Properties of bounded stochastic processes employed in biophysics

Abstract

Realistic stochastic modeling is increasingly requiring the use of bounded noises. In this work, properties and relationships of commonly employed bounded stochastic processes are investigated within a solid mathematical ground. Four families are object of investigation: the Sine-Wiener (SW), the Doering–Cai–Lin (DCL), the Tsallis–Stariolo–Borland (TSB), and the Kessler–Sørensen (KS) families. We address mathematical questions on existence and uniqueness of the processes defined through Stochastic Differential Equations, which often conceal non-obvious behavior, and we explore the behavior of the solutions near the boundaries of the state space. The expression of the time-dependent probability density of the Sine-Wiener noise is provided in closed form, and a close connection with the Doering–Cai–Lin noise is shown. Further relationships among the different families are explored, pathwise and in distribution. Finally, we illustrate an analogy between the Kessler–Sørensen family and Bessel processes, which allows to relate the respective local times at the boundaries.     

DNS of premixed turbulent V-flame: coupling spectral and finite difference methods

To allow for a reliable examination of the interaction between velocity fluctuations, acoustics and combustion, a novel numerical procedure is discussed in which a spectral solution of the Navier–Stokes equations is directly associated to a high-order finite difference fully compressible DNS solver (sixth order PADE). Using this combination of high-order solvers with accurate boundary conditions, simulations have been performed where a turbulent premixed V-shape flame develops in grid turbulence. In the light of the DNS results, a sub-model for premixed turbulent combustion is analyzed. To cite this article: R. Hauguel et al., C. R. Mecanique 333 (2005).     

Synthesis and Characterization of Canola-Based Cholesteryl Ester and Nematic E7 Mixture

Abstract

The fatty acid of Canola Oil, 61% of which is Oleic acid, was extracted. Fourier Transform Infrared Spectrophotometry (FTIR) confirmed the fatty acid extraction. Canola-based Cholesteryl Ester (CANCE) was obtained through esterification. FTIR scans of the CANCE and the fatty acid were compared to verify the complete esterification. The resulting crude product is a yellow wax with some crystals embedded on it. Thin layer chromatography was then performed to determine the appropriate solvent for the column chromatography to purify the crude sample. The purified product was characterized using Optical Polarizing Microscopy and Differential Scanning Calorimetry. Mixtures of the Nematic E7 and CANCE in different ratios were prepared. Transition temperatures of each mixture were determined using differential scanning calorimetry and verified using optical polarizing microscopy.     

Multiscale Approach to the Study of the Electronic Properties of Two Thiophene Curcuminoid Molecules

We studied the electronic and conductance properties of two thiophene–curcuminoid molecules, 2‐thphCCM ( 1 ) and 3‐thphCCM ( 2 ), in which the only structural difference is the position of the sulfur atoms in the thiophene terminal groups. We used electrochemical techniques as well as UV/Vis absorption studies to obtain the values of the HOMO–LUMO band gap energies, showing that molecule 1 has lower values than 2 . Theoretical calculations show the same trend. Self‐assembled monolayers (SAMs) of these molecules were studied by using electrochemistry, showing that the interaction with gold reduces drastically the HOMO–LUMO gap in both molecules to almost the same value. Single‐molecule conductance measurements show that molecule 2 has two different conductance values, whereas molecule 1 exhibits only one. Based on theoretical calculations, we conclude that the lowest conductance value, similar in both molecules, corresponds to a van der Waals interaction between the thiophene ring and the electrodes. The one order of magnitude higher conductance value for molecule 2 corresponds to a coordinate (dative covalent) interaction between the sulfur atoms and the gold electrodes.     

Synthesis of Densely Functionalised 5‐Halogen‐1,3‐oxazin‐2‐ones by Halogen‐Mediated Regioselective Cyclisation of N‐Cbz‐Protected Propargylic Amines: A Combined Experimental and Theoretical Study

A very efficient synthesis of 5‐halogen‐1,3‐oxazin‐2‐ones has been accomplished by the halocyclisation reaction of chiral nonracemic N‐carbobenzyloxy (N‐Cbz)‐protected propargylic amines by using I₂, Br₂ and Cl₂ as electrophile sources. The nature of the halogen influences the reaction time and yield. However, in all cases the reaction is totally regioselective taking place through a 6‐endo‐dig process regardless of the nature of the halogen and of the substituents in the starting material. To rationalise the experimental results, theoretical studies at the B3LYP/6‐311G* level have been performed.     

Structural Diversity from the Transannular Cyclizations of Natural Germacrone and Epoxy Derivatives: A Theoretical–Experimental Study

Treatment of germacrone ( 1 ) with different electrophiles, and of its epoxy derivatives germacrone‐4,5‐epoxide ( 2 ), germacrone‐1,10‐epoxide ( 3 ) and isogermacrone‐4,5‐epoxide ( 4 ) with Brönsted/Lewis acids and Ti^III, gives rise to a great structural diversity. Thus, by using a maximum of two steps, the production of more than 40 compounds corresponding to 14 skeletons is described. Computational calculations rationalizing the structural divergence produced are also described. Finally, since some of the compounds generated are bioactive natural sesquiterpenes, the mechanisms of formation of these substances will provide new insights in their biosynthesis.