Phase diagram of the ABC model with nonconserving processes

The three species ABC model of driven particles on a ring is generalized to include vacancies and particle-nonconserving processes. The model exhibits phase separation at high densities. For equal average densities of the three species, it is shown that although the dynamics is {\it local}, it obeys detailed balance with respect to a Hamiltonian with {\it long-range interactions}, yielding a nonadditive free energy. The phase diagrams of the conserving and nonconserving models, corresponding to the canonical and grand-canonical ensembles, respectively, are calculated in the thermodynamic limit. Both models exhibit a transition from a homogeneous to a phase-separated state, although the phase diagrams are shown to differ from each other. This conforms with the expected inequivalence of ensembles in equilibrium systems with long-range interactions. These results are based on a stability analysis of the homogeneous phase and exact solution of the hydrodynamic equations of the models. They are supported by Monte-Carlo simulations. This study may serve as a useful starting point for analyzing the phase diagram for unequal densities, where detailed balance is not satisfied and thus a Hamiltonian cannot be defined.Comment: 32 page, 7 figures. The paper was presented at Statphys24, held in Cairns, Australia, July 201

Exact Quantum Solutions of Extraordinary N-body Problems

The wave functions of Boson and Fermion gases are known even when the particles have harmonic interactions. Here we generalise these results by solving exactly the N-body Schrodinger equation for potentials V that can be any function of the sum of the squares of the distances of the particles from one another in 3 dimensions. For the harmonic case that function is linear in r^2. Explicit N-body solutions are given when U(r) = -2M \hbar^{-2} V(r) = \zeta r^{-1} - \zeta_2 r^{-2}. Here M is the sum of the masses and r^2 = 1/2 M^{-2} Sigma Sigma m_I m_J ({\bf x}_I - {\bf x}_J)^2. For general U(r) the solution is given in terms of the one or two body problem with potential U(r) in 3 dimensions. The degeneracies of the levels are derived for distinguishable particles, for Bosons of spin zero and for spin 1/2 Fermions. The latter involve significant combinatorial analysis which may have application to the shell model of atomic nuclei. For large N the Fermionic ground state gives the binding energy of a degenerate white dwarf star treated as a giant atom with an N-body wave function. The N-body forces involved in these extraordinary N-body problems are not the usual sums of two body interactions, but nor are forces between quarks or molecules. Bose-Einstein condensation of particles in 3 dimensions interacting via these strange potentials can be treated by this method.Comment: 24 pages, Latex. Accepted for publication in Proceedings of the Royal Societ

Combination of fluorescent and spin labels: a powerful method for the optimization of hydrophilic membranes for the separation of oil-in-water emulsions

A new method for assessing the quality of fibre coating based on a combination of fluorescence microscopy and electron paramagnetic resonance is presented in this work. An influence of the carboxymethylcellulose/polyvinylamine gel preparation method on the mobility of the spin label was established. The mobility of the spin label changes from 3.5 ns in the case of a polyvinylamine solution to 12.8 ns in the case of a cross-linked gel on the surface of the glass fibre. A qualitative relationship was found between the mobility of the spin label in the gel applied to the glass fibre and the rate of spreading of crude oil over its surface. This method can be used to make membranes for the separation of water-in-oil emulsions

Ensemble Inequivalence and the Spin-Glass Transition

We report on the ensemble inequivalence in a many-body spin-glass model with integer spin. The spin-glass phase transition is of first order for certain values of the crystal field strength and is dependent whether it was derived in the microcanonical or the canonical ensemble. In the limit of infinitely many-body interactions, the model is the integer-spin equivalent of the random-energy model, and is solved exactly. We also derive the integer-spin equivalent of the de Almeida-Thouless line.Comment: 19 pages, 7 figure

Synthesis of Cu(II)-containing TiO2-SiO2 binary xerogels by hydrolysis of a mixture of tetrabutoxytitanium, tetraethoxysilane, and copper(II) chloride in a water-ammonia atmosphere

A Cu(II)-containing binary xerogel TiO2-SiO2 was synthesized by joint hydrolysis of tetrabutoxytitanium, teraethoxysilane and copper(II) chloride dissolved in their mixture. The synthesis was performed in a vapor of 10% aqueous ammonia under static conditions. EPR spectroscopy was used to examine the state of Cu(II) in the xerogel matrix. Data on specific features of the behavior of saccharose within xerogel pores under heating were obtained. The catalytic activity of the xerogel was tested by the kinetic method on model reactions of hydrogen peroxide decomposition and oxidative dehydrogenation of trimethylhydroquinone. © 2013 Pleiades Publishing, Ltd

Conductive Atomic Force Microscopy study of local resistive switching by a complex signal in the yttria stabilized zirconia films

This work was supported by RFBR (18-42-520059р_а)