I point out that for lattice fermions which retain some chiral
symmetry on the lattice, e.g. staggered fermions, the leading order prediction
of the chiral expansion is that the mass of the pion depends only on , and
is independent of . This surprising result is shown to receive corrections
from loop effects which are of relative size , and which thus
diverge when the valence quark mass vanishes. Using partially quenched chiral
perturbation theory, I calculate the full one-loop correction to the mass and
decay constant of pions composed of two non-degenerate quarks, and suggest
various combinations for which the prediction is independent of the unknown
coefficients of the analytic terms in the chiral Lagrangian. These results can
also be tested with Wilson fermions if one uses a non-perturbative definition
of the quark mass.Comment: 14 pages, 3 figures, uses psfig. Typos in eqs (18)-(20) corrected
(alpha_4 is replaced by alpha_4/2
Chiral perturbation theory for K+ to pi+ pi0 decay in the continuum and on the lattice
In this paper we use one-loop chiral perturbation theory in order to compare
lattice computations of the K+ to pi+ pi0 decay amplitude with the experimental
value. This makes it possible to investigate three systematic effects that
plague lattice computations: quenching, finite-volume effects, and the fact
that lattice computations have been done at unphysical values of the quark
masses and pion external momenta (only this latter effect shows up at tree
level). We apply our results to the most recent lattice computation, and find
that all three effects are substantial. We conclude that one-loop corrections
in chiral perturbation theory help in explaining the discrepancy between
lattice results and the real-world value. We also revisit B_K, which is closely
related to the K+ to pi+ pi0 decay amplitude by chiral symmetry.Comment: 50 pages, TeX, two eps figures included, minor changes, no changes in
results or conclusions, version to appear in Phys.Rev.
Lattice QCD at the end of 2003
I review recent developments in lattice QCD. I first give an overview of its
formalism, and then discuss lattice discretizations of fermions. We then turn
to a description of the quenched approximation and why it is disappearing as a
vehicle for QCD phenomenology. I describe recent claims for progress in
simulations which include dynamical fermions and the interesting theoretical
problems they raise. I conclude with brief descriptions of the calculations of
matrix elements in heavy flavor systems and for kaons.Comment: Review for Int J Mod Phys A. 58 pages, latex, WSPC macros,, 22
postscript figure
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