New exact solutions to the high dispersive cubic–quintic nonlinear Schrödinger equation

The complete discrimination system method is employed to find exact solutions for a dispersive cubic–quintic nonlinear Schrödinger equation with third order and fourth order time derivatives. As a result, we derive a range of solutions which include triangular function solutions, kink solitary wave solutions, dark solitary wave solutions, Jacobian elliptic function solutions, rational function solutions and implicit analytical solutions. Numerical simulations are presented to visualize the mechanism of Eq. (1) by selecting appropriate parameters of the solutions. The comparison between our results and other's works are also given.     

Corrigendum to “Wave-particle interactions in a resonant system of photons and ion-solvated water” [Phys. Lett. A 381 (2017) 762–766]

Two corrections to Ref. [1] are presented. In particular, a correct version of the derivation of Eq. (14) is given. These corrections do not have any effect on the main results of the original article.     

Remark on Landau quantization,Aharonov–Bohm effect and two-dimensional pseudoharmonic quantum dot around a screw dislocation

We investigate the influence of a screw dislocation on the energy levels and the wavefunctions of an electron confined in a two-dimensional pseudoharmonic quantum dot under the influence of an external magnetic field inside a dot and Aharonov–Bohm field inside a pseudodot. Filgueiras et al. (2016) [1] showed that the Schrödinger equation is separable in cylindrical coordinates when the motion along the z axis is unbounded. We show that it is not separable under box confinement as those authors claim but it is separable in the case of periodic boundary conditions along that axis.     

Antiproton annihilation as a deconfinement process

N¯N annihilation into mesons through the deconfinement stage is analysed. Behaviour of deconfined quark-gluon plasma describes an equation of state, with first order quark and gluon interactions. The effects of pion structure and threshold irregularities are considered.Invited talk to the symposium Mesons and Light Nuclei IV, Bechyn, Czechoslovakia, September 5–10, 1988.     

Superstatistics and temperature fluctuations

Superstatistics [Beck and Cohen (2003) [1]] is a formalism aimed at describing statistical properties of a generic extensive quantity E in complex out-of-equilibrium systems in terms of a linear superposition of equilibrium canonical distributions. The weight function $P(\beta )$ is argued to be provided by the statistics of the intensive thermodynamic quantity β conjugate to E [Beck (2011) [14]], and therefore is expected to be determined by the spatiotemporal dynamics alone of the system under consideration. In this paper, recalling a previous work [Beck (2006) [21]], I show by examples that, in some cases fulfilling all the conditions for the superstatistics formalism to be applicable, $P(\beta )$ cannot be defined uniquely, but rather depends upon the way the measurement of E is performed.     

High energy radiation precursors to the collapse of black holes binaries based on resonating plasma modes

The presence of well organized plasma structures around binary systems of collapsed objects [1], [2] (black holes and neutron stars) is proposed in which processes can develop [3] leading to high energy electromagnetic radiation emission immediately before the binary collapse. The formulated theoretical model supporting this argument shows that resonating plasma collective modes can be excited in the relevant magnetized plasma structure. Accordingly, the collapse of the binary approaches, with the loss of angular momentum by emission of gravitational waves [2], the resonance conditions with vertically standing plasma density and magnetic field oscillations are met. Then, secondary plasma modes propagating along the magnetic field are envisioned to be sustained with mode-particle interactions producing the particle populations responsible for the observable electromagnetic radiation emission. Weak evidence for a precursor to the binary collapse reported in Ref. [2], has been offered by the Agile X-γ-ray observatory [4] while the August 17 (2017) event, identified first by the LIGO-Virgo detection of gravitational waves and featuring the inferred collapse of a neutron star binary, improves the evidence of such a precursor. A new set of experimental observations is needed to reassess the presented theory.     

Quantum confinement and interface structure of Si nanocrystals of sizes 3–5 nm embedded in a-SiO2

Spectroscopic ellipsometry and Monte Carlo simulations are employed to answer the fundamental question whether the energy gaps of Si nanocrystals with sizes in the range of 3–5 nm, which are embedded in amorphous silica, follow or deviate from the quantum confinement model, and to examine their interfacial structure. It is shown that the optical properties of these nanocrystals are well described by the Forouhi–Bloomer interband model. Analysis of the optical measurements over a photon-energy range of 1.5–5 eV shows that the gap of embedded nanocrystals with a mean size of 3.9 nm follows closely quantum confinement theory. A large band gap expansion (0.65 eV) compared to bulk Si is observed. The Monte Carlo simulations reveal a non-abrupt interface and a large fraction of interface oxygen bonds. This, in conjunction with the experimental observations, indicates that oxygen states and the chemical disorder at the interface have a negligible influence on the optical properties of the material in this size regime.     

Stability criterion for solitons of the Zakharov–Kuznetsov-type equations

Early results concerning the linear stability of the solitons in equation of the KDV-type [1] are generalized to solitons describing by the Zakharov–Kuznetsov-type equation. The linear stability criterion for ground solitons in the Vakhitov–Kolokolov form is derived for such equations with arbitrary nonlinearity. For the power nonlinearity the instability criterion coincides with the condition of the Hamiltonian unboundedness from below. The latter represents the main feature for appearance of collapse in such systems.     

Structure and thermodynamic stability of carbon clathrates: A Monte Carlo study

Clathrates are strong, low density, fully sp³ structures that have been found for several elements of the IV group. Carbon clathrates however are, as of now, hypothetical materials. Ab initio calculations at $T=0K$ predict carbon clathrates to be metastable with remarkable mechanical and electronic properties. Here we study the behavior and structural stability of the type I C₄₆ carbon clathrates up to high temperature and pressure by means of Monte Carlo simulations based on an accurate model for the interatomic interactions. We find that the clathrate structure remains mechanically stable up to melting and we report the equilibrium structural parameters, thermal expansion, and equation of state.     

Slow light engineering in a photonic crystal slab waveguide through optofluidic infiltration and geometric modulation

In this paper, a new type of flat-band slow light structure with high group index (n _g) and large normalized delay-bandwidth product (NDBP) in a silicon on insulator (SOI) based photonic crystal (PC) slab waveguide with a triangular lattice of circular holes is demonstrated. The dispersion engineering is performed by infiltrating optical fluids with different refractive indices n _f in the first row and shifting the second row of air holes adjacent to the PC waveguide (PCW) in the longitudinal direction. In the optimized case, a high NDBP of 0.32 with a group index of 54.55 and a bandwidth of 9.13 nm could be obtained. Furthermore, an ultra-low group velocity dispersion (GVD) in the range of 10^–20 s²/m is achieved in all of the structures. These results are obtained by numerical simulations based on three-dimensional (3D) plane wave expansion (PWE) method.     

Mean-field gauge interactions in five dimensions II. The orbifold

We study Gauge–Higgs Unification in five dimensions on the lattice by means of the mean-field expansion. We formulate it for the case of an SU(2)$\mathit{SU}(2)$ pure gauge theory and orbifold boundary conditions along the extra dimension, which explicitly break the gauge symmetry to U(1)$U(1)$ on the boundaries. Our main result is that the gauge boson mass computed from the static potential along four-dimensional hyperplanes is non-zero implying spontaneous symmetry breaking. This observation supports earlier data from Monte Carlo simulations in Irges and Knechtli (2007) [12].     

Equation of State in the Fugacity Format for the Two-Dimensional Coulomb Gas

We derive the general form of the equation of state, in the fugacity format, for the two-dimensional Coulomb gas. Our results are valid in the conducting phase of the Coulomb gas, for temperatures above the Kosterlitz–Thouless transition. The derivation of the equation of state is based on the knowledge of the general form of the short-distance expansion of the correlation functions of the Coulomb gas. We explicitly compute the expansion up to order in the activity ζ. Our results are in very good agreement with Monte Carlo simulations at very low density.     

Power law decay of correlations in stationary nonequilibrium lattice gases with conservative dynamics

We report computer simulations and high-temperature approximations of the pair correlation in a stationary nonequilibrium system, a lattice gas subject to a strong uniform driving fieldE. The dynamics of the system is given by hoppings of particles to adjacent empty sites with rates biased for jumps in the direction ofE. We study the anisotropic short-distance behavior as well as the long-distance decay properties of the two-point correlations along the principal axes. The simulations as well as the (approximate) expansion in strongly suggest that the correlations in this system have a power law decay,r ^–D for dimensionsD=2 and 3, even at high temperatures.     

Anomalous transport from holography: part II

This is a second study of chiral anomaly-induced transport within a holographic model consisting of anomalous \(U(1)_V\times U(1)_A\) Maxwell theory in Schwarzschild–AdS\(_5\) spacetime. In the first part, chiral magnetic/separation effects (CME/CSE) are considered in the presence of a static spatially inhomogeneous external magnetic field. Gradient corrections to CME/CSE are analytically evaluated up to third order in the derivative expansion. Some of the third order gradient corrections lead to an anomaly-induced negative \(B^2\)-correction to the diffusion constant. We also find modifications to the chiral magnetic wave nonlinear in B. In the second part, we focus on the experimentally interesting case of the axial chemical potential being induced dynamically by a constant magnetic and time-dependent electric fields. Constitutive relations for the vector/axial currents are computed employing two different approximations: (a) derivative expansion (up to third order) but fully nonlinear in the external fields, and (b) weak electric field limit but resuming all orders in the derivative expansion. A non-vanishing nonlinear axial current (CSE) is found in the first case. The dependence on magnetic field and frequency of linear transport coefficient functions is explored in the second.     

Perturbational blowup solutions to the compressible 1-dimensional Euler equations

We construct non-radially symmetry solutions for the compressible 1-dimensional adiabatic Euler equations in this Letter. In detail, we perturb the linear velocity with a drifting term:

(1)     

Experiments in PT-Symmetric Quantum Mechanics

Extended quantum mechanics using non-Hermitian (pseudo-Hermitian) Hamiltonians H = H is briefly reviewed. A few related mathematical experiments concerning supersymmetric regularizations, solvable simulations and large-N expansion techniques are summarized. We suggest that they could initiate a deeper study of nonlocalized structures (quasi-particles) and/or of their unstable and many-particle generalizations. Using the Klein-Gordon example for illustration, we show how the PT symmetry of its Feshbach-Villars Hamiltonian H ^FV might clarify experimental aspects of relativistic quantum mechanics.     

A renormalization group analysis of turbulent transport

The field-theoretic renormalization group is used to derive scaling relations for the transport of passive scalars by an incompressible velocity field with a specified energy spectrum. Results are obtained with the analog of the expansion of critical phenomena and compared to exact results which are available for shear flows in two dimensions.A 1/N expansion is proposed for the regions in which the expansion fails.     

Computer Simulation of Irreversible Expansions via Molecular Dynamics, Smooth Particle Applied Mechanics, Eulerian, and Lagrangian Continuum Mechanics

We simulate the far-from-equilibrium irreversible expansion of a compressed ideal gas in two space dimensions. For this problem the particle trajectories from conventional smooth particle applied mechanics are isomorphic to those from a corresponding molecular dynamics simulation. The smooth-particle weight function used to describe the expanding gas is identical to the pair potential governing the molecular dynamics simulation. These many-body particle simulations are compared with those using a modified smooth-particle algorithm invented by Monaghan, as well as with those based on conventional grid-based Eulerian and Lagrangian methods.