Approximate symmetries in viscoelasticity

In the framework of approximate symmetries, we investigate a perturbed system of partial differential equations for viscoelastic media with nonlinear dissipation. We completely classify the approximate symmetries and prove a theorem on the relation between the symmetries of two related models. In some physical cases, we find approximate solutions using the generator of the group of transformations taken in the first-order approximation.     

SEFE without Mapping via Large Induced Outerplane Graphs in Plane Graphs

We show that every n‐vertex planar graph admits a simultaneous embedding without mapping and with fixed edges with any ‐vertex planar graph. In order to achieve this result, we prove that every n‐vertex plane graph has an induced outerplane subgraph containing at least vertices. Also, we show that every n‐vertex planar graph and every n‐vertex planar partial 3‐tree admit a simultaneous embedding without mapping and with fixed edges.     

Approximate Entropy of Brain Network in the Study of Hemispheric Differences

Human brain, a dynamic complex system, can be studied with different approaches, including linear and nonlinear ones. One of the nonlinear approaches widely used in electroencephalographic (EEG) analyses is the entropy, the measurement of disorder in a system. The present study investigates brain networks applying approximate entropy (ApEn) measure for assessing the hemispheric EEG differences; reproducibility and stability of ApEn data across separate recording sessions were evaluated. Twenty healthy adult volunteers were submitted to eyes-closed resting EEG recordings, for 80 recordings. Significant differences in the occipital region, with higher values of entropy in the left hemisphere than in the right one, show that the hemispheres become active with different intensities according to the performed function. Besides, the present methodology proved to be reproducible and stable, when carried out on relatively brief EEG epochs but also at a 1-week distance in a group of 36 subjects. Nonlinear approaches represent an interesting probe to study the dynamics of brain networks. ApEn technique might provide more insight into the pathophysiological processes underlying age-related brain disconnection as well as for monitoring the impact of pharmacological and rehabilitation treatments.     

Landau quantization and spin polarization of cold magnetized quark matter

The magnetic field and density behaviors of various thermodynamic quantities of strange quark matter under compact star conditions are investigated in the framework of the thermodynamically self-consistent quasiparticle model. For individual species, a larger number density \begin{document}$ n_i $\end{document} leads to a larger magnetic field strength threshold that aligns all particles parallel or antiparallel to the magnetic field. Accordingly, in contrast to the finite baryon density effect which reduces the spin polarization of magnetized strange quark matter, the magnetic field effect leads to an enhancement of it. We also compute the sound velocity as a function of the baryon density and find the sound velocity shows an obvious oscillation with increasing density. Except for the oscillation, the sound velocity grows with increasing density, similar to the zero-magnetic field case, and approaches the conformal limit \begin{document}$ V_s^2=1/3 $\end{document} at high densities from below.     

Kinetic parameters,collision rates,energy exchanges and transport coefficients of non-thermal electrons in premixed flames at sub-breakdown electric field strengths

The effects of an electric field on the collision rates, energy exchanges and transport properties of electrons in premixed flames are investigated via solutions to the Boltzmann kinetic equation. The case of high electric field strength, which results in high-energy, non-thermal electrons, is analysed in detail at sub-breakdown conditions. The rates of inelastic collisions and the energy exchange between electrons and neutrals in the reaction zone of the flame are characterised quantitatively. The analysis includes attachment, ionisation, impact dissociation, and vibrational and electronic excitation processes. Our results suggest that Townsend breakdown occurs for E/N = 140 Td. Vibrational excitation is the dominant process up to breakdown, despite important rates of electronic excitation of CO, CO₂ and N₂ as well as impact dissociation of O₂ being apparent from 50 Td onwards. Ohmic heating in the reaction zone is found to be negligible (less than 2% of peak heat release rate) up to breakdown field strengths for realistic electron densities equal to 10¹⁰ cm^?3. The observed trends are largely independent of equivalence ratio. In the non-thermal regime, electron transport coefficients are insensitive to mixture composition and approximately constant across the flame, but are highly dependent on the electric field strength. In the thermal limit, kinetic parameters and transport coefficients vary substantially across the flame due to the spatially inhomogeneous concentration of water vapour. A practical approach for identifying the plasma regime (thermal versus non-thermal) in studies of electric field effects on flames is proposed.     

Objective bayesian analysis of the Yule–Simon distribution with applications

The Yule–Simon distribution is usually employed in the analysis of frequency data. As the Bayesian literature, so far, has ignored this distribution, here we show the derivation of two objective priors for the parameter of the Yule–Simon distribution. In particular, we discuss the Jeffreys prior and a loss-based prior, which has recently appeared in the literature. We illustrate the performance of the derived priors through a simulation study and the analysis of real datasets.     

On the motion of a phase interface by surface diffusion

Mullins, in a series of papers, developed a surface dynamics for phase interfaces whose evolution is controlled by mass diffusion within the interface. It is our purpose here to embed Mullins's theory within a general framework based on balance laws for mass and capillary forces in conjunction with a version of the second law, appropriate to a purely mechanical theory, which asserts that the rate at which the free energy increases cannot be greater than the energy inflow plus the power supplied. We develop an appropriate constitutive theory, and deduce general and approximate equations for the evolution of the interface.

---

Sommario Mullins, in una serie di articoli inerenti la morfologia delle superfici di interfaccia tra fasi, ha sviluppato una dinamica delle superfici la cui evoluzione è governata dal fenomeno di diffusione di massa all'interno dell'interfaccia. Scopo di questo articolo è inscrire la teoria di Mullins in uno schema più generale basato su leggi di bilancio della massa e delle azioni capillari nonchè su una formulazione puramente meccanica del secondo principio della termodinamica, asserente ehe l'incremento di energia libera non possa essere superiore al flusso di energia ed alla potenza fornite all'interfaccia. Viene successivamente sviluppata una appropriata teoria costitutiva, e vengono dedotte le equazioni di evoluzione sia in forma generale che approssimata.

     

Sub-Rayleigh imaging via N-photon detection

The Rayleigh diffraction bound sets the minimum separation for two point objects to be distinguishable in a conventional imaging system. We demonstrate sub-Rayleigh resolution by scanning a focused beam--in an arbitrary, object-covering pattern that is unknown to the imager--and using N-photon photodetection implemented with a single-photon avalanche detector array. Experiments show resolution improvement by a factor ～(N-N(max))(?) beyond the Rayleigh bound, where N(max) is the maximum average detected photon number in the image, in good agreement with theory.     

Extension results for slice regular functions of a quaternionic variable

In this paper we prove a new Representation Formula for slice regular functions, which shows that the value of a slice regular function f at a point q=x+yI can be recovered by the values of f at the points q+yJ and q+yK for any choice of imaginary units I,J,K. This result allows us to extend the known properties of slice regular functions defined on balls centered on the real axis to a much larger class of domains, called axially symmetric domains. We show, in particular, that axially symmetric domains play, for slice regular functions, the role played by domains of holomorphy for holomorphic functions.     

Chemical and Mechanical Characterization of Licorice Root and Palm Leaf Waste Incorporated into Poly(urethane-acrylate) (PUA)

A poly(urethane-acrylate) polymer (PUA) was synthesized, and a sufficiently high molecular weight starting from urethane-acrylate oligomer (UAO) was obtained. PUA was then loaded with two types of powdered ligno-cellulosic waste, namely from licorice root and palm leaf, in amounts of 1, 5 and 10%, and the obtained composites were chemically and mechanically characterized. FTIR analysis of final PUA synthesized used for the composite production confirmed the new bonds formed during the polymerization process. The degradation temperatures of the two types of waste used were in line with what observed in most common natural fibers with an onset at 270 °C for licorice waste, and at 290 °C for palm leaf one. The former was more abundant in cellulose (44% vs. 12% lignin), whilst the latter was richer in lignin (30% vs. 26% cellulose). In the composites, only a limited reduction of degradation temperature was observed for palm leaf waste addition and some dispersion issues are observed for licorice root, leading to fluctuating results. Tensile performance of the composites indicates some reduction with respect to the pure polymer in terms of tensile strength, though stabilizing between data with 5 and 10% filler. In contrast, Shore A hardness of both composites slightly increases with higher filler content, while in stiffness-driven applications licorice-based composites showed potential due to an increase up to 50% compared to neat PUA. In general terms, the fracture surfaces tend to become rougher with filler introduction, which indicates the need for optimizing interfacial adhesion.