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This work analyzes the nucleation and stabilization of torons in cylindrical nanopillars with bulk DMI and easy-plane anisotropy. A micromagnetic study reveals the dependence of toron chains on the nanopillar length and the different behaviors when nucleating an even or odd number of torons in a magnetic nanopillar. Spin wave resonant modes in these systems are explored, evidencing differences according to the number of torons. The interplay between torons, chiral bobbers, and their associated spin wave modes is analyzed, which is relevant for applications demanding dynamical modes in the range of gigahertz. [ABSTRACT FROM AUTHOR]

The linear and weakly nonlinear stability analyses of Darcy–Bénard convection of a Newtonian fluid experiencing a uniform vertical cross-flow is investigated in the paper for various aspect ratios. Making use of the Maclaurin series representation, an expression for axial eigenfunctions is obtained with the radial eigenfunction being a Bessel function of first kind. These eigenfunctions are influenced by the Peclet number, Pe, the non-dimensional number that signifies the rate of vertical cross-flow. The modified-Vadasz-Lorenz model obtained in this paper has newly defined non-dimensional parameters that capture the influence of vertical cross-flow. From the linear stability analysis, it is found that the effect of introducing vertical cross-flow is to stabilize the system. Using a weakly nonlinear stability analysis, the closed-form expression of the Hopf-Rayleigh number as a function of Pe is obtained. Furthermore, the behavior of the modified-Vadasz–Lorenz model is analyzed using the largest Lyapunov exponent and the bifurcation diagram. This gives information about the intensity of chaos and occurrence of the periodic motion. We observe that the influence of vertical cross-flow is to increase the value of the Hopf–Rayleigh number and thereby to delay the onset of chaos. Furthermore, the appearance of the first periodic point is preponed due to the vertical cross-flow. As the rate of vertical cross-flow increases, the intensity of chaos decreases, thereby indicating that the effect of introducing vertical cross-flow is to suppress chaos. [ABSTRACT FROM AUTHOR]

Possibility of chaos is studied in Darcy–Bénard convection using the Dirichlet and the Robin boundary condition at the lower and upper boundaries, respectively. Comparison is made with the results of Dirichlet (classical-Darcy–Bénard convection, CDBC) and Neumann boundary condition (Barletta–Darcy–Bénard convection, BDBC). It is found that the cell size at onset is bigger in the case of BDBC compared to the generalized-Darcy–Bénard convection (GDBC) and much bigger compared to CDBC. The critical-Darcy–Rayleigh number of BDBC is found to be the least and that of CDBC is the largest. Nonlinear-stability-analysis is performed leading to the scaled-generalized-Vadasz–Lorenz model (SGVLM). In deriving this model, help is sought from a local-nonlinear-stability-analysis that yields the form of the convective-mode. The SGVLM is shown to be dissipative and conservative, with its bounded solution trapped within an ellipsoid. Onset of chaos and its characteristics are studied using the Hopf–Rayleigh-number, the Lorenz-butterfly-diagram, and the plot of the amplitude of the convective-mode vs the control-parameter, R, which is the eigenvalue. Chaos sets in earlier in CDBC and much later in BDBC when compared to that in GDBC. Beyond the onset of chaos is seen a sequence of chaotic and periodic motions, with the latter sometimes being present for an extended period. [ABSTRACT FROM AUTHOR]

The effect of suction-injection-combination (SIC) on the linear and weakly nonlinear stability of Rayleigh–Bénard convection is considered in the paper for the cases of symmetric and asymmetric boundary conditions. Using the Maclaurin series with an appropriate number of terms, expression for eigenfunctions is obtained. The linear theory corroborates the results obtained using the chosen eigenfunctions in the limiting case of the no-SIC effect by matching accurately with the exact values concerning the critical Rayleigh number (Rac) and the wave number (αc). It is found that the effect of SIC is to stabilize the system in the case of symmetric boundaries irrespective of SIC being pro-gravity or anti-gravity. However, the effect of SIC is to stabilize/destabilize the system depending on SIC being pro-gravity or anti-gravity in the case of the asymmetric boundaries. We also noted a similar effect in the case of αc wherein a maximum error of order 10 − 4 was observed. The main novelty of the present work is studying the influence of SIC on the nonlinear dynamics of the considered problem. It is shown that the effect of SIC is to hasten the onset of chaos. Using various indicators (the largest Lyapunov exponent, the time series solution, the amplitude spectrum, and the phase-space plots), the dynamical behavior of the system is analyzed and the influence of SIC on the dynamics is recorded. The change due to the boundary effect and the SIC on the size of convection rolls and the trapping region where the dynamical system evolves within a bound is highlighted in the paper. [ABSTRACT FROM AUTHOR]

Using Fourier representations, an elaborate study of regular cellular-convective and chaotic motions in a ferrofluid is made. Investigation is made on the adequacy or otherwise of the minimal mode in studying such motions. Higher-order modes are also considered by adding modes (vertical/horizontal/combined extension). For higher modes, the extensions yield a dynamical system of order greater than three. The characteristic features of extended ferromagnetic-Lorenz models are analyzed using the largest Lyapunov exponent(LE), second largest LE, bifurcation diagram, and phase-space plots. The effect of additional modes on critical modal-Rayleigh (infinitesimal and finite-amplitude ones) numbers and the Rayleigh number at which transition to chaos occurs are examined to report features of ferroconvection hitherto unseen in previous studies. As both horizontal and vertical modes are increased, our findings infer that the dynamical system displays advanced onset of regular convection and delayed chaotic motion. Vigorous-chaotic motion is seen on adding vertical modes, whereas on adding horizontal modes, intense chaos appears with decreased intensity for large values of the scaled Rayleigh number. Most important finding from the study is that as modes are increased (vertical/horizontal), the transition from regular to chaotic motion is greatly modified and leads the system to a hyper-chaotic state. Conventionally, the chaotic or hyper-chaotic state is intermittent with a periodic/quasi-periodic state but it can be retained in the chaotic or hyper-chaotic state by considering moderate values of the Prandtl number and/or by bringing in the ferromagnetic effect. [ABSTRACT FROM AUTHOR]

Analytical study of linear and weakly nonlinear stability analyses of Rayleigh–Bénard convection in a chemically reactive two-component fluid system is reported by considering physically realistic and idealistic boundaries. Analytical expression for the eigenvalue as functions of the chemical potential and the relaxation parameter is reported in the cases of stationary, oscillatory, and subcritical instabilities. The preferred stationary mode at onset is attributed to the assumption of a chemical reaction. The possibility of subcritical motion in a specific range of values of the relaxation parameter is reported and the threshold value of this parameter at which the transition from the subcritical to the critical motion takes place is documented for different values of the chemical reaction rate. The higher-order generalized Lorenz model leads to the reduced-order cubic–quintic, Ginzburg–Landau equation (GLE), and using its solution, the heat transport is quantified in steady and unsteady convective regimes. The drawback of the cubic GLE and the need for the cubic–quintic GLE for studying the heat transfer in the case of subcritical regime is explained. The possibility of having pitchfork and inverted bifurcations at various values of the relaxation parameter is highlighted. The steady Nusselt number plots clearly show that in the case of a supercritical bifurcation, a smooth transition takes place from unity in the conduction state to a higher value as the Rayleigh number exceeds its critical value predicted by linear theory. In the case of subcritical bifurcation, however, a discontinuous transition is observed. [ABSTRACT FROM AUTHOR]

In this paper, we study the propagation of the cardiac action potential in a one-dimensional fiber, where cells are electrically coupled through gap junctions (GJs). We consider gap junctional gate dynamics that depend on the intercellular potential. We find that different GJs in the tissue can end up in two different states: a low conducting state and a high conducting state. We first present evidence of the dynamical multistability that occurs by setting specific parameters of the GJ dynamics. Subsequently, we explain how the multistability is a direct consequence of the GJ stability problem by reducing the dynamical system's dimensions. The conductance dispersion usually occurs on a large time scale, i.e., thousands of heartbeats. The full cardiac model simulations are computationally demanding, and we derive a simplified model that allows for a reduction in the computational cost of four orders of magnitude. This simplified model reproduces nearly quantitatively the results provided by the original full model. We explain the discrepancies between the two models due to the simplified model's lack of spatial correlations. This simplified model provides a valuable tool to explore cardiac dynamics over very long time scales. That is highly relevant in studying diseases that develop on a large time scale compared to the basic heartbeat. As in the brain, plasticity and tissue remodeling are crucial parameters in determining the action potential wave propagation's stability. [ABSTRACT FROM AUTHOR]

The interplay between curvature and magnetization is a cornerstone in magnetism. Thus, in this work, we address the role of curvature on the propagation of magnetic skyrmions along a curved race track. Using a micromagnetic approach and simulations, we observed the creation of a curvature-induced force (CIF) that acts on the skyrmion while traveling along the track. We also show that curvature can stop the skyrmion if the current density is below a critical value. Above this limit, the skyrmion goes through the defect, a direct consequence of the CIF. Our results allow a better definition of the electric current needed for moving skyrmions along curved tracks. [ABSTRACT FROM AUTHOR]

The onset of Darcy–Bénard regular and chaotic convection in a porous medium is studied by considering phase-lag effects that naturally arise in the thermal non-equilibrium heat transfer problem between the fluid and solid phases. A new type of heat equation is derived for both the phases. Using a double Fourier series and a novel decomposition, an extended Vadasz–Lorenz model with three phase-lag effects is derived. New parameters arise due to the phase-lag effects between local acceleration, convective acceleration, and thermal diffusion. The principle of exchange of stabilities is found to be valid and the subcritical instability is discounted. The new perspective supports the finding of an analytical expression for the critical Darcy–Rayleigh numbers representing, respectively, the onset of regular and chaotic convection. The understanding of the transition from the local thermal non-equilibrium situation to the local thermal equilibrium one is also best explained through the new perspective. In its present elegant form, the extended Vadasz–Lorenz system with three phase-lag effects is analyzed using the largest Lyapunov exponent and the bifurcation diagram. It is found that the lag effects not only give rise to a quantitative difference in the above two metrics concerning chaos, but also present a qualitative difference as well in the form of the very nature of chaos. [ABSTRACT FROM AUTHOR]

Natural convection in nanoliquid-saturated porous cylindrical annuli due to uniform heat and mass influxes from the solid cylinder and effluxes from the outer hollow cylinder is investigated analytically. The Darcy model and the modified version of the Buongiorno two-phase model are used, and local thermal non-equilibrium between the phases is assumed. A nanoliquid-saturated porous medium made up of glass balls with a dilute concentration of AA7075 alloy nanoparticles well-dispersed in water is considered. Out of three types of annuli considered, shallow annuli provide the best heat transport and tall annuli show the worst performance. The presence of a dilute concentration of nanoparticles significantly enhances the heat transport in the system. Of nine nanoparticle shapes considered, lamina-shaped nanoparticles enhance heat transport the most. Heat transport is enhanced in the case of heat-and-mass-driven convection compared to the case of purely heat-driven convection. The results for a rectangular enclosure are obtained as a particular case of the present study. Two asymptotic routes that take us to the results of thermal equilibrium are shown. The vanishing limit of the concentration Rayleigh number yields the result for a single-phase model. Results for the base-liquid-saturated porous medium form a limiting case of the present study. We conclude that a shallow cylindrical annulus saturated with water-AA7075 lamina-shaped alloy nanoparticles is best suited for heat transfer due to its high effective thermal conductivity in comparison with that of other shaped nanoparticles and a tall rectangular enclosure saturated by water is best suited for heat storage applications. [ABSTRACT FROM AUTHOR]

The influence of an intense laser field on one-electron states and intraband optical absorption coefficients is investigated in two-dimensional GaAs/Ga0.7Al0.3As quantum rings. An analytical expression of the effective lateral confining potential induced by the laser field is obtained. The one-electron energy spectrum and wave functions are found using the effective mass approximation and exact diagonalization technique. We have shown that changes in the incident light polarization lead to blue- or redshifts in the intraband optical absorption spectrum. Moreover, we found that only blueshift is obtained with increasing outer radius of the quantum ring. [ABSTRACT FROM AUTHOR]

In this paper, we study the spin-dependent electron transport through aromatic molecular chains attached to two semi-infinite leads. We model this system taking into account different geometrical configurations which are all characterized by a tight binding Hamiltonian. Based on the Green's function approach with a Landauer formalism, we find spin-dependent transport in short aromatic molecules by applying external magnetic fields. Additionally, we find that the magnetoresistance of aromatic molecules can reach different values, which are dependent on the variations in the applied magnetic field, length of the molecules, and the interactions between the contacts and the aromatic molecule. [ABSTRACT FROM AUTHOR]

In this paper, we study the electronic transport properties through aromatic molecules connected to two semi-infinite leads. The molecules are in different geometrical configurations including arrays. Using a nearest neighbor tight-binding approach, the transport properties are analyzed into a Green's function technique within a real-space renormalization scheme. We calculate the transmission probability and the Current-Voltage characteristics as a function of a molecule-leads coupling parameter. Our results show different transport regimes for these systems, exhibiting metal-semiconductor-insulator transitions and the possibility to employ them in molecular devices. [ABSTRACT FROM AUTHOR]

In this work, we study numerically the periodicity of regular regions embedded in chaotic states for the case of an anisotropic magnetic particle. The particle is in the monodomain regime and subject to an applied magnetic field that depends on time. The dissipative Landau–Lifshitz–Gilbert equation models the particle. To perform the characterization, we compute several two-dimensional phase diagrams in the parameter space for the Lyapunov exponents and the isospikes. We observe multiple transitions among periodic states, revealing complex topological structures in the parameter space typical of dynamic systems. To show the finer details of the regular structures, iterative zooms are performed. In particular, we find islands of synchronization for the magnetization and the driven field and several shrimp structures with different periods. [ABSTRACT FROM AUTHOR]

The control effects on the convection dynamics in a viscoelastic fluid-saturated porous medium heated from below and cooled from above are studied. A truncated Galerkin expansion was applied to balance equations to obtain a four-dimensional generalized Lorenz system. The dynamical behavior is mainly characterized by the Lyapunov exponents, bifurcation, and isospike diagrams. The results show that within a range of moderate and high Rayleigh numbers, proportional controller gain is found to enhance the stabilization and destabilization effects on the thermal convection. Furthermore, due to the effect of viscoelasticity, the system exhibits remarkable topological structures of regular regions embedded in chaotic domains. [ABSTRACT FROM AUTHOR]

Thermal convection of binary mixtures in a porous medium is studied with stress-free boundary conditions. The linear stability analysis is studied by using the normal mode method. The effects of the material parameters have been studied at the onset of convection. Using a multiple scale analysis near the onset of the stationary convection, a cubic-quintic amplitude equation is derived. The influence of the Lewis number and the separation ratio on the supercritical-subcritical transition is discussed. Stationary front solutions and localized states are analyzed at the Maxwell point. Near the threshold of the oscillatory convection, a set of two coupled complex cubic-quintic Ginzburg-Landau type amplitude equations is derived, and implicit analytical expressions for the coefficients are given. [ABSTRACT FROM AUTHOR]

All online versions of the article were corrected on 22 April 2021. This article was originally published online and in print on 20 April 2021 with a typographical error in the acknowledgment. Publisher's Note: "A study of Darcy-Bénard regular and chaotic convection using a new local thermal non-equilibrium formulation" [Phys. [Extracted from the article]

The pattern formation in a magnetic wire forced by a time dependent magnetic field is studied. This system is described in the continuum limit by the Landau-Lifshitz-Gilbert equation. The spatio-temporal magnetization field exhibits two-soliton bound state solutions. Close to the parametric resonance instability, an amplitude equation allows us to understand and characterize these localized states. [ABSTRACT FROM AUTHOR]