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.     

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.     

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.     

BiGlobal stability analysis in curvilinear coordinates of massively separated lifting bodies

A methodology based on spectral collocation numerical methods for global flow stability analysis of incompressible external flows is presented. A potential shortcoming of spectral methods, namely the handling of the complex geometries encountered in global stability analysis, has been dealt with successfully in past works by the development of spectral-element methods on unstructured meshes. The present contribution shows that a certain degree of regularity of the geometry may be exploited in order to build a global stability analysis approach based on a regular spectral rectangular grid in curvilinear coordinates and conformal mappings. The derivation of the stability linear operator in curvilinear coordinates is presented along with the discretisation method. Unlike common practice to the solution of the same problem, the matrix discretising the eigenvalue problem is formed and stored. Subspace iteration and massive parallelisation are used in order to recover a wide window of its leading Ritz system. The method is applied to two external flows, both of which are lifting bodies with separation occurring just downstream of the leading edge. Specifically the flow configurations are a NACA 0015 airfoil, and an ellipse of aspect ratio 8 chosen to closely approximate the geometry of the airfoil. Both flow configurations are at an angle of attack of 18° with a Reynolds number based on the chord length of 200. The results of the stability analysis for both geometries are presented and illustrate analogous features.     

High-affinity tags fused to s-layer proteins probed by atomic force microscopy

Two-dimensional, crystalline bacterial cell surface layers, termed S-layers, are one of the most commonly observed cell surface structures of prokaryotic organisms. In the present study, genetically modified S-layer protein SbpA of Bacillus sphaericus CCM 2177 carrying the short affinity peptide Strep-tag I or Strep-tag II at the C terminus was used to generate a 2D crystalline monomolecular protein lattice on a silicon surface. Because of the genetic modification, the 2D crystals were addressable via Strep-tag through streptavidin molecules. Atomic force microscopy (AFM) was used to investigate the topography of the single-molecules array and the functionality of the fused Strep-tags. In high-resolution imaging under near-physiological conditions, structural details such as protein alignment and spacing were resolved. By applying molecular recognition force microscopy, the Strep-tag moieties were proven to be fully functional and accessible. For this purpose, streptavidin molecules were tethered to AFM tips via approximately 8-nm-long flexible polyethylene glycol (PEG) linkers. These functionalized tips showed specific interactions with 2D protein crystals containing either the Strep-tag I or Strep-tag II, with similar energetic and kinetic behavior in both cases.     

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.     

Symmetric Stable Laws and Stable-Like Jump-Diffusions

Asymptotic expansions are obtained for finite-dimensional symmetricstable distributions. They are used to prove the existence ofcontinuous transition probability densities of stable and stable-likejump-diffusions, and to construct local multiplicative asymptoticsandglobal two-sided estimates for these densities. As a consequence,the distribution of the first passage times for stable jump-diffusionsis estimated and the integral test for the limsup behaviourof their sample paths as t 0 is provided. 1991 MathematicsSubject Classification: 60E07, 60G17, 60J35, 47D07.     

A Note on the Long Time Asymptotics of the Brownian Motion with Application to the Theory of Quantum Measurement

Estimates of growth of the standard d-dimensional Brownian motion W(t) and its integral V(t) = ^t ₀ W (s) ds are obtained, as t , and an application is discussed to the long time asymptotics of the solutions of the nonlinear stochastic equation of the quantum filtering theory.