Density outbursts in a food web model with a closed nutrient cycle

A spatial three level food web model with a closed nutrient cycle is presented and analyzed via Monte Carlo simulations. The food web consists of three trophic levels. The basal level species (called resources  , R$R$) corresponds to primary producers in real ecosystems. The species at an intermediate level (consumers  , C$C$) relates to herbivores. It feeds on the resources. The consumers themselves constitute food for the top level species (predators  , P$P$), which corresponds to carnivores. The remains of the consumers and predators (detritus  , D$D$) provide nutrient for the resources. The time evolution of the model reveals two asymptotic states: an absorbing one with all species being extinct, and a coexisting one, in which concentrations of all species are non-zero. There are two possible ways for the system to reach the absorbing state. In some cases the densities increase very quickly at the beginning of a simulation and then decline slowly and almost monotonically. In others, well pronounced peaks in the R$R$, C$C$ and D$D$ densities appear regularly before the extinction. Those peaks correspond to density outbursts (waves) traveling through the system. We investigate the mechanisms leading to the waves. In particular, we show that the percolation of the detritus (i.e. the accumulation of nutrients) is necessary for the emergence of the waves. Moreover, our results corroborate the hypothesis that top-level predators play an essential role in maintaining the stability of a food web (top-down control).     

Food web model with detritus path

We present and study a lattice (Monte Carlo) model of a food web consisting of three levels. Agents on the lowest level produce food from dead agents (detritus) of the upper levels and are themselves eaten by the first level species, which in turn are prey for the top level species. Agents which do not find food in a given time, die with a given probability, while eating enables them to produce offspring in their neighborhood. This rule applies to species on all levels, including the lowest one. The dynamics is therefore nutrient limited. We are considering two pathways — grazers and detritus (using dead organic matter). We show that the emerging dynamics is more complex than the ordinary predator-prey systems in which bottom species are indestructible. We investigate the viability of our model and we construct appropriate (extinct-alive) phase diagrams. We demonstrate how the temporal fluctuations in the densities of the three populations are correlated. We show also that the density of the middle level agents plays the key role in the viability of the investigated food web.     

Computer simulations of history of life: speciation, emergence of complex species from simpler organisms, and extinctions

We propose a generic model of eco-systems, with a hierarchical food web structure. In our computer simulations, we let the eco-system evolve continuously for so long that we can monitor extinctions as well as speciations over geological time scales. Speciation leads not only to horizontal diversification of species at any given trophic level but also to vertical bio-diversity that accounts for the emergence of complex species from simpler forms of life. We find that five or six trophic levels appear as the eco-system evolves for sufficiently long time, starting initially from just one single level. Moreover, the time intervals between the successive collections of ecological data is so short that we could also study “micro”-evolution of the eco-system, i.e., the birth, ageing and death of individual organisms.     

Kinetics of the maintenance of the epidermis

The epidermis is the outermost layer of skin. It is comprised of keratin-containing cells called keratinocytes. Functionally, the epidermis serves as a physical barrier that can prevent infection and regulate body hydration. Maintenance and repair of the epidermis are important for human health. Mechanistically, these processes occur primarily via proliferation and differentiation of stem cells located in the basal monolayer. These processes are believed to depend on cell-cell communication and spatial constraints but existing kinetic models focus mainly on proliferation and differentiation. To address this issue, we present a mean-field kinetic model that takes these additional factors into account and describes the epidermis at a biosystem level. The corresponding equations operate with the populations of stem cells and differentiated cells in the basal layer. The keratinocytes located above the basal layer are treated at a more coarse-grained level by considering the thickness of the epidermis. The model clarifies the likely role of various negative feedbacks that may control the epidermis and, accordingly, provides insight into the cellular mechanisms underlying complex biological phenomena such as wound healing.     

Detonation front structure and the competition for radicals

We examine the role of competition for radical species in determining detonation front structure for hydrogen and selected hydrocarbon fuels in air and oxygen. Numerical simulations and detailed reaction mechanisms are used to characterize the reaction zone length, shape, and sensitivity to temperature variation. We find that the effect of the competition for radicals on the energy release rate characteristics varies significantly for the chosen mixtures. Hydrogen exhibits a strong effect while in methane and ethane mixtures the effect is absent. Other hydrocarbons including acetylene, ethylene, and propane fall between these extreme cases. This competition is manifested by a peak in effective activation energy associated with a shift in the dominant reaction pathway in the initial portion of the reaction zone. The peak of the effective activation energy is centered on the extended second explosion limit. A five-step, four species reaction model of this competition process has been developed and calibrated against numerical simulations with detailed chemistry for hydrogen. The model includes a notional radical species and reactive intermediate in addition to reactants and products. The radical species undergoes chain-branching and there is a competing pathway through the reactive intermediate that is mediated by a three-body reaction followed by decomposition of the intermediate back to the radical species. We have used this model in two-dimensional unsteady simulations of detonation propagation to examine the qualitative differences in the cellular instability of detonation fronts corresponding to various degrees of competition between the chain-branching and reactive intermediate production. As the post-shock state approaches the region of competition between the radical and reactive intermediate, the detonation front becomes irregular and pockets of the reactive intermediate appear behind the front, but the detonation continues to propagate.     

Paradox of enrichment: A fractional differential approach with memory

The paradox of enrichment (PoE) proposed by Rosenzweig [M. Rosenzweig, The paradox of enrichment, Science 171 (1971) 385–387] is still a fundamental problem in ecology. Most of the solutions have been proposed at an individual species level of organization and solutions at community level are lacking. Knowledge of how learning and memory modify behavioral responses to species is a key factor in making a crucial link between species and community levels. PoE resolution via these two organizational levels can be interpreted as a microscopic- and macroscopic-level solution. Fractional derivatives provide an excellent tool for describing this memory and the hereditary properties of various materials and processes. The derivatives can be physically interpreted via two time scales that are considered simultaneously: the ideal, equably flowing homogeneous local time, and the cosmic (inhomogeneous) non-local time. Several mechanisms and theories have been proposed to resolve the PoE problem, but a universally accepted theory is still lacking because most studies have focused on local effects and ignored non-local effects, which capture memory. Here we formulate the fractional counterpart of the Rosenzweig model and analyze the stability behavior of a system. We conclude that there is a threshold for the memory effect parameter beyond which the Rosenzweig model is stable and may be used as a potential agent to resolve PoE from a new perspective via fractional differential equations.     

On the relationship between cyclic and hierarchical three-species predator-prey systems and the two-species Lotka-Volterra model

Stochastic spatial predator-prey competition models represent paradigmatic systems to understand the emergence of biodiversity and the stability of ecosystems. We aim to clarify the relationship and connections between interacting three-species models and the classic two-species Lotka-Volterra (LV) model that entails predator-prey coexistence with long-lived population oscillations. To this end, we utilize mean-field theory and Monte Carlo simulations on two-dimensional square lattices to explore the temporal evolution characteristics of two different interacting three-species predator-prey systems, namely: (1) a cyclic rock-paper-scissors (RPS) model with conserved total particle number but strongly asymmetric reaction rates that lets the system evolve towards one “corner” of configuration space; (2) a hierarchical “food chain” where an additional intermediate species is inserted between the predator and prey in the LV model. For the asymmetric cyclic model variant (1), we demonstrate that the evolutionary properties of both minority species in the (quasi-)steady state of this stochastic spatial three-species “corner” RPS model are well approximated by the two-species LV system, with its emerging characteristic features of localized population clustering, persistent oscillatory dynamics, correlated spatio-temporal patterns, and fitness enhancement through quenched spatial disorder in the predation rates. In contrast, we could not identify any regime where the hierarchical three-species model (2) would reduce to the two-species LV system. In the presence of pair exchange processes, the system remains essentially well-mixed, and we generally find the Monte Carlo simulation results for the spatially extended hierarchical model (2) to be consistent with the predictions from the corresponding mean-field rate equations. If spreading occurs only through nearest-neighbor hopping, small population clusters emerge; yet the requirement of an intermediate species cluster obviously disrupts spatio-temporal correlations between predator and prey, and correspondingly eliminates many of the intriguing fluctuation phenomena that characterize the stochastic spatial LV system.     

Dissipative oscillations in spatially restricted ecosystems due to long range migration

An ecosystem containing three interacting species is studied using both Mean Field approach and Kinetic Monte Carlo simulations on a lattice substrate. The so called 3rd order LLV model involves birth, death and reaction processes with 3rd order nonlinearities and feedbacks. At the mean field level this system exhibits conservative oscillations; the analytic form of the constant of motion is presented. The stochastic simulations show that the density oscillations disappear for sufficiently large lattices, while they are present locally, on small lattice windows. Introduction of mixing via long range migration in the two reacting species changes this picture. For small migration rates p, the behavior remains as with p = 0 and the system is divided into local asynchronous oscillators. As p increases the system passes through a phase transition and exhibits a weak disorder limit cycle through a supercritical Hopf-like bifurcation. The amplitude of the limit cycle depends on the rate p, on the range of migration r and on the system kinetic rates k₁, k₂ and k₃.     

A priori investigation of the constructed PDF model

The constructed probability density function (PDF) model approximates the species and temperature at a point in a general turbulent reacting flow by the species and temperature that evolved in an independent homogeneous turbulent flow. The thermo-chemical PDF is parameterized by a suitable set of lower moments, and tabulated for retrieval in 3D CFD codes. The Linear Eddy Model is used to resolve, affordably, detailed kinetic calculations in the homogeneous turbulence geometry. In this work, the constructed PDF is parameterized by the first two moments of the mixture fraction, and tested against the equilibrium, assumed-shape PDF model, which is parameterized by the same two moments. The models are evaluated by comparing mean species and temperature predictions with experimental measurements at three points in a turbulent, piloted, jet diffusion flame. The constructed PDF model exhibits consistently improved predictions, and is able to capture super-equilibrium intermediate species as well as species governed by slow kinetics, such as the pollutant NO. The advantage of the constructed PDF model is the capability to decouple the finite-rate chemistry from the multi-dimensional CFD simulation, allowing rapid CFD simulations on large meshes.     

Shear localization in a model glass

Using molecular dynamics simulations, we show that a simple model of a glassy material exhibits the shear localization phenomenon observed in many complex fluids. At low shear rates, the system separates into a fluidized shear band and an unsheared part. The two bands are characterized by a very different dynamics probed by a local intermediate scattering function. Furthermore, a stick-slip motion is observed at very small shear rates. Our results, which open the possibility of exploring complex rheological behavior using simulations, are compared to recent experiments on various soft glasses.     

Food chain chaos with canard explosion

The "tea-cup" attractor of a classical prey-predator-superpredator food chain model is studied analytically. Under the assumption that each species has its own time scale, ranging from fast for the prey to intermediate for the predator and to slow for the superpredator, the model is transformed into a singular perturbed system. It is demonstrated that the singular limit of the attractor contains a canard singularity. Singular return maps are constructed for which some subdynamics are shown to be equivalent to chaotic shift maps. Parameter regions in which the described chaotic dynamics exist are explicitly given.     

Theoretical study of the cracking mechanisms of linear α-olefins catalyzed by zeolites

The cracking reactions of linear C₄-C₁₀ α-olefins over zeolites have been studied by using density functional theory at the B3LYP/6-31G(d,p) level. The obtained results reveal that the β-scission processes of C₄-C₁₀ olefins have the same reaction mechanism. Every pathway only involves a transition state corresponding to the rupture of the C-C bond, while the intrinsic reaction coordinate analysis indicates that the protonated intermediate species is formed during the reaction process. Furthermore, it is found that this intermediate species is not usually highly stable alkoxy group but adsorbed short-lifetime carbocation. This phenomenon can well explain why the carbocations are seldom observed inside the zeolite's cavities. The calculated real activation energy for this pathway is lower than the experimental value for corresponding alkane cracking contrary to the previously reported pathway via an alkoxide intermediate. Therefore, the reaction pathway via a carbocation intermediate species is energetically much more favorable. In addition, the study also shows that the real activation energies of olefin cracking are nearly independent of the olefin chain length, which is in agreement with the existing experimental results of alkane cracking.     

Monte Carlo simulation of age-dependent host-parasite relations

The death of a biological population is an extreme event which we investigate here for a host-parasitoid system. Our simulations using the Penna ageing model show how biological evolution can “teach” the parasitoids to avoid extinction by waiting for the right age of the host. We also show the dependence of extinction time on the population size.     

Large eddy simulation of turbulent premixed combustion using tabulated detailed chemistry and presumed probability density function

A method of chemistry tabulation combined with presumed probability density function (PDF) is applied to simulate piloted premixed jet burner flames with high Karlovitz number using large eddy simulation. Thermo-chemistry states are tabulated by the combination of auto-ignition and extended auto-ignition model. To evaluate the predictive capability of the proposed tabulation method to represent the thermo-chemistry states under the condition of different fresh gases temperature, a-priori study is conducted by performing idealised transient one-dimensional premixed flame simulations. Presumed PDF is used to involve the interaction of turbulence and flame with beta PDF to model the reaction progress variable distribution. Two presumed PDF models, Dirichlet distribution and independent beta distribution, respectively, are applied for representing the interaction between two mixture fractions that are associated with three inlet streams. Comparisons of statistical results show that two presumed PDF models for the two mixture fractions are both capable of predicting temperature and major species profiles, however, they are shown to have a significant effect on the predictions for intermediate species. An analysis of the thermo-chemical state-space representation of the sub-grid scale (SGS) combustion model is performed by comparing correlations between the carbon monoxide mass fraction and temperature. The SGS combustion model based on the proposed chemistry tabulation can reasonably capture the peak value and change trend of intermediate species. Aspects regarding model extensions to adequately predict the peak location of intermediate species are discussed.     

在线捕集分离联用技术对食品调料中砷形态分析方法研究

成功建立了冷捕集-气相色谱-氢化物发生-原子荧光光谱分析测定食品调料(酱油和醋)中砷形态的方法。以脱脂棉为分离介质,用液氮对样品中生成的气态砷化合物进行冷捕集,常温下不同砷形态化合物即可以实现基线分离,随后被原子荧光光谱检测。实验考查了酸介质的种类和酸度、KBH₄溶液的浓度、反应时间以及载气(He)的流量等实验条件对测定结果的影响。结果表明,在优化后的实验条件下,方法对As(Ⅲ),As(Ⅴ),MMA(Ⅴ)和DMA(Ⅴ)的检出限分别为0.2,0.2,0.3,0.8 ng·mL-1,对酱油和醋As(Ⅲ),As(Ⅴ),MMA(Ⅴ)和DMA(Ⅴ)的回收率为93.07%～103.54%。与传统的液相色谱分离方法相比,该方法不用对样品进行特殊前处理,分析速度快,灵敏度高,适合于对食品调料中砷形态尤其是无机砷形态的准确、快速分析测定。     

Experimental evidence of anomalous phase synchronization in two diffusively coupled Chua oscillators

We study the transition to phase synchronization in two diffusively coupled, nonidentical Chua oscillators. In the experiments, depending on the used parameterization, we observe several distinct routes to phase synchronization, including states of either in-phase, out-of-phase, or antiphase synchronization, which may be intersected by an intermediate desynchronization regime with large fluctuations of the frequency difference. Furthermore, we report the first experimental evidence of an anomalous transition to phase synchronization, which is characterized by an initial enlargement of the natural frequency difference with coupling strength. This results in a maximal frequency disorder at intermediate coupling levels, whereas usual phase synchronization via monotonic decrease in frequency difference sets in only for larger coupling values. All experimental results are supported by numerical simulations of two coupled Chua models.     

Effect of ultrasound on the techno-functional properties of food components/ingredients: A review

Ultrasound (US) has been used in many food systems and model systems, such as starch, whey protein concentrates and soy, to modify their chemical and techno-functional properties. At present, the use of ultrasound has yielded diverse results, ranging from potentiating the technological and functional properties of various foods to different operating conditions. Similarly, the results that were obtained vary according to the ultrasonic equipment used and the power, frequency and times of sonication, as well as the characteristics of the food system used. However, not all results have been favourable because US can cause damage to the structure of some food components, such as starch, and affect the technological and functional properties of the food. In the literature, there is little research on the effect of sonication on fibre; this gap in the literature is worrisome because fibre is found in a wide variety of foods and provides health benefits. Such research would represent an opportunity for researchers to make use of this technology for the generation of knowledge and improve the techno-functional properties in fibre, which could benefit the human population and the food industry. In this review, we present current results obtained with US in different treatments affecting processes of strong importance in the food industry, emphasizing the effects in the different model systems.     

Nucleophilic aromatic substitution in chlorinated aromatic systems with a glutathione thiolate model

The conjugation of glutathione with chlorobenzene and di‐, tri‐, tetra‐, and hexa‐chlorinated benzenes via nucleophilic aromatic substitution was modeled for isolated reacting species by ab initio molecular orbital theory to provide an understanding of the intrinsic reactivity of unactivated chloroaromatic systems. Computations at the HF/6‐31+G(d,p) level were augmented with electron correlation corrections using MP2 theory and density functional theory at the B3LYP level. Features of the reaction hypersurface were elaborated using thiolate (thiomethoxide) as the model for an enzyme‐activated glutathione molecule. Unlike the similar reaction with 1‐chloro‐2, 4‐dinitrobenzene a known substrate with glutathione, no σ‐complex or Meisenheimer complex was isolated as a true intermediate on the hypersurface. Instead, the σ‐complex appears as a transition state, preceded and followed by two ion‐molecule complexes in which the approaching and departing anions reside in the plane of the aromatic ring. Solvent calculations show a very similar hypersurface landscape with only one transition state and no intermediate. Activation energies are somewhat greater than for 1‐chloro‐2, 4‐dinitrobenzene owing to the lack of nitro substituents, which provide stabilization in these systems. Nevertheless, activation energies calculated at correlated levels indicate that these reactions are still feasible and consistent with experiment. Transition states and activation energies for dichlorobenzenes and polychlorobenzenes are lower in energy than for chlorobenzene implying greater stability conferred to the transition state by ortho and para substituents.     

Critical and tricritical behavior of a selectively diluted triangular Ising antiferromagnet in a field

We study a geometrically frustrated triangular Ising antiferromagnet in an external magnetic field which is selectively diluted with nonmagnetic impurities employing an effective-field theory with correlations and Monte Carlo simulations. We focus on the frustration-relieving effects of such a selective dilution on the phase diagram and find that it can lead to rather intricate phase diagrams in the dilution-field parameters space. In particular, in a highly (weakly) diluted system the frustration is greatly (little) relieved and such a system is found to display only the second(first)-order phase transitions at any field. On the other hand, for a wide interval of intermediate dilution values the transition remains second-order at low fields but it changes to first-order at higher fields and the system displays a tricritical behavior. The existence of the first-order transition in the region of intermediate dilution and high fields is verified by Monte Carlo simulations.     

Multiphonon-resonance quantum Rabi model and adiabatic passage in a cavity-optomechanical system

In this paper,we propose a scheme to achieve a multiphonon-resonance quantum Rabi model and adiabatic passage in a strong-coupling cavity optomechanical system.In the scheme,when the driving bichromatic laser beam is adjusted to the off-resonant j-order red-and blue-sideband,the interaction between the cavity and mechanical oscillator leads to a j-phonon resonance quantum Rabi model.Moreover,we show that there exists a resonant multi-phonon coupling via intermediate states connected by counter-rotating processes when the frequency of the simulated bosonic mode is near a fraction of the transition frequency of the simulated two-level system.As a typical example,we theoretically analyze the two-phonon resonance quantum Rabi model,and derive an effective Hamiltonian of the six-phonon coupling.Finally,we present a method of six-phonon generation based on adiabatic passage across the resonance.Numerical simulations confirm the validity of the proposed scheme.Theoretically,the proposed scheme can be extended to the realization of 3j-phonon state.