2,115 research outputs found
Revisiting the stability of spatially heterogeneous predator-prey systems under eutrophication
We employ partial integro-differential equations to model trophic interaction
in a spatially extended heterogeneous environment. Compared to classical
reaction-diffusion models, this framework allows us to more realistically
describe the situation where movement of individuals occurs on a faster time
scale than the demographic (population) time scale, and we cannot determine
population growth based on local density. However, most of the results reported
so far for such systems have only been verified numerically and for a
particular choice of model functions, which obviously casts doubts about these
findings. In this paper, we analyse a class of integro-differential
predator-prey models with a highly mobile predator in a heterogeneous
environment, and we reveal the main factors stabilizing such systems. In
particular, we explore an ecologically relevant case of interactions in a
highly eutrophic environment, where the prey carrying capacity can be formally
set to 'infinity'. We investigate two main scenarios: (i) the spatial gradient
of the growth rate is due to abiotic factors only, and (ii) the local growth
rate depends on the global density distribution across the environment (e.g.
due to non-local self-shading). For an arbitrary spatial gradient of the prey
growth rate, we analytically investigate the possibility of the predator-prey
equilibrium in such systems and we explore the conditions of stability of this
equilibrium. In particular, we demonstrate that for a Holling type I (linear)
functional response, the predator can stabilize the system at low prey density
even for an 'unlimited' carrying capacity. We conclude that the interplay
between spatial heterogeneity in the prey growth and fast displacement of the
predator across the habitat works as an efficient stabilizing mechanism.Comment: 2 figures; appendices available on request. To appear in the Bulletin
of Mathematical Biolog
Dynamical lattice instability versus spin liquid state in a frustrated spin chain system
The low-dimensional s=1/2 compound (NO)[Cu(NO3)3] has recently been suggested
to follow the Nersesyan-Tsvelik model of coupled spin chains. Such a system
shows unbound spinon excitations and a resonating valence bond ground state due
spin frustration. Our Raman scattering study demonstrates phonon anomalies as
well as the suppression of a broad magnetic scattering continuum for
temperatures below a characteristic temperature, T<T*=100K. We interpret these
effects as evidence for a dynamical interplay of spin and lattice degrees of
freedom that might lead to a further transition into a dimerized or
structurally distorted phase at lower temperatures.Comment: 5 pages, 6 figure
Dynamic Properties of Molecular Motors in Burnt-Bridge Models
Dynamic properties of molecular motors that fuel their motion by actively
interacting with underlying molecular tracks are studied theoretically via
discrete-state stochastic ``burnt-bridge'' models. The transport of the
particles is viewed as an effective diffusion along one-dimensional lattices
with periodically distributed weak links. When an unbiased random walker passes
the weak link it can be destroyed (``burned'') with probability p, providing a
bias in the motion of the molecular motor. A new theoretical approach that
allows one to calculate exactly all dynamic properties of motor proteins, such
as velocity and dispersion, at general conditions is presented. It is found
that dispersion is a decreasing function of the concentration of bridges, while
the dependence of dispersion on the burning probability is more complex. Our
calculations also show a gap in dispersion for very low concentrations of weak
links which indicates a dynamic phase transition between unbiased and biased
diffusion regimes. Theoretical findings are supported by Monte Carlo computer
simulations.Comment: 14 pages. Submitted to J. Stat. Mec
Application of Johnson disribution to the problemof aerospace images classification
Solving the problem of aerospace images classification it was suggested to approximate distribution density of image characteristics by Johnson distribution. The possibilities of such approach were investigated and its availability was show
M-Theory of Matrix Models
Small M-theories unify various models of a given family in the same way as
the M-theory unifies a variety of superstring models. We consider this idea in
application to the family of eigenvalue matrix models: their M-theory unifies
various branches of Hermitean matrix model (including Dijkgraaf-Vafa partition
functions) with Kontsevich tau-function. Moreover, the corresponding duality
relations look like direct analogues of instanton and meron decompositions,
familiar from Yang-Mills theory.Comment: 12 pages, contribution to the Proceedings of the Workshop "Classical
and Quantum Integrable Systems", Protvino, Russia, January, 200
Calculation of the energy J -integral for bodies with notches and cracks
Abstract. The approximate solutions for calculation of the energy J -integral of a body both with a notch and with a crack under elastic-plastic loading have been obtained. The crack is considered as the limit case of a sharp notch. The method is based on stress concentration analysis near a notch/crack tip and the modified Neuber's approach. The HRR-model and the method based on an equation of equilibrium were also employed to calculate the J -integral. The influence of the strain hardening exponent on the J -integral is discussed. New aspects of the two-parameter J * c -fracture criterion for a body with a short crack are studied. A theoretical investigation of the effect of the applied critical stress (or the crack length) on the strain fields ahead of the crack tip has been carried out
Strong-coupling effects in the relaxation dynamics of ultracold neutral plasmas
We describe a hybrid molecular dynamics approach for the description of
ultracold neutral plasmas, based on an adiabatic treatment of the electron gas
and a full molecular dynamics simulation of the ions, which allows us to follow
the long-time evolution of the plasma including the effect of the strongly
coupled ion motion. The plasma shows a rather complex relaxation behavior,
connected with temporal as well as spatial oscillations of the ion temperature.
Furthermore, additional laser cooling of the ions during the plasma evolution
drastically modifies the expansion dynamics, so that crystallization of the ion
component can occur in this nonequilibrium system, leading to lattice-like
structures or even long-range order resulting in concentric shells
Layer-by-layer laser synthesis of Cu–Al–Ni intermetallic compounds and shape memory effect
Published ArticleWe have studied conditions for the synthesis of intermetallic phases in the Cu–Al–Ni system by selective laser sintering/melting, in particular by heating a powder mixture to 300°C. The effects of laser synthesis and heating on the microstructure of the intermetallic phases in the samples obtained have been studied using electron microscopy, optical metallography, and X-ray diffraction analysis. The results demonstrate high sinterability of stoichiometric mixtures. Resistivity measurements indicate that the samples exhibit a shape memory effect. We discuss the feasibility of producing biomicroelectromechanical systems using layerby- layer synthesis
SU(2) Gluodynamics and HP1 sigma-model embedding: Scaling, Topology and Confinement
We investigate recently proposed HP1 sigma-model embedding method aimed to
study the topology of SU(2) gauge fields. The HP1 based topological charge is
shown to be fairly compatible with various known definitions. We study the
corresponding topological susceptibility and estimate its value in the
continuum limit. The geometrical clarity of HP1 approach allows to investigate
non-perturbative aspects of SU(2) gauge theory on qualitatively new level. In
particular, we obtain numerically precise estimation of gluon condensate and
its leading quadratic correction. Furthermore, we present clear evidences that
the string tension is to be associated with global (percolating) regions of
sign-coherent topological charge. As a byproduct of our analysis we estimate
the continuum value of quenched chiral condensate and the dimensionality of
regions, which localize the lowest eigenmodes of overlap Dirac operator.Comment: 22 pages, 18 ps figures, revtex4. Replaced to match published version
(PRD, to appear
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