Abelian vortices from sinh-Gordon and Tzitzeica equations

It is shown that both the sinh-Gordon equation and the elliptic Tzitzeica equation can be interpreted as the Taubes equation for Abelian vortices on a CMC surface embedded in R^2,1${\mathbb{R}}^{2,1}$, or on a surface conformally related to a hyperbolic affine sphere in R³${\mathbb{R}}^3$. In both cases the Higgs field and the U(1)$U(1)$ vortex connection are constructed directly from the Riemannian data of the surface corresponding to the sinh-Gordon or the Tzitzeica equation. Radially symmetric solutions lead to vortices with a topological charge equal to one, and the connection formulae for the resulting third Painlevé transcendents are used to compute explicit values for the strength of the vortices.     

On vortices and rings in extended Abelian models

A numerical search for straight superconducting vortices in a U(1) model with a Ginzburg-Landau potential containing a cubic term is presented. Such vortices exist in a small numerically determined region. The reasons of their existence in that narrow region of the parameter space, as well as of their instability in the rest of the parameter space, are explained. Then, the results of a numerical search for axially symmetric solitons in a U(1)×U(1) model with higher derivative terms, which is based on [C.G. Doudoulakis, Physica D 228 (2007) 159], are presented and discussed.     

Ginzburg–Landau vortices,Coulomb gases,and Abrikosov lattices

This is a review of a mathematical analysis of vortices in the Ginzburg–Landau model: phase transitions and effective energies that govern optimal patterns formed by the vortices, in particular the Abrikosov lattice, are discussed. Analogies with Coulomb gases are also mentioned.     

Non-Abrikosov vortices in liquid metallic hydrogen

We consider non-Abrikosov vortex solutions in liquid metallic hydrogen (LMH) in the framework of two-component Ginzburg–Landau model. We have shown that there are three types of non-Abrikosov vortices depending on chosen boundary conditions at the core of vortices, namely, Neumann (N)-type, Dirichlet (D)-type and Gross–Pitaevskii (GP)-type vortices. The Neumann-type vortex has a non-vanishing condensation at the core, that is different from the ordinary vortex, and the magnetic flux could be reversed as well in LMH. Furthermore, we have obtained a new type of a neutral vortex which has no magnetic field. The presence of such a vortex is related to metallic superfluid state suggested by Babaev (2004) [1].     

Periodic and Chaotic Exploding Dissipative Solitons

Abstract

This article shows for the first time the existence of periodic exploding dissipative solitons. These non-chaotic explosions appear when higher-order non-linear and dispersive effects are added to the complex cubic–quintic Ginzburg–Landau equation modeling soliton transmission lines. This counter-intuitive phenomenon is the result of period-halving bifurcations leading to order (periodic explosions), followed by period-doubling bifurcations leading to chaos (chaotic explosions). This periodic behavior is persistent even when small amounts of noise are added to the system. Since for ultrashort optical pulses it is necessary to include these higher-order effects, it is conjectured that the predictions can be tested in mode-locked lasers.     

Lifshitz tricritical point and its relation to the FFLO superconducting state

We study the phase diagram of spatially inhomogeneous Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) superconducting state using the Ginzburg–Landau (GL) free energy, derived from the microscopic Hamiltonian of the system, and notice that it has a very clear Lifshitz tricritical point. We find the specific heat jumps abruptly near the first-order line in the emergent phase diagram which is very similar to the recent experimental observation in layered organic superconductor. Comparison with experimental data allows us to obtain quantitative relations between the parameters of phenomenological free energy. The region of the phase diagram where the specific heat jumps can be probed by doing a dynamical analysis of the free energy.     

Analytic soliton solutions of cubic‐quintic Ginzburg‐Landau equation with variable nonlinearity and spectral filtering in fiber lasers

In fiber lasers, the study of the cubic‐quintic complex Ginzburg‐Landau equations (CGLE) has attracted much attention. In this paper, four families (kink solitons, gray solitons, Y‐type solitons and combined solitons) of exact soliton solutions for the variable‐coefficient cubic‐quintic CGLE are obtained via the modified Hirota method. Appropriate parameters are chosen to investigate the properties of solitons. The influences of nonlinearity and spectral filtering effect are discussed in these obtained exact soliton solutions, respectively. Methods to amplify the amplitude and compress the width of solitons are put forward. Numerical simulation with split‐step Fourier method and fourth‐order Runge‐Kutta algorithm are carried out to validate some of the analytic results. Transformation from the variable‐coefficient cubic‐quintic CGLE to the constant coefficients one is proposed. The results obtained may have certain applications in soliton control in fiber lasers, and may have guiding value in experiments in the future.

     

Structure Development via Reaction-Induced Phase Separation in Polymer Mixtures: Analysis of Early- and Late-Stage Demixing and Computer Simulations at Non-Isoquench Depths

The effects of phase separation during polymerization of a monomer/polymer mixture were studied. The kinetics of the spinodal decomposition of glycidyl phenyl ether/polystyrene (95/5) during polymerization was investigated using a light-scattering technique. This phase separation during polymerization was comparatively different from the one observed at the isoquench depth such that (i) there was significantly more time before any observable fluctuation, and (ii) the periodic distance of the resulting two-phase structure in the later stages decreased with time. To further investigate the influence of a continually increasing quench depth on phase separation, a diglycidyl aminophenol/diglycidyl ether of bisphenol A (50/50) system with a simple phase diagram was investigated using ultra-small-angle X-ray scattering analysis, and a similar phase separation behavior was observed. Furthermore, computer simulations using the dynamic self-consistent field method were performed to interpret polymer morphology during the demixing driven by chemical reactions. The simulation results suggested that the periodic distance of the resulting two-phase structure formed in the later stages decreases with time. The time dependence of the concentration fluctuations observed in these simulations provided a satisfying explanation for the morphologies formed as a result of a continuously increasing quench depth.     

Dynamics of a quantum phase transition and relaxation to a steady state

We review recent theoretical work on two closely related issues: excitation of an isolated quantum condensed matter system driven adiabatically across a continuous quantum phase transition or a gapless phase, and apparent relaxation of an excited system after a sudden quench of a parameter in its Hamiltonian. Accordingly, the review is divided into two parts. The first part revolves around a quantum version of the Kibble–Zurek mechanism including also phenomena that go beyond this simple paradigm. What they have in common is that excitation of a gapless many-body system scales with a power of the driving rate. The second part attempts a systematic presentation of recent results and conjectures on apparent relaxation of a pure state of an isolated quantum many-body system after its excitation by a sudden quench. This research is motivated in part by recent experimental developments in the physics of ultracold atoms with potential applications in the adiabatic quantum state preparation and quantum computation.     

Nearest-neighbour interaction from an Abelian symmetry and deviations from Hermiticity

We show that Nearest-Neighbour Interaction (NNI) textures for the quark mass matrices can be obtained through the introduction of an Abelian flavour symmetry. The minimal realisation requires a Z₄${\mathsf{Z}}_4$ symmetry in the context of a two Higgs doublet model. It is further shown that the NNI textures can be in agreement with all present experimental data on quark masses and mixings, provided one allows for deviations of Hermiticity in the quark mass matrices at the 20% level.     

Bounded multi-soliton solutions and their asymptotic analysis for the reversal-time nonlocal nonlinear Schrödinger equation

In this paper, we construct the Darboux transformation (DT) for the reverse-time integrable nonlocal nonlinear Schrödinger equation by loop group method. Then we utilize the DT to derive soliton solutions with zero seed. We investigate the dynamical properties for those solutions and present a sufficient condition for the non-singularity of multi-soliton solutions. Furthermore, the asymptotic analysis of bounded multi-solutions has also been established by the determinant formula.     

Similarity reductions and new nonlinear exact solutions for the 2D incompressible Euler equations

For the 2D and 3D Euler equations, their existing exact solutions are often in linear form with respect to variables x, y, z. In this paper, the Clarkson–Kruskal reduction method is applied to reduce the 2D incompressible Euler equations to a system of completely solvable ordinary equations, from which several novel nonlinear exact solutions with respect to the variables x and y are found.     

Study on analytical solutions and their simplification for one-component multi-Yukawa fluids and test by Monte-Carlo simulation

Using the mean spherical approximation, an explicit analytical equation of state with non-dimensional variables for one-component multi-Yukawa fluids is established based on the work of Blum and Ubriaco. Two simplified calculation methods (one is the linear summation method and the other is the negligible entropy method) are proposed. The compressibility factors for one-component 1–4 Yukawa fluids are simulated with the Monte-Carlo method. Comparisons between various methods under different range parameters are listed and discussed for 1–4 Yukawa fluids. These indicate that our methods are reliable for a wide range of parameters and can be used conveniently.     

Optical properties and bandgaps from low loss EELS: pitfalls and solutions

We investigate the impacts of zero loss peak (ZLP) removal and retardation effects altering the electron energy loss spectrum on the optical properties obtained by using Kramers-Kronig analysis and on the determination of the bandgap. For this purpose we use amorphous SiN(x):H having a bandgap of Eg(SiNx:H)= 5.5 eV. We demonstrate that for bandgap determination not only the accurate removal of the ZLP is crucial, moreover also retardation losses have to be taken into account. The same is valid for an accurate determination of the optical properties of semiconductors which can be done if the retardation effects are treated correctly or avoided at all before Kramers-Kronig analysis is applied. Beside the detailed study on using SiN(x):H we discuss the impact of the retardation effects on several other semiconductors and insulators, like GaP.     

Energy transfer and photoextinction from Ln to Tb and Eu in aqueous chloride solutions

Energy transfer and photoextinction from Ln³⁺ to Tb³⁺ and Eu³⁺ in aqueous chloride solutions were studied by absorption, emission and excitation spectra. The energy gaps below the luminescent terms of Gd³⁺, Tb³⁺ and Eu³⁺ are spanned by 10, 5 and 4 quanta, respectively, of the highest energy vibration in aqueous solution, and luminescence is observed in each case. This is not so for other Ln³⁺ where nonradiative deactivation dominates over luminescence. It was verified that only Gd³⁺ could transfer energy to Tb³⁺ and Eu³⁺ ions in aqueous or acid solutions. The ions Pr³⁺, Nd³⁺, Sm³⁺, Dy³⁺, Ho³⁺ and Er³⁺ exhibited strong competitive absorption at certain wavelengths, resulting in the photoextinction of Tb³⁺ and Eu³⁺ emission.     

Dynamic properties of aqueous electrolyte solutions from non-polarisable,polarisable, and scaled-charge models

We investigated the dynamic properties of alkali halide solutions (NaCl, NaF, NaBr, NaI, LiCl, and KCl) using molecular dynamics simulations and several non-polarisable, polarisable, and scaled-charge models. The concentration dependence of shear viscosity was obtained with low statistical uncertainties to allow for calculation of the viscosity Jones-Dole B-coefficients. No prior values are available for the B-coefficients from molecular simulations of fully atomistic models for electrolyte solutions. In addition, we obtained diffusion coefficients with rigorous finite-size corrections to access ion mobilities; these provide insights on single ion hydration behaviour. We find that all models studied, even polarisable and scaled-charge models, quantitatively over-predict water structuring but qualitatively follow the experimentally determined Hofmeister series. All ion models considered are kosmotropes based on their calculated B-coefficient and diffusion coefficients, even for ions experimentally found to be chaotropes. These observations indicate that the water-ion interactions in these models are not adequately represented; additional interactions such as charge transfer must be incorporated in future models in order to better represent electrolyte solution properties.     

Grain boundary behavior in metallic solid solutions as deduced from diffusion and segregation experiments

Grain boundary diffusion and segregation experiments have been carried out in the same metallic solid solutions by means of radio-isotopes and Auger techniques. It was shown that the mass transport parameters could only be understood by assuming the formation of “2D phases” in “segregated grain boundaries” where the main bonds between atoms were identical to those which limit the bulk solid solubility of the solutes.     

Vapour–liquid equilibria from molecular simulations: some issues affecting reliability and reproducibility

ABSTRACT

Molecular simulation data of the vapour–liquid equilibria (VLE) published in the period 2005–2016 and listed in the Web-of-Science collection have been scrutinised and their correctness examined using the recently proposed exact compressibility factor criterion [I. Nezbeda, J. Chem. Eng. Data 61, 3964 (2016)]. It turns out that a large number of the examined data are very inaccurate, if not completely wrong, and this is illustrated by several examples. This problem goes, unfortunately, unnoticed and the data are further used by other researchers. The finding goes hand-in-hand with the becoming practice of ignoring the common etiquette of presenting (pseudo)experimental data, i.e. to provide sufficient information both on technical details and on data post-simulation processing which could enable anyone their independent check and further reliable use. Moreover, the problem of the correctness of published data does not concern only VLE data but any simulation results and these cases along with potential reasons are therefore also briefly discussed. An appeal is therefore made both to the community of simulators and users to examine data using available tools before publishing or using them. Similarly, an appeal is made also to reviewers to insist that the submitted papers with simulation data do contain all necessary details.     

Adsorption and solid phase extraction of 8-hydroxyquinoline from aqueous solutions by using natural bentonite

The nitrogen-heterocyclic compound 8-hydroxyquinoline (8HQ) is one of the components of coal tar and has a wide variety of uses in industry. Because of its toxicity for aquatic organisms and harmful effects for human health, the removal of 8HQ from aqueous solutions by adsorption onto natural bentonite was investigated in the present work. The experimental results show that the optimum pH value of 2.5 is favourable for the 8HQ adsorption. The experimental data were fitted well with the pseudo-second-order kinetic and Langmuir adsorption isotherm models at all studied temperatures. The maximum adsorption capacity obtained from the Langmuir isotherm model at 20 °C was 120.6 mg g⁻¹. The calculated thermodynamic results such as ΔG° (−24.3 kJ mol⁻¹) and ΔH° (−9.56 kJ mol⁻¹) indicate that the adsorption process is spontaneous and exothermic in nature. Solid phase extraction of 8HQ was also performed. The X-ray diffractometry (XRD), Fourier Transform Infrared (FTIR) and thermogravimetric (TG) analyses were carried out in order to confirm the 8HQ adsorption onto bentonite. According to the obtained results, natural bentonite can be a reusable and effective adsorbent for the removal of 8HQ.     

Breather and double-pole solutions of the derivative nonlinear Schrödinger equation from optical fibers

The derivative nonlinear Schrödinger (DNLS) equation, which governs the propagation of the femtosecond optical pulse in a monomodal optical fiber, is analytically studied in this Letter. Breather and double-pole solutions are derived from the two-soliton solution with the choice of parameters. It is found that the parameters in the DNLS equation cannot only control the phase and propagation direction of the breather and double pole, but also influence the interaction period of the breather. Elastic collisions between a breather and a dark/anti-dark soliton are studied by the qualitative analysis and graphical illustration. The stability of the breather and double-pole solutions is also analyzed.