Showing papers in "Zeitschrift für Naturforschung A in 2016"

Quasi-periodically driven quantum systems

Abstract: Floquet theory provides rigorous foundations for the theory of periodically driven quantum systems. In the case of non-periodic driving, however, the situation is not so well understood. Here, we provide a critical review of the theoretical framework developed for quasi-periodically driven quantum systems. Although the theoretical footing is still under development, we argue that quasi-periodically driven quantum systems can be treated with generalisations of Floquet theory in suitable parameter regimes. Moreover, we provide a generalisation of the Floquet-Magnus expansion and argue that quasi-periodic driving offers a promising route for quantum simulations.

Multi-Soliton Solutions of the Generalized Sawada–Kotera Equation

Abstract: Abstract Korteweg–de Vries (KdV)-type equations can describe the nonlinear phenomena in shallow water waves, stratified internal waves, and ion-acoustic waves in plasmas. In this article, the two-dimensional generalization of the Sawada–Kotera equation, one of the KdV-type equations, is discussed by virtue of the Bell polynomials and Hirota method. The results show that there exist multi-soliton solutions for such an equation. Relations between the direction of the soliton propagation and coordinate axes are shown. Elastic interaction with the multi-soliton solutions are analysed.

Impact of Entropy Generation on Stagnation-Point Flow of Sutterby Nanofluid: A Numerical Analysis

Abstract: Abstract The present article dicusses the computational analysis of entropy generation for the stagnation-point flow of Sutterby nanofluid over a linear stretching plate. The Sutterby fluid is chosen to study the effect for three major classes of non-Newtonian fluids, i.e. pseudoplastic, Newtonian, and dilatant. The effects of pertinent physical parameters are examined under the approximation of boundary layer. The system of coupled nonlinear partial differential equations is simplified by incorporating suitable similarity transformation into a system of non-linear-coupled ordinary differential equations. Entropy generation analysis is conducted numerically, and the results are displayed through graphs and tables. Significant findings are listed in the closing remarks.

The Modified Simple Equation Method, the Exp-Function Method, and the Method of Soliton Ansatz for Solving the Long-Short Wave Resonance Equations

Abstract: Abstract The modified simple equation method, the exp-function method, and the method of soliton ansatz for solving nonlinear partial differential equations are presented. Based on these three different methods, we obtain the exact solutions and the bright–dark soliton solutions with parameters of the long-short wave resonance equations which describe the resonance interaction between the long wave and the short wave. When these parameters take special values, the solitary wave solutions are derived from the exact solutions. We compare the results obtained using the three methods. Also, a comparison between our results and the well-known results is given.

Solitons, Bäcklund Transformation, Lax Pair, and Infinitely Many Conservation Law for a (2+1)-Dimensional Generalised Variable-Coefficient Shallow Water Wave Equation

Abstract: Abstract Under investigation in this article is a (2+1)-dimensional generalised variable-coefficient shallow water wave equation, which describes the interaction of the Riemann wave propagating along the y axis with a long-wave propagating along the x axis in a fluid, where x and y are the scaled space coordinates. Bilinear forms, Bäcklund transformation, Lax pair, and infinitely many conservation law are derived based on the binary Bell polynomials. Multi-soliton solutions are constructed via the Hirota method. Propagation and interaction of the solitons are illustrated graphically: (i) variable coefficients affect the shape of the multi-soliton interaction in the scaled space and time coordinates. (ii) Positions of the solitons depend on the sign of wave numbers after each interaction. (iii) Interaction of the solitons is elastic, i.e. the amplitude, velocity, and shape of each soliton remain invariant after each interaction except for a phase shift.

Conservation laws and Exact Solutions of Phi-Four (Phi-4) Equation via the (G′/G, 1/G)-Expansion Method

Abstract: Abstract In this article, we constructed formal Lagrangian of Phi-4 equation, and then via this formal Lagrangian, we found adjoint equation. We investigated if the Lie point symmetries of the equation satisfy invariance condition or not. Then we used conservation theorem to find conservation laws of Phi-4 equation. Finally, the exact solutions of the equation were obtained through the (G′/G, 1/G)-expansion method.

On Symmetry Analysis and Conservation Laws of the AKNS System

Abstract: Abstract The Lie symmetry analysis is applied to study the Ablowitz–Kaup–Newell–Segur (AKNS) system of water wave model. The AKNS system can be obtained from a dispersive-wave system via a variable transformation. Lie point symmetries and corresponding point transformations are determined. The optimal system of one-dimensional subalgebras is presented. On the basis of the optimal system, the similarity reductions and the invariant solutions are obtained. Some conservation laws are derived using the multipliers. In addition, the AKNS system is quasi self-adjoint. The conservation laws associated with the symmetries are also constructed.

Soliton, Breather, and Rogue Wave for a (2+1)-Dimensional Nonlinear Schrödinger Equation

Abstract: Abstract In this paper, a (2+1)-dimensional nonlinear Schrödinger (NLS) equation, which is a generalisation of the NLS equation, is under investigation. The classical and generalised N-fold Darboux transformations are constructed in terms of determinant representations. With the non-vanishing background and iterated formula, a family of the analytical solutions of the (2+1)-dimensional NLS equation are systematically generated, including the bright-line solitons, breathers, and rogue waves. The interaction mechanisms between two bright-line solitons and among three bright-line solitons are both elastic. Several patterns for first-, second, and higher-order rogue wave solutions fixed at space are displayed, namely, the fundamental pattern, triangular pattern, and circular pattern. The two-dimensional space structures of first-, second-, and third-order rogue waves fixed at time are also demonstrated.

Interband Heating Processes in a Periodically Driven Optical Lattice

Abstract: We investigate multi-"photon" interband excitation processes in an optical lattice that is driven periodically in time by a modulation of the lattice depth. Assuming the system to be prepared in the lowest band, we compute the excitation spectrum numerically. Moreover, we estimate the effective coupling parameters for resonant interband excitation processes analytically, employing degenerate perturbation theory in Floquet space. We find that below a threshold driving strength, interband excitations are suppressed exponentially with respect to the inverse driving frequency. For sufficiently low frequencies, this leads to a rather sudden onset of interband heating, once the driving strength reaches the threshold. We argue that this behavior is rather generic and should also be found in lattice systems that are driven by other forms of periodic forcing. Our results are relevant for Floquet engineering, where a lattice system is driven periodically in time in order to endow it with novel properties like the emergence of a strong artificial magnetic field or a topological band structure. In this context, interband excitation processes correspond to detrimental heating.

Unexpected Behavior on Nonlinear Tunneling of Chirped Ultrashort Soliton Pulse in Non-Kerr Media with Raman Effect

Abstract: Abstract In this manuscript, the ultrashort soliton pulse propagation through nonlinear tunneling in cubic quintic media is investigated. The effect of chirping on propagation characteristics of the soliton pulse is analytically investigated using similarity transformation. In particular, we investigate the propagation dynamics of ultrashort soliton pulse through dispersion barrier for both chirp and chirp-free soliton. By investigating the obtained soliton solution, we found that chirping has strong influence on soliton dynamics such as pulse compression with amplification. These two important dynamics of chirped soliton in cubic quintic media open new possibilities to improve the solitonic communication system. Moreover, we surprisingly observe that a dispersion well is formed for the chirped case whereas a barrier is formed for the chirp-free case, which has certain applications in the construction of logic gate devices to achieve ultrafast switching.

Rogue-Wave Interaction of a Nonlinear Schrödinger Model for the Alpha Helical Protein

Abstract: Abstract In this article, we investigate a fourth-order nonlinear Schrödinger equation, which governs the Davydov solitons in the alpha helical protein with higher-order effects. By virtue of the generalised Darboux transformation, higher-order rogue-wave solutions are derived. Propagation and interaction of the rogue waves are analysed: (i) Coefficients affect the existence time of the first-order rogue waves; (ii) coefficients affect the interaction time of the second- and third-order rogue waves; (iii) direction of the rogue-wave propagation remain unchanged after interaction.

Mechanical and Electronic Properties of P42/mnm Silicon Carbides

Abstract: Abstract Two new phases of Si8C4 and Si4C8 with the P42/mnm symmetry are proposed. Using first principles calculations based on density functional theory, the structural, elastic, and electronic properties of Si8C4 and Si4C8 are studied systematically. Both Si8C4 and Si4C8 are proved to be mechanically and dynamically stable. The elastic anisotropies of Si8C4 and Si4C8 are studied in detail. Electronic structure calculations show that Si8C4 and Si4C8 are indirect semiconductors with the band gap of 0.74 and 0.15 eV, respectively.

Qualitative Behaviour of Generalised Beddington Model

Abstract: Abstract This work is related to the dynamics of a discrete-time density-dependent generalised Beddington model. Moreover, we investigate the existence and uniqueness of positive equilibrium point, boundedness character, local and global behaviours of unique positive equilibrium point, and the rate of convergence of positive solutions that converge to the unique positive equilibrium point of this model. Numerical examples are provided to illustrate theoretical discussion.

Unsteady Mixed Bioconvection Flow of a Nanofluid Between Two Contracting or Expanding Rotating Discs

Abstract: Abstract An investigation is made for a three-dimensional unsteady mixed nano-bioconvection flow between two contracting or expanding rotating discs. The passively controlled nanofluid model in which Brownian diffusion and thermophoresis are considered as the two dominant factors for nanoparticle/base-fluid slip mechanisms is introduced for description of this flow problem. A novel similarity transformation is introduced so that the governing equations embodying the conservation of total mass, momentum, thermal energy, nanoparticle volume fraction, and microorganisms are reduced to a set of five fully coupled ordinary differential equations. Exact solutions are then obtained analytically for this complex nonlinear system. Besides, the influences of various physical parameters on distributions of velocity, temperature, nanoparticle volume fraction, and the density of motile microorganisms, along with the local Nusselt number and the local wall motile microorganisms flux, are presented and discussed. It is expected that this study can provide a theoretical base for understanding the transport mechanisms of unsteady bioconvection in nanofluids.

Robust Finite-Time Passivity for Discrete-Time Genetic Regulatory Networks with Markovian Jumping Parameters

Abstract: Abstract This article addresses the issue of robust finite-time passivity for a class of uncertain discrete-time genetic regulatory networks (GRNs) with time-varying delays and Markovian jumping parameters. By constructing a proper Lyapunov–Krasovskii functional involving the lower and upper bounds of time delays, a new set of sufficient conditions is obtained in terms of linear matrix inequalities (LMIs), which guarantees the finite-time boundedness and finite-time passivity of the addressed GRNs for all admissible uncertainties and satisfies the given passive performance index. More precisely, the conditions are obtained with respect to the finite-time interval, while the exogenous disturbances are unknown but energy bounded. Furthermore, the Schur complement together with reciprocally convex optimisation approach is used to simplify the derivation in the main results. Finally, three numerical examples are provided to illustrate the validity of the obtained results.

Exact solutions for Stokes' Flow of a non-Newtonian nanofluid model: a Lie Similarity approach

Abstract: Abstract The fully developed time-dependent flow of an incompressible, thermodynamically compatible non-Newtonian third-grade nanofluid is investigated. The classical Stokes model is considered in which the flow is generated due to the motion of the plate in its own plane with an impulsive velocity. The Lie symmetry approach is utilised to convert the governing nonlinear partial differential equation into different linear and nonlinear ordinary differential equations. The reduced ordinary differential equations are then solved by using the compatibility and generalised group method. Exact solutions for the model equation are deduced in the form of closed-form exponential functions which are not available in the literature before. In addition, we also derived the conservation laws associated with the governing model. Finally, the physical features of the pertinent parameters are discussed in detail through several graphs.

Oscillations in the Interactions Among Multiple Solitons in an Optical Fibre

Abstract: Abstract In this article, under the investigation on the interactions among multiple solitons for an eighth-order nonlinear Schrödinger equation in an optical fibre, oscillations in the interaction zones are observed theoretically. With different coefficients of the operators in this equation, we find that (1) the oscillations in the solitonic interaction zones have different forms with different spectral parameters of this equation; (2) the oscillations in the interactions among the multiple solitons are affected by the choice of spectral parameters, the dispersive effects and nonlinearity of the eighth-order operator; (3) the second-, fifth-, sixth-, and seventh-order operators restrain oscillations in the solitonic interaction zones and the higher-order operators have stronger attenuated effects than the lower ones, while the third- and fourth-order operators stimulate and extend the scope of oscillations.

Nonlocal Symmetry and Consistent Tanh Expansion Method for the Coupled Integrable Dispersionless Equation

Abstract: Abstract Nonlocal symmetries are obtained for the coupled integrable dispersionless (CID) equation. The CID equation is proved to be consistent, tanh-expansion solvable. New, exact interaction excitations such as soliton–cnoidal wave solutions, soliton–periodic wave solutions, and multiple resonant soliton solutions are discussed analytically and shown graphically.

Negative Energies in the Dirac Equation

Abstract: It is easy to check that both algebraic equation Det (hat p - m) =0 and Det (hat p + m) =0 for u- and v- 4-spinors have solutions with p_0= pm E_p = pm sqrt bf p^2 +m^2. The same is true for higher-spin equations. Meanwhile, every book considers the equality p_0=E_p for both u- and v- spinors of the (1/2,0)+(0,1/2)) representation only, thus applying the Dirac-Feynman-Stueckelberg procedure for elimination of the negative-energy solutions. The recent Ziino works (and, independently, the articles of several others) show that the Fock space can be doubled. We re-consider this possibility on the quantum field level for both s=1/2 and higher spin particles.

Multi-Scale Morphological Analysis of Conductance Signals in Vertical Upward Gas–Liquid Two-Phase Flow

Abstract: Abstract The multi-scale analysis is an important method for detecting nonlinear systems. In this study, we carry out experiments and measure the fluctuation signals from a rotating electric field conductance sensor with eight electrodes. We first use a recurrence plot to recognise flow patterns in vertical upward gas–liquid two-phase pipe flow from measured signals. Then we apply a multi-scale morphological analysis based on the first-order difference scatter plot to investigate the signals captured from the vertical upward gas–liquid two-phase flow loop test. We find that the invariant scaling exponent extracted from the multi-scale first-order difference scatter plot with the bisector of the second-fourth quadrant as the reference line is sensitive to the inhomogeneous distribution characteristics of the flow structure, and the variation trend of the exponent is helpful to understand the process of breakup and coalescence of the gas phase. In addition, we explore the dynamic mechanism influencing the inhomogeneous distribution of the gas phase in terms of adaptive optimal kernel time–frequency representation. The research indicates that the system energy is a factor influencing the distribution of the gas phase and the multi-scale morphological analysis based on the first-order difference scatter plot is an effective method for indicating the inhomogeneous distribution of the gas phase in gas–liquid two-phase flow.

Soliton and Shock Profiles in Electron-positron-ion Degenerate Plasmas for Both Nonrelativistic and Ultra-Relativistic Limits

Abstract: Abstract An attempt has been taken to find a general equation for degenerate pressure of Chandrasekhar and constants, by using which one can study nonrelativistic as well as ultra-relativistic cases instead of two different equations and constants. Using the general equation, ion-acoustic solitary and shock waves have been studied and compared, numerically and graphically, the two cases in same situation of electron-positron-ion plasmas. Korteweg–de Vries (KdV) and KdV–Barger equations have been derived as well as their solution to study the soliton and shock profiles, respectively.

Lump Solutions for the (3+1)-Dimensional Kadomtsev–Petviashvili Equation

Abstract: Abstract In this article, we investigate the lump solutions for the Kadomtsev–Petviashvili equation in (3+1) dimensions that describe the dynamics of plasmas or fluids. Via the symbolic computation, lump solutions for the (3+1)-dimensional Kadomtsev–Petviashvili equation are derived based on the bilinear forms. The conditions to guarantee analyticity and rational localisation of the lump solutions are presented. The lump solutions contain eight parameters, two of which are totally free, and the other six of which need to satisfy the presented conditions. Plots with particular choices of the involved parameters are made to show the lump solutions and their energy distributions.

Cooling of Moving Wavy Surface through MHD Nanofluid

Abstract: Abstract Heat transfer analysis has been carried out in the Magnetohydrodynamic (MHD) boundary layer formed near the wavy rough plate moving in x-direction. Due to the presence of metallic nanoparticle in the fluid and enhanced surface area of the plate as a consequence of surface texture, an increase in heat transfer rates is expected. However, the calculation of these enhanced rates of heat transfer is not straightforward because the convection phenomena become more complicated due to the motion of nanoparticle in the base fluid and also the waviness of the plate surface. The contribution of nanoparticle toward convective heat transfer is manifold which requires a suitable model in order to capture the correct physics. Famous Tiwari and Das model has been utilised in the current study. Percent increase in the rate of heat transfer is calculated for the nanoparticle of different metals, such as MWCNT, SWCNT, Al2O3, TiO2 and Ag. Appreciable increase in the rate of heat transfer is observed, which is 24% at the most for Al2O3 nanoparticle. The effect of applied magnetic field on the velocity profile, skin friction coefficient, and Nusselt number has also been presented through graphs. The concentration of the nanoparticle has been limited up to 10%.

Anatomy of a Periodically Driven p-Wave Superconductor

Abstract: The topological properties of periodically driven many-body systems often have no static analogs and defy a simple description based on the effective Hamiltonian. To explore the emergent edge modes in driven p-wave superconductors in two dimensions, we analyze a toy model of Kitaev chains (one-dimensional spinless p-wave superconductors with Majorana edge states) coupled by time-periodic hopping. We show that with proper driving, the coupled Kitaev chains can turn into a fully gapped superconductor which is analogous to the $p_x+ip_y$ state but has two, rather than one, chiral edge modes. A different driving protocol turns it into a gapless superconductor with isolated point nodes and completely flat edge states at quasienergy $\omega=0$ or $\pi/T$, with $T$ the driving period. The time evolution operator $U(k_x,k_y,t)$ of the toy model is computed exactly to yield the phase bands. And the "topological singularities" of the phase bands are exhausted and compared to those of a periodically driven Hofstadter model which features counter-propagating chiral edge modes. These examples demonstrate the unique edge states in driven superconducting systems and suggest driving as a potentially fruitful route to engineer new topological superconductors.

First-Principles Study of Lattice Dynamics, Structural Phase Transition, and Thermodynamic Properties of Barium Titanate

Abstract: Abstract Lattice dynamics, structural phase transition, and the thermodynamic properties of barium titanate (BaTiO3) are investigated by using first-principles calculations within the density functional theory (DFT). It is found that the GGA-WC exchange-correlation functional can produce better results. The imaginary frequencies that indicate structural instability are observed for the cubic, tetragonal, and orthorhombic phases of BaTiO3 and no imaginary frequencies emerge in the rhombohedral phase. By examining the partial phonon density of states (PDOSs), we find that the main contribution to the imaginary frequencies is the distortions of the perovskite cage (Ti-O). On the basis of the site-symmetry consideration and group theory, we give the comparative phonon symmetry analysis in four phases, which is useful to analyze the role of different atomic displacements in the vibrational modes of different symmetry. The calculated optical phonon frequencies at Γ point for the four phases are in good agreement with other theoretical and experimental data. The pressure-induced phase transition of BaTiO3 among four phases and the thermodynamic properties of BaTiO3 in rhombohedral phase have been investigated within the quasi-harmonic approximation (QHA). The sequence of the pressure-induced phase transition is rhombohedral→orthorhombic→tetragonal→cubic, and the corresponding transition pressure is 5.17, 5.92, 6.65 GPa, respectively. At zero pressure, the thermal expansion coefficient αV, heat capacity CV, Grüneisen parameter γ, and bulk modulus B of the rhombohedral phase BaTiO3 are estimated from 0 K to 200 K.

The Non-Alignment Stagnation-Point Flow Towards a Permeable Stretching/Shrinking Sheet in a Nanofluid Using Buongiorno's Model: A Revised Model

Abstract: Abstract A numerical study on the stagnation-point boundary layer flow of a viscous and incompressible (Newtonian) fluid past a stretching/shrinking sheet with the fluid suction using Buongiorno’s model is considered. The main focus of this article is the effects of the non-alignment of the flow and the surface of the sheet. We have also studied the problem using a new boundary condition that is more physically realistic which assumes that the nanoparticle fraction at the surface is passively controlled. The governing equations of this problem are reduced to the ordinary differential equations using some similarity transformations which are then solved using the bvp4c function in Matlab. From the results obtained, we concluded that the effect of the non-alignment function is the same as in the regular fluid or nanofluid. However, it is found that the fluid suction can reduce the effect of the non-alignment at the surface. Dual solutions have also been discovered in this problem and from the stability analysis it is found that the first solution is stable while the second solution is not stable.

Multi-Scale Long-Range Magnitude and Sign Correlations in Vertical Upward Oil-Gas-Water Three-Phase Flow

Abstract: Abstract In this article we apply an approach to identify the oil–gas–water three-phase flow patterns in vertical upwards 20 mm inner-diameter pipe based on the conductance fluctuating signals. We use the approach to analyse the signals with long-range correlations by decomposing the signal increment series into magnitude and sign series and extracting their scaling properties. We find that the magnitude series relates to nonlinear properties of the original time series, whereas the sign series relates to the linear properties. The research shows that the oil–gas–water three-phase flows (slug flow, churn flow, bubble flow) can be classified by a combination of scaling exponents of magnitude and sign series. This study provides a new way of characterising linear and nonlinear properties embedded in oil–gas–water three-phase flows.

Bäcklund Transformation and Soliton Solutions for a (3+1)-Dimensional Variable-Coefficient Breaking Soliton Equation

Abstract: Abstract In this article, a (3+1)-dimensional variable-coefficient breaking soliton equation is investigated. Based on the Bell polynomials and symbolic computation, the bilinear forms and Bäcklund transformation for the equation are derived. One-, two-, and three-soliton solutions are obtained via the Hirota method. N-soliton solutions are also constructed. Propagation characteristics and interaction behaviors of the solitons are discussed graphically: (i) solitonic direction and position depend on the sign of the wave numbers; (ii) shapes of the multisoliton interactions in the scaled space and time coordinates are affected by the variable coefficients; (iii) multisoliton interactions are elastic for that the velocity and amplitude of each soliton remain unchanged after each interaction except for a phase shift.

Closed analytical solutions of the d-dimensional Schr\"odinger equation with deformed Woods-Saxon potential plus double ring-shaped potential

Abstract: By employing the Pekeris approximation, the D-dimensional Schr\"odinger equation is solved for the nuclear deformed Woods-Saxon potential plus double ring-shaped potential within the framework of the Asymptotic Iteration Method (AIM). The energy eingenvalues are given in a closed form and the corresponding normalized eigenfunctions are obtained in terms of hypergeometric functions. Our general results reproduce many predictions obtained in the literature, using the Nikiforov-Uvarov method (NU) and the Improved Quantization Rule approach, particulary those derived by considering Woods-Saxon potential without deformation and/or without ring shape interaction.

Flow and Heat Transfer of Bingham Plastic Fluid over a Rotating Disk with Variable Thickness

Abstract: Abstract This paper studies the steady flow and heat transfer of Bingham plastic fluid over a rotating disk of finite radius with variable thickness radially in boundary layer. The boundary layer flow is caused by the rotating disk when the extra stress is greater than the yield stress of the Bingham fluid. The analyses of the velocity and temperature field related to the variable thickness disk have not been investigated in current literatures. The governing equations are first simplified into ordinary differential equations owing to the generalized von Kármán transformation for seeking solutions easily. Then semi-similarity approximate analytical solutions are obtained by using the homotopy analysis method for different physical parameters. It is found that the Bingham number clearly influences the velocity field distribution, and the skin friction coefficient Cfr is nonlinear growth with respect to the shape parameter m. Additionally, the effects of the involved parameters (i.e. shape parameter m, variable thickness parameter β, Reynolds number Rev, and Prandtl number Pr) on velocity and temperature distribution are investigated and analyzed in detail.