Phase uniqueness and correlation length in diluted-field Ising models

The diluted-field Ising model, a random nonnegative field ferromagnetic model, is shown to have a unique Gibbs measure with probability I when the field mean is positive. Our methods involve comparisons with ordinary uniform field Ising models. They yield as a corollary a way of obtaining spontaneous magnetization through the application of a vanishing random magnetic field. The correlation lengths of this model defined as (lim _n-(1/n) log ₀; _n)^-1, wheren is the site on the first coordinate axis at distancen from the origin and ₀; _n is the origin ton two-point truncated correlation function, is non-random. We derive an upper bound for it in terms of the correlation length of an ordinary nonrandom model with uniform field related to the field distribution of the diluted model.     

Insertion of a Single‐Molecule Magnet inside a Ferromagnetic Lattice Based on a 3D Bimetallic Oxalate Network: Towards Molecular Analogues of Permanent Magnets

The insertion of the single‐molecule magnet (SMM) [Mn^III(salen)(H₂O)]₂²⁺ (salen^2?=N,N′‐ethylenebis‐(salicylideneiminate)) into a ferromagnetic bimetallic oxalate network affords the hybrid compound [Mn^III(salen)(H₂O)]₂[Mn^IICr^III(ox)₃]₂ ? (CH₃OH) ? (CH₃CN)₂ ( 1 ). This cationic Mn₂ cluster templates the growth of crystals formed by an unusual achiral 3D oxalate network. The magnetic properties of this hybrid magnet are compared with those of the analogous compounds [Mn^III(salen)(H₂O)]₂[Zn^IICr^III(ox)₃]₂ ? (CH₃OH) ? (CH₃CN)₂ ( 2 ) and [In^III(sal₂‐trien)][Mn^IICr^III(ox)₃] ? (H₂O)_0.25 ? (CH₃OH)_0.25 ? (CH₃CN)_0.25 ( 3 ), which are used as reference compounds. In 2 it has been shown that the magnetic isolation of the Mn₂ clusters provided by their insertion into a paramagnetic oxalate network of Cr^III affords a SMM behavior, albeit with blocking temperatures well below 500 mK even for frequencies as high as 160 kHz. In 3 the onset of ferromagnetism in the bimetallic Mn^IICr^III network is observed at T_c=5 K. Finally, in the hybrid compound 1 the interaction between the two magnetic networks leads to the antiparallel arrangement of their respective magnetizations, that is, to a ferrimagnetic phase. This coupling induces also important changes on the magnetic properties of 1 with respect to those of the reference compounds 2 and 3 . In particular, compound 1 shows a large magnetization hysteresis below 1 K, which is in sharp contrast with the near‐reversible magnetizations that the SMMs and the oxalate ferromagnetic lattice show under the same conditions.     

Triple flame: Inherent asymmetries and pentasectional character

A two-dimensional triple-flame numerical model of a laminar combustion process reflects flame asymmetric structural features that other analytical models do not generate. It reveals the pentasectional character of the triple flame, composed of the central pure diffusion-flame branch and the fuel-rich and fuel-lean branches, each of which is divided into two sections: a near-stoichiometric section and a previously unreported near-flammability-limits section with combined diffusion and premixed character. Results include propagation velocity, fuel and oxidiser mass fractions, temperature and reaction rates. Realistic stoichiometric ratios and reaction orders match experimental planar flame characteristics. Constant density, a one-step reaction, and a mixture fraction gradient at the inlet as the simulation parameter are imposed. The upstream equivalence ratio or the upstream reactant mass fractions are linear or hyperbolic functions of the transverse coordinate. The use here of experimental kinetics data differs from previous analytical works and results in flame asymmetry and different flammability limits. Upstream mixture composition gradient affects propagation velocity, flame curvature, diffusion flame reaction rate, and flammability limits. Flammability limits extend beyond those of a planar flame due to transverse heat and mass diffusion causing the pentasectional character.     

Duality Between Multi-Output Production Correspondences and Cost Functions

Set-Valued and Variational Analysis - The production correspondence associated with a technology maps every input vector into the set of output vectors that may be obtained by means of those...