Clusters,metastability, and nucleation: Kinetics of first-order phase transitions

We describe and interpret computer simulations of the time evolution of a binary alloy on a cubic lattice, with nearest neighbor interactions favoring like pairs of atoms. Initially the atoms are arranged at random; the time evolution proceeds by random interchanges of nearest neighbor pairs, using probabilities compatible with the equilibrium Gibbs distribution at temperatureT. For temperatures 0.59T_c, 0.81 T_c, and 0.89T _c, with density of A atoms equal to that in the B-rich phase at coexistence, the density C₁ of clusters ofl A atoms approximately satisfies the following empirical formulas: C₁ w(1 –)³ andC ₁, (1 –)⁴Q₁w¹ (2 l 10). Herew is a parameter and we defineQ _l = _K e ^–E(K) , where the sum goes over all translationally nonequivalentl-particle clusters andE(K) is the energy of formation of the clusterK. Forl > 10,Q ₁ is not known exactly; so we use an extrapolation formulaQ _l Aw _s ^–l l ^– exp(–bl ), wherew _s is the value ofw at coexistence. The same formula (withw > w _s) also fits the observed values of C, (for small values ofl) at densities greater than the coexistence density (forT=0.59T_c): When the supersaturation is small, the simulations show apparently metastable states, a theoretical estimate of whose lifetime is compatible with the observations. For higher supersaturation the system is observed to undergo a slow process of segregation into two coexisting phases (andw therefore changes slowly with time). These results may be interpreted as a more quantitative formulation (and confirmation) of ideas used in standard nucleation theory. No evidence for a spinodal transition is found.Supported by AFOSR Grant No. 73-2430D and by ERDA Contract No. EY-76-C-02-3077*000.     

Growth of clusters in a first-order phase transition

The results of computer simulations of phase separation kinetics in a binary alloy quenched from a high temperature are analyzed in detail, using the ideas of Lifshitz and Slyozov. The alloy was modeled by a three-dimensional Ising model with Kawasaki dynamics. The temperature after quenching was 0.59T _c, whereT _c is the critical temperature, and the concentration of minority atoms was=0.075, which is about five times their largest possible single-phase equilibrium concentration at that temperature. The time interval covered by our analysis goes from about 1000 to 6000 attempted interchanges per site. The size distribution of small clusters of minority atoms is fitted approximately byc ₁(1-)³ w(t),c ₁ (1–)⁴ Q _l w(t)^l(2l10); wherec _l is the concentration of clusters of sizel;Q ₂,...,Q ₁₀ are known constants, the cluster partition functions;t is the time; andw(t)=0.015(1+7.17t ^–1/3). The distribution of large clusters (l20) is fitted approximately by the type of distribution proposed by Lifshitz and Slyozov,c _l ,(t)=–(d/dl) [lnt+p (l/t)], where is a function given by those authors and is defined by(x)=C _o e–x-C ₁ e ^–4x/3-C ₂ e ^–5x/3;C ₀,C ₁,C ₂ are constants determined by considering how the total number of particles in large clusters changes with time.Supported by the U.S. Air Force Office of Scientific Research under Grant No. 78-3522 and by the U.S. Department of Energy under Contract No. EY-76-C-02-3077*000.     

Non-Existence of Black Hole Solutions¶for a Spherically Symmetric, Static Einstein–Dirac–Maxwell System

We consider for j=?, … a spherically symmetric, static system of (2j+1) Dirac particles, each having total angular momentum j. The Dirac particles interact via a classical gravitational and electromagnetic field. The Einstein–Dirac–Maxwell equations for this system are derived. It is shown that, under weak regularity conditions on the form of the horizon, the only black hole solutions of the EDM equations are the Reissner–Nordstr?m solutions. In other words, the spinors must vanish identically. Applied to the gravitational collapse of a “cloud” of spin-?-particles to a black hole, our result indicates that the Dirac particles must eventually disappear inside the event horizon. Received: 2 November 1998 / Accepted: 23 February 1999     

Tracking regression and progression of atherosclerosis in human carotid arteries using high-resolution magnetic resonance imaging

BACKGROUND AND PURPOSE: Magnetic resonance imaging (MRI) can accurately and reproducibly measure the volume of atherosclerotic plaque in human carotid arteries. Atherosclerotic plaques may either progress or regress over time, depending on individual risk factors and treatment regimens. This study was designed to determine if regression or progression of human carotid atherosclerosis in patients receiving statin therapy over 24 months can be detected by high-resolution MRI. METHODS: In 11 subjects who had undergone unilateral carotid endarterectomy and were on statin therapy, volumes for total carotid artery, concentric wall (normal wall), eccentric wall (plaque), and lumen were quantified at 0, 16 and 24 months using a 1.5-T human imager equipped with 6-cm phased array coils. RESULTS: The interobserver mean coefficient of variation (CV) was lowest for the lumen volume (3.1%) and highest for the plaque volume (9.8%). The interscan mean CV was lowest for the total artery volume (3.2%) and highest for the plaque volume (9.9%). As much as 26% regression and 35% progression were observed in individual subject's carotid artery eccentric wall (plaque) volumes over time. Mean eccentric wall volume increased 5% by 16 months and 8% by 24 months. Mean total wall volume increased slightly at both 16 and 24 months (+1.2% and +1.8%). CONCLUSIONS: High-resolution MRI provides a noninvasive reproducible method of tracking changes in carotid atherosclerosis. This pilot study detected changes in individual subjects at both 16 and 24 months. MRI tracking of changes in atherosclerotic plaques should prove useful in assessing vascular disease risk and monitoring the efficacy of interventions designed to induce regression or retard progression.     

Vortex locking in direct numerical simulations of quantum turbulence

Direct numerical simulations are used to examine the locking of quantized superfluid vortices and normal fluid vorticity in evolving turbulent flows. The superfluid is driven by the normal fluid, which undergoes either a decaying Taylor-Green flow or a linearly forced homogeneous isotropic turbulent flow, although the back reaction of the superfluid on the normal fluid flow is omitted. Using correlation functions and wavelet transforms, we present numerical and visual evidence for vortex locking on length scales above the intervortex spacing.     

Interplay of thermochemistry and Structural Chemistry,the journal (volume 29, 2018, issues 3–4) and the discipline

The contents of issues 3 and 4 of Structural Chemistry from the calendar year 2018 are summarized in the present review. A brief thermochemical commentary and recommendations for future research have been added to the summary of each paper.

     

Differential evolution with enhanced diversity maintenance

Optimization Letters - Differential evolution (de) is a popular population-based meta-heuristic that has been successfully used in complex optimization problems. Premature convergence is one of the...     

Noble gas halides: The B → X and D → X systems of 136Xe35Cl

The B → X (2870–3100 Å) and D → X (2250–2370 Å) band systems of ¹³⁶Xe³⁵Cl are photographed and vibrationally analyzed. A simultaneous least-squares fit of 41 band-heads in the B-X system and 35 in D-X yields, in part, the following constants (in cm^?1): T_eB = 32 405.8, T_eD = 42 347.9, ω_eB = 194.75, ω_eD = 204.34, ω_eX = 26.22. The ground state dissociation energy ($\text{D}$″_e) is estimated to be 281 ± 10 cm^?1. Potential curves are derived for all three states through Franck-Condon calculations. From these curves the D-state internuclear distance is 0.09 ± .02 Å smaller than the B-state distance.     

An optimization approach for planning daily drayage operations

Daily drayage operations involve moving loaded or empty equipment between customer locations and rail ramps. Our goal is to minimize the cost of daily drayage operations in a region on a given day. Drayage orders are generally pickup and delivery requests with time windows. The repositioning of empty equipment may also be required in order to facilitate loaded movements. The drayage orders are satisfied by a heterogeneous fleet of drivers. Driver routes must satisfy various operational constraints. We present an optimization methodology for finding cost-effective schedules for regional daily drayage operations. The core of the formulation is a set partitioning model whose columns represent routes. Routes are added to the formulation by column generation. We present numerical results for real-world data which demonstrate that our methodology produces low cost solutions in a reasonably short time.     

The crystal structure on the set of Mirkovi?-Vilonen polytopes

In an earlier work, we proved that MV polytopes parameterize both Lusztig's canonical basis and the Mirkovi?-Vilonen cycles on the affine Grassmannian. Each of these sets has a crystal structure (due to Kashiwara-Lusztig on the canonical basis side and due to Braverman-Finkelberg-Gaitsgory on the MV cycles side). We show that these two crystal structures agree. As an application, we consider a conjecture of Anderson-Mirkovi? which describes the BFG crystal structure on the level of MV polytopes. We prove their conjecture for sln and give a counterexample for sp₆. Finally we explain how Kashiwara data can be recovered from MV polytopes.