Positive Solutions Bifurcating from Zero Solution in a Lotka-Volterra Competitive System with Cross-Diffusion Effects

A strongly coupled elliptic system under the homogeneous Dirichlet boundary condition denoting the steady-state system of the Lotka-Volterra two-species competitive system with cross-diffusion effects is considered. By using the implicit function theorem and the Lyapunov- Schmidt reduction method, the existence of the positive solutions bifurcating from the trivial solution is obtained. Furthermore, the stability of the bifurcating positive solutions is also investigated by analyzing the associated characteristic equation.

Pattern formation induced by cross-diffusion in a predator-prey system

This paper considers the Holling-Tanner model for predator-prey with self and cross-diffusion. From the Turing theory, it is believed that there is no Turing pattern formation for the equal self-diffusion coefficients. However, combined with cross-diffusion, it shows that the system will exhibit spotted pattern by both mathematical analysis and numerical simulations. Furthermore, asynchrony of the predator and the prey in the space. The obtained results show that cross-diffusion plays an important role on the pattern formation of the predator-prey system.

Spatial Pattern Induced by Cross-Diffusion in a Chemostat Model with Maintenance Energy

A chemostat model with maintenance energy and crossdiffusion is considered,and the formation of patterns is caused by the cross-diffusion. First, through linear stability analysis, the necessary conditions for the formation of the spatial patterns are given. Then numerical simulations by changing the values of crossdiffusions in the unstable domain are performed. The results showthat the cross-diffusion coefficient plays an important role in the formation of the pattern, and the different values of the crossdiffusion coefficients may lead to different types of pattern formation.

Pattern dynamics of network-organized system with cross-diffusion

Cross-diffusion is a ubiquitous phenomenon in complex networks, but it is often neglected in the study of reaction–diffusion networks. In fact, network connections are often random. In this paper, we investigate pattern dynamics of random networks with cross-diffusion by using the method of network analysis and obtain a condition under which the network loses stability and Turing bifurcation occurs. In addition, we also derive the amplitude equation for the network and prove the stability of the amplitude equation which is also an effective tool to investigate pattern dynamics of the random network with cross diffusion. In the meantime, the pattern formation consistently matches the stability of the system and the amplitude equation is verified by simulations. A novel approach to the investigation of specific real systems was presented in this paper. Finally, the example and simulation used in this paper validate our theoretical results.

Modulation of Anti-Microbial Resistant <i>Salmonella heidelberg</i>Using Synbiotics (Probiotics and Prebiotics) in Two <i>In-Vitro</i>Assays (Cross-Streaking and Agar Wells Diffusion)

Salmonellosis is the most prevalent bacterial foodborne disease in many countries worldwide. Utilization of probiotics is one of the most accepted ways to reduce Salmonella, especially lactic acid bacteria, as it has proven to reduce the enteric pathogens in monogastric and ruminant livestock animals through different mechanisms such as antimicrobials production, competitive adhesion to the gastrointestinal tract, and immune stimulation. Prebiotics could be utilized solely for health benefits as an alternative to probiotics or in addition to probiotics for a synergistic effect known as synbiotics. The aim of this study was to compare effects of different probiotic strains (Lactobacillus acidophilus (La-14), Lactobacillus paracasei (Lpc-37), Streptococcus thermophiles (St-21), Bifidobacterium bifidum (Bb-06), and Aspergillus niger (ATCC®16888TM) and without prebiotics (Mannose;Xylose;Galactooligosaccharides GOS;Inulin;and Dandelion extract) on lowering Salmonella heidelberg CFU in vitro. Different inhibition levels probiotic strains were assessed and compared in the presence and absence of 2.5% prebiotic compounds using cross-streaking and agar well diffusion assays. Recommendations for the growth of selected microorganisms such as temperature and oxygen conditions were taken into consideration. All the analysis was conducted in triplicates. The results showed that all the probiotics strains except S. thermophiles were able to significantly (P < 0.05) inhibit the growth of S. heidelberg in at least one of the assays. The difference in inhibition percentage confirms that probiotic strains have multiple inhibition mechanisms, such as production of antimicrobials, lower pH by producing organic acids (acetic acid, lactic acid, etc.), and inhibition of pathogen’s virulence factor expression, and production of lipopolysaccharide solubilizing compounds.

Effects of signal modulation and coloured cross-correlation of coloured noises on the diffusion of a harmonic oscillator

The diffusion in a harmonic oscillator driven by coloured noises ξ（t） and η（t） with coloured cross-correlation in which one of the noises is modulated by a biased periodic signal is investigated. The exact expression of diffusion coefficient d as a function of noise parameter, signal parameter, and oscillator frequency is derived. The findings in this paper are as follows. 1） The curves of d versus noise intensity D and d versus noises cross-correlation time z3 exist as two different phases. The transition between the two phases arises from the change of the cross-correlation coefficient A of the two Ornstein-Uhlenbeck （O-U） noises. 2） Changing the value of T3, the curves of d versus Q, the intensity of colored noise that is modulated by the signal, can transform from a phase having a minimum to a monotonic phase. 3） Changing the value of signal amplitude A, d versus Q curves can transform from a phase having a minimum to a monotonic phase. The above-mentioned results demonstrate that a like noise-induced transition appears in the model.

Turing Instability and Pattern Induced by Cross-Diffusion for a Nonlinear Reaction-Diffusion System of Turbulence-Shear Flow Interaction

The Turing instability and the phenomena of pattern formation for a nonlinear reaction-diffusion(RD) system of turbulence-shear flowinteraction are investigated.By the linear stability analysis,the essential conditions for Turing instability are obtained.It indicates that the emergence of cross-diffusion terms leads to the destabilizing mechanism.Then the amplitude equations and the asymptotic solutions of the model closed to the onset of instability are derived by using the weakly nonlinear analysis.

Global existence of weak solutions to a prey-predator model with strong cross-diffusion

Using finite differences and entropy inequalities, the global existence of weak solutions to a multidimensional parabolic strongly coupled prey-predator model is obtained. The nonnegativity of the solutions is also shown.

Diffusion bonded transition joint of TC4 to QAl10-3-1.5

Solid-state diffusion bonding has been done to produce transition joint between TC4 and QAl10-3-1.5 at the temperature 850℃ for 60 min. The produced diffusion bonded couples were evaluated by scanning electron microscopy （SEM）, energy dispersive spectroscopy （EDS） and X-ray diffraction （XRD）. SEM revealed the presences of the different reaction regions in the diffusion zone and “kirkendall voids” were observed in the interface. This study indicated the existences of Cu3 Ti, Cu and Ti phases in the diffusion zone of the joint confirmed by XRD. The microhardness tests revealed that the microhardness of TC4 jointing affected zone （ JAZ） is higher than the TC4 base materials, and transition zone close to TC4 possesses the highest microhardness value.

Diffusion bonding of Ti-6Al-4V to ZQSn10-10 in vacuum

The experimental investigation of the direct diffusion bonding of Ti-6Al-4V to ZQSn10-10 was carried out in vacuum. The microstructure of bonded joint was studied by scanning electron microscopy （SEM）, energy dispersive spectroscopy （ EDS ） and the mechanical properties were detected by the tensile experiments. The microstructure and tensile strength of the joint mainly depend on the bonding temperature and bonding time. A satisfying diffusion bonded interface with a tensile strength of 73.9 MPa can be obtained under the condition of bonding temperature 850℃ for 30 rain. Three kinds of reaction products were observed in the bonded interface, namely β-Ti, CoaTi and CuSn3Ti5. And the brittle Cu3Ti and CuSn3 Ti5 are mainly responsible for lowering the strength of the bonded joint. The diffusion distances of Sn , Cu and Ti and square root of bonding time are approximately linear relationship. And diffusion velocity of Sn, Cu and Ti in the diffusion reaction layer are 0. 013 9,0. 069 7 and 0. 056 4 mm^2/s.

A Numerical Algorithm Based on Quadratic Finite Element for Two-Dimensional Nonlinear Time Fractional Thermal Diffusion Model

In this article,a high-order scheme,which is formulated by combining the quadratic finite element method in space with a second-order time discrete scheme,is developed for looking for the numerical solution of a two-dimensional nonlinear time fractional thermal diffusion model.The time Caputo fractional derivative is approximated by using the L2-1formula,the first-order derivative and nonlinear term are discretized by some second-order approximation formulas,and the quadratic finite element is used to approximate the spatial direction.The error accuracy O(h3+
t2)is obtained,which is verified by the numerical results.

Traveling waves in nonlocal diffusion systems with delays and partial quasi-monotonicity

This paper is devoted to the study of a three-dimensional delayed system with nonlocal diffusion and partial quasi-monotonicity. By developing a new definition of upper-lower solutions and a new cross iteration scheme, we establish some existence results of traveling wave solutions. The results are applied to a nonlocal diffusion model which takes the three-species Lotka-Volterra model as its special case.

Superplastic Forming and Diffusion Bonding for Sandwich Structure of Ti-6Al-4V Alloy

Superplastic forming and diffusion bonding (SPF/DB) is a well-established process for the manufacture of components almost exclusively from Ti-6AI-4V sheet material. The sandwich structure of Ti-6AI-4V alloy is investigated. The effects of the microstructure on the SPF/DB process were discussed. The microstructure at the interfaces and the distribution of thickness were researched.

Diffusion bonding behaviour of β-γTiAl alloys containing high niobium with Ti interlayer by spark plasma sintering

High niobium β-γ TiAl alloy(HNBG) was diffusion bonded using spark plasma sintering with pure Ti as interlayer. The joint microstructural evolution, growth kinetics and mechanical properties were investigated. The joint included three diffusion zones. The β/B2 phase formed in the Zone Ⅰ, α_(2)phase in the Zone Ⅱ, and β-Ti and α-Ti phases in the Zone Ⅲ. The thickness of β/B2 phase, the average grain size of α_(2)phase and the amount of β-Ti phase increased with the increase of bonding temperature or bonding time. The growth activation energies of β/B2 and α_(2)phases were 582 and 253 kJ/mol, respectively. The joint acquired at 1000 °C, 10 min and 10 MPa showed the maximum shear strength of 308 MPa. Fracture mainly occurred along the interfaces between Zone Ⅰ and HNBG alloy, and between Zone I and Zone Ⅱ. Fracture mechanism of the joint was characterized by brittleness rupture along the phase boundary.

Investigation of Intrachain Exciton Diffusion of MEH-PPV in Solution with Different Polarity

Femtosecond time-resolved transient grating technique was adopted to insight into the intra-chain exciton diffusion of MEH-PPV in solution with different polarity. Broadband white-light continuum was introduced as the probe to observe the transient absorption and the femtosecond time-resolved transient grating information simultaneously. The vibrational dephasing behaviors, single exciton relaxation, and population relaxation dynamics of MEH-PPV were systematically investigated. The result shows that the relaxation processes of the sample solution will be accelerated in the solvent with larger polarity.

Pattern selection in a predation model with self and cross diffusion

In this paper, we present the amplitude equations for the excited modes in a cross-diffusive predator-prey model with zero-flux boundary conditions. From these equations, the stability of patterns towards uniform and inhomogenous perturbations is determined. Furthermore, we present novel numerical evidence of six typical turing patterns, and find that the model dynamics exhibits complex pattern replications： for μ1 〈μ ≤μ2, the steady state is the only stable solution of the model; for μ2 〈 μ ≤ μ4, by increasing the control parameter μ, the sequence Hπ-hexagons→ Hπ- hexagon-stripe mixtures → stripes → H0-hexagon-stripe mixtures → H0-hexagons is observed; for μ 〉 μ4, the stripe pattern emerges. This may enrich the pattern formation in the cross-diffusive predatorprey model.

Cross-Linked Alginate Film Pore Size Determination Using Atomic Force Microscopy and Validation Using Diffusivity Determinations

The deficit of organ donors has fueled the need for advances in tissue engineering and regenerative medicine. Microencapsulation in alginate immuno-isolation membranes has been used to treat many disabling metabolic disorders, namely, phenylketonuria, kidney failure and diabetes mellitus. Systematic nutrient flux determinations are hindered by the lack of experimental data on alginate-based membrane topography and the pore size thus preventing the full therapeutic potential of the bio-membranes to be reached. In this study, samples of cross-linked alginate membranes were subjected to the following analytical characterization: 1) pore size characterization using atomic force microscopy operated in contact mode to detect and measure pore size;2) differential scanning calorimetry to confirm biopolymer cross-linking;and 3) diffusivity measurements using spectrophotometry and fluorescence microscopy to confirm the presence of through pores and to calculate reflection coefficients. The pore sizes for the pre-clinical standard formulation of 1.5% (w/v) medium viscosity alginate cross-linked with 1.5% CaCl2 and 0.5% (w/v) alginate and chitosan cross-linked with 20% CaCl2 are 5.2 nm ± 0.9 nm and 7.0 nm ± 3.1 nm, respectively. An increase in the glass transition temperatures as a function of cross-linker concentration was observed. Diffusivity values obtained from the inward diffusivity of creatinine into macrocapsules (d = 1000 μm ± 75 μm) and the outward diffusivity of FITC dextrans from macrocapsules (d = 1000 μm ± 75 μm) and microcapsules (d = 40 μm ± 5 μm) were shown to correlate strongly (R2 = 0.9835) with the ratio of solute to pore sizes, confirming the presence of through pores. Reflection coefficients approaching and exceeding unity correlate with the lack of permeability of the membranes to MW markers that are 70 kDa and greater.

Qualitative Properties and Numerical Solution of the Kolmogorov-Fisher Type Biological Population Task with Double Nonlinear Diffusion

In the present work we study the global solvability of the Kolmogorov-Fisher type biological population task with double nonlinear diffusion and qualitative properties of the solution of the task based on the self-similar analysis. In additional, in this paper we consider the model of two competing population with dual nonlinear cross-diffusion.

Interface of solid steel and liquid aluminum under nonequilibrium diffusion

The nonequilibrium diffusion of liquid aluminum atoms in cross direction in the innerpart of the solid steel base has been realized by using methods such as roughening steel plate surface, immersing flux on steel plate surface and short time diffusion, and the interface of solid steel and liquid aluminum under nonequilibrium diffusion in cross direction was formed by using rapid solidification. The interfacial structure was studied by means of electron probe microanalysis. The results showed that the interfacial structure of solid steel and liquid aluminum under nonequilibrium diffusion in cross direction is quite different from that of solid steel and liquid aluminum under conventional diffusion, that is, the interface of solid steel and liquid aluminum under nonequilibrium diffusion in cross direction is made up of groups of Al 13 Fe 4 teeth (which grew from the contact surface to steel base inner) at the bulges of steel plate surface and Fe Al solid solution (whose Al content is less than 3.5%) at the concaves of steel plate surface between the groups of Al 13 Fe 4 teeth.

Diffusion coefficients of natural gas in foamy oil systems under high pressures

The diffusion coefficient of natural gas in foamy oil is one of the key parameters to evaluate the feasibility of gas injection for enhanced oil recovery in foamy oil reservoirs. In this paper, a PVT cell was used to measure diffusion coefficients of natural gas in Venezuela foamy oil at high pressures, and a new method for deter- mining the diffusion coefficient in the foamy oil was de- veloped on the basis of experimental data. The effects of pressure and the types of the liquid phase on the diffusion coefficient of the natural gas were discussed. The results indicate that the diffusion coefficients of natural gas in foamy oil, saturated oil, and dead oil increase linearly with increasing pressure. The diffusion coefficient of natural gas in the foamy oil at 20 MPa was 2.93 times larger than that at 8.65 MPa. The diffusion coefficient of the natural gas in dead oil was 3.02 and 4.02 times than that of the natural gas in saturated oil and foamy oil when the pressure was 20 MPa. However, the gas content of foamy oil was 16.9 times higher than that of dead oil when the dissolution time and pressure were 20 MPa and 35.22 h, respectively.