International Journal of Modern Physics B

Although the paradigm of criticality is centered around spatial correlations and their anomalous scaling, not many studies of self-organized criticality (SOC) focus on spatial correlations. Often, integrated observables, such as avalanche size and duration, are used, not least as to avoid complications due to the unavoidable lack of translational invariance. The present work is a survey of spatio-temporal correlation functions in the Manna Model of SOC, measured numerically in detail in $d$ = 1,3 and 5 dimensions and compared to theoretical results, in particular relating them to “integrated” observables such as avalanche size and duration scaling, that measure them indirectly. Contrary to the notion held by some of SOC models organizing into a critical state by re-arranging their spatial structure avalanche by avalanche, which may be expected to result in large, nontrivial, system-spanning spatial correlations in the quiescent state (between avalanches), correlations of inactive particles in the quiescent state have a small amplitude that does not and cannot increase with the system size, although they display (noisy) power law scaling over a range linear in the system size. Self-organization, however, does take place as the (one-point) density of inactive particles organizes into a particular profile that is asymptotically independent of the driving location, also demonstrated analytically in one dimension. Activity and its correlations, on the other hand, display nontrivial long-ranged spatio-temporal scaling with exponents that can be related to established results, in particular avalanche size and duration exponents. The correlation length and amplitude are set by the system size (confirmed analytically for some observables), as expected in systems displaying finite size scaling. In one dimension, we find some surprising inconsistencies of the dynamical exponent. A (spatially extended) mean field theory (MFT) is recovered, with some corrections, in five dimensions.

Bursting discharge is a ubiquitous behavior in neurons, and abundant bursting patterns imply many physiological information. There exists a closely potential link between bifurcation phenomenon and the number of spikes per burst as well as mixed-mode oscillations (MMOs). In this paper, we have mainly explored the dynamical behavior of the reduced Purkinje cell and the existence of MMOs. First, we adopted the codimension-one bifurcation to illustrate the generation mechanism of bursting in the reduced Purkinje cell model via slow–fast dynamics analysis and demonstrate the process of spike-adding. Furthermore, we have computed the first Lyapunov coefficient of Hopf bifurcation to determine whether it is subcritical or supercritical and depicted the diagrams of inter-spike intervals (ISIs) to examine the chaos. Moreover, the bifurcation diagram near the cusp point is obtained by making the codimension-two bifurcation analysis for the fast subsystem. Finally, we have a discussion on mixed-mode oscillations and it is further investigated using the characteristic index that is Devil’s staircase.

We studied the thermo-elastic properties of Ru₂FeZ (Z=Si, Ge, Sn) Heusler alloys within the framework of density functional theory. Thermo-elastic properties corresponding to elastic modulus, anisotropy, phase stability, elastic wave velocities, thermal stability, Debye temperature, melting temperature, thermal conductivity and formation energy are calculated. The elastic constants C${}_{ij}$ predict the structural and dynamical stabilities while the formation energies show thermal stability of the alloys at 0 K. Pugh’s and Poisson’s ratios display the ductile nature of alloys. All alloys are anisotropic and we also observed that Ru₂FeSn is the hardest material than Ru₂FeSi and Ru₂FeGe. Moreover, longitudinal mode of vibrations are also observed and are maximum along [100], [110] and [111] directions than the transverse mode of vibrations.

The steady-state work fluctuations for an overdamped Brownian particle driven by an external stochastic force are analyzed by using the Langevin approach. The first two moments of the work distribution are given analytically, both are proportional to the time duration of the work injection. The first two moments determine a unique Gaussian function, and the deviations of the probability density functions (PDFs) of work from the Gaussian functions are measured. The tails of the PDFs are shown to approximate the Gaussian functions. In the limit of weak external force and large time interval, the PDF can be approximated by the Gaussian form and the steady-state fluctuation theorem is held.

First principles and quasi-harmonic Debye model have been used to study the thermodynamic properties, enthalpies, electronic and optical properties of MgO up to the core–mantle boundary (CMB) condition (137 GPa and 3700 K). Thermodynamic properties calculation includes thermal expansion coefficient and capacity, which have been studied up to the CMB pressure (137 GPa) and temperature (3700 K) by the Debye model with generalized gradient approximation (GGA) and local-density approximation (LDA). First principles with hybrid functional method (PBE0) has been used to calculate the electronic and optical properties under pressure up to 137 GPa and 0 K. Our results show the Debye model with LDA and first principles with PBE0 can provide accurate thermodynamic properties, enthalpies, electronic and optical properties. Calculated enthalpies show that MgO keep NaCl (B1) structure up to 137 GPa. And MgO is a direct bandgap insulator with a 7.23 eV calculated bandgap. The bandgap increased with increasing pressure, which will induce a blue shift of optical properties. We also calculated the density of states (DOS) and discussed the relation between DOS and band, optical properties. Equations were used to fit the relations between pressure and bandgaps, absorption coefficient ($\alpha$($\omega$)) of MgO. The equations can be used to evaluate pressure after careful calibration. Our calculations can not only be used to identify some geological processes, but also offer a reference to the applications of MgO in the future.

Using the first-principles calculations within the Korringa–Kohn–Rostoker (KKR) method combined with the coherent potential approximation (CPA), the structural, optical and magnetic properties of rare-earth nitride Ho${}_{0.95}$TM${}_{0.05}$N doped with transition metal (TM) atoms (Ti, V, Cr, Mn, Co and Ni) are investigated as a function the generalized gradient approximation and self-interaction correction (GGA–SIC) approximation. The optical properties are studied in detail by using ab-initio calculations. Using GGA–SIC we have showed that the bandgap value is in good agreement with the experimental value. Using GGA–SIC approximation for HoN, we have obtained a bandgap of 0.9 eV. Some of the dilute magnetic semiconductors (DMS) like Ho${}_{0.95}$TM${}_{0.05}$N under study exhibit a half-metallic behavior, which makes them suitable for spintronic applications. Moreover, the optical absorption spectra confirm the ferromagnetic stability based on the charge state of magnetic impurities.

Based on the photon localization and the photonic bandgap characteristics of photonic crystals (PCs), one-dimensional (1D) ring mirror-defect photonic crystal structure is proposed. Due to the introduction of mirror structure, a defect cavity is formed in the center of the photonic crystal, and then the resonant transmission peak can be obtained in the bandgap of transmission spectrum. The transfer matrix method is used to establish the relationship model between the resonant transmission peak and the structure parameters of the photonic crystals. Using the rectangular air gate photonic crystal structure, the dynamic monitoring of the detected gas sample parameters can be achieved from the shift of the resonant transmission peak. The simulation results show that the Q-value can attain to 1739.48 and the sensitivity can attain to 1642 nm ⋅ RIU${}^{-1}$, which demonstrates the effectiveness of the sensing structure. The structure can provide certain theoretical reference for air pollution monitoring and gas component analysis.

In this paper, Fisher information for an accelerated system initially prepared in the X-state is discussed. An analytical solution, which consists of three parts: classical, the average over all pure states and a mixture of pure states, is derived for the general state and for Werner state. It is shown that the Unruh acceleration has a depleting effect on the Fisher information. This depletion depends on the degree of entanglement of the initial state settings. For the X-state, for some intervals of Unruh acceleration, the Fisher information remains constant, irrespective to the Unruh acceleration. In general, the possibility of estimating the state’s parameters decreases as the acceleration increases. However, the precision of estimation can be maximized for certain values of the Unruh acceleration. We also investigate the contribution of the different parts of the Fisher information on the dynamics of the total Fisher information.

Molecular dynamics (MD) simulations are employed to study the elastic properties of gallium nitride (GaN) nanosheets. Young’s and bulk moduli of GaN nanosheets with different side lengths and height/width ratio are obtained. Besides, the configuration of the nanosheet at different strains is represented until the fracture initiation and final fracture are observed. It is seen that the zigzag nanosheets have larger elastic moduli than armchair ones with the same sizes. Moreover, increasing the length size of the nanosheets results in decreasing Young’s modulus. Bulk moduli of GaN nanosheets are also obtained by applying biaxial loading on all edges. It is seen that under the biaxial tensile force, the fracture is initiated at the nanosheet corners and is continued toward the nanosheet center. A nonlinear relation between the bulk modulus and nanosheet size is observed.

In this paper, the optical and electronic properties of asymmetric triple quantum well (ATQW) structures are studied depending on the indium concentrations while quantum well (QW) thicknesses and barrier widths are kept constant. Calculation of electronic properties are done within the framework of the effective mass approximation. The indium concentrations in left quantum well (LQW) and right quantum well (RQW) are varied in order to see the change of energy levels. Then, interband transition energies, wavelengths, oscillator strengths and radiative decay times are determined depending on barrier height. The scope of this study, for the first time in the literature, covers converged interband transition energies for the asymmetric quantum well structures.

We proposed the nonperturbative scheme for the calculation of the impurity spectrum in the Bose system at zero temperature. The method is based on the path-integral formulation and describes an impurity as a zero-density ideal Fermi gas interacting with Bose system for which the action is written in terms of density fluctuations. On the example of the ³He atom immersed in the liquid helium-4 a good consistency with experimental data and results of Monte Carlo simulations is shown.

The high-pressure deformation and polymerization of peapod structure (C${}_{10}$H${}_{16}$ filled into (13, 0) single-walled carbon nanotube) is studied by using density function theory. The guest–host interaction mechanism under pressure is analyzed by combining the van der Waals (vdW) potential with the electron localization function (ELF). Our studies show that the cross-section of the filled single-walled carbon nanotube changes from a circle into an ellipse shape, and then into a walnut shape with the transition pressures of 3 GPa and 10 GPa, respectively. The intertubular bonding of adjacent tubes occurs at 17 GPa, 30 GPa, 32 GPa, 82 GPa and 152 GPa. The attractive and repulsive guest–host interactions are exhibited for the pressures lower and higher than 10 GPa, respectively. Except for the ambient pressure structure, six stable high pressure structures, which can hold their structures when the pressure is released, are identified by combining the systematic binding energy with geometry optimization.

The spin–orbit splitting (E${}_{\mathrm{\text{so}}}$) of valence band maximum at the $\mathrm{\Gamma }$ point is significantly smaller in 2D planner honeycomb structures of graphene, silicene, germanene and BN than that in the corresponding 3D bulk counterparts. For 2D planner honeycomb structure of SiC, it is almost same as that for 3D bulk cubic SiC. The bandgap which opens at the K and K${}^{\prime }$ points due to spin–orbit coupling (SOC) is very small in flat honeycomb structures of graphene and silicene, while in germanene it is about 2 meV. The buckling in these structures of graphene, silicene and germanene increases the bandgap opened at the K and K${}^{\prime }$ points due to SOC quadratically, while the E${}_{\mathrm{\text{so}}}$ of valence band maximum at the $\mathrm{\Gamma }$ point decreases quadratically with an increase in the magnitude of buckling.

In the present work, we discuss the transmittance properties of one-dimensional (1D) superconductor nanocomposite photonic crystals (PCs) in THz frequency regions. Our modeling is essentially based on the two-fluid model, Maxwell–Garnett model and the characteristic matrix method. The numerical results investigate the appearance of the so-called cutoff frequency. We have obtained the significant effect of some parameters such as the volume fraction, the permittivity of the host material, the size of the nanoparticles and the permittivity of the superconductor material on the properties of the cutoff frequency. The present results may be useful in the optical communications and photonic applications to act as tunable antenna in THz, reflectors and high-pass filter.