Analysis of Dynamics in a Complex Food Chain with Ratio-Dependent Functional Response

In this paper, we study a new model obtained as an extension of athree-species food chain model with ratio-dependent functional response. We provide non-persistence and permanence results and investigate the stability of all possible equilibria in relation tothe ecological parameters. Results are obtained for the trivial andprey-only equilibria where the singularity of the model prevents linearization, and the remaining semi-trivial equilibria are studiedusing linearization. We provide a detailed analysis of conditionsfor existence, uniqueness, and multiplicity of coexistencee quilibria, as well as permanent effect for all species. The complexity of the dynamics in this model is theoretically discussedand graphically demonstrated through various examples and numerical simulations.     

A Theoretical Study of the Hard-Sphere Fluid-Solid Interface II. Test of an Alternative Variational Form

Abstract

We examine the hard-sphere fluid-solid interface using a form for the inhomogeneous density that differs significantly from those in our previous paper. As before, our approach avoids the square-gradient approximation. We present results for the [111] interface which qualitatively support our earlier findings. While the new density profile closely resembles those observed in computer simulations of Lennard-Jones systems, the surface free energy calculated from this an satz is almost 2.5 times as large as the earlier estimates.     

Corrigendum to “Coexistence states of a Holling type-II predator-prey system” [J. Math. Anal. Appl. 369 (2) (2010) 555-563]

We present the asymptotic behavior of the coexistence states near the point of bifurcation from infinity of the form

(0.1)     

Thermal transport in the oxygenated magnetic superconductor, Eu1.5Ce0.5RuSr2Cu2O10+δ

The thermal conductivity and thermopower are reported for a hole doped Eu_1.5Ce_0.5RuSr₂Cu₂O_10+δ sample that has been annealed at 1100 K under an oxygen pressure of 54 atm. At T_c=45 K superconductivity and weak ferromagnetism coexist (T_m=180 K). Weak features in the thermopower, S(T), and thermal conductivity, κ(T), are observed both at T_m and at T^*=140 K. The thermopower begins to decrease sharply toward zero at T_c, and there is an extremely sharp increase of about 30% in the thermal conductivity at T_c. This “first order” transition may be related to the sudden appearance of a spontaneous vortex phase at T_c. A small shoulder is observed in κ(T) in the temperature range T=5–13 K.     

Magnetic and electronic phase transitions and magnetoresistance effect in the Pr0.5−xLaxSr0.5MnO3 (, 0.15) system

The electronic and magnetic phase transitions of Pr_0.5−xLa_xSr_0.5MnO₃ with x=0.10 and 0.15 were investigated. The M(T) and ρ(T) curves for these samples clearly show transitions from antiferromagnetic insulator to ferromagnetic semiconductor, ferromagnetic metal and finally to paramagnetic semiconductor as the temperature is increased from 5 to 300 K. Especially, two obvious protrudent peaks in the magnetoresistance curves MR(T) for these samples were clearly observed in the relative low magnetic field, 1 T. One peak appears at around the antiferromagnet-ferromagnet transition temperature T_N (150 K) with MR≈−23%, another occurs at around the ferromagnet-paramagnet transition temperature T_C(275 K ) with MR≈−8.2%. In addition, when the magnetic field was increased, the temperature corresponding to the MR peak at T_N shifts to lower temperature while the temperature corresponding to the MR peak at T_C is fixed.     

Phase Behavior of Poly(Oxyethylene)–Poly(Oxypropylene)–Poly(Oxyethylene) Block Copolymer in Water and Water–C12EO5 Systems

Abstract

The binary phase diagram of a triblock copolymer poly(oxyethylene) (PEO) poly(oxypropylene) (PPO) poly(oxyethylene) (PEO), (PEO)₃₇(PPO)₅₈(PEO)₃₇ or P105 in water and the ternary system of P105, water, and pentaoxyethylene dodecyl ether (C₁₂EO₅) has been studied to understand the miscibility of a small amphiphile, C₁₂EO₅ and a copolymer, as well as the mixing effect on the formed liquid crystalline structures. Phase diagrams, small angle x‐ray scattering (SAXS) and differential scanning calorimetry (DSC) were used to characterize these systems. The phase diagram of the binary system is presented together with the characteristic parameters for founded phases, namely, cubic, hexagonal, and lamellar phases. In the ternary system it was found that the small amphiphile and the block copolymer, despite having very different chain lengths are essentially miscible forming single phases. A large amount of C₁₂EO₅ can be solubilized in the P105 aggregates whereas P105 is most difficult to dissolve in the C₁₂EO₅ aggregates because of the difference in the molecular size. The copolymer is practically insoluble in the lamellar phase of C₁₂EO₅ due to the packing constraint. Hence, two lamellar phases coexist in a surfactant‐rich region, at W _s  = 0.66, where W _s is the weight fraction of the total amphiphile in the system. This indicates that the thickness of the lipophilic part of the C₁₂EO₅ lamellar phase is too small to allocate the large lipophilic chain of the P105 triblock copolymer.     

De-mixing of polydisperse fluids: experimental test of a universal relation

Colloids, emulsions, polymer blends, and other important complex fluids, are polydisperse, i.e. there are variations among their constituent particles. Polydispersity is usually regarded as an ubiquitous, uncontrollable nuisance causing experimental inconsistencies. We have varied the polydispersity of a complex fluid, whilst keeping all other parameters constant, and report the first measurements of some universal physics. At coexistence (e.g. between liquid and vapour), fractionation occurs—each phase receives a different mix of the various ingredients, e.g. with the liquid disproportionately abundant with larger particles. Theory predicts, at low polydispersity, that this de-mixing becomes universal, irrespective of the material, with chemical differences between the phases proportional to polydispersity to the power two. We have studied colloid–polymer suspensions at two-phase coexistence and, using light scattering, measured the exponent as 2.16±0.44.     

The complete closed coexistence curves for 2H,3H,6H,7H,8H-5,8-(Dimethylmethano)-5(R)-methylquinoxaline with water and with deuterium oxide

The complete closed solubility curves for 2H, 3H, 6H, 7H, 8H-5,8-(dimethylmethano)-5(R)-methylquinoxaline with water and with deuterium oxide have been determined. With water the lower critical solution temperature (LCST) was found to be 51.4°C and the critical solution temperature (CST) was found to be 215.0°C. With deuterium oxide the values were 40.4°C for the LSCT and 221.7°C for the CST. The deuterium oxide curve completely encompassed the water curve. Solution compositions at the critical temperatures were also determined.     

Existence and asymptotic behavior of positive solutions for a one-prey and two-competing-predators system with diffusion

A diffusive one-prey and two-competing-predators system under homogeneous Dirichlet boundary conditions is studied. First, we obtain sufficient conditions for the extinction and existence of global attractor of the time-dependent system by means of the comparison principle. Second, we discuss the existence and nonexistence of coexistence states, and give sufficient conditions for the existence of coexistence states by using the fixed point index theory. In addition, we investigate the bifurcation from a double eigenvalue by virtue of space decomposition and implicit function theorem. Finally, some numerical simulations are made to verify and complement the theoretical analysis.     

Collaboration in R&D activities: Firm-specific decisions

In this paper, we study the strategic R&D collaboration by introducing a virtual player to reveal cooperative incentives and keeping investment share and market share independent of each other. Not consistently with the traditional opinions, we show that the superiority of the R&D cartel is due to the coexistence of cooperation and competition when spillovers are exogenous. Moreover, we conclude that high R&D input share must be reflected implicitly by high market share, and that firms’ R&D decisions vary with firms’ specific characteristics when spillovers is endogenous.