A mathematical analysis of a fish school model

A model proposed in the literature for fish schools of relatively large size is studied for mathematical and qualitative properties. Existence, uniqueness and positivity of solutions are established and bifurcation properties relative to diffusion and alignment parameters are studied.     

Formation of Long,Multicenter π‐[TCNE]22− Dimers in Solution: Solvation and Stability Assessed through Molecular Dynamics Simulations

Purely organic radical ions dimerize in solution at low temperature, forming long, multicenter bonds, despite the metastability of the isolated dimers. Here, we present the first computational study of these π‐dimers in solution, with explicit consideration of solvent molecules and finite temperature effects. By means of force‐field and ab initio molecular dynamics and free energy simulations, the structure and stability of π‐[TCNE]₂^2? (TCNE=tetracyanoethylene) dimers in dichloromethane have been evaluated. Although the dimers dissociate at room temperature, they are stable at 175 K and their structure is similar to the one in the solid state, with a cofacial arrangement of the radicals at an interplanar separation of approximately 3.0 Å. The π‐[TCNE]₂^2? dimers form dissociated ion pairs with the NBu₄⁺ counterions, and their first solvation shell comprises approximately 20 CH₂Cl₂ molecules. Among them, the eight molecules distributed along the equatorial plane of the dimer play a key role in stabilizing the dimer through bridging C?H???N contacts. The calculated free energy of dimerization of TCNE ^{. ?} in solution at 175 K is ?5.5 kcal mol^?1. These results provide the first quantitative model describing the pairing of radical ions in solution, and demonstrate the key role of solvation forces on the dimerization process.     

S=1/2 One‐Dimensional Random‐Exchange Ferromagnetic Zigzag Ladder,Which Exhibits Competing Interactions in a Critical Regime

The synthesis, crystal structure, and magnetic properties (from a combined experimental and First‐Principles Bottom‐Up theoretical study) of the new compound catena‐dichloro(2‐Cl‐3Mpy)copper(II), 1 , [2‐Cl‐3Mpy=2‐chloro‐3‐methylpyridine] are described and rationalized. Crystals of 1 present well isolated magnetic 1D chains (no 3D order was experimentally observed down to 1.8 K) and magnetic frustration stemming from competing ferromagnetic nearest‐neighbor (J_NN) interactions and antiferromagnetic next‐nearest neighbor (J_NNN) interactions, in which α=J_NNN/J_NN <?0.25. These magnetic interactions give rise to a unique magnetic topology: a two‐leg zigzag ladder composed of edge‐sharing up‐down triangles with antiferromagnetic interactions along the rails and ferromagnetic interactions along the zigzag chain that connects the rails. Crystals of 1 also present a random distribution of the 2‐Cl‐3Mpy groups, which are arranged in two different orientations, each with a 50 % occupancy. This translates into a random static structural disorder within each chain by virtue of which the value of the J_NN magnetic interactions can randomly take one of the following three values: 53, 36, and 16 cm^?1. The structural disorder does not affect the J_NNN value, which in all cases is approximately ?9 cm^?1. A proper statistical treatment of this disorder provides a computed magnetic susceptibility curve that reproduces the main features of the experimental data.     

Nonlinear mathematical model of pulsed-therapy of heterogeneous tumors

In this paper, we deal with a nonlinear impulsive differential equations modelling the chemotherapy of a heterogeneous tumor. We consider the case of several drugs with instantaneous effects. We take into account the interactions between sensitive cells and drug resistant cells. We are interested in the stability of the disease. We also study the loss of stability and the bifurcation of nontrivial solutions.     

Anodic behaviour of 2-mercaptoethanol at a mercury electrode

The anodic processes which occur at the mercury electrode in 2-mercaptoethanol solutions are studied by various polarographic techniques (d.c., a.c. and differential pulse), controlled-potential coulometry, cyclic voltammetry and differential capacity curves. Two steps are distinguished in the process: a one-electron charge transfer and a dismutation step leading to the formation of a mercury(II) mercaptide. The final product is isolated and analyzed. Differential-pulse polarography can be used to determine ?10^?4 M 2-mercaptoethanol with a limit of M.     

Estimates for periodic solutions of differential equations

A class of infinite delay equations which are per- turbations of finitely delayed equations is considered. Asymptotic estimates are obtained for the solutions from which we get the existence of periodic solutions. We review a few technics for fixed point theorems     

Polypropylene nanofiber sheets prepared by CO2 laser supersonic multi-drawing

Isotactic polypropylene (iPP) nanofiber sheets were fabricated by winding nanofibers onto a spool. The nanofibers were prepared by irradiation of the iPP fibers with a carbon dioxide laser while drawing them at supersonic velocities. A supersonic jet was generated by blowing air into a vacuum chamber through the fiber injection orifice. The vacuum chamber used to produce nanosheets has seven fiber injection orifices and a spool to collect the nanofibers. A 17 × 18 cm², 17 μm-thick rectangular nanofiber sheet was obtained by collecting nanofibers for 10 min. The nanosheet is composed of nanofibers with an average diameter of 350 nm. This technique is a novel method for the production of nanosheets without using a solvent, and therefore, without the need to remove a second component.     

Semigroup Properties and the Crandall Liggett Approximation for a Class of Differential Equations with State-Dependent Delays

We present an approach for the resolution of a class of differential equations with state-dependent delays by the theory of strongly continuous nonlinear semigroups. We show that this class determines a strongly continuous semigroup in a closed subset of C^0, 1. We characterize the infinitesimal generator of this semigroup through its domain. Finally, an approximation of the Crandall-Liggett type for the semigroup is obtained in a dense subset of (C, ‖·‖_∞). As far as we know this approach is new in the context of state-dependent delay equations while it is classical in the case of constant delay differential equations.     

Estimation of the Rate of Convergence of Semigroups to an Asynchronous Equilibrium

Perturbations leading to an estimate of the rate of convergence to an asynchronous equilibrium of general semigroups with boundary conditions are given. The particular case of translation semigroups is examined. The results obtained are applied to a demographic model.