910 research outputs found
Moment Equations for a Spatially Extended System of Two Competing Species
The dynamics of a spatially extended system of two competing species in the
presence of two noise sources is studied. A correlated dichotomous noise acts
on the interaction parameter and a multiplicative white noise affects directly
the dynamics of the two species. To describe the spatial distribution of the
species we use a model based on Lotka-Volterra (LV) equations. By writing them
in a mean field form, the corresponding moment equations for the species
concentrations are obtained in Gaussian approximation. In this formalism the
system dynamics is analyzed for different values of the multiplicative noise
intensity. Finally by comparing these results with those obtained by direct
simulations of the time discrete version of LV equations, that is coupled map
lattice (CML) model, we conclude that the anticorrelated oscillations of the
species densities are strictly related to non-overlapping spatial patterns.Comment: 10 pages, 3 figure
Moment equations in a Lotka-Volterra extended system with time correlated noise
A spatially extended Lotka-Volterra system of two competing species in the
presence of two correlated noise sources is analyzed: (i) an external
multiplicative time correlated noise, which mimics the interaction between the
system and the environment; (ii) a dichotomous stochastic process, whose jump
rate is a periodic function, which represents the interaction parameter between
the species. The moment equations for the species densities are derived in
Gaussian approximation, using a mean field approach. Within this formalism we
study the effect of the external time correlated noise on the ecosystem
dynamics. We find that the time behavior of the order moments are
independent on the multiplicative noise source. However the behavior of the
order moments is strongly affected both by the intensity and the
correlation time of the multiplicative noise. Finally we compare our results
with those obtained studying the system dynamics by a coupled map lattice
model.Comment: 12 pages, 7 figures, to appear in Acta Phys. Pol.
A practical method for calculating thermally-induced stresses in pile foundations used as heat exchangers
Thermo-active piles are capable of providing both structural stability as foundations and low carbon heating and cooling as ground source heat exchangers. When subjected to heating or cooling, the soil surrounding the pile restricts its expansion or contraction, giving rise to thermally-induced axial stresses, which need to be considered during design. Previous numerical studies often assume axisymmetry of the problem and/or a simplification of the heating or cooling mechanism of the pile. To simulate accurately the development of thermallyinduced axial stresses, this paper presents a computational study comprising three dimensional fully coupled thermo-hydro-mechanical finite element analyses conducted using the Imperial College Finite Element Program (ICFEP), where the heating of a thermo-active pile is simulated by prescribing a flow of hot water through the heat exchanger pipes within the pile. The effects of pipe arrangement on thermally-induced axial stresses are investigated by considering three different cases – single U loop, double U-loop and triple U-loop. Since threedimensional analyses are computationally expensive, a simplified method using a combination of two-dimensional analyses is proposed to estimate the thermally-induced axial stresses, which is subsequently validated and shown to yield accurate results
Finite element modelling of heat transfer in ground source energy systems with heat exchanger pipes
Ground source energy systems (GSES) utilise low enthalpy geothermal energy and have been recognised as an efficient means of providing low carbon space heating and cooling. This study focuses on GSES where the exchange of heat between the ground and the building is achieved by circulating a fluid through heat exchanger pipes. Although numerical analysis is a powerful tool for exploring the performance of such systems, simulating the highly advective flows inside the heat exchanger pipes can be problematic. This paper presents an efficient approach for modelling these systems using the finite element method (FEM). The pipes are discretised with line elements and the conductive-advective heat flux along them is solved using the Petrov-Galerkin FEM instead of the conventional Galerkin FEM. Following extensive numerical studies, a modelling approach for simulating heat exchanger pipes, which employs line elements and a special material with enhanced thermal properties, is developed. The modelling approach is then adopted in three-dimensional simulations of two thermal response tests, with an excellent match between the computed and measured temperatures being obtained
Interplay of fixed points in scalar models
We performed the renormalization group analysis of scalar models exhibiting
spontaneous symmetry breaking. It is shown that an infrared fixed point appears
in the broken symmetric phase of the models, which induces a dynamical scale,
that can be identified with the correlation length. This enables one to
identify the type of the phase transition which shows similarity to the one
appearing in the crossover scale. The critical exponent of the
correlation length also proved to be equal in the crossover and the infrared
scaling regimes.Comment: 11 pages, 4 figure
Noise Induced Complexity: From Subthreshold Oscillations to Spiking in Coupled Excitable Systems
We study stochastic dynamics of an ensemble of N globally coupled excitable
elements. Each element is modeled by a FitzHugh-Nagumo oscillator and is
disturbed by independent Gaussian noise. In simulations of the Langevin
dynamics we characterize the collective behavior of the ensemble in terms of
its mean field and show that with the increase of noise the mean field displays
a transition from a steady equilibrium to global oscillations and then, for
sufficiently large noise, back to another equilibrium. Diverse regimes of
collective dynamics ranging from periodic subthreshold oscillations to
large-amplitude oscillations and chaos are observed in the course of this
transition. In order to understand details and mechanisms of noise-induced
dynamics we consider a thermodynamic limit of the ensemble, and
derive the cumulant expansion describing temporal evolution of the mean field
fluctuations. In the Gaussian approximation this allows us to perform the
bifurcation analysis; its results are in good agreement with dynamical
scenarios observed in the stochastic simulations of large ensembles
Collapse of Flux Tubes
The dynamics of an idealized, infinite, MIT-type flux tube is followed in
time as the interior evolves from a pure gluon field to a
plasma. We work in color U(1). pair formation is evaluated
according to the Schwinger mechanism using the results of Brink and Pavel. The
motion of the quarks toward the tube endcaps is calculated by a Boltzmann
equation including collisions. The tube undergoes damped radial oscillations
until the electric field settles down to zero. The electric field stabilizes
the tube against pinch instabilities; when the field vanishes, the tube
disintegrates into mesons. There is only one free parameter in the problem,
namely the initial flux tube radius, to which the results are very sensitive.
Among various quantities calculated is the mean energy of the emitted pions.Comment: 16 pages plus 12 figures. RevTex3. DOE/ER/40427-160N9
The Rarita-Schwinger Particles Under de Influence of Strong Magnetic Fields
In this work, we calculate the solutions of the Rarita-Schwinger equation
with the inclusion of the eletromagnetic interaction. Our gauge and coupling
prescription choices lead to Dirac-type solutions. One of the consequences of
our results are the Landau level occupation of particles, quite different from
the usual spin 1/2 particle system occupation numbers.Comment: 12 page
Comparison of renormalization group schemes for sine-Gordon type models
The scheme-dependence of the renormalization group (RG) flow has been
investigated in the local potential approximation for two-dimensional periodic,
sine-Gordon type field-theoric models discussing the applicability of various
functional RG methods in detail. It was shown that scheme-independent
determination of such physical parameters is possible as the critical frequency
(temperature) at which Kosterlitz-Thouless-Berezinskii type phase transition
takes place in the sine-Gordon and the layered sine-Gordon models, and the
critical ratio characterizing the Ising type phase transition of the massive
sine-Gordon model. For the latter case the Maxwell construction represents a
strong constraint on the RG flow which results in a scheme-independent infrared
value for the critical ratio. For the massive sine-Gordon model also the
shrinking of the domain of the phase with spontaneously broken periodicity is
shown to take place due to the quantum fluctuations.Comment: 17 pages, 8 figures, revised version, to be published in Phys. Rev.
Periodic ground state for the charged massive Schwinger model
It is shown that the charged massive Schwinger model supports a periodic
vacuum structure for arbitrary charge density, similar to the common
crystalline layout known in solid state physics. The dynamical origin of the
inhomogeneity is identified in the framework of the bozonized model and in
terms of the original fermionic variables.Comment: 19 pages, 10 figures, revised version, accepted in Phys. Rev.
- …