Transient bimodality in interacting particle systems

We consider a system of spins which have values ±1 and evolve according to a jump Markov process whose generator is the sum of two generators, one describing a spin-flipGlauber process, the other aKawasaki (stirring) evolution. It was proven elsewhere that if the Kawasaki dynamics is speeded up by a factor ^–2, then, in the limit 0 (continuum limit), propagation of chaos holds and the local magnetization solves a reaction-diffusion equation. We choose the parameters of the Glauber interaction so that the potential of the reaction term in the reaction-diffusion equation is a double-well potential with quartic maximum at the origin. We assume further that for each the system is in a finite interval ofZ with ^–1 sites and periodic boundary conditions. We specify the initial measure as the product measure with 0 spin average, thus obtaining, in the continuum limit, a constant magnetic profile equal to 0, which is a stationary unstable solution to the reaction-diffusion equation. We prove that at times of the order ^–1/2 propagation of chaos does not hold any more and, in the limit as 0, the state becomes a nontrivial superposition of Bernoulli measures with parameters corresponding to the minima of the reaction potential. The coefficients of such a superposition depend on time (on the scale ^–1/2) and at large times (on this scale) the coefficient of the term corresponding to the initial magnetization vanishes (transient bimodality). This differs from what was observed by De Masi, Presutti, and Vares, who considered a reaction potential with quadratic maximum and no bimodal effect was seen, as predicted by Broggi, Lugiato, and Colombo.     

The class reconstruction number of maximal planar graphs

The reconstruction numberrn(G) of a graphG was introduced by Harary and Plantholt as the smallest number of vertex-deleted subgraphsG _i =G – v _i in the deck ofG which do not all appear in the deck of any other graph. For any graph theoretic propertyP, Harary defined theP-reconstruction number of a graph G P as the smallest number of theG _i in the deck ofG, which do not all appear in the deck of any other graph inP We now study the maximal planar graph reconstruction numberrn(G), proving that its value is either 1 or 2 and characterizing those with value 1.     

Hydrodynamic equations for attractive particle systems on ℤ

Hydrodynamic properties for a class of nondiffusive particle systems are investigated. The method allows one to study local equilibria for a class of asymmetric zero-range processes, and applies as well to other models, such as asymmetric simple exclusion and misanthropes. Attractiveness is an essential ingredient. The hydrodynamic equations present shock wave phenomena. Preservation of local equilibrium is proven to hold away from the shocks. The problem of breakdown of local ergodicity at the shocks, which was investigated by D. Wick in a particular model, remains open in this more general setup.     

Escape from the unstable equilibrium in a random process with infinitely many interacting particles

We consider a one-dimensional version of the model introduced in Ref. l. At each site of Z there is a particle with spin ± 1. Particles move according to the Stirring Process and spins change according to the Glauber dynamics. In the hydrodynamical limit, with the stirring process suitably speeded up, the local magnetic densitym _t(r) is proven in Ref. 1 to satisfy the reaction-diffusion equation (*) $$\partial _t m_t (r) = \tfrac{1}{2}\partial _r^2 m_t (r) - V'(m_t )$$ \(V(m) = - \tfrac{1}{2}\alpha m^2 + \tfrac{1}{4}\beta m^4 \) ,α andβ being determined by the parameters of the Glauber dynamics. In the present paper we consider an initial state with zero magnetization,m ₀(r)=0. We then prove that at long times, before taking the hydrodynamical limit, the evolution departs from that predicted by (*) and that the microscopic state becomes a nontrivial mixture of states with different magnetizations.     

Determination of lead concentration and film thickness in electroluminescent calcium sulfide thin films by X-ray fluorescence

Summary For the analysis of electroluminescent thin films, X-ray fluorescence (XRF) provides a convenient method as both the concentration of the dopant and the film thickness can be determined rapidly and non-destructively. An XRF method for the determination of thickness and lead concentration in lead doped calcium sulfide thin films was developed. Calibration standards made of polyvinyl alcohol and gelatin as well as filter paper standards were used. In addition, the applicability of a fundamental parameter program UniQuant was investigated. For comparison, the concentrations of lead and calcium were determined after dissolution by atomic absorption spectrometry. Generally, the correlation between the different methods excluding the use of filter paper standards was satisfactory. When the dopant concentration was very low or very high, however, the fundamental parameter program yielded best results. Determination of thicknesses by XRF was made by comparing the sulfur K intensities of the sample and those of a zinc sulfide standard. A correction factor for molar masses and densities was applied. The thicknesses obtained were compared to those measured with a profilometer after etching and the deviations were found to be less than 10%.Dedicated to Professor Dr. Wilhelm Fresenius on the occasion of his 80th birthday     

Computation of the physio-chemical properties and data mining of large molecular collections

Very large data sets of molecules screened against a broad range of targets have become available due to the advent of combinatorial chemistry. This information has led to the realization that ADME (absorption, distribution, metabolism, and excretion) and toxicity issues are important to consider prior to library synthesis. Furthermore, these large data sets provide a unique and important source of information regarding what types of molecular shapes may interact with specific receptor or target classes. Thus, the requirement for rapid and accurate data mining tools became paramount. To address these issues Pharmacopeia, Inc. formed a computational research group, The Center for Informatics and Drug Discovery (CIDD).* In this review we cover the work done by this group to address both in silico ADME modeling and data mining issues faced by Pharmacopeia because of the availability of a large and diverse collection (over 6 million discrete compounds) of drug-like molecules. In particular, in the data mining arena we discuss rapid docking tools and how we employ them, and we describe a novel data mining tool based on a ID representation of a molecule followed by a molecular sequence alignment step. For the ADME area we discuss the development and application of absorption, blood-brain barrier (BBB) and solubility models. Finally, we summarize the impact the tools and approaches might have on the drug discovery process.     

An NMR-Based Approach to the Measurement of High Log K HL Values at Low Ionic Strength. 31P NMR Study of 1,2-Diaminoethane-N,N,N′,N′-tetra(methylenephosphonic Acid) Protonation Equilibrium at pH > 12

A sequential NMR based approach is proposed for measurements of high log K values at low ionic strength. [³¹P] NMR technique is used to determine the protonation constants of 1,2-diaminoethane-N,N,N,N-tetra(methylenephosphonic acid) (EDTPH, H₈L) at 25°C in 0.1 mol-dm^–3 KNO₃ and at 37°C in 0.15 mol-dm^–3 NaCl at pH 11–14. For equilibrium L + H HL log K are found to be 13.3 (0.1) and 12.9 (0.1), respectively.     

H2S-sensing properties of SnO2 produced by ball milling and different chemical reactions

In this work, the mechanochemical synthesis of a moderately agglomerated tin oxide (SnO₂) powders and the subsequent preparation of semiconductor gas sensors as prototypes, were studied. Tin (II) chloride (SnCl₂) powder was milled with calcium hydroxide (Ca(OH)₂) and potassium carbonate, (K₂CO₃) powder, respectively, in a ball mill at room temperature and in an air atmosphere. Heat treatment of milled mixtures at 400 °C resulted in the formation of a tetragonal phase, confirmed by X-ray diffraction (XRD). During milling in the presence of water, a high number of hydroxide (OH) groups are formed at the surface. When SnCl₂ was milled with K₂CO₃, no water was produced and the Fourier-transform infrared spectrum (FT-IR) of the powder has no surface hydroxyl deformations. On exposure to hydrogen sulfide (H₂S) gas, the particles, prepared from anhydrous powder, have higher sensitivity than these, prepared from hydrated powder. The SnO₂ thick film, prepared from anhydrous powder may be successfully applied to a H₂S gas sensor.