<i>Equilibrium and Non-equilibrium Statistical Mechanics</i>

Balescu, Radu; Kaufman, Allan N.

doi:10.1063/1.3024522

Cited by 247 publications

(231 citation statements)

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“…As a result, even if the response to each stimulus is well defined and perfectly deterministic, the resultant response is likely to be complicated. This is exactly the context where Newtonian mechanics gives way to statistical mechanics [10]. Especially when the focus is on the path 'as a whole', as it often is in the dispersal studies [175], it is not instructive to look for a particular reason behind every animal's turn or move.…”

Section: Individual-based Approachmentioning

confidence: 99%

Multiscale approach to pest insect monitoring: Random walks, pattern formation, synchronization, and networks

Petrovskii

Petrovskaya

Bearup

2014

Physics of Life Reviews

104

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Pest insects pose a significant threat to food production worldwide resulting in annual losses worth hundreds of billions of dollars. Pest control attempts to prevent pest outbreaks that could otherwise destroy a sward. It is good practice in integrated pest management to recommend control actions (usually pesticides application) only when the pest density exceeds a certain threshold. Accurate estimation of pest population density in ecosystems, especially in agro-ecosystems, is therefore very important, and this is the overall goal of the pest insect monitoring. However, this is a complex and challenging task; providing accurate information about pest abundance is hardly possible without taking into account the complexity of ecosystems' dynamics, in particular, the existence of multiple scales. In the case of pest insects, monitoring has three different spatial scales, each of them having their own scale-specific goal and their own approaches to data collection and interpretation. In this paper, we review recent progress in mathematical models and methods applied at each of these scales and show how it helps to improve the accuracy and robustness of pest population density estimation.

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Section: Individual-based Approachmentioning

confidence: 99%

Multiscale approach to pest insect monitoring: Random walks, pattern formation, synchronization, and networks

Petrovskii

Petrovskaya

Bearup

2014

Physics of Life Reviews

104

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“…Time dependent diffusion as a mean field counterpart of Lévy type random walk [2]. The magnitude of the stochastic fluctuations must be small enough for adequate comparisons with the diffusive flux.…”

Section: Da Ahmed S Petrovskiimentioning

confidence: 99%

Time Dependent Diffusion as a Mean Field Counterpart of Lévy Type Random Walk

Ahmed

Petrovskii

2015

Math. Model. Nat. Phenom.

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Abstract. Insect trapping is commonly used in various pest insect monitoring programs as well as in many ecological field studies. An individual is said to be trapped if it falls within a well defined capturing zone, which it cannot escape. The accumulation of trapped individuals over time forms trap counts or alternatively, the flux of the population density into the trap. In this paper, we study the movement of insects whose dynamics are governed by time dependent diffusion and Lévy walks. We demonstrate that the diffusion model provides an alternative framework for the Cauchy type random walk (Lévy walk with Cauchy distributed steps). Furthermore, by calculating the trap counts using these two conceptually different movement models, we propose that trap counts for pests whose dynamics may be Lévy by nature can effectively be predicted by diffusive flux curves with time-dependent diffusivity.

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“…The motion of Brownian particle in the framework of classical dynamics can be modeled by the force three-vector [28] …”

Section: Force Field Modelingmentioning

confidence: 99%

Curvature Coupling and Accelerated Expansion of the Universe

Balakin

2004

General Relativity and Gravitation

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A new exactly solvable model for the evolution of relativistic kinetic system interacting with an internal stochastic reservoir under the influence of a gravitational background expansion is established. This model of selfinteraction is based on the relativistic kinetic equation for the distribution function defined in the extended phase space. The supplementary degree of freedom is described by the scalar stochastic variable (Langevin source), which is considered to be the constructive element of the effective oneparticle force. The expansion of the Universe is shown to be accelerated for the suitable choice of the non-minimal self-interaction force.

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Equilibrium and Non-equilibrium Statistical Mechanics

Cited by 247 publications

References 0 publications

Multiscale approach to pest insect monitoring: Random walks, pattern formation, synchronization, and networks

Multiscale approach to pest insect monitoring: Random walks, pattern formation, synchronization, and networks

Time Dependent Diffusion as a Mean Field Counterpart of Lévy Type Random Walk

Curvature Coupling and Accelerated Expansion of the Universe

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