Twist-grain boundary phase induced by Au nanoparticles in a chiral liquid crystal host

We report on the stabilisation of the liquid-crystalline, twist-grain boundary A (TGB_A) phase in mixtures of a chiral liquid crystal and surface-functionalised spherical Au nanoparticles (NPs) of 10 nm diameter. The results, obtained by calorimetric, optical, small-angle X-ray and plasmon resonance measurements, demonstrate that a TGB_A phase, which is metastable for the pure liquid crystal host, can be effectively stabilised for a 3 K range in the presence of NPs. Moreover, the role of NPs size on the TGB_A stabilisation is briefly discussed.     

Dissipation of the herbicide active ingredient glyphosate in natural water samples in the presence of biofilms

Dissipation of the herbicide active ingredient glyphosate was investigated in natural waters. To assess combined effects, glyphosate was applied in its pure form (glyphosate isopropylammonium salt) and in preparation Roundup Classic® formulated with polyethoxylated tallowamines (POEA). Standing and running surface water samples originated from Lake Balaton and River Danube between early May and mid-June of 2015. The kinetics of dissipation of glyphosate, measured by high-performance liquid chromatography combined with UV-VIS absorbance detection or tandem mass spectrometry, was investigated under laboratory conditions in aquaria with or without the presence of biofilms. The quantity and the biofilm structure of algal biomass were determined by in vivo fluorimetry and scanning electron microscopy. The presence of POEA affected the dissipation of glyphosate, and dissipation profiles differed in the investigated natural waters. Significantly higher initial concentrations of glyphosate were measured in River Danube for treatment with formulated glyphosate (101.4 ± 6.2 µg L^?1), than with glyphosate alone (79.9 ± 6.6 µg L^?1), and dissipation to a residual level (57.6 ± 1.4 µg L^?1) consequently took longer (approximately by 1 day). Degradation of glyphosate from the initial level (91.24 ± 5.9 µg L^?1) in Lake Balaton was not detected. Phytotoxic effects of glyphosate, particularly if enhanced by a formulant on algal biomass, were observed. Thus, 5–18% and 11–33% of algal biomass reduction was determined in River Danube upon treatments with glyphosate and Roundup Classic®, respectively. Corresponding biomass decreases in Lake Balaton were 1.3–13% and 9–14%, respectively, accompanied by an overall decay in the algal biofilms. In River Danube, treatments resulted in the occurrence of 1.4–5.8% of green algae in the algal biomass in 28 days, while green algae were not detected in the untreated control. The results indicate that glyphosate is capable of modifying the structure of the algal community and to induce increased secretion of extracellular polymeric substances matrix in the biofilms assessed.     

Entropy-stable and entropy-dissipative approximations of a fourth-order quantum diffusion equation

Structure-preserving numerical schemes for a nonlinear parabolic fourth-order equation, modeling the electron transport in quantum semiconductors, with periodic boundary conditions are analyzed. First, a two-step backward differentiation formula (BDF) semi-discretization in time is investigated. The scheme preserves the nonnegativity of the solution, is entropy stable and dissipates a modified entropy functional. The existence of a weak semi-discrete solution and, in a particular case, its temporal second-order convergence to the continuous solution is proved. The proofs employ an algebraic relation which implies the G-stability of the two-step BDF. Second, an implicit Euler and $q$ -step BDF discrete variational derivative method are considered. This scheme, which exploits the variational structure of the equation, dissipates the discrete Fisher information (or energy). Numerical experiments show that the discrete (relative) entropies and Fisher information decay even exponentially fast to zero.     

On almost periodic processes in impulsive competitive systems with delay and impulsive perturbations

In the present paper we investigate the existence of almost periodic processes of ecological systems which are presented with the general impulsive nonautonomous Lotka–Volterra system of integro-differential equations with infinite delay. The impulses are at fixed moments of time, and by using the techniques of piecewise continuous Lyapunov’s functions, new sufficient conditions for the global exponential stability of the unique positive almost periodic solutions of these systems are given.     

A system of parabolic equations in nonequilibrium thermodynamics including thermal and electrical effects

The time-dependent equations for a charged gas or fluid consisting of several components, exposed to an electric field, are considered. These equations form a system of strongly coupled, quasilinear parabolic equations which in some situations can be derived from the Boltzmann equation. The model uses the duality between the thermodynamic fluxes and the thermodynamic forces. Physically motivated mixed Dirichlet-Neumann boundary conditions and initial conditions are prescribed.The existence of weak solutions is proven. The key of the proof is (i) a transformation of the problem by using the entropic variables, or electro-chemical potentials, which symmetrizes the equations, and (ii) a priori estimates obtained by using the entropy function. Finally, the entropy inequality is employed to show the convergence of the solutions to the thermal equilibrium state as the time tends to infinity.     

A Nonlinear Drift - Diffusion System with Electric Convection Arising in Electrophoretic and Semiconductor Modeling

A multi-dimensional transient drift-diffusion model for (at most) three charged particles, consisting of the continuity equations for the concentrations of the species and the Poisson equation for the electric potential, is considered. The diffusion terms depend on the concentrations. Such a system arises in electrophoretic modeling of three species (neutrally, positively and negatively charged) and in semiconductor theory for two species (positively charged holes and negatively charged electrons). Diffusion terms of degenerate type are also possible in semiconductor modeling. For the initial boundary value problem with mixed Dirichlet - Neumann boundary conditions and general reaction rates, a global existence result is proved. Uniqueness of solutions follows in the Dirichlet boundary case if the diffusion terms are uniformly parabolic or if the initial and boundary densities are strictly positive. Finally, we prove that solutions exist which are positive uniformly in time and globally bounded if the reaction rates satisfy appropriate growth conditions.     

Second-Order Necessary Optimality Conditions for Some State-Constrained Control Problems of Semilinear Elliptic Equations

In this paper we are concerned with some optimal control problems governed by semilinear elliptic equations. The case of a boundary control is studied. We consider pointwise constraints on the control and a finite number of equality and inequality constraints on the state. The goal is to derive first- and second-order optimality conditions satisfied by locally optimal solutions of the problem. Accepted 6 May 1997