Fractal scaling mechanisms in biomembranes

A modified model of the Cohen-Turnbull free volume theory for lateral transport processes in biomembranes is presented. The model which is based on renormalization group theoretical concepts incorporates fractal rather than Markovian diffusion kinetics. It predicts harmonic oscillations in the lateral diffusion coefficient around a dominant power-law trend and clarifies, in addition, recently observed deviations from the Cohen-Turnbull exponential law.     

Non-normal Statistics of DNA Sequences of Prokaryotes

The n-rule of Schrödinger in his discussion of DNA is based onnormal statistics and equilibrium physics. Herein the kurtosis is used tomeasure the deviation from normality of the stistics of non-equilibrium DNAsequences. A pattern for this deviation from normality is identified andthis signature is found in prokaryotes. The signature is explained by atheory of DNA sequences that involves finite length DNA walks withdynamically generated long-range correlations.     

Apoptosis in virus infection dynamics models

In this paper, on the basis of the simplified two-dimensional virus infection dynamics model, we propose two extended models that aim at incorporating the influence of activation-induced apoptosis which directly affects the population of uninfected cells. The theoretical analysis shows that increasing apoptosis plays a positive role in control of virus infection. However, after being included the third population of cytotoxic T lymphocytes immune response in HIV-infected patients, it shows that depending on intensity of the apoptosis of healthy cells, the apoptosis can either promote or comfort the long-term evolution of HIV infection. Further, the discrete-time delay of apoptosis is incorporated into the pervious model. Stability switching occurs as the time delay in apoptosis increases. Numerical simulations are performed to illustrate the theoretical results and display the different impacts of a delay in apoptosis.     

Peak-to-peak dynamics in food chain models

We show in this paper that the chaotic regimes of many food chain models often enjoy a very peculiar property, known as peak-to-peak dynamics. This means that the maximum (peak) density of the populations of any trophic level can be easily forecasted provided the last two peaks of the same population are known. Moreover, extensive simulation shows that only the last peak is needed if the forecast concerns the population at the top of the food chain and that peaks variability often increases from bottom to top. All these findings bring naturally to the conclusion that top populations should be sampled in order to have higher chances to detect peak-to-peak dynamics. The analysis is carried out by studying ditrophic food chain models with seasonally varying parameters, tritrophic food chain models with constant parameters, and more complex food chain and food web models.     

Understanding movement data and movement processes: current and emerging directions

Animal movement has been the focus on much theoretical and empirical work in ecology over the last 25 years. By studying the causes and consequences of individual movement, ecologists have gained greater insight into the behavior of individuals and the spatial dynamics of populations at increasingly higher levels of organization. In particular, ecologists have focused on the interaction between individuals and their environment in an effort to understand future impacts from habitat loss and climate change. Tools to examine this interaction have included: fractal analysis, first passage time, Lévy flights, multi‐behavioral analysis, hidden markov models, and state‐space models. Concurrent with the development of movement models has been an increase in the sophistication and availability of hierarchical bayesian models. In this review we bring these two threads together by using hierarchical structures as a framework for reviewing individual models. We synthesize emerging themes in movement ecology, and propose a new hierarchical model for animal movement that builds on these emerging themes. This model moves away from traditional random walks, and instead focuses inference on how moving animals with complex behavior interact with their landscape and make choices about its suitability.     

Steady states in population models with monotone,stochastic dynamics

Existence, uniqueness and asymptotic stability of stochastic equilibrium are established in multi-dimensional population models with monotone dynamics.     

玉米田截形叶螨种群动态的研究

1999～2001年于内蒙古巴彦卓尔盟杭锦后旗研究了玉米田截形叶螨田间种群动态。结果表明．截形叶螨在玉米田的空间格局为聚集格局,随着叶螨种群密度的上升,其聚集强度下降应用最优分割法将玉米截形叶螨田间种群动态划分为5个阶段：①7月上旬前为种群初建期,叶螨在玉米田刚开始发生,种群数量很低,只分布在极少数植株上;②7月中旬为种群缓慢增长期,种群数量低,增长缓慢,聚集强度高;③从7月下旬至8月中旬为种群快速增长期,种群数量高,增长迅速,叶螨分布至全田,聚集强度下降;④8月下旬为种群高峰期,种群数量最高,聚集强度较低;⑤9月以后为玉米截形叶螨种群的衰落期,由于玉米受害严重及玉米进入生长后期,中下部叶片大部分均已枯死,上部叶片也已老化营养水平下降,加之气温下降,叶螨种群数量迅速下降。     

Role of chemical short-range order in atomic dynamics decoupling

Abstract

Using molecular dynamics simulation, α-relaxation times τ_α and self-diffusion coefficients D for Al₉₀Fe₁₀, Al₈₀Fe₂₀, Al₇₀Fe₃₀, Al₆₀Fe₄₀ and Al₈₀Ni₂₀ (as a contrast system) melts have been systematically computed over a wide temperature range (1000–2000 K). The computed results reveal that τ_Fe/τ_Al (or D_Al/D_Fe) for the Al₉₀Fe₁₀ and Al₈₀Fe₂₀ melts exhibit an accelerating increase with cooling at temperatures lower than 1400 K, implying a clear decoupling of dynamics of Al and Fe (here referred to as component decoupling). This component decoupling diminishes in Al₇₀Fe₃₀ melt and disappears in Al₆₀Fe₄₀ melt. We simultaneously checked the relaxation decoupling (i.e. the decoupling between α-relaxation and diffusion). The relaxation decoupling is clear in Al₆₀Fe₄₀ melt, less clear in Al₇₀Fe₃₀ melt and not shown in Al₈₀Fe₂₀ and Al₉₀Fe₁₀ melt. It exhibits a tendency counter to that of component decoupling with changing composition, arguing that relaxation decoupling does not necessarily lead to component decoupling. This finding is contradicted against the conventional view that component decoupling is believed as a result of relaxation decoupling. We further attributed such a contradiction to the difference in the degree of chemical short-range order (CSRO) in melts. The existence of CSRO can increase the cooperativity in dynamics of different components. So it is better to consider component decoupling as a combined effect of relaxation decoupling and CSRO. This work would be helpful in improving our understanding of the relationship between the two kinds of decoupling.     

Segregation and mixing in degenerate diffusion in population dynamics

 We study the qualitative properties of degenerate diffusion equations used to describe dispersal processes in population dynamics. For systems of interacting populations, the forms of the diffusion models used determine if the population will intermix or remain disjoint (segregated). The dynamics and stability of segregation boundaries between competing populations is analyzed. General population models with segregation and mixing interactions are derived and connections to behavior in fluid mechanical systems are addressed. Received 19 January 1996; received in revised form 4 April 1996     

Investigation of moisture diffusion in cross-linked epoxy moulding compound by molecular dynamics simulation

Molecular dynamics (MD) simulation was carried out to study the moisture diffusion in cross-linked epoxy resin, with the influence of temperature, water concentration and polymer conversion taken into account. The simulation results showed that the moisture diffusion coefficients increased with the increase in temperature. And generally, with the increased moisture concentration or decreased polymer conversion, the moisture diffusion coefficients reduced. However, the moisture diffusion was strongly inhibited when the number of epoxy groups in completely reacted epoxy resins was equal to the number of water molecules.     

Molecular dynamics simulation of O2 diffusion in polydimethylsiloxane (PDMS) and end-linked PDMS networks

Molecular dynamics simulations are used to compute diffusion coefficients for O₂ molecules in polydimethylsiloxane (PDMS) and end-linked PDMS networks. The PDMS chains and penetrants are modelled using a hybrid interatomic potential which treats the Si and O atoms along the chain backbone explicitly while coarse-graining the methyl side groups and penetrants. In PDMS models with different molecular weights, diffusivity of the O₂ penetrants is found to modestly decrease with an increase in chain length. To match typical experimental conditions, the end-linked PDMS networks are constructed with a PDMS to crosslinking (CL) molecule mass ratio of 5:1 or 10:1, demanding that the number of CL molecules exceeds the number of PDMS chains in each model. Despite end-linking, the presence of non-bonded CL molecules promotes increased O₂ diffusivity in comparison with uncrosslinked PDMS. Temperature dependence is captured using the Williams–Landel–Ferry equation.     

Transport diffusivities of fluids in nanopores by non-equilibrium molecular dynamics simulation

We present a method to study fluid transport through nanoporous materials using highly efficient non-equilibrium molecular dynamics simulations. A steady flow is induced by applying an external field to the fluid particles within a small slab of the simulation cell. The external field generates a density gradient between both sides of the porous material, which in turn triggers a convective flux through the porous medium. The heat dissipated by the fluid flow is released by a Gaussian thermostat applied to the wall particles. This method is effective for studying diffusivities in a slit pore as well as more natural, complex wall geometries. The dependence of the diffusive flux on the external field sheds light on the transport diffusivities and allows a direct calculation of effective diffusivities. Both pore and fluid particle interactions are represented by coarse-grained molecular models in order to present a proof-of-concept and to retain computational efficiency in the simulations. The application of the method is demonstrated in two different scenarios, namely the effective mass transport through a slit pore and the calculation of the effective self-diffusion through this system. The method allows for a distinction between diffusive and convective contributions of the mass transport.     

Stochastic models for phytoplankton dynamics in Mediterranean Sea

In this paper, we review some results obtained from three one-dimensional stochastic models, which were used to analyze picophytoplankton dynamics in two sites of the Mediterranean Sea. Firstly, we present a stochastic advection–reaction–diffusion model to describe the vertical spatial distribution of picoeukaryotes in a site of the Sicily Channel. The second model, which is an extended version of the first one, is used to obtain the vertical stationary profiles of two groups of picophytoplankton, i.e. Pelagophytes and Prochlorococcus, in the same marine site as in the previous case. Here, we include intraspecific competition of picophytoplanktonic groups for limiting factors, i.e. light intensity and nutrient concentration. Finally, we analyze the spatio-temporal behaviour of five picophytoplankton populations in a site of the Tyrrhenian Sea by using a reaction–diffusion–taxis model. The study is performed, taking into account the seasonal changes of environmental variables, obtained starting from experimental findings. The multiplicative noise source, present in all three models, mimics the random fluctuations of temperature and velocity field. The vertical profiles of chlorophyll concentration obtained from the stochastic models show a good agreement with experimental data sampled in the two marine sites considered. The results could be useful to devise a new class of models based on a stochastic approach and able to predict future changes in biomass primary production.     

Dispersal and transient dynamics in metapopulations

Abstract Recent studies of spatially explicit metapopulation models have shown the existence of complex transient behaviour (supertransients and mesotransients) characterized by spontaneous changes in the system's dynamics after thousands or hundreds of generations, respectively. Their detection in simple ecological models has been taken as evidence that transient dynamics may be common in nature. In this study, we explore the generality of these phenomena in a simple one‐dimensional spatially explicit metapopulation model. We investigate how frequently supertransient behaviour emerges in relation to the shape and type of the dispersal kernel used (normal and Laplace), system size, boundary conditions and how sensitive they are to initial conditions. Our results show that supertransients are rare, are heavily affected by initial conditions and occur for a small set of dispersal parameter values, which vary according to kernel type, system size, and boundary conditions. Similarly, mesotransients emerge over a very narrow range of dispersal parameter values and are rare under all circumstances. Thus, transient dynamics are not likely to be either common or widespread in simple models of ecological systems.     

From local interactions to population dynamics in site-based models of ecology

A central problem in ecology is relating the interactions of individuals-described in terms of competition, predation, interference, etc.-to the dynamics of the populations of these individuals-in terms of change in numbers of individuals over time. Here, we address this problem for a class of site-based ecological models, where local interactions between individuals take place at a finite number of discrete resource sites over non-overlapping generations and, between generations, individuals move randomly between sites over the entire system. Such site-based models have previously been applied to a wide range of ecological systems: from those involving contest or scramble competition for resources to host-parasite interactions and meta-populations. We show how the population dynamics of site-based models can be accurately approximated by and understood through deterministic and stochastic difference equations. Conversely, we use the inverse of this approximation to show what implicit assumptions are made about individual interactions by modelling of population dynamics in terms of difference equations. To this end, we prove a useful and general theorem: that any model in our class of site-based models has a corresponding stochastic difference equation population model, by which it can be approximated. This theorem allows us to calculate long-term population dynamics, evolutionary stable strategies and, by extending our theory to account for large deviations, extinction probabilities for a wide range of site-based systems. Our methodology is then illustrated to various examples of between species competition, predator-prey interactions and co-operation.