The ground state of the Frenkel–Kontorova model

The continual approximation of the ground state of the discrete Frenkel–Kontorova model is tested using a symmetric algorithm of numerical simulation. A “kaleidoscope effect” is found, which means that the curves representing the dependences of the relative extension of an N-atom chain vary periodically with increasing N. Stairs of structural transitions for N ? 1 are analyzed by the channel selection method with the approximation N = ∞. Images of commensurable and incommensurable structures are constructed. The commensurable–incommensurable phase transitions are stepwise.     

Voltage–current characteristics and current instability conditions of a high-temperature superconductor in non-uniform temperature distribution

The influence of non-uniform temperature distribution in the cross section of a high-temperature superconductor (thermal size effect) on its voltage–current characteristic and the instability conditions of charged current is investigated. The boundary values of the electric field and the current above which the charged current is unstable are defined taking into account the size effect. It is shown that the calculated current of the instability determining the maximum allowable value of the charged current is reduced, if the thermal heterogeneity of the electrodynamics states is taken into consideration in the theoretical analysis of the stability conditions. As a result, the limiting stable values of the electric field and current depend nonlinearly on the thickness of the superconductor, its critical properties as well as on the external cooling conditions. Therefore, the current of instability will not increase proportionally to the increase in the thickness of superconductor or its critical current density at the intensive cooling conditions.     

Properties of the ground state in a spin—2 transverse Ising model with the presence of a srystal field

The properties of the ground state in the spin-2 transverse Ising model with the presence of a crystal of a crystal field are studied by using the effective-field theory with correlations,The longitudinal and transverse magnetizations,the phase diagram and the internal energy in the ground state are given numerically for a honeycomb lattice(z=3).     

Topological self-dual configurations in a Maxwell–Higgs model with a CPT-odd and Lorentz-violating nonminimal coupling

We have studied the existence of topological self-dual configurations in a nonminimal CPT-odd and Lorentz-violating (LV) Maxwell–Higgs model, where the LV interaction is introduced by modifying the minimal covariant derivative. The Bogomol’nyi–Prasad–Sommerfield formalism has been implemented, revealing that the scalar self-interaction implying self-dual equations contains a derivative coupling. The CPT-odd self-dual equations describe electrically neutral configurations with finite total energy proportional to the total magnetic flux, which differ from the charged solutions of other CPT-odd and LV models previously studied. In particular, we have investigated the axially symmetrical self-dual vortex solutions altered by the LV parameter. For large distances, the profiles possess general behavior similar to the vortices of Abrikosov–Nielsen–Olesen. However, within the vortex core, the profiles of the magnetic field and energy can differ substantially from ones of the Maxwell–Higgs model depending if the LV parameter is negative or positive.     

Electron temperature and ion density measurements in a glow discharge of an Ar–N2 mixture

A DC glow discharge produced in N₂ gas can generate several species that are important in different applications, such as the modification of surface properties of materials. A low-pressure glow discharge apparatus was used for the the analysis of the Ar–N₂ mixture at a total pressure of 2.0 Torr, a power of 20 W and 40 l/min flow rate of gases. The emission bands were measured in the wavelength range of 200–1100 nm. The principal elements are N₂, N ₂⁺ and Ar I. The electron temperature was found in the range of 1.72–2.08 eV, and the ion density was in the order of 10¹⁰ cm^?3.     

Equation of state and liquid–vapour equilibrium in a triangle-well fluid

The second-order thermodynamic perturbation theory formulation of Barker and Henderson is used to derive the equation of state of the triangle-well fluid. This is combined with the rational function approximation to the radial distribution function of the hard-sphere fluid. Results are obtained for the critical parameters and the liquid–vapour coexistence curve for various values of the range of the potential. A comparison with available simulation data is presented.     

Fermi field and Dirac oscillator in a Som–Raychaudhuri space-time

We investigate the relativistic dynamics of a Dirac field in the Som–Raychaudhuri space-time, which is described by a Gödel-type metric and a stationary cylindrical symmetric solution of Einstein field equations for a charged dust distribution in rigid rotation. In order to analyze the effect of various physical parameters of this space-time, we solve the Dirac equation in the Som–Raychaudhuri space-time and obtain the energy levels and eigenfunctions of the Dirac operator by using the Nikiforov–Uvarov method. We also examine the behaviour of the Dirac oscillator in the Som–Raychaudhuri space-time, in particular, the effect of its frequency and the vorticity parameter.     

Simulation of dynamic temperature evolution in an underground coal fire area based on an optimised Thermal–Hydraulic–Chemical model

Underground coal fires (UCFs) exist in almost all coal mining countries. In this paper, an optimised Thermal–Hydraulic–Chemical model, which includes variable reaction kinetics of coal and permeability variation in UCF zones, was developed for the simulation of dynamic temperature evolution of an actual UCF in Xinjiang, China. The model was also adopted in the analysis of the effect of surface coverage permeability on the temperature field, providing a theoretical reference for UCFs control. The results demonstrate that the temperature evolution included three distinct stages which were slow-heating stage, rapid-heating stage and stable-development stage. The slow-heating stage was occupied by the low-temperature oxidation of residual coal. During the rapid-heating stage, a hotspot (combustion centre) formed in residual coal zone and moved toward the air inlet side when the temperature reached a certain threshold. And before moving back into the deeper coal seam, the hotspot developed the temperature to the maximum when it got to the air inlet side. In the stable-development stage, the hotspot spread along the coal seam with the maximum temperature staying between about 800°C and 1000°C, creating elliptical temperature anomalies around the combustion centre. The simulation proved to be in good agreement with the in situ measurements. Surface covering will extinguish the UCF when the permeability of the coverage layer is lower than 10^–10?m², otherwise the fire will persist and continue to spread.     

Numerical approximation of the Euler–Maxwell model in the quasineutral limit

We derive and analyze an Asymptotic-Preserving scheme for the Euler–Maxwell system in the quasi-neutral limit. We prove that the linear stability condition on the time-step is independent of the scaled Debye length λ when λ → 0. Numerical validation performed on Riemann initial data and for a model plasma opening switch device show that the AP-scheme is convergent to the Euler–Maxwell solution when Δx/λ → 0 where Δx is the spatial discretization. But, when λ/Δx → 0, the AP-scheme is consistent with the quasi-neutral Euler–Maxwell system. The scheme is also perfectly consistent with the Gauss equation. The possibility of using large time and space steps leads to several orders of magnitude reductions in computer time and storage.     

Motion of charged particles in a NUTty Einstein–Maxwell spacetime and causality violation

We investigate the motion of electrically charged test particles in spacetimes with closed timelike curves, a subset of the black hole or wormhole Reissner–Nordström-NUT spacetimes without periodic identification of time. We show that, while in the wormhole case there are closed worldlines inside a potential well, the wordlines of initially distant charged observers moving under the action of the Lorentz force can never close or self-intersect. This means that for these observers causality is preserved, which is an instance of our weak chronology protection criterion.     

On the computation of ground state and dynamics of Schrödinger–Poisson–Slater system

In this paper, we deal with the computation of ground state and dynamics of the Schrödinger–Poisson–Slater (SPS) system. To this end, backward Euler and time-splitting pseudospectral methods are proposed for the nonlinear Schrödinger equation with the nonlocal Hartree potential approximated by solving a Poisson equation. The approximation approaches for the Hartree potential include fast convolution algorithms, which are accelerated by using FFT in 1D and fast multipole method (FMM) in 2D and 3D, and sine/Fourier pseudospectral methods. The inconsistency in 0-mode in Fourier pseudospectral approach is pointed out, which results in a significant loss of high-order of accuracy as expected for spectral methods. Numerical comparisons show that in 1D the fast convolution and sine pseudospectral approaches are compatible. While, in 3D the fast convolution approach based on FMM is second-order accurate and the Fourier pseudospectral approach is better than it from both efficiency and accuracy point of view. Among all these approaches, the sine pseudospectral one is the best candidate in the numerics of the SPS system. Finally, we apply the backward Euler and time-splitting sine pseudospectral methods to study the ground state and dynamics of 3D SPS system in different setups.     

The quantum ground state of a Heisenberg ferromagnet with an “easy-plane” type anisotropy

For the Heisenberg ferromagnet with the easy-plane type anisotropy the ground state energy and the magnetization are found with the help of perturbation theory supposing that the anisotropy energy is less than the exchange one. The study is carried out exactly without using any spin operators representation. Therefore, it is valid for a spin of any magnitude.     

Measurement Uncertainty and Its Connection to Quantum Coherence in an Inertial Unruh–DeWitt Detector

The dynamic characteristics of measured uncertainty and quantum coherence are explored for an inertial Unruh–DeWitt detector model in an expanding de Sitter space. Using the entropic uncertainty relation, the uncertainty of interest is correlated with the evolving time t, the energy level spacing δ, and the Hubble parameter H. The investigation shows that, for short time, a strong energy level spacing and small Hubble parameter can result in a relatively small uncertainty. The evolution of quantum coherence versus the evolving time and Hubble parameter, which varies almost inversely to that of the uncertainty, is then discussed, and the relationship between uncertainty and the coherence is explicitly derived. With respect to the l₁ norm of coherence, it is found that the environment for the quantum system considered possesses a strong non-Markovian property. The dynamic behavior of coherence non-monotonously decreases with the growth of evolving time. The dynamic features of uncertainty and coherence in the expanding space with those in flat space are also compared. Furthermore, quantum weak measurement is utilized to effectively reduce the magnitude of uncertainty, which offers realistic and important support for quantum precision measurements during the undertaking of quantum tasks.     

Thoughts on entropic gravity in the Parikh–Wilczek tunneling model of Hawking radiation

In this letter, we use the Parikh–Wilczek tunneling model of Hawking radiation to illustrate that a reformulation of Verlinde’s entropic gravity is needed to derive Newton’s law for a temperature-varying screen, required by the conservation of energy. Furthermore, the entropy stored in the holographic screen is shown to be additive and its temperature dependence can be obtained.     

Hawking Radiation of Photons in a Vaidya–de Sitter Black Hole

Hawking evaporation of photons in a Vaidya–de Sitter black hole is investigated by using the method of generalized tortoise coordinate transformation. Both the location and the temperature of the event horizon depend on the time. It is shown that Hawking radiation of photons exists only for the complex Maxwell scalar ₀ in the advanced Eddington–Finkelstein coordinate system. This asymmetry of Hawking radiation for different components of Maxwell fields probably arises from the asymmetry of spacetime in the advanced Eddington–Finkelstein coordinate system. It is shown that the black body radiant spectrum of photons resembles that of Klein–Gordon particles.     

Precipitation and solute distribution in an interrupted-aged Al–Mg–Si–Cu alloy

Quantitative analysis of the precipitate species and solute distribution was carried out on Al–Mg–Si–Cu alloy 6061 aged to peak hardness using a conventional T6 heat treatment and the so-called T6I6 heat treatments. In this latter, a dwell period at reduced temperature (65°C) is introduced into the T6 ageing cycle (at 177°C or 150°C) which modifies the microstructure and results in the simultaneous improvement of both tensile properties and fracture toughness. Analysis of three-dimensional atom probe data reveals that the superior mechanical properties of the T6I6/177 temper are achieved by a combined effect of a greater consumption of solute atoms by precipitates, an increased number density of fine precipitates and the presence of greater fractions of the effective strengthening precipitates in the final microstructure. Three types of precipitates were found to be characteristic of the peak aged conditions: β′′ precipitates, Guinier–Preston zones and Mg–Si(–Cu) co-clusters. The composition of the strengthening precipitates was found to vary over a wide range for the different heat treatment schedules, corresponding to a variation in the number density of stable nuclei, without any accompanying change in their morphology. All precipitates were found to contain substantial quantities of aluminium. The results also indicate that the strengthening precipitates are preferentially formed from Si-rich nuclei that contain Cu atoms, as opposed to Cu-free nuclei.     

An improved radial temperature model of a high-powered He–SrBr2 laser

When designing and modeling metal vapor and metal halide vapor lasers, the radial distribution of the gas temperature is found by solving the steady-state heat conduction equation for the internal tube at mixed boundary conditions. The volume power density is usually taken as a constant and the unknown value for the temperature of the inner wall is substituted by the measured temperature of the outer wall of the composite laser tube. In this paper, these inaccuracies are overcome. A general solution of the steady-state heat conduction problem has been suggested for an arbitrary volume power density. In order to determine the temperature of the inner wall, a complete model of the radial heat flow has been constructed. The resulting model has been applied in order to evaluate the gas temperature of a new high-powered strontium laser at different qualitative distributions of volume power density. The results have been compared with the known simple models. The presented model could be used on its own for existing and future lasers or as part of other types of theoretical or computer models.     

Effects of temperature and electromagnetic induction on action potential of Hodgkin–Huxley model

Based on an improved the Hodgkin–Huxley (HH) neuron model which is driven by the electromagnetic induction, the effects of temperature and electromagnetic induction on the action potential of neuron are investigated by numerical computations. It is very interesting that, under the fixed condition of electromagnetic induction, there is a region for the electrical activity of neuron in the external current and temperature parameters plane, the region of electrical firing is similar to the Arnold’ tongue-like structure, and the Arnold’ tongue originates from the nonlinear variation of temperature with the increasing of threshold external current. The effects of temperature and electromagnetic induction on neuronic electrical activity are respectively discussed by using numerical simulations. Our results provide new insights into the roles of temperature in the improved HH neuron model, the existence of Arnold’ tongue-like structure might give some insights for the treatment of neurological diseases such as the epilepsia.