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.
•We formulate the fractional counterpart of the Rosenzweig model.•We analyze the stability of this fractional order model.•We identify a threshold for the memory effect parameter.•Below this threshold value the system is always stable independent of enrichment.•Fractional differential equations may be an important tool for resolving the paradox of enrichment.
•The principle of system equilibrium is used to model the macroscopic dynamics of bee colony.•The mathematical criterions for the benign development of bee colonies are presented.•The effects of ...multiple factors are revealed for diagnosing the health of bee colonies.
In recent years, frequent outbreaks of bee colony collapse have seriously threatened food production and ecological balance. Many scholars have studied different factors and formed a consensus that multiple factors jointly cause the colony collapse. However, it is still a challenge to understand the effects of multiple factors on bee colony development due to the complex microcosmic mechanism of each factor. Based on the principle of system equilibrium, this paper models the macroscopic dynamics of bee colony with three core states: the stocks of food, the population of adult bees and the population of larval bees, and the internal and external factors have been abstracted as the model parameters. The mathematical criteria for the benign development of bee colonies are presented from the idea of system stability, and the effects of multiple factors are studied by critical parameter perturbation and Monte Carlo simulation. The results show that the population of adults is most likely to be influenced by multiple factors, that is to say, the observations related to adults, such as the total number of adults and the number/frequency of adults entering and leaving the nest, can more quickly reflect the health status of bee colony, which provides a theoretical basis for experimental studies. Meanwhile, this study reveals the effects of multiple factors on the development of bee colonies from the level of system equilibrium, which is of great significance for understanding the collapse of bee colonies in recent years. Further, according to monitoring the three core states, the trend changes of them could be used to diagnose the healthy problems of actual bee colonies.
Anode slime is produced by electrolytic manganese production enterprises. The effects of anode slime particle size, leaching temperature, leaching agent concentration, and leaching time on the extent ...of lead leaching were investigated using ammonium acetate as the leaching agent. The lead leaching mechanism and kinetics in the anode slime were also studied. The extent of lead leaching of anode slimes with different particle sizes is significantly different. The extent of lead leaching was increased by elevating the leaching temperature. The extent of leaching reaches 99.3% after 30 min of leaching when the average particle size of anode slime approaches 10 μm, the leaching temperature is 80 °C, and the concentration of ammonium acetate is 2 mol/L. Due to the high-temperature roasting, the high valence state of the lead is changed. Then, both the compact structure between the wrapped lead and the external anode slime and the dense structure between the coated lead and the anode mud outside are destroyed. A multidimensional tunnel and a porous network structure with cracks are formed. Under the mechanism of the complex, lead is transferred from the solid phase to the liquid phase. The lead leaching process followed the “shrinkage particle model”. The reaction is mainly controlled by the diffusion of solid product layers. The apparent activation energy of the reaction Ea (28.521 kJ/mol), the pre-exponential factor A (13.34), and the macroscopic kinetic equation are obtained by establishing a macroscopic dynamic model based on the experimental data.
•The leaching rate of lead can be increased by reducing the size of anode mud by ball milling.•Roasting will destroy the original dense structure of anode mud and form porous network structure.•The best leaching temperature is 80C, and the leaching rate of lead can reach 99.3%.•The leaching process of lead is mainly controlled by solid product layer, the macroscopic kinetics equation is determined.
Experiments have shown that spatial heterogeneities can arise when the glass transition in polymers as well as in a number of low molecular weight compounds is approached by lowering the temperature. ...This formation of “clusters” has been detected predominantly by small angle light scattering and ultrasmall angle x-ray scattering from the central peak on length scales up to about 200 nm and by mechanical measurements including, in particular, piezorheometry for length scales up to several microns. Here we use a macroscopic two-fluid model to study the formation of clusters observed by the various experimental techniques. As additional macroscopic variables, when compared to simple fluids, we use a transient strain field to incorporate transient positional order, along with the velocity difference and a relaxing concentration field for the two subsystems. We show that an external homogeneous shear, as it is applied in piezorheometry, can lead to the onset of spatial pattern formation. To address the issue of additional spectral weight under the central peak we investigate the coupling to all macroscopic variables. We find that there are additional static as well as dissipative contributions from both, transient positional order, as well as from concentration variations due to cluster formation, and additional reversible couplings from the velocity difference. We also briefly discuss the influence of transient orientational order. Finally, we point out that our description is more general, and could be applied above continuous or almost continuous transitions
We discuss the time-reversal behavior of dynamic cross-couplings among various hydrodynamic degrees of freedom in liquid crystal systems. Using a standard hydrodynamic description including linear ...irreversible thermodynamics, we show that the distinct thermodynamic requirements for reversible and irreversible couplings lead to experimentally accessible differences. We critically compare our descriptions with those of existing standard continuum mechanics theories, where time-reversal symmetry is not adequately invoked. The motivation comes from recent experimental progress allowing to discriminate between the hydrodynamic description and the continuum mechanics approach. This concerns the dynamics of Lehmann-type effects in chiral liquid crystals and the dynamic magneto-electric response in ferronematics and ferromagnetic nematics, a liquid multiferroic system. In addition, we discuss the consequences of time-reversal symmetry for flow alignment of the director in nematics (or pretransitional nematic domains) and for the dynamic thermo-mechanical and electro-mechanical couplings in textured nematic liquid crystals.
We present the macroscopic dynamics of nematic liquid crystals in a two-fluid context. We investigate the case of a nematic in a chiral solvent as well as of a cholesteric in a non-chiral solvent. In ...addition, we analyze how the incorporation of a strain field for nematic gels and elastomers in a chiral solvent modifies the macroscopic dynamics. It turns out that the relative velocity between the nematic subsystem and the chiral solvent gives rise to a number of cross-coupling terms, reversible as well as irreversible, unknown from other two-fluid systems considered so far. Possible experiments to study those novel dynamic cross-coupling terms are suggested. As examples we just mention that gradients of the relative velocity lead, in cholesterics to heat currents. We also find that in cholesterics shear flows give rise to a temporal variation in the velocity difference perpendicular to the shear plane, and in cholesteric gels uniaxial stresses or strains generate temporal variations of the velocity difference. Finally, the exotic chiral
Q
phase of tetragonal (
D
4
) symmetry is analyzed for an isotropic non-chiral solvent in a two-fluid scenario.
Stimulating the receptors of a single cell generates stochastic intracellular signaling. The fluctuating response has been attributed to the low abundance of signaling molecules and the ...spatio-temporal effects of diffusion and crowding. At population level, however, cells are able to execute well-defined deterministic biological processes such as growth, division, differentiation and immune response. These data reflect biology as a system possessing microscopic and macroscopic dynamics. This commentary discusses the average population response of the Toll-like receptor (TLR) 3 and 4 signaling. Without requiring detailed experimental data, linear response equations together with the fundamental law of information conservation have been used to decipher novel network features such as unknown intermediates, processes and cross-talk mechanisms. For single cell response, however, such simplicity seems far from reality. Thus, as observed in any other complex systems, biology can be considered to possess order and disorder, inheriting a mixture of predictable population level and unpredictable single cell outcomes.
We investigate the macroscopic dynamics of sets of an arbitrary finite number of weakly amplitude-modulated pulses in a multidimensional lattice of particles. The latter are assumed to exhibit scalar ...displacement under pairwise nonlinear interaction potentials of arbitrary range and are embedded in a nonlinear background field. By an appropriate multiscale ansatz, we derive formally the explicit evolution equations for the macroscopic amplitudes up to an arbitrarily high-order of the scaling parameter, thereby deducing the resonance and nonresonance conditions on the fixed wave vectors and frequencies of the pulses, which are required for that. The derived equations are justified rigorously in time intervals of macroscopic length. Finally, for sets of up to three pulses we present a complete list of all possible interactions and discuss their ramifications for the corresponding, explicitly given macroscopic systems.
Digital snowflakes are solidifying cellular automata on the triangular lattice with the property that a site having exactly one occupied neighbor always becomes occupied at the next time step. We ...demonstrate that each such rule fills the lattice with an asymptotic density that is independent of the initial finite set. There are some cases in which this density can be computed exactly, and others in which it can only be approximated. We also characterize when the final occupied set comes within a uniformly bounded distance of every lattice point. Other issues addressed include macroscopic dynamics and exact solvability.
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