Shock waves for the hyperbolic balance laws with discontinuous sources

In this paper, we are concerned with the behavior of shock waves in a 2 × 2 balance law with discontinuous source terms. We obtain the existence of a local shock wave solution of this problem and deduce that the discontinuous source terms create a weak discontinuity in this solution. Copyright © 2013 John Wiley & Sons, Ltd.     

A numerical analysis of a class of generalized Boussinesq‐type equations using continuous/discontinuous FEM

An improved class of Boussinesq systems of an arbitrary order using a wave surface elevation and velocity potential formulation is derived. Dissipative effects and wave generation due to a time‐dependent varying seabed are included. Thus, high‐order source functions are considered. For the reduction of the system order and maintenance of some dispersive characteristics of the higher‐order models, an extra O(μ²ⁿ⁺²) term (n ∈ ?) is included in the velocity potential expansion. We introduce a nonlocal continuous/discontinuous Galerkin FEM with inner penalty terms to calculate the numerical solutions of the improved fourth‐order models. The discretization of the spatial variables is made using continuous P₂ Lagrange elements. A predictor‐corrector scheme with an initialization given by an explicit Runge–Kutta method is also used for the time‐variable integration. Moreover, a CFL‐type condition is deduced for the linear problem with a constant bathymetry. To demonstrate the applicability of the model, we considered several test cases. Improved stability is achieved. Copyright © 2011 John Wiley & Sons, Ltd.     

Adaptation of a load-inject valve for a flow injection chemiluminescence system enabling dual-reagent injection enhances understanding of environmental Fenton chemistry

Environmental Fenton chemistry has been poorly constrained within the marine environment at a multi-component level. A simple, unique, reconfiguration of a flow-injection analytical system combined with luminol chemiluminescence allows quasi-simultaneously the measurement, using a single load-inject valve and a single photon multiplier tube, of reduced iron, Fe(II), and hydrogen peroxide. The system enables rapid, every 22 s, measurements with good accuracy at environmentally relevant concentrations, less than 5% relative standard deviations on both a 5 nM Fe(II) standard and a 60 nM hydrogen peroxide standard. Limits of detection were as low as 40 pM Fe(II) and 100 pM hydrogen peroxide. The system showed excellent capability by measuring from within an organic rich seawater the photochemically induced production of Fe(II) and hydrogen peroxide and their subsequent cycling and Fenton like interactions.     

Chemical modification of poly(lactic acid) and its use as matrix in poly(lactic acid) poly(butylene adipate-co-terephthalate) blends

Poly(lactic acid), PLA, was chemically modified with maleic anhydride (MA) by reactive extrusion. The effect of this modification on molar mass (MM) and acidity was assessed by means of size-exclusion chromatography (SEC) and titration, respectively. PLA MM decreased in the presence of MA solely and of MA and peroxide. Reduction in MM was monitored by the increase in acidity. PLA blends containing poly(butylene adipate-co-terephthalate) (PBAT) were prepared through different mixing protocols, PLA/PBAT, PLA-g-MA/PBAT and PLA/PBAT/MA/peroxide (PLA/PBAT in situ). SEC results and rheological properties revealed reduction in MM and viscosity of the modified blends. PLA/PBAT presented increase in MM and bimodal MM distribution. The calculated interfacial tension was significantly lower for the modified blends, despite the lower average particle area of PLA/PBAT. Surprisingly, the modified blends presented higher yield strength than that predicted by the rule of mixtures, which might indicate interfacial reactions.     

Anisotropic sound and shock waves in dipolar Bose-Einstein condensate

We study the propagation of anisotropic sound and shock waves in dipolar Bose-Einstein condensate in three dimensions (3D) as well as in quasi-two (2D, disk shape) and quasi-one (1D, cigar shape) dimensions using the mean-field approach. In 3D, the propagation of sound and shock waves are distinct in directions parallel and perpendicular to dipole axis with the appearance of instability above a critical value corresponding to attraction. Similar instability appears in 1D and not in 2D. The numerical anisotropic Mach angle agrees with theoretical prediction. The numerical sound velocity in all cases agrees with that calculated from Bogoliubov theory. A movie of the anisotropic wave propagation in a dipolar condensate is made available as supplementary material.     

Computational analysis of glycolytic reaction in open spatial reactor

We consider the computational analysis of processes within the spatially-distributed model simulating the glycolytic reaction taking place in the one-side fed open chemical reactor. The main point of the simulation is the decomposition of the reaction–diffusion system into unidirectional reaction in a bulk supplied by feedback terms stated as boundary conditions on the lower boundary of the reactor, i.e. the unique plane where an exchange with an outer medium is possible within the real experimental situation. Analysis of the curvature of the reagents distribution curves proves kinematic character of the observed lateral waves corresponding to the picture of experimentally observed glycolytic traveling waves. At the same time, their origin relates to diffusion of the reagents in a vertical cross-section of the reactor. Study of the solutions for the concerned reaction–diffusion model in the case of stochastically different diffusion coefficients reveals the Turing structures.     

Disjoining pressure and the film-height-dependent surface tension of thin liquid films: New insight from capillary wave fluctuations

In this paper we review simulation and experimental studies of thermal capillary wave fluctuations as an ideal means for probing the underlying disjoining pressure and surface tensions, and more generally, fine details of the Interfacial Hamiltonian Model. We discuss recent simulation results that reveal a film-height-dependent surface tension not accounted for in the classical Interfacial Hamiltonian Model. We show how this observation may be explained bottom-up from sound principles of statistical thermodynamics and discuss some of its implications.     

Novel nonlinear wave equation: Regulated rogue waves and accelerated soliton solutions

A new exactly solvable ($1+1$)-dimensional complex nonlinear wave equation exhibiting rich analytic properties has been introduced. A rogue wave (RW), localized in space–time like Peregrine RW solution, though richer due to the presence of free parameters is discovered. This freedom allows to regulate amplitude and width of the RW as needed. The proposed equation allows also an intriguing topology changing accelerated dark soliton solution in spite of constant coefficients in the equation.