The Distribution of the Free Path Lengths in the Periodic Two-Dimensional Lorentz Gas in the Small-Scatterer Limit

We study the free path length and the geometric free path length in the model of the periodic two-dimensional Lorentz gas (Sinai billiard). We give a complete and rigorous proof for the existence of their distributions in the small-scatterer limit and explicitly compute them. As a corollary one gets a complete proof for the existence of the constant term in the asymptotic formula of the KS entropy of the billiard map in this model, as conjectured by P. Dahlqvist.In memory of Walter Philipp     

On the Caffarelli‐Kohn‐Nirenberg inequalities: Sharp constants,existence (and nonexistence), and symmetry of extremal functions

Consider the following inequalities due to Caffarelli, Kohn, and Nirenberg [6] where, for N ≥ 3, −∞ < a < (N − 2)/2, a ≤ b ≤ a + 1, and p = 2N/(N − 2 + 2(b − a)). We shall answer some fundamental questions concerning these inequalities such as the best embedding constants, the existence and nonexistence of extremal functions, and their qualitative properties. While the case a ≥ 0 has been studied extensively and a complete solution is known, little has been known for the case a < 0. Our results for the case a < 0 reveal some new phenomena which are in striking contrast with those for the case a ≥ 0. Results for N = 1 and N = 2 are also given. © 2001 John Wiley & Sons, Inc.     

Stochastic simulations based on mixed finite elements for solute transport in groundwater

An accurate mixed finite element method to solve both flow and transport is developed for stochastic simulations of transport in saturated aquifers characterized by random log-hydraulic conductivity fields. The main advantage of the mixed finite element is that it is local mass conservative. Unlike in stochastic finite element methods, this approach yields concentration fields and concentration moments for samples of the random field. In this way, it will be possible to analyze the behavior of different ensemble average observables of the transport process as well as the behavior of their fluctuations. Results of the stochastic simulations described here can be used to assess the reliability for real cases of the ensemble average quantities provided by stochastic modeling of transport in groundwater. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical analyis of turbulent flow in a Coanda ejector

The task of this study is to investigate the influence of various geometric parameters and pressure ratios on the Coanda ejector performance. For numerically investigations we use an implicit formulation of the compressible Reynolds-average Navier-Stokes equations (RANS) for axisymmetric flow with a shear stress transport k − ω (SST model) turbulence model. The numerically results was obtained for a total pressure range 1-5 Bars, imposed at the reservoir inlet. The effect of various factors, such as, the pressure ratio, primary nozzle and ejector configurations on the system performance has been evaluated based on defined performance parameters. The numerical results have been compared with theoretical and experimental results for a given Coanda ejector configuration. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Supramolecular Structure - A Key Parameter for Cellulose Biodegradation

Summary: Three different cellulosic substrata, like microcrystalline cellulose, cotton cellulose and spruce dissolving pulp, were chosen for biodegradation. The kinetics of the enzymatic hydrolysis of these celluloses by Trichoderma reesei, has been investigated. The experiments proved the fact that both the morphological structure and the crystalline one are crucial to the process and the ratio of the reactions. In addition, in order to obtain the most accessible cellulose substratum it was studied the biodegradation of cellulose allomorphs of spruce dissolving pulp. The insoluble cellulose fraction remaining after enzymatic hydrolysis was examined by X-ray diffraction method and it was established the degree of crystallinity and the average crystallite size. The enzymatic degradation is also proved by the decrease in the degree of polymerization of hydrolyzed samples.     

Novel nanocomposite membranes from cellulose acetate and clay‐silica nanowires

In this study, a new class of heterogeneous membranes based on cellulose acetate (CA) polymer and a complex filler clay‐silica nanowires (SiO₂NWs) was investigated for potential biomedical applications. SiO₂NWs were synthesized using natural clay through a facile sol–gel method and were dispersed in the polymer solution by sonication in the 1.25, 2.5, and 5% weight ratio to the CA acetate polymer. Membranes were subsequently prepared via phase inversion by precipitation of the CA polymer in water. The pristine CA membrane and SiO₂NWs based nanocomposites membranes were characterized using different characterization techniques. The presence of the SiO₂NWs in the CA membrane was found to significantly enhance the protein retention, water wettability and thermal as well as mechanical properties in comparison to the pristine CA membrane. Water flows studies at different temperatures and the retention of bovine serum albumin have been studied and the nanocomposite membranes were found to exhibit superior performances compared with the pristine CA membranes. SiO₂NWs‐CA membranes showed a much higher stability to the water temperature change during separation than CA membranes. Morphological changes clearly revealed that the composite membrane were much more compact than the pristine CA membranes. The rabbit dermal fibroblasts cell viability in cultures after 72 hr of incubation was found to be greater than 80%. These newly synthesized composite membranes exhibit a high potential to be used for various medical applications because of their non‐cytotoxic characteristics. Copyright © 2016 John Wiley & Sons, Ltd.     

Validation of protein structural models using THz spectroscopy: a promising approach to solve three-dimensional structures

Terahertz (THz) spectroscopy is a promising technique for the study of protein structure and internal flexibility. Here, we used THz spectroscopy and molecular modeling for bovine serum albumin (BSA) structure investigation. BSA molecule was built using homology modeling methods and 30 different more relaxed models were obtained by molecular dynamics simulations of the hydrated protein. As the experimental and simulated THz spectra are linear, we compared them by comparing the slopes of the lines that fit them. Six BSA structures had slope values in the range given by the slope of the experimental spectrum $\pm $  0.2 and a total of sixteen BSA structures had slope values in the 0.6 interval near the experimental slope value. BSA average structures were calculated over the six and the sixteen identified BSA molecules. Based on the similarity with the crystal structure of BSA, we validated the average structure calculated over the sixteen BSA conformations. The comparison with the crystal structure showed that the structure validated using THz spectroscopy is a coarse model of BSA, as its root-mean-square deviation relative to the crystal structure is 1.9 Å. The regions from our model that present the highest deviation from the crystal structure are exterior loops. The results presented here show that using THz spectroscopy and molecular modeling is a promising approach to determine the structure of proteins.     

Linearization of the MS response function: case study for metformin assay in plasma samples for bioequivalence purposes

Calibration data of LC-MS/MS rarely fit the pure least square regression model, especially for large concentration intervals. The response function of the MS instrument is corrected by weighted regression models or logarithms. The choice of a response linearization method is based on results produced through back-interpolation of experimental data and/or evaluation of correlation coefficients. Two bioequivalence studies carried out for pharmaceutical formulations containing metformin gave us the opportunity to appreciate the impact of the MS response linearization method (logarithm and 1/x weighted linear regression) on method quality characteristics. The sample preparation was based on protein precipitation with acetonitrile. Chromatographic separation was achieved on a Zorbax CN column (mobile phase acetonitrile and aqueous 10 m m ammonium acetate solution, pH 3.5). Tandem MS detection was performed on a triple quadrupole spectrometer equipped with an electrospray source, operated under positive-ion mode. The method was validated and used for evaluation of the bioequivalence of formulations containing 500 and 1000 mg metformin. The 500 mg metformin study used logarithms for linearization of the detector response, while the 1000 mg metformin study was based on 1/x linear weighted regression. Data resulting from validations and studies completion were compared with evaluate the impact of the response linearization on the method quality characteristics.