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The current paper is devoted to the study of spreading speeds and linear determinacy of diffusive cooperative/competitive systems of the form u t ( t , x ) = ( A u ) ( t , x ) + F ( t , u ( t , x ) ) , x ∈ H , where H = R N or Z N , A is a random or nonlocal dispersal operator in the cases H = R N , and is a discrete dispersal operator in the case H = Z N , F ( t , u ) is cooperative or competitive in u and is recurrent in t , which includes F ( t , u ) is periodic and almost periodic in t as special cases. First, the notion of spreading speed intervals for diffusive cooperative systems is introduced via the natural features of spreading speeds and some basic spreading properties are established. Next, some principal Lyapunov exponent and principal Floquent bundle theory for linear cooperative systems of ordinary differential equations is developed, which plays an important role in the study of spreading speeds of diffusive cooperative/competitive systems with time dependence and is also of independent interest. In terms of the principal Lyapunov exponent and principal Floquent bundle theory, some upper and lower bounds for the spreading speed intervals for diffusive cooperative systems are then established. Under certain conditions, it is proved that a diffusive cooperative system has a single spreading speed and is linearly determinant. Finally, by transforming a diffusive competitive system to a diffusive cooperative system and applying established results for diffusive cooperative systems, upper and lower bounds for the spreading speed intervals for diffusive competitive systems are obtained and linearly determinacy for such systems is discussed. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we consider the positive steady state problem of a spatially heterogeneous cross-diffusion prey–predator model with modified Leslie–Gower and Holling-Type II schemes. The heterogeneity here is created by a protection zone for the prey. By the bifurcation method and a priori estimates, we discuss the existence and non-existence of positive steady states. Moreover, uniqueness and stability of positive steady states for small birth rate of the predator are shown as well as the asymptotic behavior of positive steady states when some coefficients tend to infinity. Our result reveals that large cross-diffusion in a heterogeneous environment has a profound effect on the positive steady state set, and the bifurcation continuum of positive steady states changes from a bounded one to an unbounded one as the cross-diffusion varies from 0 to a large number for suitable ranges of the parameter. Whereas it has little effect in the homogeneous environment. The impact of the protection zone is also quite important, and it deduces a critical number for the birth rate of the prey which determines the bifurcation continuum of positive steady states to be bounded or unbounded. Furthermore, the modified Leslie–Gower term yields essentially different results of positive solutions from the Leslie–Gower term. [Copyright &y& Elsevier]

Abstract: This paper is concerned with a diffusive Holling–Tanner predator–prey model subject to homogeneous Neumann boundary condition. By choosing the ratio of intrinsic growth rates of predator to prey λ as the bifurcation parameter, we find that spatially homogeneous and non-homogeneous Hopf bifurcation occur at the positive constant steady state as λ varies. The steady state bifurcation of simple and double eigenvalues are intensively investigated. The techniques of space decomposition and the implicit function theorem are adopted to deal with the case of double eigenvalues. Our results show that this model can exhibit spatially non-homogeneous periodic and stationary patterns induced by the parameter λ. Numerical simulations are presented to illustrate our theoretical results. [Copyright &y& Elsevier]

This paper is concerned with the asymptotic spreading of competition diffusion systems, with the purpose of formulating the propagation modes of a co-invasion–coexistence process of two competitors. Using the comparison principle for competitive systems, some results on asymptotic spreading are obtained. Our conclusions imply that the interspecific competitions slow the invasion of one species and decrease the population densities in the coexistence domain. Therefore, the interspecific competitions play a negative role in the evolution of competitive communities. [ABSTRACT FROM PUBLISHER]

Abstract: In this paper, we will consider the following strongly coupled cooperative system in a spatially heterogeneous environment with Neumann boundary condition where Ω is a bounded domain in () with smooth boundary ∂Ω; k is a positive constant, λ and μ are real constants which may be non-positive; and are continuous functions in ; is a smooth positive function in with ; ν is the outward unit normal vector on ∂Ω and . For the case , we show that if is small and k is large, a spatial segregation of and can cause the positive solution curve to form an unbounded fish–hook (⊂) shaped curve with parameter λ. For the case , if is small and k is large, and the cooperative effect is strong for species u and very weak for species v, then the positive solution set also forms an unbounded fish–hook shaped continuum. These results are quite different from those of predator–prey systems and the cooperative system under Dirichlet boundary condition, both of which can form a bounded continuum. Our results deduce that the spatial heterogeneity of environments can produce multiple coexistence states. Our method of analysis is based on the bifurcation theory and the Lyapunov–Schmidt procedure. [Copyright &y& Elsevier]

This paper is concerned with a ratio-dependent predator-prey system with diffusion and cross-diffusion in a bounded domain with no flux boundary condition. We establish the existence and non-existence of non-constant positive steady states (patterns). In particular, we show that under certain hypotheses, the cross-diffusion can create stationary patterns even though the corresponding model without cross-diffusion fails. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with an inhomogeneous nonlocal dispersal equation. We study the limit of the re-scaled problem of this nonlocal operator and prove that the solutions of the re-scaled equation converge to a solution of the Fokker–Planck equation uniformly. We then analyze the nonlocal dispersal equation of an inhomogeneous diffusion kernel and find that the heterogeneity in the classical diffusion term coincides with the inhomogeneous kernel when the scaling parameter goes to zero. [Copyright &y& Elsevier]

This paper is concerned with a two-species predator-prey reaction-diffusion system with Beddington-DeAngelis functional response and subject to homogeneous Neumann boundary conditions. By linearizing the system at the positive constant steady-state solution and analyzing the associated characteristic equation in detail, the asymptotic stability of the positive constant steady-state solution and the existence of local Hopf bifurcations are investigated. Also, it is shown that the appearance of the diffusion and homogeneous Neumann boundary conditions can lead to the appearance of codimension two Bagdanov-Takens bifurcation. Moreover, by applying the normal form theory and the center manifold reduction for partial differential equations (PDEs), the explicit algorithm determining the direction of Hopf bifurcations and the stability of bifurcating periodic solutions is given. Finally, numerical simulations supporting the theoretical analysis are also included. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with the stability of traveling wave fronts of a monostable reaction–diffusion epidemic system with delay. The existence and comparison theorem of solutions of the corresponding Cauchy problem in a weighted space are established for the system on by appealing to the theories of semigroup and abstract functional differential equations. When the initial perturbation around the traveling wave decays exponentially as (but the initial perturbation can be arbitrarily large in other locations), we prove the exponential stability of all traveling wave fronts for the monostable epidemic system with delay. This is probably the first time the weighted-energy method combining comparison principle is applied to reaction–diffusion systems to solve the stability of traveling fronts in some appropriate exponentially weighted space. [ABSTRACT FROM AUTHOR]

Abstract: The main purpose of this work is to investigate the effects of cross-diffusion in a strongly coupled predator–prey system. By a linear stability analysis we find the conditions which allow a homogeneous steady state (stable for the kinetics) to become unstable through a Turing mechanism. In particular, it is shown that Turing instability of the reaction–diffusion system can disappear due to the presence of the cross-diffusion, which implies that the cross-diffusion induced stability can be regarded as the cross-stability of the corresponding reaction–diffusion system. Furthermore, we consider the existence and non-existence results concerning non-constant positive steady states (patterns) of the system. We demonstrate that cross-diffusion can create non-constant positive steady-state solutions. These results exhibit interesting and very different roles of the cross-diffusion in the formation and the disappearance of the Turing instability. [Copyright &y& Elsevier]

Abstract: This paper is concerned with a delayed predator–prey diffusive system with Neumann boundary conditions. The bifurcation analysis of the model shows that Hopf bifurcation can occur by regarding the delay as the bifurcation parameter. In addition, the direction of Hopf bifurcation and the stability of bifurcated periodic solution are also discussed by employing the normal form theory and the center manifold reduction for partial functional differential equations (PFDEs). Finally, the effect of the diffusion on bifurcated periodic solution is considered. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the monotonicity and uniqueness of traveling waves for a reaction–diffusion model with quiescent stage. We first obtain the exponential decay rate of wave profiles, and then we show that any profile is strictly monotone by using the strong comparison principle. Furthermore, we prove the uniqueness (up to translation) of all traveling waves including even the waves with minimal speed. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the existence, nonexistence and minimal wave speed of the travelling wavefronts of Belousov–Zhabotinskii system with diffusion and delay. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the existence of traveling wave solutions of a delayed predator–prey system with stage structure and nonlocal diffusion. By introducing the partial quasi-monotone condition and cross-iteration scheme, we first consider a class of delayed systems with nonlocal diffusion and deduce the existence of traveling wave solutions to the existence of a pair of upper–lower solutions. When the result is applied to the predator–prey system, we establish the existence of traveling wave solutions, as well as its precisely asymptotic behavior. Our result implies that there is a transition zone moving from the steady state with no species to the steady state with the coexistence of both species. [Copyright &y& Elsevier]

The main purpose of this paper is to investigate the stability and Hopf bifurcation for a delayed two-species cooperative diffusion system with Neumann boundary conditions. By linearizing the system at the positive equilibrium and analyzing the corresponding characteristic equation, the asymptotic stability of positive equilibrium and the existence of Hopf oscillations are demonstrated. It is shown that, under certain conditions, the system undergoes only a spatially homogeneous Hopf bifurcation at the positive equilibrium when the delay crosses through a sequence of critical values; under the other conditions, except for the previous spatially homogeneous Hopf bifurcations, the system also undergoes a spatially inhomogeneous Hopf bifurcation at the positive equilibrium when the delay crosses through another sequence of critical values. In particular, in order to determine the direction and stability of periodic solutions bifurcating from spatially homogeneous Hopf bifurcations, the explicit formulas are given by using the normal form theory and the center manifold reduction for partial functional differential equations (PFDEs). Finally, to verify our theoretical predictions, some numerical simulations are also included. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with a predator–prey system with diffusion. The global asymptotic stability of the unique positive constant equilibrium is obtained under certain conditions. The method used here is the upper and lower solutions combined with the monotone iteration and constructing suitable Lyapunov functions. [Copyright &y& Elsevier]

Mineral phenocrysts/megacrysts convey important information about deep magmatic evolution and volcanic eruption especially with respect to magmatic water content. Clinopyroxene (cpx) is generally considered to be less susceptible to diffusive hydrogen loss than olivine and orthopyroxene. We analyzed hydrogen concentration profiles alongside major and trace element compositions of a suite of cpx megacrysts (1–4 cm in size) hosted in basanitic scoria from the Gezi volcano, central Inner Mongolia of north China. The anhydrous composition within each megacryst is homogeneous, but comparison between different grains shows clear elemental covariation, suggesting that these cpx megacrysts progressively crystallized from a common parental magma. The cpx megacrysts contain hydrogen contents in the range of 0–410 wt ppm H 2 O at their cores, and some of them show a smooth decrease of hydrogen from the core to the rim. Those with the highest hydrogen contents (290–410 wt ppm H 2 O) have long plateau at the core, in contrast with long dehydration profiles and no plateau in some low-hydrogen megacrysts. These observations suggest that the cpx megacrysts experienced variable extent of dehydration during volcanic eruption, arising from variable H diffusivity probably associated with differences in the composition and microstructure of cpx megacrysts. Cpx megacrysts with the lowest degree of dehydration and good diffusion profiles are the most informative. Their plateau hydrogen contents at the core are used to infer ~2 wt% H 2 O in the parental magma. Quantitative modeling of the diffusion profiles at the rim yields a dehydration duration of 3–28 h, suggesting an ascent rate of 1–6 m/s for the host basanitic magma. • Profiles across cpx megacrysts show heterogeneous hydrogen distribution. • Differences in H contents and profiles indicate variable extent of dehydration. • Hydrogen content profiles are used to estimate ascent rates and yield 1–6 m/s. [ABSTRACT FROM AUTHOR]

• Experiments determined high Ag diffusivity in granitic melt and T - P -H 2 O effects. • Rapid diffusion implies efficient transfer of Ag from melt to exsolved phases. • Melt inclusions can record bulk Ag concentration if no modification. Element diffusion in silicate melts is an important process in the transport and enrichment of metals in magmatic and magmatic-hydrothermal systems, but the diffusivity of Ag, unlike other metals such as Cu, Mo, and W, is still unknown. In this study, Ag diffusion in granitic melts with up to 6.9 wt% H 2 O was investigated at 973–1673 K and 0.1–1 GPa in a piston cylinder apparatus and a cold seal vessel, using both a diffusion couple approach and an argentite (Ag 2 S) dissolution approach. Silver concentration profiles were analyzed by LA-ICP-MS on recovered samples. Silver solubility, determined by Ag concentration at melt-argentite interface, increases with increasing temperature. Silver diffusivity is found to increase with increasing temperature and water content but to decrease with pressure. At 1 GPa, Ag diffusivity in granitic melt can be described by the following expression: ln D Ag , 1 GPa = - 13.77 ± 0.46 - 13341 ± 534 - 700 ± 39 w T where D is Ag diffusivity in m2/s, w is the water content in wt%, and T is the temperature in K. The pressure effect over 0.1–1 GPa gives an activation volume of 11.3 cm3/mol for Ag diffusion. While not being on a par with the mobility of Na and Li, Ag diffusion is among the most rapid, comparable to Cu and faster than other species including H 2 O and Fe. This implies that Ag diffusion in melt is unlikely to be a rate-limiting step for Ag enrichment into exsolved fluid bubbles or sulfide blobs. Furthermore, melt inclusions in silicate minerals are expected to record Ag concentration in the bulk melt instead of an elevated concentration in the presence of an Ag-rich boundary layer. Our Ag diffusivity data also suggest that a few tens of hours are long enough to homogenize Ag concentration in melt in solubility or partition experiments at temperatures above 800 °C. [ABSTRACT FROM AUTHOR]

We consider an epidemic model with nonlocal diffusion and free boundaries, which describes the evolution of an infectious agents with nonlocal diffusion and the infected humans without diffusion, where humans get infected by the agents, and infected humans in return contribute to the growth of the agents. The model can be viewed as a nonlocal version of the free boundary model studied by Ahn, Beak and Lin [2] , with its origin tracing back to Capasso et al. [5,6]. We prove that the problem has a unique solution defined for all t > 0 , and its long-time dynamical behaviour is governed by a spreading-vanishing dichotomy. Sharp criteria for spreading and vanishing are also obtained, which reveal significant differences from the local diffusion model in [2]. Depending on the choice of the kernel function in the nonlocal diffusion operator, it is expected that the nonlocal model here may have accelerated spreading, which would contrast sharply to the model of [2] , where the spreading has finite speed whenever spreading happens [33]. [ABSTRACT FROM AUTHOR]

We introduce and study a class of free boundary models with "nonlocal diffusion", which are natural extensions of the free boundary models in [16] and elsewhere, where "local diffusion" is used to describe the population dispersal, with the free boundary representing the spreading front of the species. We show that this nonlocal problem has a unique solution defined for all time, and then examine its long-time dynamical behavior when the growth function is of Fisher-KPP type. We prove that a spreading-vanishing dichotomy holds, though for the spreading-vanishing criteria significant differences arise from the well known local diffusion model in [16]. [ABSTRACT FROM AUTHOR]

Graphical abstract A power-free imaging box was proposed to establish ideal diffuse light conditions for on-site imaging, highlighting the potential of smartphone-based colorimetric analysis systems in point-of-care testing applications. Abstract Smartphones-based colorimetric analysis systems are favoured for point-of-care testing applications. However, the image quality typically suffers from nonuniform and non-reproducible lighting, which negatively affects the accuracy of analyses. The present work proposed a power-free imaging box to utilize the light source of smartphone. The imaging box effectively eliminated interference arising from ambient light, while a V-shaped optical pipe coupled to the light source of smartphone was adopted to redirect the light to the sides of the box to eliminate the direct reflection of light from the surface of the target. This configuration was verified by numerical simulations. The specular reflection of the microfluidic chip was eliminated by establishing ideal diffuse light conditions. Moreover, the color images of a glucose testing on a paper strip and an enzyme-linked immunosorbent assay (ELISA) on transparent microchannels were captured with the proposed configuration, resulting a reduced assay variation and improving the lowest detection limit. The proposed imaging box improves the detection limit of colorimetric analysis, which highlights the potential of smartphone-based colorimetric analysis systems in point-of-care testing applications. [ABSTRACT FROM AUTHOR]

We report new experimental data of Cu diffusivity in granite porphyry melts with 0.01 and 3.9 wt% H2O at 0.15-1.0 GPa and 973-1523 K. A diffusion couple method was used for the nominally anhydrous granitic melt, whereas a Cu diffusion-in method using Pt95Cu5 as the source of Cu was applied to the hydrous granitic melt. The diffusion couple experiments also generate Cu diffusion-out profiles due to Cu loss to Pt capsule walls. Cu diffusivities were extracted from error function fits of the Cu concentration profiles measured by LA-ICP-MS. At 1 GPa, we obtain DCu, dry, 1 GPa=exp(-13.89±0.42)-12878±540T, and DCu, 3.9 wt\%H2O,1 GPa=exp(-16.31±1.30)-8148±1670T, where D is Cu diffusivity in m2/s and T is temperature in K. The above expressions are in good agreement with a recent study on Cu diffusion in rhyolitic melt using the approach of Cu2S dissolution. The observed pressure effect over 0.15-1.0 GPa can be described by an activation volume of 5.9 cm3/mol for Cu diffusion. Comparison of Cu diffusivity to alkali diffusivity and its variation with melt composition implies fourfold-coordinated Cu+ in silicate melts. Our experimental results indicate that in the formation of porphyry Cu deposits, the diffusive transport of magmatic Cu to sulfide liquids or fluid bubbles is highly efficient. The obtained Cu diffusivity data can also be used to assess whether equilibrium Cu partitioning can be reached within certain experimental durations. [ABSTRACT FROM AUTHOR]