Corticonic models of brain mechanisms underlying cognition and intelligence

The concern of this review is brain theory or more specifically, in its first part, a model of the cerebral cortex and the way it:(a) interacts with subcortical regions like the thalamus and the hippocampus to provide higher-level-brain functions that underlie cognition and intelligence, (b) handles and represents dynamical sensory patterns imposed by a constantly changing environment, (c) copes with the enormous number of such patterns encountered in a lifetime bymeans of dynamic memory that offers an immense number of stimulus-specific attractors for input patterns (stimuli) to select from, (d) selects an attractor through a process of “conjugation” of the input pattern with the dynamics of the thalamo–cortical loop, (e) distinguishes between redundant (structured)and non-redundant (random) inputs that are void of information, (f) can do categorical perception when there is access to vast associative memory laid out in the association cortex with the help of the hippocampus, and (g) makes use of “computation” at the edge of chaos and information driven annealing to achieve all this. Other features and implications of the concepts presented for the design of computational algorithms and machines with brain-like intelligence are also discussed. The material and results presented suggest, that a Parametrically Coupled Logistic Map network (PCLMN) is a minimal model of the thalamo–cortical complex and that marrying such a network to a suitable associative memory with re-entry or feedback forms a useful, albeit, abstract model of a cortical module of the brain that could facilitate building a simple artificial brain. In the second part of the review, the results of numerical simulations and drawn conclusions in the first part are linked to the most directly relevant works and views of other workers. What emerges is a picture of brain dynamics on the mesoscopic and macroscopic scales that gives a glimpse of the nature of the long sought after brain code underlying intelligence and other higher level brain functions. Physics of Life Reviews 4 (2007) 223–252 © 2007 Elsevier B.V. All rights reserved

Anticipating Critical Transitions with Nonlinearity, Periodicity and Heterogeneity

Many natural and engineering systems may switch abruptly from one stable state to another due to a small perturbation to the system's state or a small change in the underlining conditions. In ecosystems, for example, extinctions of species or desertification can occur rapidly. Therefore, critical transitions can be dangerous to a number of systems, and it could be very beneficial if monitoring or early warning methods were available while the system is still in the healthy regime. The approach of critical transitions in many natural and engineering systems is accompanied by a phenomenon called critical slowing down. Theoretical and experimental studies have suggested that responses to small perturbations become increasingly slow when these systems are near critical transitions. Statistics such as variance, autocorrelation calculated from time series data have been proposed as early warning signals to anticipate the system's approach to a transition point. The problem of anticipating critical transitions becomes more complicated when other factors come into play. Factors such as nonlinearity, periodicity and heterogeneity can alter the behavior of the system, and thus affect the applicability of generic early warning signals. This thesis examines the effect of these factors on the critical transition of a system, and develops new data-driven approaches accordingly. To deal with and exploit the existence of nonlinearity in the system, recoveries from large instead of small perturbations are used to calculate the recovery rates of the system versus amplitudes. Under the circumstances of periodicity, recovery rates are calculated discretely via the Poincare section. Using experimental and computational data, we show that a combination of using recoveries from large perturbations and calculating recovery rates using the Poincare section can be highly effective in terms of anticipating critical transitions for systems with parametric resonance. Moreover, this thesis develops new early warning signals for spatially extended systems based on the eigenvalues of the covariance matrix. We mathematically show that the dominance of the largest eigenvalue of the covariance matrix can be used as an early warning signal by establishing the relationship between the eigenvalues of the covariance matrix and the eigenvalues of the force matrix. This new set of early warning signals are especially useful when the system has strong spatial heterogeneity. Lastly, this thesis investigates the influence of the choice of hyper-parameters, such as moving window size, sample rate, detrending methods, on the robustness of several early warning signals. General rules regarding data preparation and hypothesis testing are proposed.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/145907/1/shychen_1.pd

Parametric Forcing of Confined and Stratified Flows

abstract: A continuously and stably stratified fluid contained in a square cavity subjected to harmonic body forcing is studied numerically by solving the Navier-Stokes equations under the Boussinesq approximation. Complex dynamics are observed near the onset of instability of the basic state, which is a flow configuration that is always an exact analytical solution of the governing equations. The instability of the basic state to perturbations is first studied with linear stability analysis (Floquet analysis), revealing a multitude of intersecting synchronous and subharmonic resonance tongues in parameter space. A modal reduction method for determining the locus of basic state instability is also shown, greatly simplifying the computational overhead normally required by a Floquet study. Then, a study of the nonlinear governing equations determines the criticality of the basic state's instability, and ultimately characterizes the dynamics of the lowest order spatial mode by the three discovered codimension-two bifurcation points within the resonance tongue. The rich dynamics include a homoclinic doubling cascade that resembles the logistic map and a multitude of gluing bifurcations. The numerical techniques and methodologies are first demonstrated on a homogeneous fluid contained within a three-dimensional lid-driven cavity. The edge state technique and linear stability analysis through Arnoldi iteration are used to resolve the complex dynamics of the canonical shear-driven benchmark problem. The techniques here lead to a dynamical description of an instability mechanism, and the work serves as a basis for the remainder of the dissertation.Dissertation/ThesisSupplemental Materials Description Filezip file containing 10 mp4 formatted video animations, as well as a text readme and the previously submitted Supplemental Materials Description FileDoctoral Dissertation Mathematics 201

Vibration analysis and intelligent control of flexible rotor systems using smart materials

Flexible rotor-bearing system stability is a very important subject impacting the design, control, maintenance and operating safety. As the rotor bearing-system dynamic nonlinearities are significantly more prominent at higher rotating speeds, the demand for better performance through higher speeds has rendered the use of linear approaches for analysis both inadequate and ineffective. To address this need, it becomes important that nonlinear rotor-dynamic responses indicative of the causes of nonlinearity, along with the bifurcated dynamic states of instabilities, be fully studied. The objectives of this research are to study rotor-dynamic instabilities induced by mass unbalance and to use smart materials to stabilise the performance of the flexible rotor-system. A comprehensive mathematical model incorporating translational and rotational inertia, bending stiffness and gyroscopic moment is developed. The dynamic end conditions of the rotor comprising of the active bearing-induced axial force is modelled, the equations of motion are derived using Lagrange equations and the Rayleigh-Ritz method is used to study the basic phenomena on simple systems. In this thesis the axial force terms included in the equations of motion provide a means for axially directed harmonic force to be introduced into the system. The Method of Multiple Scales is applied to study the nonlinear equations obtained and their stabilities. The Dynamics 2 software is used to numerically explore the inception and progression of bifurcations suggestive of the changing rotor-dynamic state and impending instability. In the context of active control of flexible rotors, smart materials particularly SMAs and piezoelectric stack actuators are introduced. The application of shape memory alloy (SMA) elements integrated within glass epoxy composite plates and shells has resulted in the design of a novel smart bearing based on the principle of antagonistic action in this thesis. Previous work has shown that a single SMA/composite active bearing can be very effective in both altering the natural frequency of the fundamental whirl mode as well as the modal amplitude. The drawback with that design has been the disparity in the time constant between the relatively fast heating phase and the much slower cooling phase which is reliant on forced air, or some other form of cooling. This thesis presents a modified design which removes the aforementioned existing shortcomings. This form of design means that the cooling phase of one half, still using forced air, is significantly assisted by switching the other half into its heating phase, and vice versa, thereby equalising the time constants, and giving a faster push-pull load on the centrally located bearing; a loading which is termed ‘antagonistic’ in this present dissertation. The piezoelectric stack actuator provides an account of an investigation into possible dynamic interactions between two nonlinear systems, each possessing nonlinear characteristics in the frequency domain. Parametric excitations are deliberately introduced into a second flexible rotor system by means of a piezoelectric exciter to moderate the response of the pre-existing mass-unbalance vibration inherent to the rotor. The intended application area for this SMA/composite and piezoelectric technologies are in industrial rotor systems, in particular very high-speed plant, such as small light pumps, motor generators, and engines for aerospace and automotive application

A preliminary investigation into the effects of nonlinear response modification within coupled oscillators

This thesis provides an account of an investigation into possible dynamic interactions between two coupled nonlinear sub-systems, each possessing opposing nonlinear overhang characteristics in the frequency domain in terms of positive and negative cubic stiffnesses. This system is a two degree-of-freedom Duffing oscillator coupled in series in which certain nonlinear effects can be advantageously neutralised under specific conditions. This theoretical vehicle has been used as a preliminary methodology for understanding the interactive behaviour within typical industrial ultrasonic cutting components. Ultrasonic energy is generated within a piezoelectric exciter, which is inherently nonlinear, and which is coupled to a bar-horn or block-horn to one, or more, material cutting blades, for example. The horn/blade configurations are also nonlinear, and within the whole system there are response features which are strongly reminiscent of positive and negative cubic stiffness effects. The two degree-of-freedom model is analysed and it is shown that a practically useful mitigating effect on the overall nonlinear response of the system can be created under certain conditions when one of the cubic stiffnesses is varied. It has also bfeen shown experimentally that coupling of ultrasonic components with different nonlinear characteristics can strongly influence the performance of the system and that the general behaviour of the hypothetical theoretical model is indeed borne out in practice

Symmetry in Chaotic Systems and Circuits

Symmetry can play an important role in the field of nonlinear systems and especially in the design of nonlinear circuits that produce chaos. Therefore, this Special Issue, titled “Symmetry in Chaotic Systems and Circuits”, presents the latest scientific advances in nonlinear chaotic systems and circuits that introduce various kinds of symmetries. Applications of chaotic systems and circuits with symmetries, or with a deliberate lack of symmetry, are also presented in this Special Issue. The volume contains 14 published papers from authors around the world. This reflects the high impact of this Special Issue

Vibration analysis of cracked aluminium plates

This research is concerned with analytical modelling of the effects of cracks in structural plates and panels within aerospace systems such as aeroplane fuselage, wing, and tail-plane structures, and, as such, is part of a larger body of research into damage detection methodologies in such systems. This study is based on generating a so-called reduced order analytical model of the behaviour of the plate panel, within which a crack with some arbitrary characteristics is present, and which is subjected to a force that causes it to vibrate. In practice such a scenario is potentially extremely dangerous as it can lead to failure, with obvious consequences. The equation that is obtained is in the form of the classical Duffing equation, in this case, the coefficients within the equation contain information about the geometrical and mass properties of the plate, the loading and boundary conditions, and the geometry, location, and potentially the orientation of the crack. This equation has been known for just over a century and has in the last few decades received very considerable attention from both the analytical dynamics community and also from the dynamical systems researchers, in particular the work of Ueda, Thompson, in the 1970s and 1980s, and Thomsen in the 1990s and beyond. An approximate analytical solution is obtained by means of the perturbation method of multiple scales. This powerful method was popularized in the 1970s by Ali H.Nayfeh, and discussed in his famous books, ‘Perturbation Methods’ (1974) and ‘Nonlinear Oscillations’ (1979, with D.T.Mook), and also by J.Murdock (1990), and M.P.Cartmell et al. (2003) and has been shown to be immensely useful for a wide range of nonlinear vibration problems. In this work it is shown that different boundary conditions can be admitted for the plate and that the modal natural frequencies are sensitive to the crack geometry. Bifurcatory behaviour of the cracked plate has then been examined numerically, for a range of parameters. The model has been tested against experimental work and against a Finite Element model, with good corroboration from both. In all events, this is a significant new result in the field and one that if implemented within a larger damage detection strategy, could be of considerable practical use