Existence of infinitely many solutions for second-order singular initial value problems with an application to nonlinear massive gravity

We prove the existence of infinitely many solutions for a second-order singular initial value problem between given lower and upper solutions. Our study is motivated by a singular problem which arises in the field of nonlinear massive gravity. Moreover, we also discuss the global behavior of solutions of the motivating problem. Our arguments lean at some steps on lower and upper solutions with corners in their graphs, thus showing the applicability of this more general definition of lower and upper solutions in the analysis of a concrete mathematical model.     

Effects of Massage Therapy and Occlusal Splint Usage on Quality of Life and Pain in Individuals with Sleep Bruxism: A Randomized Controlled Trial

Purpose: The aim of the present study was to investigate the effects of massage therapy on the masticatory muscles and occlusal splint usage on quality of life and pain in individuals with sleep bruxism. Method: A randomized, controlled, blinded, clinical trial was conducted involving 78 volunteers aged 18 to 40 years with sleep bruxism. Quality of life and pain assessments were performed. Results: Significant differences (p < 0.05) were found on the physical functioning, general health state, vitality, role emotional and mental health subscales. A large effect size was found for all treatment protocols with regard to pain. The largest effect was found in the combined treatment group. Conclusions: The findings of the present study reveal that the occlusal splint usage alone led to improvements in components of quality of life among individuals with sleep bruxism. Moreover, both treatments (occlusal splint usage and massage therapy on the masticatory muscles) led to a reduction in pain.     

Experimental and computational exploration of indolizinyl carbene generation. A route to biindolizines

In previous work, (E)-2-enynyl pyridines were reported to yield indolizinyl singlet carbenes through base-catalyzed E/Z isomerization followed by a 5-exo-dig pseudocoarctate cyclization. We report herein that in the presence of ethyl acrylate these carbenes undergo stereoselective cis-cyclopropanation due mainly to electrostatic interactions in the transition state. The scope of this carbene generation scheme has been further explored through the preparation of a symmetric bis(pyridylenyl)alkyne which spontaneously furnished the biindolizine core in a one-pot reaction. Computational characterization of this transformation suggests a highly asynchronous double cyclization.     

Nonlinear refractive index measurements in antimony–sulfide glass films using a single beam nonlinear image technique

The nonlinear refractive index, n₂, of films based on the new glass system Sb₂O₃–Sb₂S₃ was measured at 1064 nm with laser pulses of 15 ps, using a single-beam nonlinear image technique in presence of a phase object. The films were prepared from bulk glasses by RF-sputtering. A large value of n₂ = 3 × 10⁻¹⁵ m²/W, which is three orders of magnitude larger than for CS₂, was determined. The result shows the strong potential of antimony–sulfide glass films for integrated nonlinear optics.     

Laser-Scanning Microscopy for Electrophoretic Mobility Characterization of Single Nanoparticles

To enable detailed studies of interactions between nanoparticles and their environment and the correlations between various nanoparticle properties, one must go beyond ensemble averages and toward single-particle measurements. However, current methodologies for the single-nanoparticle analysis of charge and size either lack the flexibility to study dynamic processes on the single-particle level or are highly specific and require complex microfluidic devices. In addition, accurate measurements of the electrophoretic mobility (or zeta-potential) based on the optical detection of single nanoparticles remain challenging due to the low photon budget, the required sampling frequency, and the fact that electroosmosis in typical microfluidic devices must be analyzed carefully. In this study, a method is investigated to accurately characterize the electrophoretic mobility of individual nanoparticles and estimate their size by simultaneously analyzing the electrokinetic- and Brownian motion in a simple microfluidic channel. Fast laser scanning excitation and sensitive detection of fluorescent photons enable single-nanoparticle velocimetry experiments in an oscillating electric field at high frame rates.     

Third-order nonlinearity of nickel oxide nanoparticles in toluene

We report measurements of the nonlinear refractive index, n(2), of nickel oxide nanoparticles (NPs) in toluene at 532 nm. The measurements were performed using the Z-scan technique with 80 ps laser pulses at 7 Hz. Large values of n(2) in the range of 10(-13)-10(-12) cm(2)/W were measured, and negligible two-photon absorption coefficient was estimated for colloids having NP filling fractions in the range of 10(-8)-10(-7).     

Near-Wake Turbulence Properties around a Circular Cylinder at High Reynolds Number

The present study investigates the turbulent properties of the flow around a circular cylinder in the near-wake and in the near-wall upstream region at the Reynolds number 140,000. A detailed cartography of the mean and turbulent velocity fields using a moderate blockage and aspect ratio is provided in order to use the present results for direct comparisons with realisable 3D Navier-Stokes computations. The flow structure is analysed by means of two experiments using respectively the LDV and the PIV techniques, both providing a refined grid of measurement points. The dynamics of the separation region, the growth and decay of turbulence in the near wake, as well as the spatial growth of the organised mode are analysed.     

Obtaining phase averaged turbulence properties in the near wake of a circular cylinder at high Reynolds number using POD

The flow past a circular cylinder at high Reynolds number is studied by means of PIV, 3C-PIV and Time-Resolved PIV techniques. One of the goals of this study was to allow comparisons with numerical simulations on a domain identical to that of the experiment. For this reason, the cylinder was placed in a confined environment, with a high blockage and a low aspect ratio, thereby allowing computations on a mesh of reasonable size, and avoiding “infinite conditions”. This paper deals with the decomposition of the flow in a coherent and random parts. To this aim, phase averaged quantities were first obtained using the wall pressure signal on the cylinder as a trigger signal. This was achieved using both conditional sampling and LSE with similar results. This decomposition is then analysed using the Time Resolved PIV measurements, as well as by comparison of the contributions of the organised and turbulent fluctuations to the time-independent Reynolds stress tensor with those estimated from velocity spectra by interpolation and integration of the continuous part. In agreement with other studies, it is found that the contribution of the turbulent motion is overestimated as a result of the occurence of phase jitter between the trigger and velocity signal. A POD analysis was then performed to extract the coherent motion and to compare this decomposition with that obtained by phase averaging. Similarly to the phase averaging, the POD allows the decomposition of the time-independent stress tensor as the sum of two contributions corresponding to the first N modes, and the rest of the modes. This decomposition is then analysed by comparing these contributions to those obtained from the velocity spectra, according to the value N chosen. It is found that these contributions are strongly dependent on N, and the contribution of the first modes greatly overestimate the coherent motion if N is too large. In order to obtain a good decomposition of the flow in coherent and random parts, the difficulty in this case lies in the choice of the modes. Finally, the POD coefficients of the first two modes are used instead of the pressure signal to determine the phase of the vortex shedding, and the phase averaging is reconsidered. It is found that the phase averaged vortices are less smeared by the averaging process, the turbulent stresses better follow the evolution of the vortices, and the contributions of both coherent and turbulent fluctuations are found to agree well with those evaluated from the velocity spectra. This enhancement is obtained because the phase angle is determined directly from the velocity fields to be averaged, thereby reducing the phase-jitter effect. A comparison with a detached eddy simulation is also briefly shown and demonstrates the high level of agreement obtainable between simulation and experiment, as well as confirming the enhancement of the phase averaging using this procedure.