Different kinds of discrete breathers in a Sine–Gordon lattice

We study a one-dimensional Sine–Gordon lattice of anharmonic oscillators with cubic and quartic nearest-neighbor interactions, in which discrete breathers can be explicitly constructed by an exact separation of their time and space dependence. DBs can stably exist in the one-dimensional Sine–Gordon lattice no matter whether the nonlinear interaction is cubic or quartic. When a parametric driving term is introduced in the factor multiplying the harmonic part of the on-site potential of the system, we can obtain the stable quasiperiodic discrete breathers and chaotic discrete breathers by changing the amplitude of the driver.     

Bound states of Klein－Gordon equation for ring-shaped harmonic oscillator scalar and vector potentials

Solving Klein－Gordon equation with equal ring-shaped harmonic oscillator scalar and vector potentials, we obtain the exact normalized bound-state wavefunction and energy equation.     

Discrete gap breathers in a diatomic K2-K3-K4 chain with cubic nonlinearity

The discrete gap breathers （DGBs） in a one-dimensional diatomic chain with K2-K3-K4 potential are analysed. Using the local anharmonicity approximation, the analytical investigation has been implemented. The dependence of the central amplitude of the discrete gap breathers on the breather frequency and the localization parameter are calculated. With increasing breather frequency, the DGB amplitudes decrease. As a function of the localization parameter, the central amplitude exhibits bistability, corresponding to the two branches of the curve ω = ω（ζ）. With a nonzero cubic term, the HS mode of DGB profiles becomes weaker. With increasing K3, the HS mode of DGB profiles becomes weaker and a bit narrower. For the LS mode, with increasing K3, the central particle amplitude becomes larger, and the DGB profile becomes much sharper. But, as k3 increases further, the central particle amplitude of the LS mode becomes smaller.     

The Klein–Gordon equation in mixture models of tumour growth

A mixture model of tumour microenvironment is considered, which consists of a solid phase for the tumour cells, a liquid phase for the interstitial fluid, and a nutrient phase. The balance equations for the three phases take into account exchange of mass between tumour and nutrients, and exchange of drag forces between the constituents. Under rather natural assumptions, the determination of the nutrient density is reduced to the solution of a Klein–Gordon equation, with source term depending on mass injection from outside. A chain of decoupled equations for the remaining unknowns is then determined in terms of the nutrient density. Finally, the growth of tumour volume is investigated under the assumption of spherical symmetry.     

Instability and noise-induced thermalization of Fermi–Pasta–Ulam recurrence in the nonlinear Schrödinger equation

We investigate the spontaneous growth of noise that accompanies the nonlinear evolution of seeded modulation instability into Fermi–Pasta–Ulam recurrence. Results from the Floquet linear stability analysis of periodic solutions of the three-wave truncation are compared with full numerical solutions of the nonlinear Schrödinger equation. The predicted initial stage of noise growth is in a good agreement with simulations, and is expected to provide further insight into the subsequent dynamics of the field evolution after recurrence breakup.     

Bound states of the Klein－Gordon and Dirac equations for scalar and vector harmonic oscillator potentials

We give the exact bound states of the Klein－Gordon and Dirac equations with equal scalar and vector harmonic oscillator potentials.     

Bound states of the Klein－Gordon and Dirac equation for scalar and vector pseudoharmonic oscillator potentials

The exact bound state solutions of the Klein－Gordon equation and Dirac equation with scalar and vector pseudoharmonic oscillator potentials are obtained in this paper. Furthermore, we have used the supersymmetric quantum mechanics, shape invariance and alternative method to obtain the required results.     

Two-Dimensional Klein–Gordon Oscillator in the Presence of a Minimal Length

Minimal length of a two-dimensional Klein–Gordon oscillator is investigated and illustrates the wave functions in the momentum space. The eigensolutions are found and the system is mapping to the wellknown Schrödinger equation in a Pöschl–Teller potential.     

Localization of an electron on a one-dimensional chain of periodically arrayed random δ potentials

A new method for exact averaging of the resistivity of a chain of periodically arrayed random short-range potentials has been developed. It is shown that the dependence of the average resistivity of the system on the length of a system having an arbitrary disorder at its centers is a sum of three exponential functions. The nature of the localization of the states as a function of the system’s disorder parameters and the energy of the single-electron states have been investigated. Fiz. Tverd. Tela (St. Petersburg) 41, 1851–1855 (October 1999)     

The virial theorem in refined Thomas－Fermi－Dirac theory for the interior of atoms in a solid

The virial theorem in refined Thomas－Fermi－Dirac theory for the interior of atoms in a solid is given and proven.     

Stability study of a model for the Klein–Gordon equation in Kerr space-time

The current early stage in the investigation of the stability of the Kerr metric is characterized by the study of appropriate model problems. Particularly interesting is the problem of the stability of the solutions of the Klein–Gordon equation, describing the propagation of a scalar field of mass $\mu $ in the background of a rotating black hole. Rigorous results prove the stability of the reduced, by separation in the azimuth angle in Boyer–Lindquist coordinates, field for sufficiently large masses. Some, but not all, numerical investigations find instability of the reduced field for rotational parameters $a$ extremely close to $1$ . Among others, the paper derives a model problem for the equation which supports the instability of the field down to $a/M \approx 0.97$ .     

Justification of the discrete nonlinear Schrödinger equation from a parametrically driven damped nonlinear Klein–Gordon equation and numerical comparisons

We consider a damped, parametrically driven discrete nonlinear Klein–Gordon equation, that models coupled pendula and micromechanical arrays, among others. To study the equation, one usually uses a small-amplitude wave ansatz, that reduces the equation into a discrete nonlinear Schrödinger equation with damping and parametric drive. Here, we justify the approximation by looking for the error bound with the method of energy estimates. Furthermore, we prove the local and global existence of solutions to the discrete nonlinear Schrödinger equation. To illustrate the main results, we consider numerical simulations showing the dynamics of errors made by the discrete nonlinear equation. We consider two types of initial conditions, with one of them being a discrete soliton of the nonlinear Schrödinger equation, that is expectedly approximate discrete breathers of the nonlinear Klein–Gordon equation.     

The use of Abell–Tersoff potentials in atomistic simulations of InGaAsSb/GaAs

In this paper we show the use of an optimally parameterized empirical potential of the Abell–Tersoff type to study the strain energy of the quaternary alloy InGaAsSb. We use our results to compute modified segregation energies in an improved kinetic model of segregation for the combined effects of group III and V exchange processes during epitaxial growth and compare with experimental data from Scanning Tunnelling Microscopy.     

The instability conditions of a gas trapped in weak weakly interacting Fermi magnetic field

In this paper the analytical expression of free energy expressed by small parameter r of a weakly interacting Fermi gas trapped in weak magnetic field is derived by using `the maximum approximation' method and the ensemble theory. Based on the derived expression, the exact instability conditions of a weakly interacting Fermi gas trapped in weak magnetic field at both high and low temperatures are given. From the instability conditions we get the following two results. (1) At the whole low-temperature extent, whether the interactions are repulsive or attractive with (ɑn + 4\varepsilon_F/3) (n and \varepsilon _F denote the particle-number density and the Fermi energy respectively, ɑ= 4π a\hbar_F/ m, and a is s-wave scattering length) positive, there is a lower-limit magnetic field of instability; in addition, there is an upper-limit magnetic field for the system of attractive interactions with (ɑ n + \varepsilon_F/3) negative. (2) At the whole high-temperature extent, the system with repulsive interactions is always stable, but for the system with attractive interactions, the greater the scattering length of attractive interactions | a | is, the stronger the magnetic field is and the larger the particle-number density is, the bigger the possibility of instability in the system will be.     

The effects of photochemical oxidation and chain conformation on green emission of poly(9,9-dioctylfluorene)

The effects of chain conformation on the photo-oxidation and green emission of poly(9,9-dioctylfluorenyl-2,7-diyl) (PFO) has been investigated at both single-molecule and ensemble levels. Single-molecule studies reveal the conformation of PFO chains to be more globular when cast from THF than from toluene solutions. Intensity transients of the single molecules show that the elongated molecules cast from toluene have more fluctuations due to limited energy transfer along the polymer chains. The more globular chains show monotonic decays with isotropic polarization. Emission spectra of the single molecules show that photochemical oxidation leads to a reduction in the emission of the molecule with no change in the emission spectra. No green emission is ever detected for single molecules, indicating that formation of emissive ketone defects is a rare event. Ensemble studies of chains show that molecules cast from THF develop some green emission upon photodegradation, while those cast from toluene do not. The increase in green emission in the globular molecules suggests that interchain contacts improve energy transfer for emissive ketone defects in the PFO cast from THF.     

Algebras of Symmetry Operators of the Klein–Gordon–Fock Equation for Groups Acting Transitively on Two-Dimensional Subspaces of a Space-Time Manifold

Russian Physics Journal - All external electromagnetic fields are found in which the Klein–Gordon–Fock equation for a charged test particle admits first-order symmetry operators...     

The effects of a static magnetic field on the microwave absorption of hydrogen plasma in carbon nanotubes： a numerical study

We theoretically investigate the microwave absorption properties of hydrogen plasma in iron-catalyzed high-pressure disproportionation-grown carbon nanotubes under an external static magnetic field in the frequency range 0.3 GHz to 30 GHz, using the Maxwell equations in conjunction with a general expression for the effective complex permittivity of magnetized plasma known as the Appleton-Hartree formula. The effects of the external static magnetic field intensity and the incident microwave propagation direction on the microwave absorption of hydrogen plasma in CNTs are studied in detail. The numerical results indicate that the microwave absorption properties of hydrogen plasma in iron-catalyzed high-pressure disproportionation-grown carbon nanotubes can be obviously improved when the exter- nal static magnetic field is applied to the material. It is found that the specified frequency microwave can be strongly absorbed by the hydrogen plasma in iron-catalyzed high-pressure disproportionation-grown carbon nanotubes over a wide range of incidence angles by adjusting the external magnetic field intensity and the parameters of the hydrogen plasma.