Faddeev–Jackiw quantization of the higher derivative Chern–Simons gauge theory in the first-order formalism

We analyse the physical constraints of the higher derivative Chern–Simons gauge model by means of Faddeev–Jackiw symplectic approach in the first-order formalism. Within such framework, we systematically determine the zero-mode structure of the corresponding symplectic matrix. In addition, we calculate the Faddeev–Jackiw quantum brackets by choosing appropriate gauge-fixing conditions and evaluate the determinant of the non-singular symplectic matrix as well as the transition-amplitude. Finally, we present a detailed Hamiltonian analysis using Dirac–Bergmann algorithm method and show that the Dirac brackets coincide with the FJ brackets when all the second-class constraints are treated as zero equations.     

On the Weak Solutions to the Maxwell–Landau–Lifshitz Equations and to the Hall–Magneto–Hydrodynamic Equations

In this paper we deal with weak solutions to the Maxwell–Landau–Lifshitz equations and to the Hall–Magneto–Hydrodynamic equations. First we prove that these solutions satisfy some weak-strong uniqueness property. Then we investigate the validity of energy identities. In particular we give a sufficient condition on the regularity of weak solutions to rule out anomalous dissipation. In the case of the Hall–Magneto–Hydrodynamic equations we also give a sufficient condition to guarantee the magneto-helicity identity. Our conditions correspond to the same heuristic scaling as the one introduced by Onsager in hydrodynamic theory. Finally we examine the sign, locally, of the anomalous dissipations of weak solutions obtained by some natural approximation processes.     

Synchrotron X-ray diffractometry and imaging of strains and defects in icosahedral quasicrystal grains

In order to better understand the long-range propagation of quasicrystalline order, as well as quasicrystal stability, it is important to know if defects are generated in the quasicrystal grains during their growth. Previously, we studied the degree of perfection of about ten icosahedral quasicrystal grains of various alloys (Al–Pd–Mn, Al–Cu–Fe, Zn–Mg–Y), as grown or annealed, and we disclosed that some of them were much more perfect than the others. In this work we have concentrated on another slice of such a grain of the Al–Pd–Mn alloy. Similarly, we have performed an extensive synchrotron X-ray topographic investigation of strain and defects in this grain, combined with phase-contrast radiography and high resolution X-ray diffraction examinations. Very few two-lobe contrasts associated with pores and no loop-shaped contrasts were observed on the X-ray topographs, but straight line segments and band contrasts have been identified. Line segments could be considered as the result of the climbing of polygonal dislocation loops, as observed by TEM by Caillard and coworkers. This would indicate that most strains and defects observed in quasicrystal grains, at room temperature, are the result of stresses (external and internal) acting after growth.     

Curvature of multiply warped products

In this paper, we study Ricci-flat and Einstein–Lorentzian multiply warped products. We also consider the case of having constant scalar curvatures for this class of warped products. Finally, after we introduce a new class of space–times called as generalized Kasner space–times, we apply our results to this kind of space–times as well as other relativistic space–times, i.e., Reissner–Nordström, Kasner space–times, Bañados–Teitelboim–Zanelli and de Sitter black hole solutions.     

High energy description of dark energy in an approximate 3-brane Brans–Dicke cosmology

We consider a Brans–Dicke cosmology in five-dimensional space–time. Neglecting the quadratic and the mixed Brans–Dicke terms in the Einstein equation, we derive a modified wave equation of the Brans–Dicke field. We show that, at high energy limit, the 3-brane Brans–Dicke cosmology could be described as the standard one by changing the equation of state. Finally as an illustration of the purpose, we show that the dark energy component of the universe agrees with the observations data.     

Higher-order solutions of a matrix AKNS system associated with a Hermitian symmetric space

In this paper, we study a matrix Ablowitz–Kaup–Newell–Segur (AKNS) system associated with a Hermitian symmetric space as a follow-up study of an earlier paper. A multi-fold generalized Darboux transformation of the matrix AKNS system associated with a Hermitian symmetric space is constructed by means of determinants. Subsequently, we derive various higher-order solutions for this system, including fan-shaped rogue wave and (truncated) Kuznetsov–Ma breather solutions. Specifically, we show the fusion and fission processes for two truncated Kuznetsov–Ma breathers by taking different free parameters.     

Design of organic supercapacitors with high performances using pore size controlled active materials

In this study, we thoroughly investigate the required properties of active materials for organic supercapacitors with high performances. In this regard, we synthesize carbon xerogels with different physical properties, including specific surface area and pore size. The carbon xerogels are prepared via the sol-gel reaction of resorcinol and formaldehyde under different gelation temperature conditions. Through Fourier-transform infrared, nitrogen adsorption–desorption, and scanning electron microscopy analysis, we can confirm that carbon xerogels with different physical properties can be successfully synthesized. We apply the prepared carbon xerogels to organic supercapacitor electrodes. As a result of electrochemical experiments, carbon xerogels with high surface area exhibit high electrochemical performances at low-rate charge?discharge processes. However, as the charge–discharge rate increases, carbon xerogels with low surface area and high conductivity exhibit higher performances. Therefore, the surface area of active materials is a key factor for supercapacitors with high performances at low-rate charge–discharge processes. However, the effects of conductivity can be more crucial as compared with those of surface area as the charge–discharge rates increase. In addition, we suggest that the physical properties of active materials should be differently optimized as the charge–discharge rate is employed.     

Exactly solving some typical Riemann-Liouville fractional models by a general method of separation of variables

Finding exact solutions for Riemann–Liouville(RL) fractional equations is very difficult. We propose a general method of separation of variables to study the problem. We obtain several general results and, as applications, we give nontrivial exact solutions for some typical RL fractional equations such as the fractional Kadomtsev–Petviashvili equation and the fractional Langmuir chain equation. In particular, we obtain non-power functions solutions for a kind of RL time-fractional reaction–diffusion equation. In addition, we find that the separation of variables method is more suited to deal with high-dimensional nonlinear RL fractional equations because we have more freedom to choose undetermined functions.     

Quantum Analogy of Poisson Geometry, Related Dendriform Algebras and Rota–Baxter Operators

We will introduce an associative (or quantum) version of Poisson structure tensors. This object is defined as an operator satisfying a “generalized” Rota–Baxter identity of weight zero. Such operators are called generalized Rota–Baxter operators. We will show that generalized Rota–Baxter operators are characterized by a cocycle condition so that Poisson structures are so. By analogy with twisted Poisson structures, we propose a new operator “twisted Rota–Baxter operators,” which is a natural generalization of generalized Rota–Baxter operators. It is known that classical Rota–Baxter operators are closely related with dendriform algebras. We will show that twisted Rota–Baxter operators induce NS-algebra, which is a twisted version of dendriform algebra. The twisted Poisson condition is considered as a Maurer–Cartan equation up to homotopy. We will show the twisted Rota–Baxter condition also is so. And we will study a Poisson-geometric reason, how the twisted Rota–Baxter condition arises.     

Freely adjusted properties in Ge–S based chalcogenide glasses with iodine incorporation

In this study, we examined the function of halogen iodine acting as a glass network modifier in green chalcogenide glasses based on the Ge–S system. We obtained a series of Ge–S–I glasses and determined their glass-forming region. We then recorded the physical, thermal, and optical properties and studied the effect of halogen iodine on Ge–S–I glasses. Results show that these glasses have relatively wide optical transmission window for infrared (IR) applications. The softening temperature of Ge–S–I glasses varies from 210.54 °C to 321.63 °C, this temperature fits well with some kinds of high-temperature polymers, such as PES and PEI, the polymers serve as protective layers with high strength and flexibility, thus simplifying the fabrication processes of IR chalcogenide glass fiber. Finally, we performed a purification process to eliminate impurities and to improve optical spectra.     

Holographic dilatonic dark energy model

In this paper, we apply the quantum anomaly cancelation method and the effective action approach as well as the method of Damour–Ruffini–Sannan to derive Hawking radiation of Dirac particles from the Myers–Perry black hole. Using the dimensional reduction technique, we find that the fermionic field in the background of the Myers–Perry black hole can be treated as an infinite collection of quantum fields in (1+1)-dimensional background coupled with the dilaton field and the U(1) gauge field near the horizon. Thus Hawking temperature and fluxes are found. The Hawking temperature obtained agrees with the surface gravity formula while the Hawking fluxes derived from the anomaly cancelation method and the effective action approach are in complete agreement with the ones obtained from integrating the Planck distribution.     

Influence of the Diagonal and Off-Diagonal Electron–Phonon Interactions on the Formation of Local Polarons and Their Band Structure in Materials with Strong Electron Correlations

For systems with strong electron correlations and strong electron–phonon interaction, we analyze the electron–phonon interaction in local variables. The effects of the mutual influence of electron–electron and electron–phonon interactions that determine the structure of local Hubbard polarons are described. Using a system containing copper–oxygen layers as an example, we consider the competition between the diagonal and off-diagonal interactions of electrons with the breathing mode as the polaron band structure is formed within a corrected formulation of the polaron version of the generalized tight-binding method. The band structure of Hubbard polarons is shown to depend strongly on the temperature due to the excitation of Franck–Condon resonances. For an undoped La₂CuO₄ compound we have described the evolution of the band structure and the spectral function from the hole dispersion in an antiferromagnetic insulator at low temperatures with the valence band maximum at point (π/2, π/2) to the spectrum with the maximum at point (π, π) typical for the paramagnetic phase. The polaron line width at the valence band top and its temperature dependence agree qualitatively with angle-resolved photoemission spectroscopy for undoped cuprates.     

Stochastic feedback,nonlinear families of Markov processes,and nonlinear Fokker–Planck equations

We discuss two fundamental aspects of Fokker–Planck equations that are nonlinear with respect to probability densities. First, we show that evolution equations of this kind describe processes involving stochastic feedback and interpret stochastic feedback processes in terms of hitchhiker processes and path integral solutions. Second, we demonstrate that nonlinear Fokker–Planck equations can be interpreted as linear Fokker–Planck equations describing nonlinear families of Markov diffusion processes. We exploit this finding in order to derive complete hierarchies of probability densities from nonlinear Fokker–Planck equations.     

Atiyah–Patodi–Singer boundary condition and a splitting formula of a spectral flow

We describe a relation between Atiyah–Patodi–Singer boundary condition and a global elliptic boundary condition, which naturally appears in formulating a splitting formula for a spectral flow, when we decompose the manifold into two components. Then we give a variant of the splitting formula with the Hörmander index as a correction term.     

Superior values of the initial permeability for electrodeposited Ni–Co–P-BaFe12O19 composite films

In this research, we detected superior values of the initial magnetic permeability for electrodeposited Ni–Co–P-M-type BaFe₁₂O₁₉ (BaM) composite films as magnetic soft–hard composites with a large amount of entrapped BaM particles. Furthermore, the initial magnetic permeability of Ni–Co–P-BaM composite films is significantly large and is comparable with corresponding values of the excellent corresponding values for permalloys, Sendust, Co-based amorphous alloys, nanocrystalline (Fe-based) and commercially sintered MnZn ferrite cores. Therefore, Ni–Co–P-BaM composite films are very attractive for magnetic devices, such as magnetic inductors, transformers, and magnetic recording heads.     

Lasing without population inversion in a four-level Y-type configuration in double quantum dot system

Klein–Gordon equation is one of the basic steps towards relativistic quantum mechanics. In this paper, we have formulated fractional Klein–Gordon equation via Jumarie fractional derivative and found two types of solutions. Zero-mass solution satisfies photon criteria and non-zero mass satisfies general theory of relativity. Further, we have developed rest mass condition which leads us to the concept of hidden wave. Classical Klein–Gordon equation fails to explain a chargeless system as well as a single-particle system. Using the fractional Klein–Gordon equation, we can overcome the problem. The fractional Klein–Gordon equation also leads to the smoothness parameter which is the measurement of the bumpiness of space. Here, by using this smoothness parameter, we have defined and interpreted the various cases.     

Nanocomposite PEO-based polymer electrolyte using a highly porous,super acid zirconia filler

In this work we report a new composite, PEO-based lithium polymer electrolyte containing a micro-sized, nanoporous zirconium–oxide–sulfate (Zr–O–SO4) filler synthesized by a surfactant templating sol–gel route. By thermal and transport studies, we show that the particular morphology of the filler enhances the properties of the material leading to a solvent-free electrolyte having unique features in terms of ionic conductivity, lithium ion transference number and thermal behaviour. Finally, the galvanostatic test of the lithium battery prepared using lithium iron phosphate, LiFePO4, as the cathode, lithium metal as the anode and the studied membrane as the electrolyte, shows enhanced performances also at the medium–low temperatures.     

Thermoelectric properties of magnetic configurations of graphene-like nanoribbons in the presence of Rashba and spin–orbit interactions

In this paper we investigate the influence of spin–orbit interaction and two types of Rashba interaction (intrinsic and extrinsic) on magnetic and thermoelectric properties of graphene-like zigzag nanoribbons based on the honeycomb lattice. We utilize the Kane-Mele model with additional Rashba interaction terms. Magnetic structure is described by the electron-electron Coulomb repulsion reduced to the on-site interaction (Hubbard term) in the mean field approximation. We consider four types of magnetic configurations: ferromagnetic and antiferromagnetic with in-plane and out-of plane direction of magnetization. Firstly, we analyze the influence of extrinsic Rashba coupling on systems with negligible spin–orbit interaction, e.g. graphene of an appropriate substrate. Secondly, we discuss the interplay between spin–orbit and intrinsic Rashba interactions. This part is relevant to materials with significant spin–orbit coupling such as silicene and stanene.     

Extremal Kähler metrics and Bach–Merkulov equations

In this paper, we study a coupled system of equations on oriented compact 4-manifolds which we call the Bach–Merkulov equations. These equations can be thought of as the conformally invariant version of the classical Einstein–Maxwell equations. Inspired by the work of C. LeBrun on Einstein–Maxwell equations on compact Kähler surfaces, we give a variational characterization of solutions to Bach–Merkulov equations as critical points of the Weyl functional. We also show that extremal Kähler metrics are solutions to these equations, although, contrary to the Einstein–Maxwell analogue, they are not necessarily minimizers of the Weyl functional. We illustrate this phenomenon by studying the Calabi action on Hirzebruch surfaces.