Mathematical study of a bacteria–fish model with level of infection structure

In this paper, we propose a mathematical model to study a bacteria–fish system, based upon the interactions between Clostridium botulinum and tilapia, Oerochromis mossambicus. The fish population is divided into susceptible and infected, and the infected fish population is considered structured by the level of infection. The model is thus a system with the infected fish equation being an evolution equation, while those corresponding to the susceptible fish and bacteria in water are ordinary differential equations. The model is firstly transformed into a system with distributed delay for susceptible fish and bacteria and, further, under some assumptions, into a system with discrete delay. The study of this system gives us some results concerning the existence, uniqueness, positivity and boundedness of solutions; we also discuss the existence and stability of its equilibrium points, including conditions for the appearance of Hopf bifurcation. The theoretical results are illustrated by some numerical simulations.     

Radical/Ion pair formation in the electrochemical reduction of arene sulfenyl chlorides

Important aspects of the electrochemical reduction of a series of substituted arene sulfenyl chlorides are investigated. A striking change is observed in the reductive cleavage mechanism as a function of the substituent on the aryl ring of the arene sulfenyl chloride. With p-substituted phenyl chlorides a "sticky" dissociative ET mechanism takes place where a concerted ET mechanism leads to the formation of a radical/anion cluster before decomposition. With o-nitropheyl sulfenyl substituted chlorides a stepwise mechanism is observed where through space S...O interactions play an important role stabilizing both the neutral molecules and their reduced forms. Disulfides are generated through a nucleophilic reaction of the two-electron reduction produced anion (arenethiolate) on the parent molecule. The dissociative electron transfer theory, as well as its extension to the case of strong in-cage interactions between the produced fragments, along with the gas phase chemical quantum calculations results helped rationalize both the observed change in the ET mechanism and the occurrence of the "sticky dissociative" ET mechanism. The radical/anion pair interactions have been determined both in solution as well as in gas phase. This study shows that despite the low magnitude of in-cage interactions in acetonitrile as compared to in the gas phase, their existence strongly affects the kinetics of the involved reactions. It also shows that, as expected, these interactions are reinforced by the existence of strong electron-withdrawing substituents.     

Coating of carbon nanotubes on flexible substrate and its adhesion study

The primary goal of this project was to develop a flexible transparent conductor with 100 Ω/sq and 90% transmittance in the wavelength range of 400-700 nm on a flexible substrate. The best result achieved so far was 110 Ω/sq at 88% transmittance using purified single-walled carbon nanotubes (SWNTs) coated on a polyethylene naphthalate (PEN) substrate. The secondary goal was to simplify the overall coating procedure; we successfully reduced the process from five (prior art method) to three steps utilizing a sonication method. We also found that the use of metallic SWNTs significantly improved the conductivity and transmittance compared with the use of mixed SWNTs, i.e., unseparated SWNTs. Furthermore, a possible adhesion mechanism between SWNTs and the surface of PEN was studied; we concluded that a π-π stacking effect and a hydrophobic interaction are the major contributing factors for SWNTs to adhere to the surface of the substrate.     

First principle calculation of accurate native defect levels in CaF<Subscript>2</Subscript>

We report on the first principle density functional calculation of the charge transition levels of native defects (vacancies and interstitials) in CaF₂ structure. The transition level was defined as the Fermi level where two charge states of given defect have the same formation energy. The common error in the band gap inherited to semiclocal density functional has been accounted for by incorporating the hybrid density functional method, leading to correct placement of the transition levels within the band gap. The band gap size from hybrid calculation has been validated using the full potential, Linearized Augmented Planewave method with the Modified-Becke-Johnson exchange potential. Prior to level calculations, we ensured that an agreement between the formation energies from small (95–97 atoms) and large (323–325 atoms) supercells was achieved after applying the Makov-Payne correction method. Our calculated transition level for the anion vacancy was 2.97 eV below the conduction band, agreeing with the experimental optical absorption band at 3.3 eV associated with the electron transition from the ground state F-center to the conduction band in CaF₂.     

Multi-shock structure of roll wavesStructure multi-chocs d'ondes à rouleaux

The special class of periodic travelling waves which is known as roll waves is investigated for nonhomogeneous hyperbolic equations of gas dynamics type. In this Note these equations are applied to shallow water flows in inclined open channels, but the results obtained are more general and far-reaching. The necessary conditions for the existence of a roll wave are derived. It is shown that for a nonconvex pressure term, multi-shock configurations of roll waves of finite amplitude exist. A new type of periodic travelling wave, which corresponds to the slug flow regime in two-layer flows, is found. To cite this article: A. Boudlal, V.Yu. Liapidevskii, C. R. Mecanique 332 (2004).     

Decreased Water Mobility Contributes To Increased α-Synuclein Aggregation**

The solvation shell is essential for the folding and function of proteins, but how it contributes to protein misfolding and aggregation has still to be elucidated. We show that the mobility of solvation shell H₂O molecules influences the aggregation rate of the amyloid protein α-synuclein (αSyn), a protein associated with Parkinson's disease. When the mobility of H₂O within the solvation shell is reduced by the presence of NaCl, αSyn aggregation rate increases. Conversely, in the presence CsI the mobility of the solvation shell is increased and αSyn aggregation is reduced. Changing the solvent from H₂O to D₂O leads to increased aggregation rates, indicating a solvent driven effect. We show the increased aggregation rate is not directly due to a change in the structural conformations of αSyn, it is also influenced by a reduction in both the H₂O mobility and αSyn mobility. We propose that reduced mobility of αSyn contributes to increased aggregation by promoting intermolecular interactions.     

Numerical approximation of the optimal control of a population dynamics model

In this paper, we present a numerical approach to an inverse problem of a population dynamics model. We propose a numerical approximation of the optimal control for obtaining the desired observation state using the augmented Lagrangian method. Moreover, the existence and uniqueness of the numerical solutions are mathematically investigated in this work. Finally, we present some numerical experiments to illustrate our theoretical results.     

Rapid Sonosynthesis of N‐Doped Nano TiO2 on Wool Fabric at Low Temperature: Introducing Self‐cleaning,Hydrophilicity, Antibacterial/Antifungal Properties with low Alkali Solubility,Yellowness and Cytotoxicity

Nano nitrogen‐doped titanium dioxide was rapidly prepared by hydrolysis of titanium isopropoxide at 75–80°C using in situ sonochemical synthesis by introducing ammonia. Various concentrations of titanium isopropoxide were examined to deposit nano nitrogen‐doped titanium dioxide through impregnation of the wool fabric in ultrasound bath followed by curing. The antibacterial/antifungal activities of wool samples were assessed against two common pathogenic bacteria including Escherichia coli and Staphylococcus aureus and the diploid fungus Candida albicans. The sonotreated wool fabrics indicated no adverse effects on human dermal fibroblasts. The presence of nanoparticles on the sonotreated wool fabrics were confirmed by FE‐SEM images and EDS patterns and X‐ray mapping and the crystalline size of nanoparticles were estimated through XRD results. The role of both pH and precursor concentration on the various properties of the fabric was investigated and the optimized conditions introduced using response surface methodology.     

A colorimetric sensor array for detection and discrimination of biothiols based on aggregation of gold nanoparticles

Developments of sensitive, rapid, and cheap systems for identification of a wide range of biomolecules have been recognized as a critical need in the biology field. Here, we introduce a simple colorimetric sensor array for detection of biological thiols, based on aggregation of three types of surface engineered gold nanoparticles (AuNPs). The low-molecular-weight biological thiols show high affinity to the surface of AuNPs; this causes replacement of AuNPs’ shells with thiol containing target molecules leading to the aggregation of the AuNPs through intermolecular electrostatic interaction or hydrogen-bonding. As a result of the predetermined aggregation, color and UV–vis spectra of AuNPs are changed. We employed the digital mapping approach to analyze the spectral variations with statistical and chemometric methods, including hierarchical cluster analysis (HCA) and principal component analysis (PCA). The proposed array could successfully differentiate biological molecules (e.g., cysteine, glutathione and glutathione disulfide) from other potential interferences such as amino acids in the concentration range of 10–800 μmol L⁻¹.     

Spectroscopic, thermal and structural studies of a new mercury(II) complex of 4′-(4-pyridyl)-2,2′:6′,2″-terpyridine (pyterpy) ligand, [Hg (hpyterpy)(SCN)2]2(MeSO4)2

A new mercury(II) complex [Hg(Hpyterpy)(SCN)₂]₂(MeSO₄)₂ was prepared from the reaction of 4′-(4-pyridyl)-2,2′:6′,2″- terpyridine (pyterpy), as a polypyridyl ligand, with mercury(II) thiocyanate. The compound was characterized by elemental analysis, IR, ¹H NMR and ¹³C NMR spectroscopy and its structure was determined by X-ray single-crystal diffraction. The thermal stability of compound was studied by thermogravimetric (TG) and differential thermal analyses (DTA).