Global solution to a phase transition model based on a microforce balance

Our aim in this article is to prove the existence and the uniqueness of a global solution to a nonisothermal Ginzburg-Landau (Allen-Cahn) system. This system is obtained by considering, in addition to the fundamental laws of thermodynamics, a balance law for internal microforces proposed by M. Gurtin.     

The Hochschild class of the Chern character for semifinite spectral triples

We provide a proof of Connes’ formula for a representative of the Hochschild class of the Chern character for (p,∞)-summable spectral triples. Our proof is valid for all semifinite von Neumann algebras, and all integral p?1. We employ the minimum possible hypotheses on the spectral triples.     

On essential extensions of reduced rings and domains

A ring is said to be a left essential extension of a reduced ring (domain) if it contains a left ideal which is a reduced ring (domain) and intersects nontrivially every nonzero twosided ideal of the ring. We prove that every ring which is a left essential extension of a reduced ring is a subdirect sum of rings which are essential extensions of domains, but the converse implication does not hold. We give some applications of this result and discuss several related questions.Received: 6 January 2003     

Medium-range structural order in liquid Ni20Al80 alloy: Experimental and molecular dynamics studies

In this Letter, structural properties of liquid Ni₂₀Al₈₀ have been studied through molecular dynamics (MD) simulations, and results agree well with X-ray experiments. The prepeak in the structure factor manifests the existence of medium-range structural order (MRSO) in liquid Ni₂₀Al₈₀. Analyses in MRSO reveal the dominance of ideal icosahedra and defective icosahedra which, furthermore, form clusters and share common atoms.     

Spectral Properties of Image Measures Under the Infinite Conflict Interaction

We introduce the conflict interaction with two positions between a couple of image probability measures and consider the associated dynamical system. We prove the existence of invariant limiting measures and find the criteria for these measures to be a pure point, absolutely continuous, or singular cotinuous as well as to have any topological type and arbitary Hausdorff dimension.     

Kraftfeldrechnungen an linearen Oligopyrrolen: 2,2′-Bipyrrol, 2,2′-Furylpyrrol und Prodigiosen

Using a specific force field model, relative stabilities of 2,2-bipyrrole and 2,2-furylpyrrole conformers as well as of prodigiosene tautomers, configurations, and conformations, are studied. 2,2-Bipyrrole adopts anantiperiplanar conformation in accord with other theoretical calculations and experimental findings. Its rotational barrier calculated by this method compares favourably to the one derived by other means. For the parent prodigiosene the (Z)sp,sp arrangement is found to be the most stable one. The two possible tautomers within its dipyrrin fragment do not show a significant energy difference.

     

Theoretical study of endohedral metallofullerenes: Sc3−nLanN@C80 (n=0–3)

To provide theoretical insight into the structures and properties of Sc₃N@C₈₀, which has been isolated in high yield and purity as a new stable endohedral metallofullerene, density functional calculations are carried out for the Sc_3?nLa_nN@C₈₀ (n=0–3) series. Because of electron transfer from Sc₃N to C₈₀, the electronic structure of Sc₃N@C₈₀ is formally described as (Sc₃N)⁶⁺C$_{80}^{6-}$. The encapsulated Sc₃N cluster takes a planar structure with long Sc–Sc distances and is highly stabilized inside the I_h cage of C₈₀, which rotates rapidly. As the number of La atoms increases, the Sc_3?nLa_nN cluster is forced to maintain a pyramidal structure in Sc_3?nLa_nN@C₈₀. In addition, the C₈₀ cage takes an open‐shell electronic structure due to an increase in the number of electrons transferring from Sc_3?nLa_nN. These make the endohedral structure less stable and more reactive. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1353–1358, 2001     

Time-asymptotic boson states from infinite mean field quantum systems coupled to the boson gas

By means of cocycle techniques in a recent paper, the global dynamics of mean field-boson couplings has been studied. Here, by restricting to the bosonic system the infinite time limit (t ) for very general initial states, one obtains time-asymptotic states on the bosonicC ^*-Weyl algebra, in which one partially rediscovers the collective ordering of the infinite mean field lattice.