Optimal Control and Stabilization for Some Fisher-Like Models

This article concerns optimal control and stabilization for some Fisher-like models with control acting in a subdomain ω. We investigate the optimal position of ω for some optimal harvesting problems. First, we refer to a logistic model with diffusion. We remember the necessary optimality conditions, and then obtain an iterative method to improve the position of ω for the optimal harvesting effort (for a simplified model without logistic term). Next, we consider the null stabilization for a controlled Fisher model and obtain a descent method to improve the position of ω in order to get a faster stabilization to zero. Numerical tests illustrating the effect of the last method are given. We also studied the null stabilization for a prey-predator system and have reduced it to the study of the null stabilizability for a related Fisher model.     

Numerical Locking Problems for Hyperbolic Equations

We investigate a time-dependent model concerning the “locking phenomenon,” namely a model for three-dimensional clamped curved rods. We show that the convergence of the numerical schemes is independent of the discretization parameters and the thickness of the rod. We present corresponding numerical experiments.     

Numerical Locking Problems for Parabolic Equations

We investigate the time evolution of a previous elliptic model. We study a parabolic model concerning the “numerical locking” phenomenon, namely a model for three-dimensional curved rods clamped at the endpoints. We show that the convergence of the numerical schemes is independent of the discretization parameters and the thickness of the rod. We present corresponding numerical experiments and we make a comparison with the results obtained for the hyperbolic model.     

Understanding the participation of quadricyclane as nucleophile in polar [2sigma + 2sigma + 2pi] cycloadditions toward electrophilic pi molecules

The formal [2sigma + 2sigma + 2pi] cycloaddition of quadricyclane, 1, with dimethyl azodicarboxylate, 2, in water has been studied using DFT methods at the B3LYP/6-31G** and MPWB1K/6-31G** levels. In the gas phase, the reaction of 1 with 2 has a two-stage mechanism with a large polar character and an activation barrier of 23.2 kcal/mol. Inclusion of water through a combined discrete-continuum model changes the mechanism to a two-step model where the first nucleophilic attack of 1 to 2 is the rate-limiting step with an activation barrier of 14.7 kcal/mol. Analysis of the electronic structure of the transition state structures points out the large zwitterionic character of these species. A DFT analysis of the global electrophilicity and nucleophilicity of the reagents provides a sound explanation about the participation of 1 as a nucleophile in these cycloadditions. This behavior is reinforced by a further study of the reaction of 1 with 1,1-dicyanoethylene.     

Understanding the reactivity and basicity of zeolites: a periodic DFT study of the disproportionation of N(2)O(4) on alkali-cation-exchanged zeolite Y

The disproportionation of N(2)O(4) into NO(3)(-) and NO(+) on Y zeolites has been studied through periodic DFT calculations to unravel 1) the role of metal cations and the framework oxygen atoms and 2) the relationship between the NO(+) stretching frequency and the basicity of zeolites. We have considered three situations: adsorption on site II cations with and without a cation at site III and adsorption on a site III cation. We observed that cations at sites II and III cooperate to stabilize N(2)O(4) and that the presence of a cation at site III is necessary to allow the disproportionation reaction. The strength of the stabilization is due to the number of stabilizing interactions increasing with the size of the cation and to the Lewis acidity of the alkali cations, which increases as the size of the cations decreases. In the product, NO(3)(-) interacts mainly with the cations and NO(+) with the basic oxygen atoms of the tetrahedral aluminium through its nitrogen atom. As the cation size increases, the NO(3)(-)...cation interaction increases. As a result, the negative charge of the framework is less well screened by the larger cations and the interaction between NO(+) and the basic oxygen atoms becomes stronger. NO(+) appears to be a good probe of zeolite basicity, in agreement with experimental observations.     

Theoretical study of the adsorption of DNA bases on the acidic external surface of montmorillonite

In the present study, DFT periodic plane wave calculations, at the PBE-D level of theory, were carried out to investigate the interaction of DNA nucleobases with acidic montmorillonite. The surface model was considered in its octahedral (Osub) and tetrahedral (Tsub) substituted forms, known to have different acidic properties. The adsorption of adenine, guanine and cytosine was considered in both orthogonal and coplanar orientations with the surface, interacting with the proton via a given heteroatom. In almost all considered cases, adsorption involved the spontaneous proton transfer to the nucleobase, with a more pronounced character in the Osub structures. The binding energy is about 10 kcal mol(-1) larger for Osub than for Tsub complexes mainly due to the larger acidity in Osub surfaces and due to the better stabilization by H-bond contacts between the negatively charged surface and the protonated base. The binding energy of coplanar orientations of the base is observed to be as large as the orthogonal ones due to a balance between electrostatic and dispersion contributions. Finally the binding of guanine and adenine on the acidic surface amounts to 50 kcal mol(-1) while that of cytosine rises to 44 kcal mol(-1).     

Metabolic profiling of mouse cerebrospinal fluid by sheathless CE-MS

The need for sensitive analytical technologies applicable to metabolic profiling of volume-restricted biological samples is high. Here, we demonstrate feasibility of capillary electrophoresis (CE) coupled to electrospray ionization mass spectrometry (MS) with sheathless nano-electrospray interface for non-targeted profiling of ionogenic metabolites in body fluids of experimental animals. A representative mixture of the metabolites and body fluids of mice such as cerebrospinal fluid (CSF), urine and plasma were used as examples of low-volume biological samples for method evaluation. An injection volume of only 9?nL resulted in limits of detection between 0.7 and 12?nM for the metabolite mixture. The method allowed the detection of ～350 molecular features in mouse CSF (an injection volume of ca. 45?nL), while ～400 features were observed in mouse plasma and ～3,500 features in mouse urine (an injection volume of ca. 9?nL). The low-volume body fluid samples were analyzed directly after only 1:1 dilution with water, thereby fully retaining sample integrity, which is of crucial importance for non-targeted metabolic profiling. As little is known about the metabolic composition of mouse CSF, we identified a fraction of the molecular features in mouse CSF using accurate mass information, migration times, MS/MS data, and comparison with authentic standards. We conclude that sheathless CE-MS can be used for sensitive metabolic profiling of volume-restricted biological samples.     

Fine-Tuning the Endcap Chemistry of Acrylated Poly(Ethylene Glycol)-Based Hydrogels for Efficient Burn Wound Exudate Management

Most commercial dressings with moderate to high exudate uptake capacities are mechanically weaker and/or require a secondary dressing. The current research article focuses on the development of hydrogel-based wound dressings combining mechanical strength with high exudate absorption capacities using acrylate-endcapped urethane-based precursors (AUPs). AUPs with varying poly(ethylene glycol) backbone molar masses (10 and 20 kg mol⁻¹) and endcap chemistries are successfully synthesized in toluene, subsequently processed into UV-cured hydrogel sheets and are benchmarked against several commercial wound dressings (Hydrosorb, Kaltostat, and Mepilex Ag). The AUP materials show high gel fractions (>90%) together with strong swelling degrees in water, phosphate buffered saline and simulated wound fluid (12.7–19.6 g g⁻¹), as well as tunable mechanical properties (e.g., Young's modulus: 0.026–0.061 MPa). The AUPs have significantly (p < 0.05) higher swelling degrees than the tested commercial dressings, while also being mechanically resistant. The elasticity of the synthesized materials leads to an increased resistance against fatigue. The di- and hexa-acrylated AUPs show excellent in vitro biocompatibility against human foreskin fibroblasts, as evidenced by indirect MTS assays and live/dead cell assays. In conclusion, the processed AUP materials demonstrate high potential for wound healing application and can even compete with commercially available dressings.