Stability of Periodic, Traveling-Wave Solutions to the Capillary-Whitham Equation

Recently, the Whitham and capillary-Whitham equations were shown to accurately model the evolution of surface waves on shallow water. In order to gain a deeper understanding of these equations, we compute periodic, traveling-wave solutions to both and study their stability. We present plots of a representative sampling of solutions for a range of wavelengths, wave speeds, wave heights, and surface tension values. Finally, we discuss the role these parameters play in the stability of the solutions

Real-Time Cure Monitoring of Unsaturated Polyester Resin from Ultra-Violet Curing

Real time Fourier transform infrared (RTFT-IR) spectroscopy reveals the influence of the nature of the photoinitiator on the kinetics for the polymerization reaction. Real time cure monitoring was used to determine the polymerization rate of ultra-violet cured unsaturated polyester resins (UPR1:2-1:5) based on palm oil and containing styrene as a cross-linking agent in the presence of IRGACURE 184 photoinitiator. Firstly, variable types of UPR1:2-1:5 were prepared using various ratios of monoglyceride (MG) monomer to maleic anhydride which used as a source of double bond using polycondensation technique. RTFT-IR spectroscopy was used to characterize the ultra-violet curing kinetics for all the systems. This technique offered a powerful approach for monitoring changes in the chemical properties of the system during the ultra-violet curing. Pseudo first order kinetics for all UPR1:2-1:5 curable systems were determined and the rate constant values and regression coefficients were calculated. Furthermore, the thermal behaviour and morphological features for the photo-fabricated UPR1:2-1:5 systems were examined. The thermal analyses for the cured films were evaluated by TGA, DTG and DSC in nitrogen atmosphere at a heating rate of 10°C/min. All the formulations showed similar degradation pattern at 40 % and 50 % weight losses (Td = 40% and Td =50% respectively) except polymer UPR1:5 which had somewhat lower degree in the same range. In addition, the morphological properties for photo-fabricated UPR1:2,1:3,1:5 were investigated by using scanning electron microscopy.

Aquatic Toxicity of Polyethylene and Microcrystalline Cellulose Microbeads Used as Abrasives in Cosmetics

Microplastics have been part of personal care products for years, but due to microplastic pollution, many companies have replaced microplastics with natural particles, such as microcrystalline cellulose. Although natural particles are considered more environmentally friendly, their ecotoxicological profile is unknown. In this context, the aim of this study was to compare the ecotoxicity of polyethylene and microcrystalline cellulose microbeads, both extracted from a cosmetic product. The effects of the two types of particles on the aquatic macrophyte Lemna minor and the crustacean Daphnia magna, as well as the bioadhesion of the particles to Lemna minor were evaluated. The results showed no significant effects of either particle on the specific growth rate, root length, and chlorophyll content of Lemna minor. The bioadhesion of both types of particles to the plant biomass was comparable. Furthermore, no significant effects were observed on the mobility and body length of Daphnia magna. Thus, the investigated polyethylene and cellulose microbeads showed no significant toxic effects on the tested organisms. However, due to the persistence of polyethylene in the environment, the use of polyethylene microbeads in cosmetics and personal care products should be avoided. This work is licensed under a Creative Commons Attribution 4.0 International License

Composite absorbing potentials

The multiple scattering interferences due to the addition of several contiguous potential units are used to construct composite absorbing potentials that absorb at an arbitrary set of incident momenta or for a broad momentum interval.Comment: 9 pages, Revtex, 2 postscript figures. Accepted in Phys. Rev. Let

Tunable linear and quadratic optomechanical coupling for a tilted membrane within an optical cavity: theory and experiment

We present an experimental study of an optomechanical system formed by a vibrating thin semi-transparent membrane within a high-finesse optical cavity. We show that the coupling between the optical cavity modes and the vibrational modes of the membrane can be tuned by varying the membrane position and orientation. In particular we demonstrate a large quadratic dispersive optomechanical coupling in correspondence with avoided crossings between optical cavity modes weakly coupled by scattering at the membrane surface. The experimental results are well explained by a first order perturbation treatment of the cavity eigenmodes.Comment: 10 pages, 6 figure

Surface Roughness and Effective Stick-Slip Motion

The effect of random surface roughness on hydrodynamics of viscous incompressible liquid is discussed. Roughness-driven contributions to hydrodynamic flows, energy dissipation, and friction force are calculated in a wide range of parameters. When the hydrodynamic decay length (the viscous wave penetration depth) is larger than the size of random surface inhomogeneities, it is possible to replace a random rough surface by effective stick-slip boundary conditions on a flat surface with two constants: the stick-slip length and the renormalization of viscosity near the boundary. The stick-slip length and the renormalization coefficient are expressed explicitly via the correlation function of random surface inhomogeneities. The effective stick-slip length is always negative signifying the effective slow-down of the hydrodynamic flows by the rough surface (stick rather than slip motion). A simple hydrodynamic model is presented as an illustration of these general hydrodynamic results. The effective boundary parameters are analyzed numerically for Gaussian, power-law and exponentially decaying correlators with various indices. The maximum on the frequency dependence of the dissipation allows one to extract the correlation radius (characteristic size) of the surface inhomogeneities directly from, for example, experiments with torsional quartz oscillators.Comment: RevTeX4, 14 pages, 3 figure

Time-Resolved Studies of Stick-Slip Friction in Sheared Granular Layers

Sensitive and fast force measurements are performed on sheared granular layers undergoing stick-slip motion, along with simultaneous imaging. A full study has been done for spherical particles with a +-20% size distribution. Stick-slip motion due to repetitive fluidization of the layer occurs for low driving velocities. Between major slip events, slight creep occurs that is variable from one event to the next. The effects of changing the stiffness k and velocity V of the driving system are studied in detail. The stick-slip motion is almost periodic for spherical particles over a wide range of parameters, but becomes irregular when k is large and V is relatively small. At larger V, the motion becomes smoother and is affected by the inertia of the upper plate bounding the layer. Measurements of the period T and amplitude A of the relative motion are presented as a function of V. At a critical value Vc, a transition to continuous sliding motion occurs that is discontinuous for k not too large. The time dependence of the instantaneous velocity of the upper plate and the frictional force produced by the granular layer are determined within individual slipping events. The force is a multi-valued function of the instantaneous velocity, with pronounced hysteresis and a sudden drop prior to resticking. Measurements of vertical displacement reveal a small dilation of the material (about one tenth of the mean particle size in a layer 20 particles deep) associated with each slip event. Finally, optical imaging reveals that localized microscopic rearrangements precede (and follow) each slip event. The behavior of smooth particles is contrasted with that of rough particles.Comment: 20, pages, 17 figures, to appear in Phys. Rev.

The Generalized Star Product and the Factorization of Scattering Matrices on Graphs

In this article we continue our analysis of Schr\"odinger operators on arbitrary graphs given as certain Laplace operators. In the present paper we give the proof of the composition rule for the scattering matrices. This composition rule gives the scattering matrix of a graph as a generalized star product of the scattering matrices corresponding to its subgraphs. We perform a detailed analysis of the generalized star product for arbitrary unitary matrices. The relation to the theory of transfer matrices is also discussed