The Picone identity: A device to get optimal uniqueness results and global dynamics in Population Dynamics

This paper infers from a generalized Picone identity the uniqueness of the stable positive solution for a class of semilinear equations of superlinear indefinite type, as well as the uniqueness and global attractivity of the coexistence state in two generalized diffusive prototypes of the symbiotic and competing species models of Lotka–Volterra. The optimality of these uniqueness theorems reveals the tremendous strength of the Picone identity.     

Bilayer studies in mixedn-decanol/n-tetradecanol complexes ofn-decylammonium beidellite

Complexes have been prepared by treatment ofn-decylammonium beidellite with mixtures ofn-decanol andn-tetradecanol with different concentrations. Measurements of the basal spacings of the obtained complexes have been performed in a wide range of temperatures. Three different bilayer phases have been established between (20 and 70°C: the _i(C₁₀) phases (=bilayers ofn-decyl chains); the _i(C₁₀/C₁₄) phases (=mixed bilayers ofn-decyl andn-tetradecyl chains in molar ratio approximately 1:1) and the _i(C₁₄) phases (=bilayer ofn-tetradecy 1 chains with then-decylammonium ions included). In all bilayer phases the chains stand perpendicular to the silicate interfaces. In definite concentration ranges two of the phases coexist, i.e., miscibility gaps occur, which disappear at temperatures higher than the temperature of the _i/ transition. The miscibility gaps are reversible with temperature. The composition of the intercalated bilayers has been studied by HPLC of the excess alkanol mixture separated from the beidellite complexes after the equilibrium has been reached. There is preferential adsorption of one of two alkanols from the mixture, which is in agreement with the observed miscibility gaps. The space filling problem as well as the structure of the three bilayer phases observed have been discussed.     

On the two-dimensional stochastic Ising model in the phase coexistence region near the critical point

We consider the two-dimensional stochastic Ising model in finite square with free boundary conditions, at inverse temperature >₀ and zero external field. Using duality and recent results of Ioffe on the Wulff construction close to the critical temperature, we extend some of the results obtained by Martinelli in the low-temperature regime to any temperature below the critical one. In particular we show that the gap in the spectrum of the generator of the dynamics goes to zero in the thermodynamic limit as an exponential of the side length of , with a rate constant determined by the surface tension along one of the coordinate axes. We also extend to the same range of temperatures the result due to Shlosman on the equilibrium large deviations of the magnetization with free boundary conditions.     

Finite-size scaling study of a first-order temperature-driven symmetry-breaking structural phase transition

We present a study of finite-size effects in a model exhibiting a first-order temperature-driven symmetry-breaking structural phase transition in theL × cylindrical geometry in theL limit. Exact studies demonstrate the applicability of our scaling ansatz even in the one-dimensional limit, making this model ideal for studying finite-size effects. The scaling ansatz, similar to the previously developed ansatz for field-driven transitions, demonstrates that latent heat is crucial in driving these transitions. This ansatz is supported by a 2×2 phenomenological transfer matrix based upon the symmetries of the system; this produces an analytic free energy which has the scaling form. Order parameter probability distributions show that the high- and low-temperature phases coexist only in a small finite-size-affected regime near the bulk transition temperature; this regime vanishes exponentially fast asL diverges.     

Structural and Thermodynamic Peculiarities of Core-Shell Particles at Fluid Interfaces from Triangular Lattice Models

A triangular lattice model for pattern formation by core-shell particles at fluid interfaces is introduced and studied for the particle to core diameter ratio equal to 3. Repulsion for overlapping shells and attraction at larger distances due to capillary forces are assumed. Ground states and thermodynamic properties are determined analytically and by Monte Carlo simulations for soft outer- and stiffer inner shells, with different decay rates of the interparticle repulsion. We find that thermodynamic properties are qualitatively the same for slow and for fast decay of the repulsive potential, but the ordered phases are stable for temperature ranges, depending strongly on the shape of the repulsive potential. More importantly, there are two types of patterns formed for fixed chemical potential—one for a slow and another one for a fast decay of the repulsion at small distances. In the first case, two different patterns—for example clusters or stripes—occur with the same probability for some range of the chemical potential. For a fixed concentration, an interface is formed between two ordered phases with the closest concentration, and the surface tension takes the same value for all stable interfaces. In the case of degeneracy, a stable interface cannot be formed for one out of four combinations of the coexisting phases, because of a larger surface tension. Our results show that by tuning the architecture of a thick polymeric shell, many different patterns can be obtained for a sufficiently low temperature.     

Study of phase coexistence in YVO3 and LaVO3

The coexistence at low temperature in YVO₃ and LaVO₃ of two competing phases with defined orbital and spin orientations is studied by Raman spectroscopy. The temperature evolution of the phonons indicates that phase coexistence, due to strain in YVO₃ and fluctuations in LaVO₃, is not restricted to small R ionic radius in RVO₃ compounds. Also, a typical temperature at 50 K is inferred from the temperature dependence of the intensities in LaVO₃. Copyright © 2015 John Wiley & Sons, Ltd.     

FURTHER INVESTIGATION OF THE VOLTERRALOTKA COMPETITION MODEL WITH DIFFUSION

In this paper, tile existence of coexistence states in the Voterra-Lotka competition model under Dirichlet boundary conditions is the major concern. Attention will be focused on the logistic equation. With a comparison theorem an inequality satistisfied by the solution of logistic equation is established. Some improved sufficient conditions for the existence of coexistence states are obtained.     

Coexistence of phases in Ising ferromagnets

We derive a new inequality for ferromagnetic Ising spin systems and then use it to obtain information about the number of phases which can coexist in such systems. We show in particular that for even interactions only two phases (up and down magnetization) can coexist below the critical temperature at zero magnetic field (h=0) whenever the energy is a continuous function of the temperature. We also prove that the derivatives with respect toh ath=0 of the odd correlation functions (triplet,...) diverge like the susceptibility in the vicinity of the critical temperature (at least for pair interactions). Our results also apply to higher order Ising spins (not just spin 1/2).Research supported in part by NSF Grant #MPS 75-20638 and USAFOR Grant #73-2430D.John Simon Guggenheim Fellow.     

Laboratory Intercomparison on the Determination of the Fe(II)/Fe(III) Ratio in Glass Using Mössbauer Spectroscopy

A Perturbed Angular Correlation (PAC) study was performed on the system that presents a rich variety of structural and magnetic phase transitions as a function of the oxygen content (δ) or as a function of temperature (T). The PAC signal at room temperature allowed the determination of the Electrical Field Gradient (EFG) parameters and to correlate them with the lattice average symmetry namely the orthorhombic (O′ or O*) Pbnm and rhombohedral (R) phases measured by X-ray diffraction.     

Coexistence and fluctuations phenomena with Davidson-like potentials in quadrupole-octupole deformed nuclei

The energy spectra of three types of two-dimensional potentials(we will call them‘Davidson-like potentials’(DLPs)),characterized by four minima separated by barriers,are investigated.The predictions for spectra and wave functions are obtained by using the nine-point finite-difference method.For these potentials,with the existence of a single configuration,a transition of spectra,as a function of barrier height,is covered from tunneling splitting modes to fluctuations phenomena,with equal peaks wave functions,crossing to the spectra of purely anharmonic oscillator potentials(AOPs).A different type of phase transition occurs when two(or more)configurations coexist.With the change of the parameters,a transition of spectra is covered from coexistence phenomena of two distinct quantum tunneling modes to fluctuations phenomena,with unequal peaks wave functions,crossing to the spectra of purely AOPs.Using DLPs,a particular application of the coherent quadropole-octupole model to describe energy bands with alternating parity of the nuclei¹⁰⁰Mo,^146,148Nd,^148,150Sm,²²⁰Ra,^220,222Rn,and^220,222Th is presented.The global parametrization of the model for the selected nuclei is achieved.