Nonlinear Theory Research Articles

Linear and nonlinear investigations of the impact of chemical reaction on the thermohaline convection in a permeable layer saturated with Casson fluid

In this effort, the consequence of chemical reaction on the thermohaline convection in a permeable layer containing Casson fluid is inspected utilizing both linear and nonlinear stability procedures. To model the momentum equation, the Casson fluid version of Darcy's law is utilized. Applying the linear stability concept, the situation for the start of stationary and oscillatory pattern of convective motion is obtained, whereas the convective heat and mass transferences are determined using nonlinear stability theory. It is found that the oscillatory type of convective flow is probable only if the evaluation of the solutal Rayleigh–Darcy number is less than zero. The effect of the chemical reacting factor, the Casson factor, the Lewis number, and the solutal Rayleigh–Darcy number is to hurry the start of convection toward both stationary and oscillatory styles of convection and also surge the size of the convective cells. The convective heat and mass transfers enhance with increasing the Casson factor, the solutal and thermal Rayleigh–Darcy numbers while both decrease with enhancing the heat capacity quotient. The effect of chemical reacting factor is to increase the mass transmission in the system, while it has no effect on the heat transmission. It is also noted that the convective heat and mass transfers in the system enhance nearly 5.4% and 3.8%, respectively, with a 50% increase in the value of Casson factor.

Effect of Helical Force on Thermal Convection of a Ferrofluid: A Weakly Non-linear Theory

Effect of Helical Force on Thermal Convection of a Ferrofluid: A Weakly Non-linear Theory

Thermal convection with a Cattaneo heat flux model

The problem of thermal convection in a layer of viscous incompressible fluid is analysed. The heat flux law is taken to be one of Cattaneo type. The time derivative of the heat flux is allowed to be a material derivative, or a general objective derivative. It is shown that only one objective derivative leads to results consistent with what one expects in real life. This objective derivative leads to a Cattaneo–Christov theory, and the results for linear instability theory are in agreement with those for a material derivative. It is further shown that none of the theories allow a standard nonlinear, energy stability analysis. A further heat flux due to P.M. Mariano is added and then an analysis is performed for stationary convection, oscillatory convection, and fully nonlinear theory. For the material derivative case, the analysis proceeds and global nonlinear stability is achieved. For Cattaneo–Christov theory, it appears necessary to add a regularization term in the equation for the heat flux, and even then the analysis only works in two space dimensions, and is conditional upon the size of the initial data. For the three-dimensional situation, it is shown how a nonlinear stability analysis may be achieved with a Navier–Stokes–Voigt fluid rather than a Navier–Stokes one.

Nonlinear Spin-wave Theory for Dynamical Spin Correlations in the Kitaev Model at Finite Temperatures

Nonlinear Spin-wave Theory for Dynamical Spin Correlations in the Kitaev Model at Finite Temperatures

A novel conservative dynamics envelope of vehicle lateral stability under different tire characteristics

This paper proposes a dynamic stability envelope based on safety maneuver margin to estimate the lateral stability of nonlinear vehicle systems with different tire characteristics (i.e. understeering (UN) and oversteering (OV) vehicles). Firstly, this study employs phase portraits and handling diagrams to investigate the number of equilibrium points and the evolution trend of state variables under various manipulation conditions. Subsequently, the nonlinear bifurcation theory is applied to analyze the characteristics of the vehicle equilibrium, aiming to derive the safe maneuver margin of the vehicle and restrict the vehicle instability. Within this proposed margin, the stability of each point of the nonlinear system is analyzed using the local linearization method. Simultaneously, a more conservative estimate of the vehicle handling stability is further obtained by applying stability criteria, resulting in the dynamic stability envelope, which ensures vehicle stability. Finally, the reliability of the dynamic stability envelope results based on the safety maneuver margin is validated under sine-with-dwell conditions (SDC) and steady-state cornering driving scenarios (SSC). The simulation results indicate that maintaining an appropriate understeering range keeps the vehicle stable.

РАСЧЕТ ЭЛЕМЕНТОВ ЖЕЛЕЗОБЕТОННЫХ КОНСТРУКЦИЙ НА ОГНЕСТОЙКОСТЬ И ОГНЕСОХРАННОСТЬ В ПРОГРАММНОМ КОМПЛЕКСЕ СТАРКОН.

RCDiagra software as a part of the domestic STARKON software is presented. The software is designed to perform fire resistance and fire safety analysis of reinforced concrete beams and columns. The strength analysis is based on the nonlinear deformation theory and enables to take into account non-stationary thermal effects changing the concrete and reinforcement properties. To determine the ultimate strength, elastic modulus for concrete and reinforcement, ultimate relative deformations, a thermal analysis is performed in accordance with SP 468.1325800.2019 and MDS 21-2.2000. The thermal engineering analysis solve the problem of determining the temperature field in the beam cross-section under non-stationary thermal action, depending on the boundary conditions and thermophysical parameters of the material. It is assumed that the coefficients of thermal conductivity and specific heat capacity of concrete depend on the current temperature at the crosssection points.

Comparative analyses of Nonlinear Optical (NLO) properties, structural characterization and density functional theory of chloro-trifluoromethyl moiety chalcone derivatives for optical limiting application

This study focuses on the impact of substitutional positions on the nonlinear optical (NLO) and photophysical properties of four novel chalcone derivatives (I–IV). The grown crystals were characterized using FT-IR, NMR and single crystal X-ray diffraction (SCXRD) techniques, and the intermolecular interactions were studied by examining the unique packing motifs. The linear and 3rd-order NLO properties were experimentally determined using UV–Vis spectrometer and Z-scan setup with 637 nm continuous wave excitation, respectively. Compounds I–IV were studied theoretically using density functional theory (DFT) to support the experimental results. B3LYP functional was used to optimize the geometries, and the molecular properties of the compounds were determined via molecular electrostatic potential (MEP), natural population analysis (NPA), and localized orbital locator-π (LOL-π) analyze. The photophysical properties were analyzed using time-dependent DFT (TDDFT) using both CAM-B3LYP and B3LYP functionals to investigate the impact of the long-range correction. Inter-fragment charge transfer (IFCT) analysis and hole-electron analysis were employed to examine the linear optical properties and charge transfer mechanism. The NLO properties such as dipole moment (μ), polarizability (α), first and second hyperpolarizabilities (β and γ) were examined with the numerically differentiate analytic method using both functionals. Z-scan NLO data shows that the nonlinear refraction (NLR) coefficient of I–IV is significantly influenced by intermolecular interactions, specifically aggregation phenomena. Compound IV exhibits an exceptional nonlinear absorption (NLA) response and superior optical limiting properties compared to others attributed to its para-substituted strong electron-acceptor group (CF3) which results in highest transition dipole moment, lowest excitation energy, and well-defined charge transfer processes within its molecule. As a result, this suggests that it could be a potential candidate for NLO applications.

Nonlinear forced vibrations of functionally graded three-phase composite cylindrical shell subjected to aerodynamic forces, external excitations and hygrothermal environment

In this paper, the new functionally graded three-phase composite cylindrical shell is assumed as a common structure in the carrier rocket in the future, and we creatively study the nonlinear forced vibration of this cylindrical shell considering the interaction of different factors in the complex operating environment, including the aerodynamic forces, external excitations, and hygrothermal environment. Based on the first-order shear deformation theory, Von-Karman geometric nonlinear theory, and Hamilton's principle, we derive the nonlinear partial differential equations of motion of the functionally graded three-phase composite cylindrical shell. Considering the axisymmetry of the perfect circular shell, there is a 1:1 internal resonance between the conjugate modes of this cylindrical shell. On this basis, the nonlinear forced vibration of the cylindrical shell is investigated by a combination of Galerkin's method and the pseudo-arc length continuation method. Matcont toolbox can directly solve the ordinary differential equations to obtain the nonlinear frequency response curves. The method can effectively obtain both stable and unstable solutions, avoiding the mathematical difficulties encountered in the formulation process, and facilitating the study of the effects of parametric variables on the resonance response in complex environments. The results show that the variation of material parameters and the complex environment have important effects on the nonlinear resonance response of functionally graded three-phase composite cylindrical shell.

Effect of Gravity Modulation on the Onset of Heat Transfer by Buoyancy Induced Convection in Boussinesq- Stokes Suspension with Temperature

The current paper considers the Boussinesq-Stokes suspensions and the temperature-dependent viscosity with the influence of gravity modulation to analyze a weak non-linear stability problem of Rayleigh Benard magnetoconvection. In the study of convective instability problems, the impact of time-periodic body force also known as gravity modulation or g-gitter is essential. In the problem of gravity modulation, the gravity field has two components: one is the constant part and another an externally imposed time periodic part, which can be produced by oscillating the fluid layer. The effect of varying frequency of gravitational oscillation on convection is examined. The truncated form of the Fourier series is used in the non-linear analysis. The effects of numerous factors on the onset of convection have been discussed in this paper. The thermal Nusselt number is computed and shown for slow time periods using non-linear theory. The impacts of gravity modulation frequency and amplitude have been investigated in order to study heat transport in the system, as well as other aspects that exist in the problem.

Nonlinear normal modes of multi-walled nanoshells with consideration of surface effect and nonlocal elasticity

System of nonlinear partial differential equations with respect to displacements is derived to describe free nonlinear vibrations of multi-walled nanoshell. The geometrically nonlinear vibrations of nanoshell, which is described by Sanders-Koiter nonlinear shell theory, are considered with account of nonlinear van der Waals forces, surface effect and nonlocal elasticity. Using the weighted residual method, the system of the partial differential equations is transformed into the system of nonlinear ordinary differential equations. The nonlinear boundary condition for the longitudinal stresses resultant is accounted in these differential equations.The essentially curvilinear Kauderer-Rosenberg nonlinear normal modes are studied numerically by combination of shooting technique and continuation algorithm. Such NNMs in double-walled nanoshell are undergone the Naimark- Sacker bifurcation. As a result, the curvilinear nonlinear modes are transformed into chaotic motions.

Experimental study on failure characteristics and rheological properties of pillar-like rock samples with different shapes

The stability of coal pillar is extremely important to the control of rock strata movement and surface subsidence. It is of great significance for mining design to analyze the stability and failure characteristics of coal and rock pillars left after mining and to study the failure characteristics and rheological properties of coal and rock with different shapes. In this paper, based on uniaxial compression and rheological tests on rock samples, the rheological properties of rock samples with different shapes were discussed by using the nonlinear theoretical mechanics and damage theory, and the rheological mechanical characteristics of coarse yellow sandstone samples under the action of different free surface areas and the same loading contact area were investigated by means of experimental research, theoretical analysis and numerical simulation. The following conclusions were drawn: the failure characteristics and dynamic change process of rock samples with different shapes under the same loading contact area are obtained by uniaxial compression test and multi-stage rheological loading. The uniaxial compressive strengths of rock samples with the same loading contact surface area and different free surface areas are inversely proportional to their free surface areas. For the round sample, the stress level in the rheological test is obviously lower than the instantaneous peak uniaxial compression strength, while for the other samples, the stress level in the rheological test is close to the instantaneous peak uniaxial compression strength. For rock all these samples, both the ratio of steady-state rheological time to final failure time and the deformation degree decrease with the increase of free surface area.

Rate-independent gradient-enhanced crystal plasticity theory — Robust algorithmic formulations based on incremental energy minimization

Numerically robust algorithmic formulations suitable for rate-independent crystal plasticity are presented. They cover classic local models as well as gradient-enhanced theories in which the gradients of the plastic slips are incorporated by means of the micromorphic approach. The elaborated algorithmic formulations rely on the underlying variational structure of (associative) crystal plasticity. To be more precise and in line with so-called variational constitutive updates or incremental energy minimization principles, an incrementally defined energy derived from the underlying time-continuous constitutive model represents the starting point of the novel numerically robust algorithmic formulations. This incrementally defined potential allows to compute all variables jointly as minimizers of this energy. While such discrete variational constitutive updates are not new in general, they are considered here in order to employ powerful techniques from non-linear constrained optimization theory in order to compute robustly the aforementioned minimizers. The analyzed prototype models are based on (1) nonlinear complementarity problem (NCP) functions as well as on (2) the augmented Lagrangian formulation. Numerical experiments show the numerical robustness of the resulting algorithmic formulations. Furthermore, it is shown that the novel algorithmic ideas can also be integrated into classic, non-variational, return-mapping schemes.

Continuum Mechanics Models for Describing the Creep and Physical Aging Behaviors of Laminated Composites

Two types of carbon fiber-reinforced epoxy composite laminates are chosen for long-term tensile creep tests under different temperatures and load levels. Their time-dependent and non-monotonic deformations indicate clearly both temperature effect and physical aging effect. To characterize these viscoelastic behavior, two phenomenological constitutive models and one physical model are developed. The linear viscoelastic model based on the Boltzmann superposition principle is able to describe reasonably the deformations at relatively lower stress levels and temperatures. The nonlinear viscoelastic model of Schapery’s single-integral form, together with a usage of effective time theory, could describe nicely all the effects of temperature, stress, and physical aging. The physical model based on Ngai’s coupling mechanism concept is further combined with the framework of Schapery’s nonlinear viscoelastic theory, which may provide certain physical understanding about the effect of aging behavior on long-term creep deformation of the laminated composites. Numerical modelling by finite element method are implemented, and comparisons between the experimental and simulation results are demonstrated.

Analysis and simulation of vehicle following behavior with consideration of multiple time delays

With the application of intelligent transportation system, drivers can receive more traffic status information in the process of driving, but they may have multiple time delays when they are presented with different information. As a result, to further research the influence of multiple time delays on vehicle following behavior, this study comes up with a modified car following model, which takes into account multiple time delays in sensing both distance and velocity information, based on the backward looking and velocity difference model. The linear stability theory is used to explore the influence of multiple time delays on the stability of the extended model. Different nonlinear equations are derived using nonlinear theory, which include Burgers, Korteweg–de Vries, and Modified Korteweg–de Vries equations and are used to depict triangular wave, soliton wave and kink–antikink wave corresponding to stable, metastable and unstable regions respectively. In the end, numerical simulation is used to further study the improved model to depict the dynamic evolution of traffic stream. The results display that the improvement of time delay in sensing distance can induce traffic congestion, conversely, the time delay in sensing velocity offsets the negative effect of time delay in sensing distance. The theoretical results and numerical simulation results are consistent with each other.

Homogeneous Dephasing in Photosynthetic Bacterial Reaction Centers: Time Correlation Function Approach.

A new tractable linear electronic transition dipole moment time correlation function (ETDMTCF) that accurately accounts for electronic dephasing, asymmetry, and width of 1-phonon profile, which the zero-phonon line (ZPL) contributes to it, in Rhodopseudomonas viridis bacterial reaction center is derived. This time correlation function proves to be superior to other frequency-domain expressions in case of strong electron-phonon coupling (which is often the case in bacterial RCs and pigment-protein complexes), many vibrational modes involved, and high temperature, whereby more vibronic and electronic (sequence) transitions would arise. The Fourier transform of this ETDMTCF leads to asymmetric multiphonon profiles composed of Lorentzian distribution and Gaussian distribution on the high- and low-energy sides, respectively, whereby the overtone widths fold themselves with that of the one-phonon profile. This ETDMTCF also features expedient computation in large systems using asymmetric phonon profiles to account correctly for dephasing and pigment-protein interaction (electron-phonon coupling). The derived ETDMTCF allows computing all nonlinear optical signals in both time and frequency domains, through the nonlinear dipole moment time correlation functions (as guided by nonlinear optical response theory) in line with the eight Liouville space pathways. The linear transition dipole moment time correlation function is of a central value as the nonlinear transition dipole moment time correlation function is expressed in terms of the linear transition dipole moment time correlation function, derived herein. One of the great advantages of presenting this ETDMTCF is its applicability to nonlinear transition dipole moment time correlation functions in line with the eight Liouville space pathways needed in computing nonlinear signals. As such, there is more to the utility and applicability of the presented ETDMTCF besides computational expediency and efficiency. Results show good agreement with the reported literature. The intimate connection between a one-phonon profile and the corresponding bath spectral density in photosynthetic complexes is discussed.

Study on Instability Change Law of Surrounding Rock of Tunnel Crossing Fault Fracture Zone Based on Cusp Point Mutation Theory

The instability process of surrounding rock is a nonlinear mutation. To truly reflect the nonlinear mutation in the failure of surrounding rock and grasp the opportunity of instability of surrounding rock, it is necessary to study the stability of surrounding rock by combining the existing methods with nonlinear scientific theory. Based on the numerical simulation results of a tunnel project crossing the fault fracture zone, the mutation theory is introduced to study the instability law of surrounding rock during tunnel excavation. The dynamic excavation process of surrounding rock tunnel in fault fracture zone is simulated by the finite difference software FLAC3D. Based on the cusp point mutation theory, the deformation law of each excavation step to the working face under different dip angles, strike angles and thicknesses of fault fracture zone is studied. Combined with the dichotomy method, curve fitting is used to analyze the instability threshold of surrounding rock and predict the opportunity of surrounding rock instability. The results indicate that (1) As the dip angle and strike angle of the fault gradually increase, the settlement of the surrounding rock arch first decreases and then increases, while as the thickness of the fault increases, the vertical displacement of the surrounding rock gradually increases. (2) When the dip angle of the fault is less than 90°, the sudden instability of the surrounding rock is advanced, while when it is greater than 90°, the time for sudden instability is delayed. (3) As the strike angle and thickness of the fault gradually increase, the excavation step for the tunnel to undergo sudden instability is gradually advanced. The research conclusion can provide theoretical guidance and suggestions for similar engineering construction in the future.

Nonlinear Optical Spectroscopy of Molecular Assemblies: What Is Gained and Lost in Action Detection?

This study elucidates the information content that is extracted from action-2D electronic spectroscopy (A-2DES) when the output intensity is not proportional to the number of excitations generated. Such a scenario can be realized in both fluorescence and photocurrent detection because of direct interaction like exciton-exciton annihilation or indirect effects in the signal generation or detection. By means of an intuitive probabilistic model supported by nonlinear response theory, the study concludes that in molecular assemblies the ground-state bleaching contribution can dominate the nonlinear signal and partially or completely hide the stimulated emission. In this case, the spectral effect resembles incoherent mixing, even in the absence of exciton-exciton annihilation, implying reduced information about the excited-state dynamics with an increasing number of chromophores. This finding has important implications for the selection of samples for A-2DES as well as for its interpretation.

An ANN-BCMO Approach for Material Distribution Optimization of Bi-Directional Functionally Graded Nanocomposite Plates with Geometrically Nonlinear Behaviors

This study commences with the application of an efficient artificial neural network (ANN)-balancing composite motion optimization (BCMO) approach for finding the optimal material distribution of bi-directional functional graded nanocomposite (FGN) thin plates considering geometrically nonlinear behaviors. To this regard, an ANN-based surrogate model of the high-fidelity isogeometric analysis (IGA) of the geometrically nonlinear Kirchhoff–Love plates based on the Von Kármán nonlinearity theory is first constructed and then employed to predict the values of objectives and constraints required in the BCMO framework. The multi-mesh design approach is utilized to form two separate nonuniform rational B-spline meshes for optimal material distribution and analysis meshes. The unknown control point values of the design mesh are herein selected as the continuous design variables. This allows a possibility to fully explore the complex distribution of optimal material profiles without requiring a significant number of variables. Selected numerical examples with different plate geometries and loading conditions are presented to illustrate the merit features of the proposed approach. Obtained results reveal not only its high accuracy and significant efficiency compared with the conventional approach coupling the BCMO with IGA direct analysis but also the stable ability of the BCMO in finding global optimum material distributions in comparison with two commonly used metaheuristics algorithms, i.e., particle swarm optimization and genetic algorithm.

Nonlinear dynamic analysis of a geometrically imperfect sandwich beam with functionally graded material facets and auxetic honeycomb core in thermal environment

In this study, a model for the nonlinear dynamic analysis of the geometrically imperfect sandwich beam with functionally graded material (FGM) facets and auxetic honeycomb core is proposed. The auxetic feature of the honeycomb material is realized by a homogenization method, which gives the expressions of the effective material coefficients in terms of material property and cellular geometric parameters. The nonlinear motion equation of the geometrically imperfect beam is derived based on the Reddy's higher shear deformation theory, von Kármán nonlinear theory, as well as general geometric imperfection function. The thermal effect on the material properties and structural rigidity is also taken into account in this model. The Newmark method and Newton–Raphson iterative method are employed to solve the nonlinear motion equation of the sandwich beam. In numerical examples, the dynamic response of the sandwich beam under two types of load, i.e. moving load and impulse load, are discussed in details. The influences of various factors (such as material parameter, geometric imperfection, and thermal condition) on the nonlinear dynamic behaviors of the sandwich beam are elaborately investigated. The numerical results show those factors can play significant roles in the bearing ability, structural stiffness, or nonlinear dynamic behaviors of the sandwich beam in certain conditions. Some key conclusions on the influences are drawn from the numerical results, which can be a useful reference for future investigations.

Controllable toughness enhancement in graphene hybrid materials via planar twist-angle of carbon nanotubes

A controllable toughness enhancement in graphene hybrid materials via twist-angle of CNTs was first investigated. The mechanical properties, such as out-of-plane deformation, stress–strain curves, strain energy and interlayer loading transfer of Gr Hybrid model coupled by twist-angle CNTs were investigated by molecular dynamics simulations and nonlinear fracture mechanics theory. We find that these mechanical properties are sensitive to the existence of twist-angle CNTs in the Gr hybrid model. The crosslinking sites can be considered as structural defects. In addition, the CNTs exert a strengthening influence on the out-of-plane deformation, interlayer loading transfer as well as bond strain energies, thereby deflecting the crack paths of Gr Hybrid model under axial tension. Nevertheless, the existence of CNTs also triggers a reduction in the in-plane stress and the associated strain due to sp2 + sp3 hybrid state. We find that this abnormal improvement in toughness derives from the localization of the stress fields arising from their out-of-plane displacements at the interface, resulting in the stress fields being localized only at the crosslinking sites. These interfacial toughening strategies can redistribute crack tip stress in a wider range, avoid stress concentration, and at the same time realize a lot of energy dissipation by promoting crack deflection, thus achieving overall high toughness.