POPULATION DYNAMICS IN HETEROGENEOUS ENVIRONMENTS: A DISCRETE MODEL

2000 ◽  
Vol 10 (08) ◽  
pp. 1993-2000 ◽  
Author(s):  
BASTIEN FERNANDEZ ◽  
VALERY TERESHKO
Keyword(s):  
Population Dynamics ◽  
Periodic Orbit ◽  
Discrete Model ◽  
Mean Field ◽  
Heterogeneous Environments ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Population Spread ◽  
Asymptotic Dynamics ◽  
Time Periodic

We study the dynamics of a multidimensional coordinate-dependent mapping governing the time evolution of a population spread over a one-dimensional lattice. The nonlinearity is of mean-field type and the dependence on coordinates, given by the so-called fitness, allows to take into account the spatial heterogeneities of the habitat. A global picture of the dynamics is given in the case without diffusion and in the case with diffusion when the fitness is homogeneous and leads to a periodic orbit. Moreover it is shown that, periodic fitnesses close to homogeneous ones impose their periodicity on the asymptotic dynamics when the latter is time-periodic.

Critical behavior of percolation and Markov fields on branching planes

1993 ◽  
Vol 30 (3) ◽  
pp. 538-547 ◽  
Author(s):  
C. Chris Wu
Keyword(s):  
Continuous Function ◽  
Critical Behavior ◽  
Mean Field ◽  
Percolation Model ◽  
Homogeneous Tree ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Percolation Probability ◽  
Triangle Condition ◽  
Markov Fields

For an independent percolation model on, whereis a homogeneous tree andis a one-dimensional lattice, it is shown, by verifying that the triangle condition is satisfied, that the percolation probabilityθ(p) is a continuous function ofpat the critical pointpc, and the critical exponents,γ,δ, and Δ exist and take their mean-field values. Some analogous results for Markov fields onare also obtained.

Critical behavior of percolation and Markov fields on branching planes

1993 ◽  
Vol 30 (03) ◽  
pp. 538-547 ◽  
Author(s):  
C. Chris Wu
Keyword(s):  
Continuous Function ◽  
Critical Behavior ◽  
Mean Field ◽  
Percolation Model ◽  
Homogeneous Tree ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Percolation Probability ◽  
Triangle Condition ◽  
Markov Fields

For an independent percolation model on , where is a homogeneous tree and is a one-dimensional lattice, it is shown, by verifying that the triangle condition is satisfied, that the percolation probability θ (p) is a continuous function of p at the critical point p c, and the critical exponents , γ, δ, and Δ exist and take their mean-field values. Some analogous results for Markov fields on are also obtained.

Limit distributions for different forms of four-state quantum walks on a two-dimensional lattice

2015 ◽  
Vol 15 (13&14) ◽  
Author(s):  
Takuya Machida ◽  
C.M. Chandrashekar ◽  
Norio Konno ◽  
Thomas Busch
Keyword(s):  
Quantum Walks ◽  
Time Limit ◽  
Two Dimensional ◽  
View Point ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Limit Distributions ◽  
The Road ◽  
Long Time ◽  
Asymptotic Dynamics

Long-time limit distributions are key quantities for understanding the asymptotic dynamics of quantum walks, and they are known for most forms of one-dimensional quantum walks using two-state coin systems. For two-dimensional quantum walks using a four-state coin system, however, the only known limit distribution is for a walk using a parameterized Grover coin operation and analytical complexities have been a major obstacle for obtaining long-time limit distributions for other coins. In this work however, we present two new types of long-time limit distributions for walks using different forms of coin-flip operations in a four-state coin system. This opens the road towards understanding the dynamics and asymptotic behaviour for higher state coin system from a mathematical view point.

Symmetry Violations in Partially Oxidized One-Dimensional (1D)Transition Metal Polymers. Metal-Ligand-Metal(M-L-M) Bridged Systems

1984 ◽  
Vol 39 (9) ◽  
pp. 807-829
Author(s):  
Michael C. Böhm
Keyword(s):  
Transition Metal ◽  
Density Wave ◽  
Tight Binding ◽  
Mean Field ◽  
Valence Bond ◽  
Hole State ◽  
One Dimensional ◽  
Metal Derivatives ◽  
A Charge ◽  
Metal Ligand

The band structure of the metal-ligand-metal (M-L-M) bridged quasi one-dimensional (1D) cyclopentadienylmanganese polymer, MnCp 1, has been studied in the unoxidized state and in a partly oxidized modification with one electron removed from each second MnCp fragment. The tight-binding approach is based on a semiempirical self-consistent-field (SCF) Hartree-Fock (HF) crystal orbital (CO) model of the INDO-type (intermediate neglect of differential overlap) combined with a statistical averaging procedure which has its origin in the grand canonical ensemble. The latter approximation allows for an efficient investigation of violations of the translation symmetries in the oxidized 1D material. The oxidation process in 1 is both ligand- and metal-centered (Mn 3d-2 states). The mean-field minimum corresponds to a charge density wave (CDW) solution with inequivalent Mn sites within the employed repeat-units. The symmetry adapted solution with electronically identical 3d centers is a maximum in the variational space. The coupling of this electronic instability to geometrical deformations is also analyzed. The ligand amplitudes encountered in the hole-state wave function prevent extremely large charge separations between the 3d centers which are found in ID systems without bridging moieties (e.g. Ni(CN)2-5 chain). The symmetry reduction in oxidized 1 is compared with violations of spatial symmetries in finite transition metal derivatives and simple solids. The stabilization of the valence bond-type (VB) solution is physically rationalized (i.e. left-right correlations between the 3d centers). The computational results derived for 1 are generalized to oxidized transition metal chains with band occupancies that are simple fractions of the number of stacking units and to 1D systems that deviate from this relation. The entropy-influence for temperatures T ≠ 0 is shortly discussed (stabilization of domain or cluster structures).

The gas-liquid surface of the penetrable sphere model. II

1978 ◽  
Vol 358 (1694) ◽  
pp. 267-280 ◽  
Keyword(s):  
Surface Tension ◽  
Correlation Function ◽  
Liquid Surface ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Intermolecular Potential ◽  
Direct Correlation Function ◽  
Sphere Model ◽  
One Dimensional

The direct correlation function between two points in the gas-liquid surface of the penetrable sphere model is obtained in a mean-field approximation. This function is used to show explicitly that three apparently different ways of calculating the surface tension all lead to the same result. They are (1) from the virial of the intermolecular potential, (2) from the direct correlation function, and (3) from the energy density. The equality of (1) and (2) is shown analytically at all temperatures 0 < T < T c where T c is the critical temperature; the equality of (2) and (3) is shown analytically for T ≈ T c , and by numerical integration at lower temperatures. The equality of (2) and (3) is shown analytically at all temperatures for a one-dimensional potential.

Sign in / Sign up

Export Citation Format

Share Document