QUALITATIVE AND QUANTITATIVE ANALYSIS OF STOCHASTIC PROCESSES BASED ON MEASURED DATA, I: THEORY AND APPLICATIONS TO SYNTHETIC DATA

Analysis of stochastic processes governed by the Langevin equation is discussed. The analysis is based on a general method for non-parametric estimation of deterministic and random terms of the Langevin equation directly from given data. Separate estimation of the terms corresponds to decomposition of process dynamics into deterministic and random components. Such decomposition provides a basis for qualitative and quantitative analysis of process dynamics. In Part I, the following analysis possibilities are described and illustrated using various synthetic datasets: (1) qualitative inspection of the estimated terms presented as fields, (2) reconstruction of the deterministic and stochastic evolution of the process and (3) approximation of the deterministic term by an analytical function and quantitative treatment of the equations obtained. In Part II, these analysis possibilities are applied to experimental datasets from metal cutting and laser-beam welding.     

Theoretical study of hyperfine coupling constants and electron spin g factors for X2Σ+ diatomics from Groups 1 and 2

The ESR parameters of the cations Be⁺ ₂, Mg⁺ ₂, Ca⁺ ₂, BeMg⁺, BeCa⁺, MgCa⁺ and the mixed radicals ZBe, ZMg, ZCa (Z = Li, Na, K), all having a X ²Σ⁺ _u(1σ² _g1σ_u)/X ²Σ⁺(1σ²2σ) ground state, have been studied theoretically. The A _iso and A _dip constants have been calculated with UHF, CISD, MP2, B3LYP, PW91PW91 wavefunctions, and 6–311+G(2df) basis sets. The electron spin g factors (magnetic moment μ_s) have been evaluated from correlated (MRDCI) wavefunctions, using a Hamiltonian based on Breit-Pauli theory with perturbation expansions up to second order, and 6–311 + G(2d) basis sets. As expected for s-rich radicals, the hyperfine spectra are governed by the A _iso terms. Both Δg∥ and Δg⊥ values are negative, but Δg∥ lies close to zero. For Δg⊥, the coupling with 1 ²Π_(u) dominates the sum-over-states expansions. Although the singly occupied MOs (SOMO) are mostly of s character, the |Δg⊥| are relatively large, up to 5200 ppm for cationic, and up to 7850 ppm for neutral radicals. These large values are caused by low excitation energies and high magnetic transition moments, the latter due to the fact that the σ?(s-s) SOMO has the same nodal properties as a pσ orbital. Of the radicals considered here, an ESR spectrum is available only for Mg⁺ ₂. Our theoretical A _iso of ?287 MHz reproduces well the matrix result (-291 MHz). Calculated values of ?10 ppm for Δg∥ and of ?1280 ppm for Δg⊥ give an average 〈Δg〉 = ?860 ppm that lies within the experimental range of ?600(±300) ppm in Ne, and of ?1300(±500) ppm in Ar matrices.     

On the Modulation of Molecular Wave Functions by the Potential

Spinless wave functions are written as the product of a modulation function that generates cusps at all loci where one electron is at one nucleus or where two electrons collide and that is independent of the electronic state, and a fundamental function that is specific for the state regarded and generates the nodes. The modulation function can be formulated in such a way that the cusps are rendered in the correct way. In this case the true potential that is singular (infinite) at these loci is transformed into a pseudopotential that is finite and continuous. The fundamental functions appear to be differentiable at these loci. The same formalism is applied to orbitals, and special modulation functions are defined for plane and linear molecules and atoms, the modulation factors now being common for all wave functions with the same symmetry. If the correct wave function of the ground state is found along these lines and taken as the modulation function itself, and if the true potential is equal for all different states, the space-dependent pseudopotential is replaced by a constant, namely the energy of the ground state. On écrit des fonctions d'onde sans spin comme le produit d'une fonction de modulation et d'une fonction fondamentale, qui est caractéristique pour l'état considéré et qui engendre les noeuds. La fonction de modulation crée des “cusps” où un électron coincide avec un noyau ou avec tin autre électron; elle est indépendante de l'état électronique. Dans ce cas-ci on transforme le vrai potentiel, qui est singulier en ces points-ci en un pseudopotentiel qui est fini et continu. Les fonctions fondamentales sont différentiables en ces points. Le même formalisme peut être appliqué à des orbitales. On définit des fonctions de modulation particulières pour des atomes et des molécules planes et linéaires avec les mêmes facteurs de modulation pour toutes les fonctions d'onde d'une même symétrie. Si on choisit comme fonction de modulation la fonction d'onde exacte de l'état fondamental, et si le vrai potentiel est le même pour les états différents, le pseudopotentiel devient une constante, c'est-à-dire l'énergie de l'état fondamental. Spinlose Wellenfunktionen werden als ein Produkt von einer Modulationsfunktion und einer fundamentalen Funktion, die spezifisch für den elektronischen Zustand ist und die die Knoten erzeugt, beschrieben. Die Modulationsfunktion erzeugt “cusps”, wo ein Elektron mit einem Kern oder einem anderen Elektron zusammentrifft; sie ist vom elektronischen Zustand unabhängig. Auf diese Weise wird das wirkliche Potential, das singulär in diesen “Cusp”-Punkten ist, in ein Pseudopotential, das endlich und stetig ist, transformiert. Die fundamentalen Funktionen sind in diesen Punkten differenzierbar. Dieselbe Methode wird auf Orbitale angewendet, und spezielle Modulationsfunktionen werden für Atome sowie ebene und lineare Moleküle definiert. Die Modulationsfaktoren sind dann gemeinsam für alle Wellenfunktionen mit derselben Symmetric. Wenn als Modulationsfunktion die exakte Wellenfunktion des Grundzustands angewendet wird, und wenn das wirkliche Potential für alle verschiedenen Zustände gleich ist, wird, das ortsabhängige Pseudopotential durch eine Konstante, nämlich die Energie des Grundzustands, ersetzt.     

Ion Channels as Sensing Elements-Investigations by Patch-Clamp Technique

Ion channels are transmembrane proteins. Their high recognition capability together with an intrinsic amplification effects makes them outstanding candidates as constituents of biosensors. The patch-clamp technique is an extremely powerful and versatile method for studying the functioning of ion channels reconstituted into biological or synthetic membranes. Two well characterized types of natural ion channels were studied, (i) the simple transmembrane protein gramicidin A and (ii) the rather complex ligand-gated nicotinic acetylcholine receptor.     

VALIDATION OF A NAVIER–STOKES SOLUTION ALGORITHM WITH EXPERIMENTAL VALUES IN A SUPERSONIC WAKE

This paper describes the validation of a finite element solver for an axisymmetric compressible flow with experimental values, especially velocities measured with a laser Doppler anemometer in the near wake of a circular cylinder. The equations under consideration are the Navier-Stokes equations with turbulent terms. A time-stepping scheme for the solution of these equations can be produced by applying a forward-time Taylor series expansion including time derivatives of second order. These time derivatives are evaluated in terms of space derivatives in the Lax–Wendroff fashion. The method is based on unstructured triangular grids with a high resolution in the radial direction. In order to predict the measured turbulent intensites more exactly, a modification of the Baldwin–Lomax model is necessary.     

ChemInform Abstract: On the Structure of S2+ 4 and its Formation from 2S+ 2. Ab initio SCF and CASSCF Studies.

ChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 100 leading journals. To access a ChemInform Abstract of an article which was published elsewhere, please select a “Full Text” option. The original article is trackable via the “References” option.     

Microtribological Studies of Poly(ether ether ketone) by Atomic Force Microscopy (AFM)

Atomic force microscopy (AFM) and its modification-lateral force microscope (LFM) are becoming increasingly important in the understanding of microfriction and nanomechanical property measurements. In the present paper, the AFM, LFM and a modified AFM-lithography technique are described, and data on microtribilogical studies of PEEK are presented. For comparisons, macro-scale friction measurements were also made on PEEK by the use of a block-on-ring testing facility. It was observed that macro-scale friction is higher than that on the microscale. Lower value of micro-scale friction as compared to macro-scale fiction may be because of less ploughing contribution in the micro-scale measurement.     

表面接枝改性纳米二氧化硅填充聚丙烯的结晶行为

应用差示扫描量热方法研究了纳米二氧化硅 (SiO2 )及其表面接枝改性对聚丙烯 (PP)结晶过程、等温与非等温结晶动力学的影响 ,并研究了上述等温结晶的熔融行为和平衡熔点 .研究发现纳米SiO2 具有明显的异相成核效应 ,能够提高PP的结晶温度、熔融温度、结晶度和结晶速率 ,但降低聚丙烯结晶的完善程度 .粒子的表面接枝处理 ,因改善了粒子与基体的亲和性而有利于粒子成核效应的提高 ,而且此效应尚与粒子的分散相关