Estimates Uniform in Time for the Transition Probability of Diffusions with Small Drift and for Stochastically Perturbed Newton Equations

An estimate uniform in time for the transition probability of diffusion processes with small drift is given. This also covers the case of a degenerate diffusion describing a stochastic perturbation of a particle moving according to the Newton's law. Moreover the random wave operator for such a particle is described and the analogue of asymptotic completeness is proven, the latter in the case of a sufficiently small drift.     

The L��vy�CKhintchine type operators with variable Lipschitz continuous coefficients generate linear or nonlinear Markov processes and semigroups

Ito??s construction of Markovian solutions to stochastic equations driven by a Lévy noise is extended to nonlinear distribution dependent integrands aiming at the effective construction of linear and nonlinear Markov semigroups and the corresponding processes with a given pseudo-differential generator. It is shown that a conditionally positive integro-differential operator (of the Lévy?CKhintchine type) with variable coefficients (diffusion, drift and Lévy measure) depending Lipschitz continuously on its parameters (position and/or its distribution) generates a linear or nonlinear Markov semigroup, where the measures are metricized by the Wasserstein?CKantorovich metrics. This is a non-trivial but natural extension to general Markov processes of a long known fact for ordinary diffusions.     

The central limit theorem for the Smoluchovski coagulation model

The general model of coagulation is considered. For basic classes of unbounded coagulation kernels the central limit theorem (CLT) is obtained for the fluctuations around the dynamic law of large numbers (LLN) described by the Smoluchovski equation. A rather precise rate of convergence is given both for LLN and CLT.     

Nonlinear Markov Semigroups and Interacting Lévy Type Processes

Semigroups of positivity preserving linear operators on measures of a measurable space X describe the evolutions of probability distributions of Markov processes on X. Their dual semigroups of positivity preserving linear operators on the space of measurable bounded functions B(X) on X describe the evolutions of averages over the trajectories of these Markov processes. In this paper we introduce and study the general class of semigroups of non-linear positivity preserving transformations on measures that is non-linear Markov or Feller semigroups. An explicit structure of generators of such groups is given in case when X is the Euclidean space R ^d (or more generally, a manifold) showing how these semigroups arise from the general kinetic equations of statistical mechanics and evolutionary biology that describe the dynamic law of large numbers for Markov models of interacting particles. Well posedness results for these equations are given together with applications to interacting particles: dynamic law of large numbers and central limit theorem, the latter being new already for the standard coagulation-fragmentation models.     

Non-PGM Electrocatalysts for PEM Fuel Cells: A DFT Study on the Effects of Fluorination of FeNx-Doped and N-Doped Carbon Catalysts

Fluorination is considered as a means of reducing the degradation of Fe/N/C, a highly active FeN_x-doped disorganized carbon catalyst for the oxygen reduction reaction (ORR) in PEM fuel cells. Our recent experiments have, however, revealed that fluorination poisons the FeN_x moiety of the Fe/N/C catalytic site, considerably reducing the activity of the resulting catalyst to that of carbon only doped with nitrogen. Using the density functional theory (DFT), we clarify in this work the mechanisms by which fluorine interacts with the catalyst. We studied 10 possible FeN_x site configurations as well as 2 metal-free sites in the absence or presence of fluorine molecules and atoms. When the FeN_x moiety is located on a single graphene layer accessible on both sides, we found that fluorine binds strongly to Fe but that two F atoms, one on each side of the FeN_x plane, are necessary to completely inhibit the catalytic activity of the FeN_x sites. When considering the more realistic model of a stack of graphene layers, only one F atom is needed to poison the FeN_x moiety on the top layer since ORR hardly takes place between carbon layers. We also found that metal-free catalytic N-sites are immune to poisoning by fluorination, in accordance with our experiments. Finally, we explain how most of the catalytic activity can be recovered by heating to 900 °C after fluorination. This research helps to clarify the role of metallic sites compared to non-metallic ones upon the fluorination of FeN_x-doped disorganized carbon catalysts.     

Influence of cyclohexane vapor on stick-slip friction between mica surfaces

Stick-slip friction between mica surfaces under cyclohexane vapor has been investigated with the Surface Force Apparatus. The dynamic shear stress decreased from 60 to 10 MPa with increasing relative vapor pressure (rvp) from 5% to 50%. Between a rvp of 50% and 80%, the shear stress remained at approximately 10 MPa, with a slight decrease on increasing the rvp. At a rvp greater than 80%, the values of shear stress were below 5 MPa. The stick-slip behavior was observed in the rvp range of 20% to saturation. When the rvp reached 20%, stick-slip appeared but faded out with sliding time. At a rvp greater than 50%, the stick-slip pattern was stable without fading. By taking into account the size of the meniscus formed by capillary condensation of the liquid around the contact area and the Laplace pressure, the dependence of shear stress and the stick-slip modulation on rvp suggests that the origin of the stick-slip observed in cyclohexane vapor is as follows: At a rvp greater than 50%, where stable sick-slip is observed, the stick-slip caused by the cyclohexane layering in the contact area is of essentially the same origin as that observed with mica surfaces sliding in bulk cyclohexane liquid. As with the bulk liquid experiment, decreasing the layer thickness (or the number of the layers) between the surfaces increases the shear stress at the onset of slip. In the vapor phase experiments, the stick-slip is enhanced by the increase of the negative Laplace pressure in the capillary condensed liquid, thereby forcing the surfaces toward each other more strongly with decreasing rvp. In the rvp range between 20% and 50%, where the fading stick-slip is observed, the condensate liquid seeps into the contact area under the influence of the applied tangential force and thus triggers the slip motion. Due to the small condensation volume, the liquid condensed around the contact area is exhausted in the process of repeating stick-slip. As the slip length is limited to the meniscus size, the stick-slip amplitude becomes smaller, and eventually the surfaces start sliding without stick-slip.     

Optimum blank design for sheet metal forming based on the interaction of high- and low-fidelity FE models

This paper deals with an optimization methodology for the design of the sheet-metal-forming process. In this study, a new design optimization system is developed which employs an iterative optimization technique and numerical simulation of a sheet-metal-forming process. The main feature of this new optimization method is that it is based on the interaction of high- and low-fidelity simulation models in order to reduce overall computing time. In the iterative optimization procedure, only the corrected low-fidelity model is used. The high-fidelity model, which requires much longer computing time, is used only for the correction of the low-fidelity analysis and validation of the final solution. To demonstrate the developed optimization method on a practical application, it is applied to the optimum blank design for deep-drawing process of a rectangular box. In deep-drawing, the flange of the drawn product is usually trimmed off to obtain the desired product geometry, and the trimmed material is wasted. Therefore, the formulation of the optimization problem is to determine the optimum initial blank geometry which minimizes the amount of the trimmed material, that is, the waste of material. It is confirmed that the blank design was optimized successfully in remarkably short computing time by the developed optimization method.     

A comparison of the enzymatic properties of three recombinant isoforms of thrombolytic and antibacterial protein—Destabilase-Lysozyme from medicinal leech

Destabilase-Lysozyme (mlDL) is a multifunctional i-type enzyme that has been found in the secretions from the salivary glands of medicinal leeches. mlDL has been shown to exhibit isopeptidase, muramidase and antibacterial activity. This enzyme attracts interest because it expresses thrombolytic activity through isopeptidolysis of the ε-(γ-Glu)-Lys bonds that cross-link polypeptide chains in stabilised fibrin. To date, three isoforms of mlDL have been identified. The enzymatic properties of pure mlDL isoforms have not yet been described because only destabilase complexes containing other proteins could be isolated from the salivary gland secretion and because low product yield from the generation of recombinant proteins has made comprehensive testing difficult. In the present study, we optimised the procedures related to the expression, isolation and purification of active mlDL isoforms (mlDL-Ds1, mlDL-Ds2, mlDL-Ds3) using an Escherichia coli expression system, and we detected and compared their muramidase, lytic, isopeptidase and antimicrobial activities. After optimisation, the product yield was 30 mg per litre of culture. The data obtained in our study led to the suggestion that the recombinant mlDL isoforms isolated from inclusion bodies form stable oligomeric complexes. Analyses of the tested activities revealed that all isoforms exhibited almost identical patterns of pH and ionic strength effects on the activities. We determined that mlDL-Ds1, 2, 3 possessed non-enzymatic antibacterial activity independent of their muramidase activity. For the first time, we demonstrated the fibrinolytic activity of the recombinant mlDL and showed that only intact proteins possessed this activity, suggesting their enzymatic nature. The recombinant Destabilase-Lysozyme isoforms obtained in our study may be considered potential thrombolytic agents that act through a mechanism different from that of common thrombolytics.