3,735 research outputs found
Biomixing by chemotaxis and efficiency of biological reactions: the critical reaction case
Many phenomena in biology involve both reactions and chemotaxis. These
processes can clearly influence each other, and chemotaxis can play an
important role in sustaining and speeding up the reaction. In continuation of
our earlier work, we consider a model with a single density function involving
diffusion, advection, chemotaxis, and absorbing reaction. The model is
motivated, in particular, by the studies of coral broadcast spawning, where
experimental observations of the efficiency of fertilization rates
significantly exceed the data obtained from numerical models that do not take
chemotaxis (attraction of sperm gametes by a chemical secreted by egg gametes)
into account. We consider the case of the weakly coupled quadratic reaction
term, which is the most natural from the biological point of view and was left
open. The result is that similarly to higher power coupling, the chemotaxis
plays a crucial role in ensuring efficiency of reaction. However,
mathematically, the picture is quite different in the quadratic reaction case
and is more subtle. The reaction is now complete even in the absence of
chemotaxis, but the timescales are very different. Without chemotaxis, the
reaction is very slow, especially for the weak reaction coupling coefficient.
With chemotaxis, the timescale and efficiency of reaction are independent of
the coupling parameter.Comment: 10 pages. arXiv admin note: text overlap with arXiv:1101.244
Particle decay in false vacuum
We revisit the problem of decay of a metastable vacuum induced by the
presence of a particle. For the bosons of the `master field' the problem is
solved in any number of dimensions in terms of the spontaneous decay rate of
the false vacuum, while for a fermion we find a closed expression for the decay
rate in (1+1) dimensions. It is shown that in the (1+1) dimensional case an
infrared problem of one-loop correction to the decay rate of a boson is
resolved due to a cancellation between soft modes of the field. We also find
the boson decay rate in the `sine-Gordon staircase' model in the limits of
strong and weak coupling.Comment: 19 pages, 2 figure
A convenient criterion under which Z_2-graded operators are Hamiltonian
We formulate a simple and convenient criterion under which skew-adjoint
Z_2-graded total differential operators are Hamiltonian, provided that their
images are closed under commutation in the Lie algebras of evolutionary vector
fields on the infinite jet spaces for vector bundles over smooth manifolds.Comment: J.Phys.Conf.Ser.: Mathematical and Physical Aspects of Symmetry.
Proc. 28th Int. colloq. on group-theoretical methods in Physics (July 26-30,
2010; Newcastle-upon-Tyne, UK), 6 pages (in press
Variational Lie algebroids and homological evolutionary vector fields
We define Lie algebroids over infinite jet spaces and establish their
equivalent representation through homological evolutionary vector fields.Comment: Int. Workshop "Nonlinear Physics: Theory and Experiment VI"
(Gallipoli, Italy; June-July 2010). Published v3 = v2 minus typos, to appear
in: Theoret. and Mathem. Phys. (2011) Vol.167:3 (168:1), 18 page
Algebraic properties of Gardner's deformations for integrable systems
An algebraic definition of Gardner's deformations for completely integrable
bi-Hamiltonian evolutionary systems is formulated. The proposed approach
extends the class of deformable equations and yields new integrable
evolutionary and hyperbolic Liouville-type systems. An exactly solvable
two-component extension of the Liouville equation is found.Comment: Proc. conf. "Nonlinear Physics: Theory and Experiment IV" (Gallipoli,
2006); Theor. Math. Phys. (2007) 151:3/152:1-2, 16p. (to appear
Gardner's deformations of the N=2 supersymmetric a=4-KdV equation
We prove that P.Mathieu's Open problem on constructing Gardner's deformation
for the N=2 supersymmetric a=4-Korteweg-de Vries equation has no supersymmetry
invariant solutions, whenever it is assumed that they retract to Gardner's
deformation of the scalar KdV equation under the component reduction. At the
same time, we propose a two-step scheme for the recursive production of the
integrals of motion for the N=2, a=4-SKdV. First, we find a new Gardner's
deformation of the Kaup-Boussinesq equation, which is contained in the bosonic
limit of the super-hierarchy. This yields the recurrence relation between the
Hamiltonians of the limit, whence we determine the bosonic super-Hamiltonians
of the full N=2, a=4-SKdV hierarchy. Our method is applicable towards the
solution of Gardner's deformation problems for other supersymmetric KdV-type
systems.Comment: Extended version of the talks given by A.V.K. at 8th International
conference `Symmetry in Nonlinear Mathematical Physics' (June 20-27, 2009,
Kiev, Ukraine) and 9th International workshop `Supersymmetry and Quantum
Symmetries' (July 29 - August 3, 2009, JINR, Dubna, Russia); 22 page
Physics of B_c mesons
In the framework of potential models for heavy quarkonium the mass spectrum
for the system () is considered. Spin-dependent splittings, taking
into account a change of a constant for effective coulomb interaction between
the quarks, and widths of radiative transitions between the () levels
are calculated. In the framework of QCD sum rules, masses of the lightest
vector and pseudoscalar states are estimated, scaling relation
for leptonic constants of heavy quarkonia is derived, and the leptonic constant
is evaluated. The decays are considered in the framework of
both the potential models and the QCD sum rules, where the significance of
Coulomb-like corrections is shown. The relations, following from the
approximate spin symmetry for the heavy quarks in the heavy quarkonium, are
analysed for the form factors of the semileptonic weak exclusive decays of
. The lifetime is evaluated with the account of the corrections to
the spectator mechanism of the decay, because of the quark binding into the
meson. The total and differential cross sections of the production in
different interactions are calculated. The analytic expressions for the
fragmentational production cross sections of are derived. The possibility
of the practical search in the current and future experiments at
electron-positron and hadron colliders is analysed.Comment: 81 page, latex, ihep.sty is required and attached in the end of the
file after \end{document}, figures are not availabl
Two-particle decays of B_c meson into charmonium states
The factorization of hard and soft contributions into the hadronic decays of
B_c meson at large recoils is explored in order to evaluate the decay rates
into the S, P and D-wave charmonia associated with rho and pi. The constraints
of approach applicability and uncertainties of numerical estimates are
discussed. The mode with the J/psi in the final state is evaluated taking into
account the cascade radiative electromagnetic decays of excited P-wave states,
that enlarges the branching ratio by 20-25%.Comment: 13 pages, LaTeX axodraw-style, 1 figure, 2 table
Mass spectra of doubly heavy Omega_QQ' baryons
We evaluate the masses of baryons composed of two heavy quarks and a strange
quark with account for spin-dependent splittings in the framework of potential
model with the KKO potential motivated by QCD with a three-loop beta-function
for the effective charge consistent with both the perturbative limit at short
distances and linear confinement term at long distances between the quarks. The
factorization of dynamics is supposed and explored in the nonrelativistic
Schroedinger equation for the motion in the system of two heavy quarks
constituting the doubly heavy diquark and the strange quark interaction with
the diquark. The limits of approach, its justification and uncertainties are
discussed. Excited quasistable states are classified by the quantum numbers of
heavy diquark composed by the heavy quarks of the same flavor.Comment: 14 pages, revtex4-file, 3 eps-figures, 5 tables, typos correcte
Forced Topological Nontrivial Field Configurations
The motion of a one-dimensional kink and its energy losses are considered as
a model of interaction of nontrivial topological field configurations with
external fields. The approach is based on the calculation of the zero modes
excitation probability in the external field. We study in the same way the
interaction of the t'Hooft-Polyakov monopole with weak external fields. The
basic idea is to treat the excitation of a monopole zero mode as the monopole
displacement. The excitation is found perturbatively. As an example we consider
the interaction of the t'Hooft-Polyakov monopole with an external uniform
magnetic field.Comment: 18 pages, 3 Postscript figures, RevTe
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