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We study the dimensionless time evolution of the logarithmic negativity and geometric quantum discord of a qubit-qutrit XXX spin model under the both Markovian and non-Markovian noise channels. We find that at a special temperature interval the quantum entanglement based on the logarithmic negativity reveals entanglement sudden deaths together with revivals. The revival phenomenon is due to the non-Markovianity resulting from the feedback effect of the environment. At high temperatures, the scenario of death and revival disappears. The geometric quantum discord evolves alternatively versus time elapsing with damped amplitudes until the system reaches steady state. It is demonstrated that the dynamics of entanglement negativity undergoes substantial changes by varying temperature, and it is much more fragile against the temperature rather than the geometric quantum discord. The real complex heterodinuclear [Ni(dpt)(H2O)Cu(pba)] · 2H2O [with pba = 1,3-propylenebis(oxamato) and dpt = bis-(3-aminopropyl)amine] is an experimental representative of our considered bipartite qubit-qutrit system that may show remarkable entanglement deaths and revivals at relatively high temperatures and high magnetic field that is comparable with the strength of the exchange interaction J between Cu+2 and Ni+2 ions, i.e., k B T ≈ J and μ B B ≈ J.

The suspension of nanoparticles in the base fluid has been tested to improve the heat transfer properties of the fluid since solid metals are characterized with higher thermal conductivity than the convectional working fluid. This present work focuses on the suspension of nanoparticles into the upper convected Maxwell fluid model (UCM) so as to improve the heat transfer efficacy of the fluid. The governing partial differential equations and their related boundary conditions are transformed and parameterized by applying appropriate transformations into a system of non-linear ordinary differential equations and the series solutions are obtained through homotopy analysis method. The impact of various parameters on velocity, temperature and nanoparticles concentration profiles are reviewed and discussed. It is discovered that increasing the Brownian motion increases the thermal conductivity of fluid and hence promotes the effective movement of the nanoparticles.

This study examines the 1 + 2 -dimensional Zoomeron equation, which has recently become popular in applied mathematics and physics. Bright soliton (non-topological), kink wave solution and traveling wave solutions are generated with the advantages of the generalized exponential rational function method. With the help of this method, it is aimed to produce different types of solutions for the Zoomeron equation compared to other traditional exponential function methods. The effects of parameters on the amplitude of the wave function are discussed, along with physical explanations backed by simulations. In addition, the advantages and disadvantages of the method for the 1 + 2 -dimensional Zoomeron equation are discussed.

We numerically investigate the dynamics of Vertical-Cavity Surface-Emitting Lasers (VCSELs) described by the current-dependent gain model and subjected to current in the form of amplitude modulation (AM) and frequency modulation (FM). Since VCSELs have two polarization modes (PMs), the competition between them offers more complex dynamical behaviors. It is found that when operating close to the threshold current, the laser converts the AM and FM currents into a series of pulse packages (PPs) that are globally irregular and modulated either in amplitude or frequency. In the particular case of FM current, both modulations occur in a unique signal. Besides, chaotic light is recovered even at low frequencies (few MHz) where it is not usually expected when sinusoidal current modulation is used. But, if the AM and the FM currents evolve over the threshold value, the laser does not alter the form of the current. Therefore, those currents are linearly converted into light signals.

Models of population dynamics are substantially non-Markovian in nature and exhibit behavior for memory effects. This research study investigates the logistic growth model from population dynamics under both classical and non-classical (fractional) differential operators using actual statistical data. For the non-classical differential operator, the operator called conformable fractional derivative having order β in the sense of Liouville-Caputo (LC) of order α is employed while taking care of its dimensional consistency. Working parameters including conformable fractional derivative order β, LC having order α, growth rate ζ, and carrying capacity Φ have been optimized, and the results are compared with those of classical one. Error rate suggests the superiority of the fractional conformable logistic model whose solutions are investigated for uniqueness via fixed point theory. Numerical simulations using Adams' iterative technique recently proposed for the conformable fractional derivative are illustrated in figures for a thorough understanding of the model's behavior, along with a statistical summary for the operators. An attractive chaotic attractor is observed in the fractional logistic model when ζ 4.023. Cumulative effects of growth rate and carrying capacity on the population's change in the logistic model are also investigated with 3D graphics.

We study the ground and first excited state of the finite one dimensional Majumdar-Ghosh model with quenched disorder about the avoided crossings. We find a relation between the shift of the first avoided crossing and average value of random numbers. For low disorder regime, the two-qubit, odd and even partition entanglement gets exchanged at avoided crossings for low spin, and former two for any value of spin. This effect has a deep relation with the dimerization nature of these states. We develop an expression sans entanglement measures to detect and study these crossings.

The (3+1)-dimensional generalized nonlinear evolution equation (gNLEE) is analyzed to model oceanic waves. One-parameter Lie group of infinitesimal transformations method is applied to the (3+1)-dimensional gNLEE. Invariant condition satisfying fourth-order prolongation and generators of infinitesimal transformations are found. The (3+1)-dimensional gNLEE is reduced to ordinary differential equations (ODEs) for the different vector fields obtained by the Lie group of transformations method. The key finding for the study of breathers and solitons that account for waveform perturbation and dispersion, including nonlinear impacts, is elaborated. Discussion of wave-wave interactions, using graphic interpretation, to explain the formation of directional large-amplitude rogue waves is explained. It is found that the scale in the crest direction becomes finite as the coherence becomes diagonal. In addition, unstable wave fields, beam dynamics, and interactions among solitons are seen.

Bioconvection for rotational flow is conceived to provide stability to improved thermal transportation for Reiner-Rivlin nano fluid over a disk with multi-slips. The nonFourier heat flux, binary chemical reaction, magnetic force, and activation energy are incorporated. A system of nonlinear differential equations in coupled form is acquired through the fundamental relations of Reiner-Rivlin fluids. The Runge-Kutta method of fourth-order is used to solved differential equations in MATLAB environment. The impact of various parameters are discussed and drawn physically with the help of graphs. The Reiner-Rivlin fluid parameter, magnetic parameter, thermophoresis, and Brownian motion parameter escalated the nanofluid temperature field. The electromagnetic parameter and Reiner-Rivlin fluid parameter decelerated the primary flow velocity and activation energy augmented the volume fraction of nanoparticles in the boundary layer region. An excellent accord among the present and previously existing solutions is establishes the validity of the current findings.

This paper studies decoherence without dissipation of charged magneto-oscillator in the framework of quantum non-demolition type interaction in non-commutative phase-space. The master equation is derived considering the non-commutativity effects of a bath of harmonic oscillators to study the dynamics of such a system, and its possible exact solution is presented. By analyzing this solution, it turns out that the process involving decoherence without energy dissipation can be observed explicitly. In addition, the decoherence factor and the measure of coherence via linear entropy dynamic are deduced for two types of reservoir, namely the ohmic and super-ohmic reservoirs at low and high temperature limits. Numerical results obtained show that the coherence is better preserved in the system when non-commutativity effects are taken into account at low temperature, while the inverse phenomenon is observed at high temperature. Moreover, by kindly adjusting the non-commutative parameters, it is possible to improve the coherence time scale of the system. Another interesting result can be observed from the system’s coherence time scale, which is very sensitive to the magnetic field and thus adding to non-commutative parameters, it may be useful to control decoherence in the system.

Carbon nanotubes are used to achieve high heat transfer rates in a variety of engineering applications include thermal storage systems, electronic component cooling, high-performance building insulation, heat exchangers and drying technologies. Hence the aim of this article is to examine the addition of single walled carbon nanotubes (SWCNT) and multi-walled carbon nanotubes (MWCNT) to water in a vertical microchannel to improve heat transfer. The effects of MHD, slip, convective boundary condition and heat source/sink are incorporated. The Brinkman-Forchheimer flow model and type II hybrid nanofluid model is adopted. Converted dimensionless differential equations are solved numerically via Dsolve command with the aid of Maple. The simulation assessment is worked out by graphs. One of the main tasks of the analysis is to compare MWCNT/water and SWCNT-MWCNT/water. It is shown that the improvement of the heat source/sink parameter improves the temperature and the rate of heat transfer in MWCNT/water is higher than SWCNT-MWCNT/water. Also larger values of Lorentz force and buoyancy force decreases the drag coefficient.

Non-equilibrium dynamics of interfaces and mixing are omnipresent in fluids, plasmas and materials, in nature and technology, at astrophysical and at molecular scales. This work investigates dynamics of an interface separating fluids of different densities and having interfacial mass flux, and being influenced by the acceleration and the surface tension. We derive solutions for the interface dynamics conserving mass, momentum and energy, find the critical acceleration values separating stable and unstable regimes, and reveal the macroscopic inertial mechanism as primary mechanism of the interface stabilization. We show that while the surface tension influences only the interface, its presence leads to formation of vortical structures in the bulk. For large accelerations the conservative dynamics is unstable, leading to the growth of interface perturbations and the growth of the interface velocity. This new instability can be unambiguously discerned from other instabilities; for strong accelerations it has the fastest growth-rate and the largest stabilizing surface tension value when compared to Landau-Darrieus and Rayleigh-Taylor instabilities. We further find the values of initial perturbation wavelengths at which the conservative dynamics can be stabilized and at which it has the fastest growth. Our results agree with existing observations, identify extensive theory benchmarks for future experiments and simulations, and outline perspectives for application problems in nature and technology.

In this current study, the steady, two-dimensional flow of an incompressible Casson fluid along a horizontal thin moving needle is investigated. Influence of Soret/Dufour effect and thermophoretic particle deposition is considered to examine the heat and mass transport analysis. This model finds application in designing of new medical equipment’s for cell delivery to the central nervous system. The efficient Runge–Kutta Fehlberg fourth fifth order method by adopting shooting technique is employed to solve the reduced non-dimensional form of equations. The impact of several non-dimensional parameters on concentration, velocity and thermal fields are discussed with the help of suitable graphs. Also, friction factor, heat passage rate and thermophoretic particle deposition velocity are analyzed graphically. Results reveal that, increase in Dufour number declines heat transfer but opposite behaviour is depicted in mass transfer. The increasing values of thermophoretic parameter improves the mass transfer. Thermophoretic diffusive deposition velocity increases for rising values of thermophoretic parameter.

We investigated theoretically the nonlinear propagation dynamics of Gaussian beams in the fractional Schrödinger equation (FSE). When the nonlinearity is introduced into FSE without invoking an external potential, the evolution behaviors of incident Gaussian beams are modulated regularly and some novel phenomena arise. In the one-dimensional case, by changing the values of Kerr or saturated nonlinear coefficient, specific localized or diffracted phenomena appear in the corresponding intensity region, where the splitting angle of one-dimensional incident beam will be modulated flexibly to become larger or smaller in weak nonlinear region, besides, when the self-focusing strength is moderate, the energy of the beam is highly concentrated to form a breathing soliton structure. For two-dimensional case, Kerr or saturated nonlinearity will modulate the energy to the middle or edge in a certain nonlinear region, corresponding to the decrease or increase of the conical diffraction radius, it should be noted that there are two evolution periods under the saturated self-focusing nonlinearity. The work may provide more possibilities for beam modulation in FSE from a nonlinear perspective.

We describe the gluon field dynamics from Unified Spinor Fields, taking into account the quantum self-interactions which come from a Ricci flow in a varied Einstein-Hilbert action. A new action to describe the Yang-Mills fields is introduced and it is obtained the nonlinear equation of motion on a curved background Riemann manifold, with self-interactions included, for the gluon field components.

In the present investigation, design of integrated numerical computing through Levenberg-Marquardt backpropagation neural network (LMBNN) is presented to examine the fluid mechanics problems governing the dynamics of expanding and contracting cylinder for Cross magneto-nanofluid flow (ECCCMNF) model in the presence of time dependent non-uniform magnetic force and permeability of the cylinder. The original system model ECCCMNF in terms of PDEs is converted to nonlinear ODEs by introducing the similarity transformations. Reference dataset of the designed LMBNN methodology is formulated with Adam numerical technique for scenarios of ECCCMNF by variation of thermophoresis temperature ratio parameter, Brownian motion, suction parameters as well as Schmidt, Prandtl, local Weissenberg and Biot numbers. To calculate the approximate solution for ECCCMNF for different scenarios, the training, testing, and validation processes are conducted in parallel to adapt neural network by reducing the mean square error (MSE) function through Levenberg-Marquardt backpropagation. The comparative studies and performance analyses based on outcomes of MSE, error histograms, correlation and regression demonstrate the effectiveness of designed LMBNN technique.

Despite numerous reports on the newly discovered hybrid nanofluid, little is known on the influence of increasing Reynolds number, stretching of lower, and upper disks on the dynamics of water conveying graphene and silver between rotating disks when Lorentz force, Joule heating, suction, thermal radiation of thermal energy, and Cattaneo-Christov heat flux are highly significant. This report provides insight into such transport phenomenon with an emphasis on the increasing effects of Reynolds number, stretching of lower, and upper disks. Initially, leading equations of motion and energy are transmuted into a system of nonlinear ordinary differential equations with the aid of suitable (Von-Karman) similarity transmutations. Later, by enforcing shooting procedure (R-K 4th order based) to obtain the numerical solutions. Based on the analysis, it is worth concluding that increasing the Reynolds number improves the thermal field but reduces the tangential velocity. Entropy generation is an increasing property of stretching lower and upper disks but these are yardsticks for decreasing Bejan number.

A generalized form of the autonomous Bonhoeffer-van der Pol (BVdP) system described by a second-order dynamical system with six independent parameters consistent with its optimal mathematical modeling, instead of three usually used, is investigated. Through its equivalent form, the generalized asymmetric van der Pol-Duffing (GAVdPD) system and the steady states of this system are derived. The analysis show that the system may exhibit one or three steady states when it is driven by an external constant impulse taken as a main control parameter. Domain ranges in which the system can function as well as monostable system as a bistable system are derived. In addition, by means of the theory of Hopf Bifurcation, it appears that there are large possibilities for the system to work as self-sustained oscillator, forced oscillator or other possibilities for which the system does not operate, indicating the richness of this generalized form of the BVdP system. Limit cycle solutions are derived at the neighboring of the Andronov-Hopf Bifurcation points even for large values of the asymmetric parameter. All these results are checked through numerical simulations. Applying these analytical investigations to the electronic circuit executing the dynamics of the basic BVdP system, two distinct working regimes are highlighted, depending on the magnitude of the capacitance with respect to a threshold value function of the characteristic parameters both of the self and of the nonlinear resistance. Through PSPICE simulations the accuracy of these analytical and numerical investigations have been confirmed.

We study dynamics of soliton waves, lump solutions and interaction solutions to a (2+1)-dimensional generalized Bogoyavlensky-Konopelchenko equation, which possesses a Hirota bilinear form. Multi-soliton solutions, one-M-lump solutions, and physical interactions between solitons and 1-M-lump solutions are presented. By using a positive quadratic function, lump solutions and their interaction solutions with kink and solitary waves are also generated. To show dynamical properties and physical behaviors of the resulting solutions, 3D-plots and contour plots at different times are made and analyzed.

We study various regimes of coherent coupled motion of a polaron and one-dimensional Bose–Einstein condensate in a harmonic potential. By using qualitative analysis, perturbation theory and direct numerical solution of the Gross–Pitaevskii equation, we show that the entire dynamics is strongly nonlinear and critically depends on the sign of the self-interaction in the condensate and the sign of the interaction between the polaron-forming embedded particle and the condensate. Strongly mutually related evolution of the condensate shape, its center of mass position, and polaron coordinate is studied for coupled nonlinear polaron-condensate oscillations and transmission/reflection of the polaron through/by the condensate.

The purpose of this paper aims to explore the mechanism of several different periodic bursting patterns based on a Mathieu-van der Pol-Duffing energy harvester with parameter excitation. These bursting patterns are categorized as ‘delayed supHopf/supHopf’ bursting, ‘delayed pitchfork/pitchfork’ bursting, ‘delayed Hopf-pitchfork/Hopf-pitchfork’ bursting, ‘delayed subHopf/supHopf’ bursting and ‘delayed subHopf/fold-cycle’ bursting, respectively. Since bursting oscillations can be created when the trajectory transfers between/among different attractors, which means the amplitude of bursting oscillations may be sufficient to overcome the potential barrier of the energy harvester, and thus it would have potential application value in energy harvesting.

The worth of the study is to explore how in the presence of Coriolis force, heat and mass transfer rates are optimized through water carrying nanoparticles of more than one type and how this force affects various factors of the flow to make them easy come easy go. The aim of the current study is to analyze the vital characteristic of flow in particular velocity, temperature, concentration, heat flux at the surface, and tangential stress for both nanofluid CuO-water and hybrid nanofluid Cu/Cuo-water over a stretching surface in presence of Coriolis force. Partial differential equations for flow, energy, and concentration are constructed and transformed into ordinary differential equations by using suitable transformations. A highly reliable numerical scheme namely midpoint integration accompanied by Richardson’s extrapolation is launched to solve these equations. A computer software MAPLE is taken in to account to tackle the problem. Results are expressed through graphs and tables. The major conclusions are that the Coriolis force declines the velocity boundary and heat transmission rate but increases the thermal boundary of nanofluid. The heat sink/source factor uplifts the thermal boundary while Schmidt number enhances the mass concentration.

We study the chaotic dynamics of the hydrogen atom in a space-dependent gradient electric field. We use the Poincaré surface of section (PSS) and the Lyapunov exponents to characterize chaotic dynamics. The dynamical character of this system is studied and the regular-chaos transition is found when the system passes from the non-integrable case to the integrable one. It is found that for a given gradient electric field, this system has a critical scaled energy ε s . When the scaled energy ε ≤ ε s , the structure of the whole phase space is nearly regular. However, as the scaled energy ε > ε s , chaotic structures appear in the PSS. As the scaled energy is very large, the whole PSS is chaotic. The chaotic property of this system is further verified by the positive value of the maximum Lyapunov exponent. In addition, we show that with increasing electric field gradient the dynamics of this system becomes increasingly chaotic. Our work provides an example to study the chaotic dynamics of the hydrogen atom by using the space-dependent electric field. We hope that our results can guide the future experimental researches about the dynamical property of the atoms or molecules in the non-uniform external fields.

When radiation fields propagate through mediums and interact with environments, the quantum characteristics of the field states usually undergo deterioration, in particular, the nonclassicality (quantumness) often decays due to photon loss. To address this issue in a quantitative way, we invoke a nonclassicality quantifier based on the Wigner-Yanase skew information and explore the dynamics of nonclassicality in the photon-loss channel for several typical initial states. We illustrate pictorially the decoherence and quantum to classical transition in the photon-loss channel from an informational perspective. It is remarkable that for certain initial states with small average photon numbers, the nonclassicality, as quantified in terms of the Wigner-Yanase skew information, may exhibit nonmonotonic behavior (revival), as compared with the general case of monotonic decaying of nonclassicality.

A redox flow battery (RFB) is an energy storage capable of contributing to grid balancing under the fluctuation of renewable power sources and loads. An RFB consists of reaction cells and tanks containing electrolytes that are pumped to the cells. Modeling of the charging/discharging dynamics is necessary for controlling the flows of the electrolytes and the current. The previous researches have assumed that the transport delay is small and negligible. However, when the transport delay appears, it affects the performance of the control systems. This paper aims to propose a model for considering charging/discharging dynamics with transport delay. The delay appears in the voltages of the cells in the tested system, and a model is introduced to simulate the delay. The model is represented by delay differential equations (DDEs) of the ion concentration in the cells with the Nernst relationship. The DDEs are derived from the mass balance equation including the transport delay translated to the time delay. The simulation result excellently agrees well with the experiment at results. In other words, the model can predict the dynamics governed by the transport delay accurately.

In a previous paper (Krumm and Vogel 2018 Phys. Rev. A 97, 043806) we presented a method to solve the nonlinear Jaynes-Cummings dynamics, describing the quantized motion of a trapped ion exactly, including detuning. Here we investigate this model with respect to nonclassical effects, such as squeezing and sub-Poisson statistics. We show that for the versatile model under study there exist quantum phenomena beyond squeezing and sub-Poisson statistics, such as anomalous quantum correlations of two non-commuting observables. In particular, it is shown that for the excitation of the zeroth sideband neither squeezing nor sub-Poisson statistics do occur, but anomalous correlations can be verified. Furthermore, it is shown how these anomalous correlation functions can be derived from measured data., Comment: 8 pages, 4 figures