Artykuły w czasopismach na temat „Non-Modal stability theory”

In the context of geologic sequestration of carbon dioxide in saline aquifers, much interest has been focused on the process of density-driven convection resulting from dissolution of CO2 in brine in the underlying medium. Recent investigations have studied the time and length scales characteristic of the onset of convection based on the framework of linear stability theory. It is well known that the non-autonomous nature of the resulting matrix does not allow a normal mode analysis and previous researchers have either used a quasi-static approximation or solved the initial-value problem with arbitrary initial conditions. In this manuscript, we describe and use the recently developed non-modal stability theory to compute maximum amplifications possible, optimized over all possible initial perturbations. Non-modal stability theory also provides us with the structure of the most-amplified (or optimal) perturbations. We also present the details of three-dimensional spectral calculations of the governing equations. The results of the amplifications predicted by non-modal theory compare well to those obtained from the spectral calculations.

Modal and non-modal perturbation growth in boundary layers subjected to time-harmonic spanwise wall motion are examined. The superposition of the streamwise Blasius flow and the spanwise Stokes layer can lead to strong modal amplification during intervals of the base-flow period. Linear stability analysis of frozen phases of the base state demonstrates that this growth is due to an inviscid instability, which is related to the inflection points of the spanwise Stokes layer. The generation of new inflection points at the wall and their propagation towards the free stream leads to mode crossing when tracing the most unstable mode as a function of phase. The fundamental mode computed in Floquet analysis has a considerably lower growth rate than the instantaneous eigenfunctions. Furthermore, the algebraic lift-up mechanism that causes the formation of Klebanoff streaks is examined in transient growth analyses. The wall forcing significantly weakens the wall-normal velocity perturbations associated with lift-up. This effect is attributed to the formation of a pressure field which redistributes energy from the wall-normal to the spanwise velocity perturbations. The results from linear theory explain observations from direct numerical simulations of breakdown to turbulence in the same flow configuration by Hack & Zaki (J. Fluid Mech., vol. 760, 2014a, pp. 63–94). When bypass mechanisms are dominant, the flow is stabilized due to the weaker non-modal growth. However, at high amplitudes of wall oscillation, transition is promoted due to fast growth of the modal instability.

In this paper, we study the linear stability of a plane Couette flow of a power-law fluid. The influence of shear-thinning effect on the stability is investigated using the classical eigenvalue analysis, the energy method and the non-modal stability theory. For the plane Couette flow, there is no stratification of viscosity. Thus, for the stability problem the stress tensor is anisotropic aligned with the strain rate perturbation. The results of the eigenvalue analysis and the energy method show that the shear-thinning effect is destabilizing. We focus on the effect of non-Newtonian viscosity on the transition from laminar flow towards turbulence in the framework of non-modal stability theory. Response to external excitations and initial conditions has been studied by examining the ε-pseudospectrum and the transient energy growth. For both Newtonian and non-Newtonian fluids, it is found that there can be a rather large transient growth even though the linear operator of the Couette flow has no unstable eigenvalue. The results show that shear-thinning significantly increases the amplitude of response to external excitations and initial conditions.

In the present work, a stability analysis of the bottom boundary layer under solitary waves based on energy bounds and non-modal theory is performed. The instability mechanism of this flow consists of a competition between streamwise streaks and two-dimensional perturbations. For lower Reynolds numbers and early times, streamwise streaks display larger amplification due to their quadratic dependence on the Reynolds number, whereas two-dimensional perturbations become dominant for larger Reynolds numbers and later times in the deceleration region of this flow, as the maximum amplification of two-dimensional perturbations grows exponentially with the Reynolds number. By means of the present findings, we can give some indications on the physical mechanism and on the interpretation of the results by direct numerical simulation in Vittori & Blondeaux (J. Fluid Mech., vol. 615, 2008, pp. 433–443) and Özdemir et al. (J. Fluid Mech., vol. 731, 2013, pp. 545–578) and by experiments in Sumer et al. (J. Fluid Mech., vol. 646, 2010, pp. 207–231). In addition, three critical Reynolds numbers can be defined for which the stability properties of the flow change. In particular, it is shown that this boundary layer changes from a monotonically stable to a non-monotonically stable flow at a Reynolds number of $Re_{\unicode[STIX]{x1D6FF}}=18$.

Layered flows that are commonly observed in stratified turbulence are susceptible to the Taylor–Caulfield Instability. While the modal stability properties of layered shear flows have been examined, the non-modal growth of perturbations has not been investigated. In this work, the tools of Generalized Stability Theory are utilized to study linear transient growth within a finite time interval of two-dimensional perturbations in an inviscid, three-layer constant shear flow under the Boussinesq approximation. It is found that, for low optimization times, small-scale perturbations utilize the Orr mechanism and achieve growth equal to that in the case of an unstratified flow. For larger optimization times, transient growth is much larger compared to growth for an unstratified flow as the Kelvin–Orr waves comprising the continuous spectrum of the dynamical operator and the gravity edge-waves comprising the discrete spectrum interact synergistically. Maximum growth is obtained for perturbations with scales within the region of instability, but significant growth is maintained for modally stable perturbations as well. For perturbations with scales within the unstable region, the unstable normal modes are excited at high amplitude by their bi-orthogonals. For perturbations with modally stable scales, the Orr mechanism is utilized to excite at high amplitude neutral propagating waves resembling the neutral Taylor–Caulfield modes.

The linear stability properties of viscous circular flows in a rotating environment are studied with respect to symmetric perturbations. Through the use of an effective energy or Lyapunov functional, we derive sufficient conditions for Lyapunov stability with respect to such perturbations. For circular flows with swirl velocity V(r) we find that Lyapunov stability is determined by the properties of the function ℱ(r) = (2V/r + f)/Q (with f the Coriolis parameter, r the radius and Q the absolute vorticity) instead of the customary Rayleigh discriminant Φ(r) = (2V/r + f)Q. The conditions for stability are valid for flows with non-zero Q everywhere. Further, the flows are presumed stationary, incompressible and velocity perturbations are required to vanish at rigid boundaries. For Lyapunov stable flows an upper bound for the increase of the total perturbation energy due to transient non-modal growth is derived which is valid for any Reynolds number. The theory is applied to Couette flow and the Lamb–Oseen vortex.

AbstractHomboe (Geophys. Publ., vol. 24, 1962, pp. 67–112) postulated that resonant interaction between two or more progressive, linear interfacial waves produces exponentially growing instabilities in idealized (broken-line profiles), homogeneous or density-stratified, inviscid shear layers. Here we have generalized Holmboe’s mechanistic picture of linear shear instabilities by (i) not initially specifying the wave type, and (ii) providing the option for non-normal growth. We have demonstrated the mechanism behind linear shear instabilities by proposing a purely kinematic model consisting of two linear, Doppler-shifted, progressive interfacial waves moving in opposite directions. Moreover, we have found a necessary and sufficient (N&S) condition for the existence of exponentially growing instabilities in idealized shear flows. The two interfacial waves, starting from arbitrary initial conditions, eventually phase-lock and resonate (grow exponentially), provided the N&S condition is satisfied. The theoretical underpinning of our wave interaction model is analogous to that of synchronization between two coupled harmonic oscillators. We have re-framed our model into a nonlinear autonomous dynamical system, the steady-state configuration of which corresponds to the resonant configuration of the wave interaction model. When interpreted in terms of the canonical normal-mode theory, the steady-state/resonant configuration corresponds to the growing normal mode of the discrete spectrum. The instability mechanism occurring prior to reaching steady state is non-modal, favouring rapid transient growth. Depending on the wavenumber and initial phase-shift, non-modal gain can exceed the corresponding modal gain by many orders of magnitude. Instability is also observed in the parameter space which is deemed stable by the normal-mode theory. Using our model we have derived the discrete spectrum non-modal stability equations for three classical examples of shear instabilities: Rayleigh/Kelvin–Helmholtz, Holmboe and Taylor–Caulfield. We have shown that the N&S condition provides a range of unstable wavenumbers for each instability type, and this range matches the predictions of the normal-mode theory.

Linear stability of the non-parallel Batchelor vortex is studied using global modes. This family of swirling wakes and jets has been extensively studied under the parallel-flow approximation, and in this paper we extend to more realistic non-parallel base flows. Our base flow is obtained as an exact steady solution of the Navier–Stokes equations by direct numerical simulation (with imposed axisymmetry to damp all instabilities). Global stability modes are computed by numerical simulation of the linearized equations, using the implicitly restarted Arnoldi method, and we discuss fully the numerical and convergence issues encountered. Emphasis is placed on exploring the general structure of the global spectrum, and in particular the correspondence between global modes and local absolute modes which is anticipated by weakly non-parallel asymptotic theory. We believe that our computed global modes for a weakly non-parallel vortex are the first to display this correspondence with local absolute modes. Superpositions of global modes are also studied, allowing an investigation of the amplifier dynamics of this unstable flow. For an illustrative case we find global non-modal transient growth via a convective mechanism. Generally amplifier dynamics, via convective growth, are prevalent over short time intervals, and resonator dynamics, via global mode growth, become prevalent at later times.

The topic of density-driven convection in porous media has been the focus of many recent studies due to its relevance as a long-term trapping mechanism during geological sequestration of carbon dioxide. Most of these studies have addressed the problem in homogeneous and anisotropic permeability fields using linear-stability analysis, and relatively little attention has been paid to the analysis for heterogeneous systems. Previous investigators have reduced the governing equations to an initial-value problem and have analysed it either with a quasi-steady-state approximation model or using numerical integration with arbitrary initial perturbations. Recently, Rapaka et al. (J. Fluid Mech., vol. 609, 2008, pp. 285–303) used the idea of non-modal stability analysis to compute the maximum amplification of perturbations in this system, optimized over the entire space of initial perturbations. This technique is a mathematically rigorous extension of the traditional normal-mode analysis to non-normal and time-dependent problems. In this work, we extend this analysis to the important cases of anisotropic and layered porous media with a permeability variation in the vertical direction. The governing equations are linearized and reduced to a set of coupled ordinary differential equations of the initial-value type using the Galerkin technique. Non-modal stability analysis is used to compute the maximum growth of perturbations along with the optimal wavenumber leading to this growth. We show that unlike the solution of the initial-value problem, results obtained using non-modal analysis are insensitive to the choice of bottom boundary condition. For the anisotropic problem, the dependence of critical time and wavenumber on the anisotropy ratio was found to be in good agreement with theoretical scalings proposed by Ennis-King et al. (Phys. Fluids, vol. 17, 2005, paper no. 084107). For heterogeneous systems, we show that uncertainty in the permeability field at low wavenumbers can influence the growth of perturbations. We use a Monte Carlo approach to compute the mean and standard deviation of the critical time for a sample permeability field. The results from theory are also compared with finite-volume simulations of the governing equations using fully heterogeneous porous media with strong layering. We show that the results from non-modal stability analysis match extremely well with those obtained from the simulations as long as the assumption of strong layering remains valid.

AbstractThe linear stability of the horizontal pipe flow of an equal density oil–water mixture, arranged as acore–annular flow(CAF), is here reconsidered from the point of view of non-modal analysis in order to assess the effects of non-normality of the linearized Navier–Stokes operator on the transient evolution of small disturbances. The aim of this investigation is to give insight into physical situations in which poor agreement occurs between the predictions of linear modal theory and classical experiments. The results exhibit high transient amplifications of the energy of three-dimensional perturbations and, in analogy with single-fluid pipe flow, the largest amplifications arise for non-axisymmetric disturbances of vanishing axial wavenumber. Energy analysis shows that the mechanisms leading to these transient phenomena mostly occur in the annulus, occupied by the less viscous fluid. Consequently, higher values of energy amplifications are obtained by increasing the gap between the core and the pipe wall and the annular Reynolds number. It is argued that these linear transient mechanisms of disturbance amplification play a key role in explaining the transition to turbulence of CAF.

A viscous extension of Arnold’s inviscid theory for planar parallel non-inflectional shear flows is developed and a viscous Arnold’s identity is obtained. Special forms of the viscous Arnold’s identity have been revealed that are closely related to the perturbation’s enstrophy identity derived by Synge (Proceedings of the Fifth International Congress for Applied Mechanics, 1938, pp. 326–332, John Wiley) (see also Fraternale et al., Phys. Rev. E, vol. 97, 2018, 063102). Firstly, an alternative derivation of the perturbation’s enstrophy identity for strictly parallel shear flows is acquired based on the viscous Arnold’s identity. The alternative derivation induces a weight function. Thereby, a novel weighted perturbation’s enstrophy identity is established, which extends the previously known enstrophy identity to include general streamwise translation-invariant shear flows. Finally, the validity of the enstrophy identity for parallel shear flows is rigorously examined and established under global nonlinear dynamics imposed with two classes of wall boundary conditions. As an application of the enstrophy identity, we quantitatively investigate the mechanism of linear instability/stability within the normal modal framework. The investigation reveals a subtle interaction between a critical layer and its adjacent boundary layer, which determines the stability nature of the disturbance. As an implementation of the relaxed wall boundary conditions imposed for the enstrophy identity, a control scheme is proposed that transitions the wall settings from the no-slip condition to the free-slip condition, through which a flow is stabilized quickly in an early stage of the transition.

AbstractWe study the linear stability of gravitationally unstable, transient, diffusive boundary layers in porous media using non-modal stability theory. We first perform a classical optimization procedure, using an adjoint-based method, to obtain the perturbations at the initial time $t= {t}_{p} $ that have a maximum amplification at a final time $t= {t}_{f} $. We then investigate the sensitivity of the optimal perturbations to the initial time, ${t}_{p} $, and the final time, ${t}_{f} $, as well as different measures of perturbation amplification. Due to the transient nature of the base state, we demonstrate that there is an optimal initial perturbation time, ${ t}_{p}^{o} $. By rescaling the problem, we develop analytical relationships for the optimal initial time and wavenumber in terms of aquifer properties. We also demonstrate that the classical optimization procedure essentially recovers the dominant perturbation structures predicted by a quasi-steady modal analysis. Although the classical optimal perturbations are mathematically valid, we observe that due to physical constraints, they are unlikely to reflect analogous laboratory experiments. Therefore, we propose a modified optimization procedure (MOP) that constrains the optimization to physically admissible initial perturbation fields. We compare the results of the classical and modified optimization procedures with quasi-steady modal analyses and initial value problems commonly used in the literature. Finally, we validate the predictions of the modified optimization scheme by performing direct numerical simulations (DNS) that emulate the onset of convection in physical systems.

In order to accurately improve and predict chatter stability region of machining process, an optimization method of machining process with non-uniform allowance of integral impeller was proposed. The modal parameters of the workpiece process system were obtained using the finite element analysis. Based on the regenerative chatter analysis theory, a limit comparison diagram of the stability with uniform allowance and non-uniform allowance was established. The simulation results showed that the non-uniform allowance natural frequency is about 1.43 times as much as the uniform allowance natural frequency, and the machining system stiffness non-uniform allowance is twice as much as the uniform allowance, while the limit of chatter stability region is increased by 3 times. This article studied uniform allowance and non-uniform allowance of milling chatter stability with experimental method. Tool path for five-axis machining and machine tool simulation based on NX CAM were planned. The comparisons of cutting processing uniform allowance and non-uniform allowance were done, and the surface profile detection of the test part with the three-dimensional scanning was carried out. The experimental results showed that the average optimization rate for manufacturing precision of blade suction surface after optimization and pressure surface was 63.8% and 48.84%. The total experiment showed that this process optimization strategy could effectively improve the stiffness of the integral impeller blade and reduce the cutting chatter of the blade during the cutting process.

AbstractWe consider the linear and nonlinear stability of two-phase density-matched but viscosity-contrasted fluids subject to laminar Poiseuille flow in a channel, paying particular attention to the formation of three-dimensional waves. A combination of Orr–Sommerfeld–Squire analysis (both modal and non-modal) with direct numerical simulation of the three-dimensional two-phase Navier–Stokes equations is used. For the parameter regimes under consideration, under linear theory, the most unstable waves are two-dimensional. Nevertheless, we demonstrate several mechanisms whereby three-dimensional waves enter the system, and dominate at late time. There exists a direct route, whereby three-dimensional waves are amplified by the standard linear mechanism; for certain parameter classes, such waves grow at a rate less than but comparable to that of the most dangerous two-dimensional mode. Additionally, there is a weakly nonlinear route, whereby a purely spanwise wave grows according to transient linear theory and subsequently couples to a streamwise mode in weakly nonlinear fashion. Consideration is also given to the ultimate state of these waves: persistent three-dimensional nonlinear waves are stretched and distorted by the base flow, thereby producing regimes of ligaments, ‘sheets’ or ‘interfacial turbulence’. Depending on the parameter regime, these regimes are observed either in isolation, or acting together.

AbstractThe stability of streamwise corner flow is investigated by means of direct numerical simulation at subcritical Reynolds numbers. The flow is harmonically forced, and global modes are extracted through a spectral decomposition. Spatial amplification in the near-corner region is observed even though the flow is shown to be subcritical in terms of spatial linear theory. This apparent discrepancy is resolved by extending the local analysis to include non-modal effects. It is demonstrated that the amplification is a result of the interaction between two coexistent spatial transient growth processes that can be associated with different parts of the linear stability spectrum. A detailed investigation of the underlying mechanisms shows that the transient amplification behaviour is caused by pseudo-resonance between the inviscid corner mode, and different sets of viscous modes. By comparison with studies of other locally inflectional flows, it is found that viscid–inviscid pseudo-resonance might be a general phenomenon leading to selective noise amplification.

Two- and three-dimensional modal and non-modal instability mechanisms of steady spanwise-homogeneous laminar separated flow over airfoil profiles, placed at large angles of attack against the oncoming flow, have been investigated using global linear stability theory. Three NACA profiles of distinct thickness and camber were considered in order to assess geometry effects on the laminar–turbulent transition paths discussed. At the conditions investigated, large-scale steady separation occurs, such that Tollmien–Schlichting and cross-flow mechanisms have not been considered. It has been found that the leading modal instability on all three airfoils is that associated with the Kelvin–Helmholtz mechanism, taking the form of the eigenmodes known from analysis of generic bluff bodies. The three-dimensional stationary eigenmode of the two-dimensional laminar separation bubble, associated in earlier analyses with the formation on the airfoil surface of large-scale separation patterns akin to stall cells, is shown to be more strongly damped than the Kelvin–Helmholtz mode at all conditions examined. Non-modal instability analysis reveals the potential of the flows considered to sustain transient growth which becomes stronger with increasing angle of attack and Reynolds number. Optimal initial conditions have been computed and found to be analogous to those on a cascade of low pressure turbine blades. By changing the time horizon of the analysis, these linear optimal initial conditions have been found to evolve into the Kelvin–Helmholtz mode. The time-periodic base flows ensuing linear amplification of the Kelvin–Helmholtz mode have been analysed via temporal Floquet theory. Two amplified modes have been discovered, having characteristic spanwise wavelengths of approximately 0.6 and 2 chord lengths, respectively. Unlike secondary instabilities on the circular cylinder, three-dimensional short-wavelength perturbations are the first to become linearly unstable on all airfoils. Long-wavelength perturbations are quasi-periodic, standing or travelling-wave perturbations that also become unstable as the Reynolds number is further increased. The dominant short-wavelength instability gives rise to spanwise periodic wall-shear patterns, akin to the separation cells encountered on airfoils at low angles of attack and the stall cells found in flight at conditions close to stall. Thickness and camber have quantitative but not qualitative effect on the secondary instability analysis results obtained.

A physics-based integral approach is adopted here to develop a theory for studying bi-modal excitation of the shear layer of a Mach 1.5 planar jet. The transverse shapes of the mean flow quantities are given by analytical functions modeling the corresponding jet experiment and Reynolds-averaged Navier–Stokes solution. The transverse shapes of the frequency modes of the coherent large-scale structure are obtained as the eigenfunctions of the locally parallel linear stability theory. The Navier–Stokes equations are then reduced to a set of ordinary differential equations. The solution of this set, subject to the initial conditions, describes the nonlinear interaction among the excited frequency modes, as well as their interaction with the mean flow and the background turbulence. Our analysis shows that the time-averaged interaction among the modes is non-zero only if the two frequency modes are related to each other by the fundamental-harmonic frequency. We label the fundamental mode here, “f,” as the most amplified mode developing nonlinearly along the jet in the absence of other imposed modes. We then use the resulting theory to study the effect of bimodal excitation by harmonically related pairs (f, f/2) or (f, 2f) to see under which conditions this bimodal excitation can suppress the fundamental. We found that the combination of fundamental and harmonic (f, 2f) can effectively reduce the fundamental at an optimized phase lag. By viewing the fundamental as the most dominant sound source in the jet, it is, thus, possible to reduce the jet noise via bi-modal excitation.

A physics-based integral approach is adopted here to develop a theory for studying bi-modal excitation of the shear layer of a Mach 1.5 planar jet. The transverse shapes of the mean flow quantities are given by analytical functions modeling the corresponding jet experiment and Reynolds-averaged Navier–Stokes solution. The transverse shapes of the frequency modes of the coherent large-scale structure are obtained as the eigenfunctions of the locally parallel linear stability theory. The Navier–Stokes equations are then reduced to a set of ordinary differential equations. The solution of this set, subject to the initial conditions, describes the nonlinear interaction among the excited frequency modes, as well as their interaction with the mean flow and the background turbulence. Our analysis shows that the time-averaged interaction among the modes is non-zero only if the two frequency modes are related to each other by the fundamental-harmonic frequency. We label the fundamental mode here, “f,” as the most amplified mode developing nonlinearly along the jet in the absence of other imposed modes. We then use the resulting theory to study the effect of bimodal excitation by harmonically related pairs (f, f/2) or (f, 2f) to see under which conditions this bimodal excitation can suppress the fundamental. We found that the combination of fundamental and harmonic (f, 2f) can effectively reduce the fundamental at an optimized phase lag. By viewing the fundamental as the most dominant sound source in the jet, it is, thus, possible to reduce the jet noise via bi-modal excitation.

A finite element formulation is presented for the prediction of nonlinear response of thin plates under a steady-state non-uniform temperature change over the thin plate and band limited Gaussian white noise. Thermal buckling temperatures and thermal deflections are obtained to explain the stability of panels, and modal frequencies of thermally buckled plate are obtained to explain the stiffness characteristics of panels. The stress responses of panels under thermo-acoustic loadings exhibit complex nonlinear characteristics. Miner linear accumulation damage theory and improved Rainflow counting cycle method are used for estimation of fatigue life of panels under combined thermo-acoustic loadings. Results show that the fatigue life decreases till the end of snap-through and then gives a rise trend. Afterward, the fatigue life reaches a steady state at low peak temperature area. As the peak temperature goes up sequentially, the fatigue life rises suddenly, and then reaches a steady state at high peak temperature area.

The vibration and dynamic instability characteristics of doubly curved panels subjected to partially distributed non-conservative follower load are studied using finite element analysis. The first-order shear deformation theory is used to model the doubly curved panels, considering the effects of shear deformation and rotary inertia. The theory used is the extension of dynamic, shear deformable theory according to Sander's first approximation for doubly curved shells, which can be reduced to Love's and Donnell's theories by means of tracers. The modal transformation technique is applied to the resulting equilibrium equation for subsequent analysis. Structural damping is introduced into the system in terms of equivalent viscous damping. The effects of load bandwidth, boundary condition, load direction control parameter and damping are considered for the stability behaviour of the panels. The results show that the load bandwidth has a significant effect on the dynamic instability characteristics of the panels. The analysis also shows that, under follower loading, the system is susceptible to instability due to flutter alone or due to both flutter and divergence, depending upon the system parameters. Structural damping significantly affects the critical flutter loads of the panels.

The article substantiates the applicability of socio-ontological approaches and methods of theoretical ontology to the study of social reality. A wide range of references to traditional research in this area conducted by sociologists, legal scholars, economists and cultural scientists are provided. From the standpoint of social ontology, the key principles of the flow of some social processes are considered, first of all, the features of the development of youth sub-cultures. Using the classical methodology of categorical analysis, the attributive characteristics of their existence are identified. The examples show how atypical contradictory aspects of a given social phenomenon can be explained, namely, how ideas about non-physical space and time relate to traditional ontological categories; the predominance of processes of "horizontal mobility" in the activities of the subculture was discovered. The intervals of "quantitative stability" are defined as those in which the development of socially dynamic processes of a new quality occurs. Using the categorical pair "identity-difference", the specific features of the manifestation of social inequality in the education and functioning of the youth movement are considered. In the course of modal analysis, the role of the necessary, random and possible in explaining the current status of a social phenomenon, which has a "floating" ontological status, combining an indication of its physical and virtual existence, was revealed. The "problematic" mode of the possible as a way of manifesting the phenomenon of youth sub-culture allows us to point out the possibility of the predominance of "online culture" features in it. Based on the results obtained, prospects for further study and practical work with "complex" social phenomena are identified. It is shown that the prevention and suppression of illegal actions by representatives of youth cultures should be based not only on sociological, legal, etc. data research but also on a deep, comprehensive theoretical and philosophical analysis.

When considering the issue of synthesis of an automatic control system by a modular method using a polynomial decomposition of the transfer functions of an object and a controller, synthesis algorithms for fully controlled systems are proposed. However, the question arises about the possibilities of using this algorithm if this condition is not met. The consideration of this is-sue turned out to be especially relevant for multichannel models of objects with a non-square transfer function (having an unequal number of input and output channels). It is shown that for some fundamental terms of the theory of automatic control, such as controllability, reachability, observability, stability and some others, there are special definitions of them in the case of considering this type of objects. The term non‒square object is proposed for use, which is used mainly in foreign literature. Some restrictions on the modal synthesis of regulators by a method using a polynomial matrix separation of the object and the regulator are considered. Examples of internally and asymptotically unstable systems are given. A hypothesis is put forward about the stability of the controlled system. An example of a multichannel system "inverted pendulum on a cart" is considered, which is an object with a non-square matrix transfer function (in this example, the number of input actions is less than the number of output parameters). Using the static characteristics of this object, it is demonstrated that not always controlled systems can be stabilized in a given position. For example, in the case of setting the desired angle of an inverted pendulum other than zero, it is impossible to hold the position of the cart in a given coordinate. At the same time, if you set the angle at the equilibrium point as the desired angle of the inverted pendulum, then stabilization of the cart at a given coordinate becomes possible.

AbstractLinear stability theory for Rayleigh-Benard convection shows that for a specified Rayleigh number, greater than some critical value, only a finite range of horizontal wave numbers support convective instability in a horizontal layer of fluid heated from below. However, it is not possible to predict the preferred horizontal scale of established motions from this approach although it is clear from observations, particularly of the solar surface, that a preferred cell size does prevail. In an endeavour to establish a preferred horizontal scale appropriate non-linear modal equations have been integrated forward in time, initially incorporating a discrete band of wave numbers equally spaced across the range that supports convection, for a specific Rayleigh number. The horizontal resolution was improved in subsequent integrations by first deleting modes that had substantially decayed and then introducing new modes on a finer horizontal mesh in the vicinity of what appeared to be the evolutionary dominant mode. Finally, the multimode integrations were continued in time until the evolution of a dominant horizontal mode from within the restricted range was evident. Both the model characteristics and numerical scheme adopted placed limits on the degree of horizontal refinement that could be undertaken with confidence.

Although boundary-layer flows over convex surfaces are exponentially stable, non-modal mechanisms may enable significant disturbance growth which can make the flow susceptible to secondary instabilities. A parametric investigation of the transient growth and secondary instabilities in flows over convex surfaces is performed. The optimal disturbance in the steady case corresponds to alternating streaks and streamwise vortices of opposite sign that reinforce one another due to lift-up and centrifugal forces, respectively. The process repeats with a constant (naturally appearing) streamwise wavelength which is proportional to the square root of the radius. Unsteady disturbances achieve a higher optimal gain, compared to the steady case, as a result of the opposing effects of the lift-up and centrifugal mechanisms. Linear analysis shows that the curvature has a negligible effect on secondary instabilities. Direct numerical simulations of transient growth with and without secondary instabilities confirm the predictions obtained by the local stability theory. It is found that the presence of a secondary instability is not sufficient, on its own, to ensure transition to turbulence. Only sufficiently long and energetic streaks trigger the breakdown to turbulence.

ABSTRACT The phoebe code was used to analyse the Kepler light-curve and to estimate the physical and geometrical parameters of a rare pulsating binary system, KIC 3858884. The analysis indicated that the system is composed of two detached and very similar main-sequence A-type stars, in a highly eccentric orbit with e = 0.47. After disentangling the binarity effect, the residual data were subjected to Fourier frequency decomposition using period04 software. The resulting frequency spectrum consists of two moderately high-amplitude nearby frequencies, F1 = 7.232199 d−1 and $F2=7.472889\, \mathrm{d}^{-1}$, which were attributed to δ Scuti-type pulsations. In addition, 18 frequencies were identified that were exact harmonics of the orbital frequency $f_{\rm orb}= 0.038533\, \mathrm{d}^{-1}$, and also 53 anharmonics. However, it was found that many of these anharmonic frequencies coupled together non-linearly to give harmonic modes of pulsation. Furthermore, some existing theoretical models of the tidal oscillations were numerically verified in general binary systems through estimations of various modal characteristics, for example mode quantum numbers ${n, l, m,}$ energies Ei, threshold energies Ei,th, damping rates γi, growth rates Γi and stability criteria, etc. The evolution of the stars in the binary system was compared with some similar single pulsating stars on the Hertzsprung–Russell diagram and it was concluded that the evolution of a single star is more rapid. Finally, the observed rate of apsidal line displacement was estimated through eclipse timing variation analysis as Uobs = 74745.2 ± 2566 yr. This was compared with the theoretically calculated rate of the line of apsides motion, UTheo = 73588 ± 2298 yr, and found to be in good agreement within errors, hence verifying general relativity theory once again.

AbstractStreamwise rolls and accompanying streamwise streaks are ubiquitous in wall-bounded shear flows, both in natural settings, such as the atmospheric boundary layer, as well as in controlled settings, such as laboratory experiments and numerical simulations. The streamwise roll and streak structure has been associated with both transition from the laminar to the turbulent state and with maintenance of the turbulent state. This close association of the streamwise roll and streak structure with the transition to and maintenance of turbulence in wall-bounded shear flow has engendered intense theoretical interest in the dynamics of this structure. In this work, stochastic structural stability theory (SSST) is applied to the problem of understanding the dynamics of the streamwise roll and streak structure. The method of analysis used in SSST comprises a stochastic turbulence model (STM) for the dynamics of perturbations from the streamwise-averaged flow coupled to the associated streamwise-averaged flow dynamics. The result is an autonomous, deterministic, nonlinear dynamical system for evolving a second-order statistical mean approximation of the turbulent state. SSST analysis reveals a robust interaction between streamwise roll and streak structures and turbulent perturbations in which the perturbations are systematically organized through their interaction with the streak to produce Reynolds stresses that coherently force the associated streamwise roll structure. If a critical value of perturbation turbulence intensity is exceeded, this feedback results in modal instability of the combined streamwise roll/streak and associated turbulence complex in the SSST system. In this instability, the perturbations producing the destabilizing Reynolds stresses are predicted by the STM to take the form of oblique structures, which is consistent with observations. In the SSST system this instability exists together with the transient growth process. These processes cooperate in determining the structure of growing streamwise roll and streak. For this reason, comparison of SSST predictions with experiments requires accounting for both the amplitude and structure of initial perturbations as well as the influence of the SSST instability. Over a range of supercritical turbulence intensities in Couette flow, this instability equilibrates to form finite amplitude time-independent streamwise roll and streak structures. At sufficiently high levels of forcing of the perturbation field, equilibration of the streamwise roll and streak structure does not occur and the flow transitions to a time-dependent state. This time-dependent state is self-sustaining in the sense that it persists when the forcing is removed. Moreover, this self-sustaining state rapidly evolves toward a minimal representation of wall-bounded shear flow turbulence in which the dynamics is limited to interaction of the streamwise-averaged flow with a perturbation structure at one streamwise wavenumber. In this minimal realization of the self-sustaining process, the time-dependent streamwise roll and streak structure is maintained by perturbation Reynolds stresses, just as is the case of the time-independent streamwise roll and streak equilibria. However, the perturbation field is maintained not by exogenously forced turbulence, but rather by an endogenous and essentially non-modal parametric growth process that is inherent to time-dependent dynamical systems.

ABSTRACT This study aims to explain and analyze the effect of product market competition, financial leverage, and risk of financing on the stability of Islamic banks in Indonesia in 2018-2022. The sampling technique used is Islamic banks listed on the Indonesia Stock Exchange. Source of data obtained from the annual report of each bank. The analytical method used is panel regression analysis with Eviews 10 software with the Common Effect Model (CEM) model as the best model. The variables used consist of product market competition (PCM), financial leverage (DER proxy), and financing risk (NPF proxy) on banking stability (proximate Natural Logarithm Z-Score). The results of this study found that product market competition did not affect bank stability. Meanwhile, financial leverage and financing risk have a negative effect on the stability of Islamic banks in Indonesia. From the results of this study, it is hoped that competition for Islamic banks in Indonesia can always run normally as it is today. In addition, the financial leverage and financing risks of Islamic banks have a negative impact on banking stability. Therefore, this research can be used as an early warning and reference for Islamic banks to make funding decisions through debt capital and excessive financing. keywords: Banking stability, product market competition, financial leverage, financing risk ABSTRAK Penelitian ini bertujuan untuk menjelaskan dan menganalisis pengaruh persaingan pasar produk, financial leverage, dan risk of financing terhadap stabilitas bank syariah di Indonesia pada 2018-2022. Teknik pengambilan sampel yang digunakan bank syariah yang terdaftar di Bursa Efek Indonesia. Sumber data diperoleh dari laporan tahunan masing masing bank. Metode analisis yang digunakan adalah analisis regresi panel dengan software Eviews 10 dengan model Common Effect Model (CEM) sebagai model terbaik .Variabel yang digunakan terdiri dari persaingan pasar produk (PCM), financial leverage (proksi DER) dan resiko pembiayaan (proksi NPF) terhadap stabilitas perbankan (doproksikan Natural Logarithm Z-Score. Hasil dari penelitian ini menemukan bahwa persaingan pasar produk tidak berpengaruh terhadap stabilitas bank. Sementara financial leverage dan resiko pembiayaan berpengaruh negative terhadap stabilitas bank syariah di Indonesia. Dari hasil penelitian ini, diharapkan persaingan bank syariah di Indonesia dapat selalu berjalan berjalan normal seperti saat ini. Selain itu, financial leverage dan resiko pembiayaan bank syariah berdampak buruk pada stabilitas perbankan. 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Kebijakan dividen, merupakan suatu topik yang menarik untuk diteliti meskipun terjadi banyak perdebatan dengan pendekatan berbagai teori mengenai dividen. Dalam penelitian ini kebijakan dividen akan dikaji melalui teori keagenan dengan memperhatikan pengaruh dari corporate governance perusahaan, khususnya melalui pemisahan mekanisme corporate governance secara internal maupun eksternal (Gillan, 2006) yang dimediasi oleh profitabilitas perusahaan. Penelitian dilakukan pada semua perusahaan non keuangan yang terdaftar di Bursa Efek Indonesia pada tahun 2007-2010. Penyelesaian estimasi path model dan pengujian hipotesis menggunakan program AMOS 16.0. Hasil penelitian menunjukkan bahwa mekanisme internal corporate governance yang diukur dari komisaris independen dan rasio kompensasi eksekutif ternyata tidak berpengaruh signifikan terhadap kinerja keuangan perusahaan, sedangkan mekanisme external corporate governance yang diukur dari stabilitas dan prosentase kepemilikan institusi berpengaruh signifikan terhadap kinerja keuangan. Kondisi ini menunjukkan bahwa external corporate governance memiliki kekuatan yang lebih besar untuk melakukan monitoring dan memberikan pengaruh atas kebijakan keuangan perusahaan. Kebijakan dividen, merupakan suatu topik yang menarik untuk diteliti meskipun terjadi banyak perdebatan dengan pendekatan berbagai teori mengenai dividen. Dalam penelitian ini kebijakan dividen akan dikaji melalui teori keagenan dengan memperhatikan pengaruh dari corporate governance perusahaan, khususnya melalui pemisahan mekanisme corporate governance secara internal maupun eksternal (Gillan, 2006) yang dimediasi oleh profitabilitas perusahaan. Penelitian dilakukan pada semua perusahaan non keuangan yang terdaftar di Bursa Efek Indonesia pada tahun 2007-2010. Penyelesaian estimasi path model dan pengujian hipotesis menggunakan program AMOS 16.0. Hasil penelitian menunjukkan bahwa mekanisme internal corporate governance yang diukur dari komisaris independen dan rasio kompensasi eksekutif ternyata tidak berpengaruh signifikan terhadap kinerja keuangan perusahaan, sedangkan mekanisme external corporate governance yang diukur dari stabilitas dan prosentase kepemilikan institusi berpengaruh signifikan terhadap kinerja keuangan. Kondisi ini menunjukkan bahwa external corporate governance memiliki kekuatan yang lebih besar untuk melakukan monitoring dan memberikan pengaruh atas kebijakan keuangan perusahaan. Dividend policy is an interesting topic to be discussed despite the fact that there are contentious arguments on theories about dividend. In this research dividend policy will be viewed through the agency theory by considering the effect of the company's corporate governance, in particular through the separation mechanism of internal and external corporate governance (Gillan, 2006) which are mediated by profitability. The study was conducted by all non-financial companies at the Indonesia Stock Exchange from 2007 to 2010. AMOS 16.0 program is used in estimating the completion path model and testing hypotesis. The results shows that the mechanisms of internal corporate governance via the existence of independent commissioner and executive compensation can not significantly influence the company's financial performance, while mechanisms of external corporate governance as measured by the stability and the percentage of institutional ownership significantly influence the companys financial performance. This indicates that the external corporate governance has a greater power to monitor and influence the financial policies of the company.

Modal and non-modal stability analyses are applied to Hagen–Poiseuille flow with a non-ideal fluid. The non-ideal fluid is defined as a fluid close to its vapor–liquid critical point. In this region, properties of the fluid deviate significantly from the assumptions of the ideal gas model. In this paper, the specific example of CO2 near the critical point is taken as a non-ideal fluid. We studied fluids at supercritical pressure and different wall temperatures so that the centerline temperatures can be lower, equal, and higher than the pseudo-critical temperature. Flow instability is characterized by the Reynolds number, and the product of the Prandtl and Eckert numbers. In modal stability analysis, we observe that there is no unstable mode in Hagen–Poiseuille flow with a non-ideal fluid. Regarding the growth rate, as the axial wavenumber increases, another mode becomes the least stable. The non-modal theory is employed to investigate the optimal response to harmonic external force and transient energy growth. The influence of axial and azimuthal wave numbers, Prandtl and Eckert numbers, and thermodynamic states are also taken into account. In this study, we identify an generalized inflection point in the transcritical base profile, causing the transcritical state to be the most unstable. In non-modal instability, we observe that the optimal response mainly occurs at time invariant axisymmetric disturbance. This suggests that the axisymmetric disturbance could potentially initiate the transition to turbulence.

AbstractThe classical problem of the stability of Core-Annular Flow (CAF) in pipes is reconsidered from the point of view of the linear non-modal analysis. An accurate Chebyshev pseudospectral code in polar coordinates has been developed in order to separately discretize the two phases of the flow. Transient amplifications of the energy of three-dimensional perturbations are computed by taking into account the effects of viscosity and volume ratios between the two liquids, as well as of Reynolds number and a surface tension parameter.A detailed investigation is conducted in wide regions of the parameters space and the occurrence of remarkable transient growths is found for asymptotically both stable and unstable configurations. Optimal perturbations (i.e. giving the maximum energy amplification) are determined and their structure is analyzed. It is shown that in conditions in which axisymmetric modes are expected to constitute the most dangerous exponential disturbances, spiral perturbations can provide higher levels of transient energy amplification. Growth rates and amplification levels relative to modal and non-modal mechanisms are compared in order to analyze more in depth previous disagreements between experiments and modal theory.

Purpose The purpose of this paper is to contribute to the solution of the fatigue damage problem of reinforced concrete frames in bending. Design/methodology/approach The problem of fatigue damage is formulated based on the rheological–dynamical analogy, including a scalar damage variable to address the reduction of stiffness in strain softening. The modal analysis is used by the finite element method for the determination of modal parameters and resonance stability of the selected frame cross-section. The objectivity of the presented method is verified by numerical examples, predicting the ductility in bending of the frame whose basic mechanical properties were obtained by non-destructive testing systems. Findings The modal analysis in the frame of the finite element method is suitable for the determination of modal parameters and resonance stability of the selected frame cross-section. It is recommended that the modulus of elasticity be determined by non-destructive methods, e.g. from the acoustic response. Originality/value The paper presents a novel method of solving the ductility in bending taking into account both the creep coefficient and the aging coefficient. The rheological-dynamical analogy (RDA) method uses the resonant method to find material properties. The characterization of the structural damping via the damping ratio is original and effective.

Abstract The analysis of the free vibration in transmission towers is aimed at better evaluating their health status. Due to the non-stationarity of the height of non-uniform wind-induced vibration, there is a sustained forced vibration response in the vibration signal of transmission towers. This will lead to a decrease in the stability of vibration characteristics, which brings great difficulty to transmission tower status identification. In order to solve this problem, this paper proposes a method for extracting the free vibration response of transmission towers. By using Void-Kalman Filtering (VKF) and generalized demodulation transform (GDT) for modal frequency tracking and pseudo-peak elimination, the signal is maximally cleaned while retaining all modal information. In addition, this paper combines variational theory and time-frequency domain features to decompose all effective modal orders in the vibration response. This not only solves the errors that exist when GDT and VKF directly process the original signal, but also makes the extraction of frequency parameters of each modal orders more convenient. The effectiveness of this approach is demonstrated by extracting the free vibration response of a 110kV cat-head type tower. And by comparing it with existing mainstream signal processing methods using the example of bolt loosening faults. The results show that the signal processed by this approach can more stably and accurately capture the fault characteristics, providing a new idea for the extraction of free vibration response in the field of transmission tower health monitoring.

IntroductionThe control of infinite-dimensional rigid-flexible robotic arms presents significant challenges, with direct truncation of first-order modal models resulting in poor control quality and second-order models leading to complex hardware implementations.MethodsTo address these issues, we propose a fuzzy super twisting mode control method based on approximate inertial manifold dimensionality reduction for the robotic arm. This innovative approach features an adjustable exponential non-singular sliding surface and a stable continuous super twisting algorithm. A novel fuzzy strategy dynamically optimizes the sliding surface coefficient in real-time, simplifying the control mechanism.ResultsOur findings, supported by various simulations and experiments, indicate that the proposed method outperforms directly truncated first-order and second-order modal models. It demonstrates effective tracking performance under bounded external disturbances and robustness to system variability.DiscussionThe method's finite-time convergence, facilitated by the modification of the nonlinear homogeneous sliding surface, along with the system's stability, confirmed via Lyapunov theory, marks a significant improvement in control quality and simplification of hardware implementation for rigid-flexible robotic arms.

Abstract A new type of non-uniform and asymmetric ultrasonic vibration system is proposed and applied to the turning process. The research results show that the design theory of the non-uniform and non-symmetric ultrasonic vibration system is accurate and reliable.The theoretical design frequency and modal simulation frequency error of Ultrasonic Vibration Turning System (UVTS) is only 2.5%. The designed non-uniform and non-symmetric ultrasonic vibration system has excellent vibration performance and stability, and the established simulation model can predict surface microtexture accurately. The vibration mode output by the non-uniform and non-symmetric ultrasonic vibration system is longitudinal-bending vibration, and the actual vibration performance is excellent. Compared with conventional cutting, the addition of longitudinal-bending ultrasonic vibration under the same conditions can give the machined surface a microscopic textured structure, reduce surface roughness and water contact angle, and improve surface wettability.The minimum surface roughness obtained in the experiment is 1.005 μm.The orthogonal experiment results show that there is a correlation between the machining parameters, surface micro-structure parameters, surface wettability, and surface roughness.

The interaction of several instabilities and the influence of free-stream turbulence on laminar-turbulent transition on a 20% thick wind-turbine blade section with a laminar separation bubble (LSB) are investigated with wall-resolved large-eddy simulations (LES). Turbulence intensities (TI) of 0%, 2.2%, 4.5%, 8.6%, and 15.6% at chord Reynolds number 105 are considered. Linear receptivity occurs for the most energetic disturbances; high-frequency perturbations are excited via non-linear mechanisms for TI≥8.6%. Unstable Tollmien–Schlichting (TS) waves appear in the inflectional flow region for TI≤4.5%, shifting to inviscid Kelvin–Helmholtz (KH) modes upon separation and forming spanwise rolls. Sub-harmonic secondary instability occurs for TI=0%, with rolls intertwining before transition. Streaks spanwise modulate the rolls and increase their growth rates with TI for TI≤4.5%, reducing separation and shifting transition upstream. The TI=4.5% case presents the highest perturbations, leading to the smallest LSB and most upstream transition. Earlier inception of TS/KH modes occurs on low-speed streaks, inducing premature transition. However, for TI=8.6%, the effect of the streaks is to stabilize the attached mean flow and front part of the LSB. This occurs due to the near-wall momentum deficit alleviation, leading to the transition delay and larger LSB than TI=4.5%. This also suppresses separation and completely stabilizes TS/KH modes for TI=15.6%. Linear stability theory predicts well the modal evolution for TI≤8.6%. Optimal perturbation analysis accurately computes the streak development upstream of the inflectional flow region but indicates higher amplification than LES downstream due to the capture of low-frequency, oblique modal instabilities from the LSB. Only low-amplitude [O(1%)] streaks displayed exponential growth in the LES since non-linearity precludes the appearance of these modes.

Low order networks are widely used for linear stability analysis of combustors in the low frequency limit. High frequency stability analysis, however, is limited to cost-intensive numerical or experimental methods, since derivation of analytical solutions is either cumbersome or impossible. The article at hand provides a quasi-two-port network model for the effective modal acoustic pressure and axial velocity normalised with the transverse acoustic field for cylindrical combustors. This network modelling approach includes transfer matrices of acoustic area jumps, ducts for longitudinal, standing and spinning transverse and mixed mode wave propagation. The purely acoustic transfer matrices are validated with a generic non-reactive experiment. On the basis of phase-locked [Formula: see text] images of an engine-similar multi-jet combustor with a forced T1 mode, a locally distributed flame response model is derived, which is reduced to a global flame transfer matrix. A locally resolved convective flame response model is implemented in a numerical model in order to verify the provided theory by the comparison of the analytical and numerical flame transfer matrix for the high-frequency regime.

Abstract The frontal pole is implicated in humans in whether to exploit resources versus explore alternatives. Effective connectivity, functional connectivity, and tractography were measured between six human frontal pole regions and for comparison 13 dorsolateral and dorsal prefrontal cortex regions, and the 360 cortical regions in the Human Connectome Project Multi-modal-parcellation atlas in 171 HCP participants. The frontal pole regions have effective connectivity with Dorsolateral Prefrontal Cortex regions, the Dorsal Prefrontal Cortex, both implicated in working memory; and with the orbitofrontal and anterior cingulate cortex reward/non-reward system. There is also connectivity with temporal lobe, inferior parietal, and posterior cingulate regions. Given this new connectivity evidence, and evidence from activations and damage, it is proposed that the frontal pole cortex contains autoassociation attractor networks that are normally stable in a short-term memory state, and maintain stability in the other prefrontal networks during stable exploitation of goals and strategies. However, if an input from the orbitofrontal or anterior cingulate cortex that expected reward, non-reward, or punishment is received, this destabilizes the frontal pole and thereby other prefrontal networks to enable exploration of competing alternative goals and strategies. The frontal pole connectivity with reward systems may be key in exploit versus explore.

AbstractWe revisit the problem of Stone duality for lattices with quasioperators, presenting a fresh duality result. The new result is an improvement over that of our previous work in two important respects. First, the axiomatization of frames is now simplified, partly by incorporating Gehrke’s proposal of section stability for relations. Second, morphisms are redefined so as to preserve Galois stable (and co-stable) sets and we rely for this, partly again, on Goldblatt’s recently proposed definition of bounded morphisms for polarities. In studying the dual algebraic structures associated to polarities with relations we demonstrate that stable/co-stable set operators result as the Galois closure of the restriction of classical (though sorted) image operators generated by the frame relations to Galois stable/co-stable sets. This provides a proof, at the representation level, that non-distributive logics can be regarded as fragments of sorted residuated (poly)modal logics, a research direction recently initiated by this author.

Рассмотрены принципы структурной и функциональной организации адаптивных систем, их возникновение из унитарных мономодальных систем (УС) и особенности эволюции. Разделение УС на консервативно (КП)-оперативную (ОП) сопряжённую пару (бинарная сопряженная дифференциация (БСД)), повышает её устойчивость (Принцип сопряжённых подсистем). Эволюция УС в БСД превращает мономодальную популяцию в бимодальную, непосредственную “экологию”: среда ↔ УС – в опосредованную: среда ↔ ОП ↔ КП (где ↔ потоки информации) и синхроннуюэволюцию – в дихронную: сначала ОП, затем КП. Рассмотрены 4 стадии эволюции признаков, характерные для всех БСД. В стабильных стадиях (нет эволюции) как отсутствия так и наличия признаков наблюдается симметрия подсистем по данному признаку. Асимметрия (диморфизм) подсистем по какому-либо признаку свидетельствует о его эволюции (признак появляется или исчезает). Приведены примеры как живых, так и неживых БСД на многих иерархических уровнях организации. Идея дихронной эволюции и аналогии между БСД позволили создать изоморфные теории пола, функциональной асимметрии мозга и половых хромосом The principles of the structural and functional organization of adaptive systems, their emergence from unitary mono modal systems (US) and the features of their evolution are considered. Dividing the US into a conservative (CS) -operative (OS) conjugated subsystems (binary conjugated differentiation (BCD)) increases its stability (Principle of conjugated subsystems). The US evolution into BSD transforms a mono modal population into a bimodal, direct “ecology”: environment ↔ US - into mediated: environment ↔ OS ↔ CS (where ↔ is the flow of information) and synchronous evolution - into asynchronous: first OS, then CS. All BCDs go through 4 stages of trait’s evolution. In stable stages (no evolution), both in the absence and the presence of a character, there is a symmetry of subsystems for this character. Asymmetry (dimorphism) of subsystems by any trait indicates its evolution (a character is appearing or disappearing). Examples of both living and non-living BSDs are given for many hierarchical levels of the organization. The idea of dichronous evolution and the analogy between BSDs allowed the creation of isomorphic theories of dioecy (The Evolutionary Theory of Sex), functional asymmetry of the brain (The Evolutionary Theory of Asymmetry) and sex chromosomes (The Evolutionary Theory of Nomadic Genes).

Based on the spectral representation method of random function and combined with memoryless nonlinear translation theory, this paper analyzes the transformation relationship between potential Gaussian random process and non-Gaussian random process, and successfully generates a stationary non-Gaussian random process that conforms to the target non-Gaussian random process. For the non-stationary non-Gaussian random process simulation, on the basis of the stationary Gaussian random process, the intensity non-stationary uniform modulation model is used to modulate it, and combined with the nonlinear translation theory, the non-stationary non-Gaussian random process conforming to the target non-Gaussian random process is obtained. Aiming at the single-leg bouncing model based on the flexible rotary hip joint, the stability of its bouncing motion under passive motion is studied, and the influence of the flexible hip rotary joint on the motion stability is analyzed by comparing the single-leg bouncing motion characteristics of the free rotary hip joint. Based on the inverse dynamic control of the air phase, the fixed point distribution of the single-leg bounce of the flexible rotary hip joint was improved, and the function of the flexible rotary hip joint in the energy conversion of the bouncing motion was studied by establishing the energy consumption evaluation function. The kinematic performance verification, dynamic performance verification, dynamic parameter identification verification, and modal experiment simulation analysis were carried out for the built experimental platform, and the comparison and analysis with its theoretical model were carried out. The results show that the theoretical motion trajectory of the test mobile platform is basically consistent with the actual motion trajectory in the X and Y directions, and there is a small error in the Z-axis direction, and the error is within an acceptable range, indicating that the experimental platform system can be used to simulate the human hip joint. There is a large error between the theoretical value of the driving torque calculated by the theoretical value of the dynamic parameters and the measured value, and the dynamic theoretical model cannot accurately predict the driving torque. The predicted value of the driving torque calculated by using the identification value of the dynamic parameters is in good agreement with the measured torque, and its confidence is increased by 10–16%, indicating that the dynamic parameter identification method in this paper has a high degree of confidence.

Spectral degeneracies where eigenvalues and eigenvectors simultaneously coalesce, also known as exceptional points, are a natural consequence of the strong non-normality of the Orr–Sommerfeld operator describing the evolution of infinitesimal disturbances in parallel shear flows. While the resonances associated with these points give rise to algebraic growth, the development of non-modal stability theory exploiting specific perturbation structures with much larger potential for transient energy growth has led to waning interest in spectral degeneracies. The appearance of subharmonic eigenvalue orbits, recently discovered in the periodic spectrum of pulsating Poiseuille flow, can be traced back to the coalescence of eigenvalues at exceptional points. We present a thorough analysis of the spectral properties of the linear operator to identify exceptional points and accurately map the prevalence of subharmonic eigenvalue orbits for a large range of pulsation amplitudes and frequencies. This information is then combined with solutions of the linear initial value problem to analyse the impact of the appearance of these orbits on the temporal evolution of linear disturbances in pulsating Poiseuille flow. The periodic amplification phases are shown to be heralded by repeated non-normal growth bursts that are intensified by the formation of subharmonic orbits involving the leading eigenvalues. These bursts are associated with the change of alignment of the perturbation from the decaying towards the amplified branch of the subharmonic eigenvalue orbits in a so-called branch transition process.

The present investigation deals with the study of vibration and dynamic instability behaviour of square isotropic/laminated composite plates with circular hole subjected to partially distributed follower edge forces using finite element method. The first order shear deformation theory is used to model the plate, considering the effects of shear deformation and rotary inertia. The modal transformation technique is applied to the resulting equilibrium equation for subsequent analysis. Structural damping is introduced into the system in terms of equivalent viscous damping to study the significance of damping on stability characteristics. The effects of cutout size, load width, boundary condition, ply orientation, direction control of the load and damping parameters are considered for the stability behaviour of the plates. The results show that under follower loading, the system is susceptible to instability due to flutter alone or due to both flutter and divergence, depending on system parameters.