Stationary Spatial Distribution Research Articles

Toward a “modern coexistence theory” for the discrete and spatial

AbstractThe usual theoretical condition for coexistence is that each species in a community can increase when it is rare (mutual invasibility). Traditional coexistence theory implicitly assumes that the invading species is common enough that we can ignore demographic stochasticity but rare enough that it does not compete with itself, even after it has reached a stationary spatial distribution. However, short‐distance dispersal of discrete individuals leads to locally dense population clusters, and existing theory breaks down. We have an intuition that when we account for invader–invader competition, shorter‐range dispersal should reduce the invader's ability to escape competition, but exactly how does this translate into lower population growth? And how will invader discreteness affect outcomes? We need a way of partitioning the contributions to coexistence, but current modern coexistence theory (MCT) does not apply under these conditions. Here we present a computationally based partitioning method to quantify the contributions to coexistence from different mechanisms, as in MCT. We also build up an intuition for how invader clumping and discreteness will affect these contributions by analyzing a case study, a lattice‐based spatial lottery model. We first consider fluctuation‐dependent coexistence, partitioning the contributions of variable environment, variable competition, demographic stochasticity, and their correlations and interactions. Our second example examines fluctuation‐independent coexistence maintained by a fecundity–survival trade‐off, and partitions the contributions to coexistence from interspecific differences in fecundity, in mortality, and in dispersal. We find that demographic stochasticity harms an invader, but only slightly. Localized invader dispersal, on the other hand, can have a strong effect. When invaders are more clumped, they compete with each other more intensely when rare, so they too become limited by environment‐competition covariance. More invader clumping also means that variation in competition changes from helping the invader to harming it. More broadly, invader clumping is likely to weaken any coexistence mechanism that relies on the invader escaping competition from the resident, because invader clumping means that the resident is no longer the only source of competition.

Search and return model for stochastic path integrators.

We extend a recently introduced prototypical stochastic model describing uniformly the search and return of objects looking for new food sources around a given home. The model describes the kinematic motion of the object with constant speed in two dimensions. The angular dynamics is driven by noise and describes a "pursuit" and "escape" behavior of the heading and the position vectors. Pursuit behavior ensures the return to the home and the escaping between the two vectors realizes exploration of space in the vicinity of the given home. Noise is originated by environmental influences and during decision making of the object. We take symmetric -stable noise since such noise is observed in experiments. We now investigate for the simplest possible case, the consequences of limited knowledge of the position angle of the home. We find that both noise type and noise strength can significantly increase the probability of returning to the home. First, we review shortly main findings of the model presented in the former manuscript. These are the stationary distance distribution of the noise driven conservative dynamics and the observation of an optimal noise for finding new food sources. Afterwards, we generalize the model by adding a constant shift within the interaction rule between the two vectors. The latter might be created by a permanent uncertainty of the correct home position. Nonvanishing shifts transform the kinematics of the searcher to a dissipative dynamics. For the latter, we discuss the novel deterministic properties and calculate the stationary spatial distribution around the home.

Convergence of an infinite dimensional stochastic process to a spatially structured trait substitution sequence

We consider an individual-based spatially structured population for Darwinian evolution in an asexual population. The individuals move randomly on a bounded continuous space according to a reflected brownian motion. The dynamics involves also a birth rate, a density-dependent logistic death rate and a probability of mutation at each birth event. We study the convergence of the microscopic process in a long time scale when the population size grows to $$+\infty $$ and the mutation probability decreases to 0. We prove the convergence towards a jump process that jumps in the infinite dimensional space containing the monomorphic stable spatial distributions. The proof requires specific studies of the microscopic model. First, we study the extinction time of the branching diffusion processes that approximate small size populations. Then, we examine the upper bound of large deviation principle around the deterministic large population limit of the microscopic process. Finally, we find a lower bound on the exit time of a neighborhood of a stationary spatial distribution.

Periodic and chaotic dynamics in a passively Q-switched Nd:GdVO4 laser with azimuthal polarization.

A period-doubling route to chaos was observed in a passively Q-switched Nd:GdVO4 laser beam with azimuthal polarization. At a period of two, the peak intensities gradually varied with the azimuthal angle. When the pump power was increased, the chaotic behavior was spatiotemporal, but the polarization was still azimuthal. To the best of our knowledge, this is the first report of spatiotemporal chaos under a stationary spatial distribution of the polarization.

Concentration of diffusional particles in viscous boundary sublayer of turbulent flow

The motion of inertial particles suspended in the viscous boundary sublayer of a wall-bounded turbulent flow is considered. We show that there is the diffusional region near the wall occupied by the particle moving in the local-equilibrium with the turbulent fluctuations which are modelled by Ornstein–Uhlenbeck process. The stationary spatial distribution of inertial particles is found for arbitrary Stokes number (dimensionless measure of the inertia). The weakly inertial particles placed in the diffusional region go away from the wall and escape the viscous sublayer. However, the direction of particle migration reverses when the Stokes number is getting larger than the critical value that we determine. The standard turbophoresis becomes more and more pronounced with the increase of Stokes number so that sufficiently inertial particles turn out to be trapped in the viscous boundary sublayer.

Patterns and scales of connectivity: temporal stability and variation within a marine metapopulation.

Because many marine invertebrates have a dispersive planktonic phase, the spatial scale of demographic, connectivity among local populations remains a key, but elusive, parameter driving population and metapopulation dynamics. However, temporal variation in the scale of connectivity remains largely undocumented, despite its recognized importance for predicting population responses to environmental changes. To assess the temporal stability of metapopulation connectivity, we conducted a large-scale survey of a blue mussel (Mytilus spp.) metapopulation for five years along a 100-km section of coastline of the Gaspé Peninsula, Québec, Canada. For each year, we estimated the scale of demographic coupling among 27-29 sites within our study region, using the spatial cross-covariance between adult abundance and recruit density across sites. Despite large interannual variability in overall recruit abundance, our analysis revealed stationary spatial distributions of adult and recruit abundance. More importantly, our analysis revealed a consistent demographic coupling among populations at a distance ranging from 12 to 24 km in all but one of the five years studied. The scale of connectivity in this system is thus temporally stable, but can occasionally show irregular fluctuations, and our results provide evidence in support of the integration of time-varying connectivity to marine metapopulation and reserve network theories.

A Novel Smooth Gauss–Semi-Markov Mobility Model for Mobile Wireless Networks

AbstractMobility model serves as the basis of protocol design and simulation in mobile wireless networks. In this paper, we propose a novel mobility model for mobile wireless networks, named smooth Gauss–semi-Markov (SGM) mobility model. Introducing Gauss and semi-Markov processes, the model can characterize the smooth movement of mobile users in accordance with the physical law of motion in order to eliminate sharp turns, abrupt speed change and sudden stops exhibited by existing mobility models. The SGM model consists of five consecutive phases: acceleration phase, stable phase, turn phase, deceleration phase and pause phase, including almost all kinds of movement states in realistic conditions. Through stochastic analysis, we prove mathematically the time stationary average speed and uniform spatial node distribution in the SGM model. The model can be easily and flexibly applied for simulating node mobility in mobile wireless networks. By adjusting parameters, many existing mobility models widely used at present, such as the Random Walk, Random Direction, Modified Random Direction, Gauss–Markov, Semi-Markov Smooth, Smooth Random mobility models, etc., can be derived from the SGM model. We show the unity and generality of the SGM model by NS-2 simulations.

The detrimental effect of hydrodynamic interactions on the process of Brownian flocculation in shear flow

AbstractThe problem of Brownian flocculation of spherical particles in strong shearing flow without hydrodynamic interactions is studied in detail using the singular perturbation method. All other types of interparticle interactions, such as van der Waals or Lennard-Jones forces, are also ignored. In the limit of strong external flow, the strength of which is measured by the Péclet number ($Pe\gg 1$), a complicated boundary layer structure for the pair probability density function ($P_{2}$) is identified and the complete stationary spatial distribution of $P_{2}(\boldsymbol {x})$ in the domain is found. The results, in particular the total mass flux in the accumulation process, are compared qualitatively and quantitatively with the case where the spheres interact hydrodynamically and it is demonstrated that the hydrodynamic interactions tend to decrease the rate of flocculation. An explicit simple formula for the flocculation rate for a general form of hydrodynamic interactions is provided. The limit of small Péclet number is also discussed to confirm the conclusion on the detrimental influence of hydrodynamic interactions on the rate of Brownian flocculation in shearing flow.

Network-coded cooperative information recovery in cellular/802.11 mobile Networks

By utilizing free WiFi transmissions, network coded cooperative peer-to-peer (P2P) information repair (NC-CPR) has been proposed to mitigate packet loss incurred during cellular Base Station (BS) broadcast. However, most of the work focuses on static network environment. While considering peer movement, the challenge part is the dynamically changed network topology, making it hard to control the transmission collisions to achieve good repair performance. In this paper, we propose the network coded cooperative information repair protocol with mobility concern (NC-CIRM) to recover the lost packets under the mobile scenario. Peer transmissions are scheduled with different channel access priorities based on their neighborhood information. Then, the NC-CIRM with known distribution (NC-CIRMD) protocol is presented which obtains neighborhood information based on the knowledge of node spatial distributions. Simulation results show that these two protocols achieve similar repair performance and work efficiently under both uniform and stationary node spatial distributions. Furthermore, a tunable parameter – coded packet generating rate based repair protocol (TP-RP) is proposed to further improve repair performance when the peers uniformly distribute within the system area. At the mean time, an analytical model is developed, then based on which parameter optimization is studied and theoretical results are derived. Extensive simulation results illustrate the improvement made by TP-RP protocol compared with the other two protocols and validate the accuracy of the optimal value of the tunable parameter.

Dynamics of two picophytoplankton groups in mediterranean sea: analysis of the deep chlorophyll maximum by a stochastic advection-reaction-diffusion model.

A stochastic advection-reaction-diffusion model with terms of multiplicative white Gaussian noise, valid for weakly mixed waters, is studied to obtain the vertical stationary spatial distributions of two groups of picophytoplankton, i.e., picoeukaryotes and Prochlorococcus, which account about for 60% of total chlorophyll on average in Mediterranean Sea. By numerically solving the equations of the model, we analyze the one-dimensional spatio-temporal dynamics of the total picophytoplankton biomass and nutrient concentration along the water column at different depths. In particular, we integrate the equations over a time interval long enough, obtaining the steady spatial distributions for the cell concentrations of the two picophytoplankton groups. The results are converted into chlorophyll a and divinil chlorophyll a concentrations and compared with experimental data collected in two different sites of the Sicily Channel (southern Mediterranean Sea). The comparison shows that real distributions are well reproduced by theoretical profiles. Specifically, position, shape and magnitude of the theoretical deep chlorophyll maximum exhibit a good agreement with the experimental values.

Fast flooding over Manhattan

We consider a Mobile Ad-hoc NETwork (MANET) formed by $$n$$ agents that move at speed $$\text{ v}$$ according to the Manhattan Random-Waypoint model over a square region of side length $$L$$ . This model has stationary properties that strongly depart from the well-studied Random-Walk model and that are typical in scenarios of vehicular traffic in urban zones. For instance, the resulting stationary (agent) spatial probability distribution is far to be uniform: the average density over the “central zone” is asymptotically higher than that over the “Suburb”. Agents exchange data if and only if they are at (Euclidean) distance at most $$R$$ within each other. We study the flooding time of this MANET: the number of time steps required to broadcast a message from one source agent to all agents of the network in the stationary phase. We prove the first asymptotical upper bound on the flooding time. This bound holds with high probability, it is a decreasing function of $$R$$ and $$\text{ v}$$ , and it is tight for a wide and relevant range of the network parameters (i.e. $$L, R$$ and $$\text{ v}$$ ). A consequence of our result is that flooding over the sparse and highly-disconnected Suburb can be as fast as flooding over the dense and connected central zone. This property holds even when $$R$$ is exponentially below the connectivity threshold of the MANET and the speed $$\text{ v}$$ is very low.

Multicast capacity scaling for inhomogeneous mobile ad hoc networks

We study multicast capacity for a large-scale spatial inhomogeneous mobile network consisting of n ad hoc nodes. Under our mobility model, the stationary spatial distribution of a node is non-uniform; each node spends most of the time in a certain region, and rarely (or never) visits out of such region. To characterize the inhomogeneity of the mobility model, we define an activity exponent γ and two clustering parameters (m(n),r(n)), where γ∈[0,1] measures the strength of node mobility, m(n) denotes the number of clusters, r(n) denotes the radius of the cluster. We classify the mobility into two cases according to the strength of mobility of each node, called strong and weak mobility, respectively. Two corresponding scheduling schemes and routing policies combined with the Manhattan multicast tree method are proposed. Suppose there are ns=Θ(n) multicast sessions. Each source has nd destinations which are selected randomly and independently. We show that under strong mobility case, the per-node multicast capacity is Θ1ndθ(n) with θ(n)=n1-γ2; under weak mobility case, when nd=Om(n)logm(n), the multicast throughput is Ω1ndm(n)n2logm(n); when nd=Ωm(n)logm(n), the multicast throughput is Ω1n. Particularly, as a special case, i.e., by letting nd=1, our results unify the previous unicast capacity bounds.

The fundamental limits of broadcasting in dense wireless mobile networks

In this paper, we investigate the fundamental properties of broadcasting in mobile wireless networks. In particular, we characterize broadcast capacity and latency of a mobile network, subject to the condition that the stationary node spatial distribution generated by the mobility model is uniform. We first study the intrinsic properties of broadcasting, and present the RippleCast broadcasting scheme that simultaneously achieves asymptotically optimal broadcast capacity and latency, subject to a weak upper bound on maximum node velocity and under the assumption of static broadcast source. We then extend RippleCast with the novel notion of center-casting, and prove that asymptotically optimal broadcast capacity and latency can be achieved also when the broadcast source is mobile. This study intendedly ignores the burden related to the selection of broadcast relay nodes within the mobile network, and shows that optimal broadcasting in mobile networks is, in principle, possible. We then investigate the broadcasting problem when the relay selection burden is taken into account, and present a combined distributed leader election and broadcasting scheme achieving a broadcast capacity and latency which is within a $$\Uptheta((\log n)^{1+\frac{2}{\alpha}})$$ factor from optimal, where n is the number of mobile nodes and ? > 2 is the path loss exponent. However, this result holds only under the assumption that the upper bound on node velocity converges to zero (although with a very slow, poly-logarithmic rate) as n grows to infinity.

Second Order Fluid Glow Discharge Model Sustained by Different Source Terms

Behavior of charged particles in a DC low pressure glow discharge is studied. The electric properties of the glow discharge in argon, maintained by a constant source term with uniform electron and ion generation, between two plane electrodes or by secondary electron emission at the cathode, are determined. A fluid model is used to solve self-consistently the first three moments of the Boltzmann equation coupled with the Poisson equation. The stationary spatial distribution of the electron and ion densities, the electric potential, the electric field, and the electron energy, in a two-dimensional (2D) configuration, are presented.

Hybrid model predictive control based on wireless sensor feedback: An experimental study

AbstractDesign and experimental validation of model predictive control (MPC) of a hybrid dynamical laboratory process with wireless sensors is presented. The laboratory process consists of four infrared lamps, controlled in pairs by two on/off switches, and of a transport belt, where moving parts equipped with wireless sensors are heated by the lamps. The process, which is motivated by heating processes in the plastic and printing industry, presents interesting hybrid dynamics. By approximating the stationary heat spatial distribution as a piecewise affine function of the position along the belt, the resulting plant model is a hybrid dynamical system. The control architecture is based on the reference governor approach: the process is actuated by a local controller, while a hybrid MPC algorithm running on a remote base station sends optimal belt velocity setpoints and lamp on/off commands over a wireless link, exploiting the sensor information received through the wireless network. A discrete‐time hybrid model of the process is used for the hybrid MPC algorithm and for the state estimator. The physical modelling of the process and the hybrid MPC algorithm are presented in detail, together with the hardware and software architectures. The experimental results show that the presented theoretical framework is well suited for control of the new laboratory process, and that the process can be used as a prototype system for evaluating hybrid and networked control strategies. Copyright © 2009 John Wiley & Sons, Ltd.

Radiation trapping in 1D using the Markov chain formalism: a computational physics project

A computational model study for atomic radiation trapping is presented with an audience non-specialized in radiation transport in mind. The level of presentation is adequate for a final undergraduate or beginning graduate project in a computational physics instruction. The dynamics of resonance radiation transport is discussed using a theoretical model known as the multiple scattering representation. This model is compared with the alternative Holstein's ansatz, reinterpreting the fundamental mode as the one associated with a relaxed stationary spatial distribution of excitation. Its computational implementation is done making use of the stochastic Markov chain formalism. A comprehensive discussion of its rationale as well as fine implementation details are presented. The simplest case of complete frequency redistribution in a two-level system is considered for a unidimensional geometry. Nevertheless, the model study discusses at length the influence of the spectral distributions, overall opacity and emission quantum yield for trapping distorted ensemble quantities stressing physical insight and using only straightforward algorithmic concepts. Overall relaxation parameters (ensemble emission yield and lifetime) as well as steady-state quantities (spectra and spatial distribution) are calculated as a function of intrinsic emission yield, opacity and external excitation mode for Doppler, Lorentz and Voigt lineshapes, respectively, with the fundamental mode contribution singled out.

Spatial node distribution of the random waypoint mobility model with applications

The random waypoint model (RWP) is one of the most widely used mobility models in performance analysis of ad hoc networks. We analyze the stationary spatial distribution of a node moving according to the RWP model in a given convex area. For this, we give an explicit expression, which is in the form of a one-dimensional integral giving the density up to a normalization constant. This result is also generalized to the case where the waypoints have a nonuniform distribution. As a special case, we study a modified RWP model, where the waypoints are on the perimeter. The analytical results are illustrated through numerical examples. Moreover, the analytical results are applied to study certain performance aspects of ad hoc networks, namely, connectivity and traffic load distribution.

Kerr-stabilized super-resonant modes in coupled-resonator optical waveguides

We investigate the effects of the optical Kerr nonlinearity in a coupled-resonator optical waveguide (CROW). Under certain conditions, there exists a stationary spatial distribution of the field whose envelope does not change with time-a super-resonant mode. The analysis does not indicate the existence of traveling hyperbolic-secant solitons of the Schrödinger type.

Flux-antiflux interface in type-II superconductors

Dynamics of vortex flux entering the superconductor containing flux of the opposite sign (antivortices) is considered. The interface point separating flux-antiflux domains is described by the solution moving inside the negative flux region. If vortices and antivortices penetrate a superconductor from the opposite sides of the sample symmetrically, the stationary flux-antiflux spatial distribution is described by the universal scaling law. Heat released by the vortex-antivortex annihilation forms a spatial temperature wave running across the sample. When velocity of the flux exceeds some critical value, it is predicted that the overheating instability will grow.

Models for Spatial Weights: A Systematic Look

General properties of spatial weights models, in particular Markovian properties, are systematically investigated. The role of stationary spatial distribution, interpretable as an importance‐centrality or prominence index, is emphasized. Spatial interaction models, and among them the gravity model, are classified with respect to the time reversal and aggregation invariance properties obeyed by the associated spatial weights. Nine examples, involving connectivity, flows and distance decay analysis, integral geometry, and Dirichlet‐Voronoi tessellations illustrate the main concepts, with a particular geometrical emphasis, and show how traditional, heuristic ingredients aimed at defining spatial weights can be recovered from general models.