Single Scalar Variable Research Articles

A discrete two time scales model of a size-structured population of parasitized trees.

The work presented a general discrete-time model of a population of trees affected by a parasite. The tree population was considered size-structured, and the parasite was represented by a single scalar variable. Parasite dynamics were assumed to act on a faster timescale than tree dynamics. The model was studied based on an associated nonlinear matrix model, in which the presence of the parasites was only reflected in the value of its parameters. For the model in all its generality, an explicit condition of viability/extinction of the parasite/tree community was found. In a simplified model with two size-classes of trees and particular forms of the vital rates, it was shown that the model undergoes a transcritical bifurcation and, likewise, a period-doubling bifurcation. It was found that, for any tree fertility rate that makes them viable without a parasite, if the parasite sufficiently reduces the survival of young trees, it can lead to the extinction of the entire community. The same cannot be assured if the parasite acts on adult trees. In situations where a high fertility rate coupled with a low survival rate of adult trees causes a non-parasitized population of trees to fluctuate, a parasite sufficiently damaging only young trees can stabilize the population. If, instead, the parasite acts on adult trees, we can find a destabilization condition on the tree population that brings them from a stable to an oscillating regime.

Adjoint-based phase reduction analysis of incompressible periodic flows

We establish the theoretical framework for adjoint-based phase reduction analysis for incompressible periodic flows. Through this adjoint-based method, we obtain spatiotemporal phase sensitivity fields through a single pair of forward and backward direct numerical simulations, as opposed to the impulse-based method that requires a very large number of simulations. Phase-based analysis involves perturbation analysis about a periodically varying base state and hence is tailored for the analysis of periodic flows. We formulate the phase description of periodic flows with respect to the potential and vortical perturbations in the flow field. The current phase-reduction analysis can also be implemented consistently in the immersed boundary projection method, which facilitates the analysis over arbitrarily-shaped bodies. We demonstrate the strength of the phase-based analysis for periodic flows over circular cylinder and symmetric airfoils at high incidence angles. The critical regions for phase modification in the cylinder flow are investigated and the locations of flow separation are shown to be the most sensitive regions. Further, the results reveal the influence of the angle of attack and airfoil thickness on the phase-sensitivity distribution of flows over various airfoils. The phase for such flows is defined based on the lift coefficient, and hence is influenced by the vortical structures responsible for lift production. The present framework sheds light on the connection between phase-sensitivity and vortex formation dynamics.

Phase-synchronization properties of laminar cylinder wake for periodic external forcings

Abstract

A Novel Kalman Filter Formulation for Improving Tracking Performance of the Extended Kernel RLS

In this paper, two contributions are presented. Firstly, a novel variant of the Kalman filter is developed and used to improve the tracking performance of the extended kernel recursive least squares algorithm (Ex-KRLS). Without resorting to the Riccati equation, the proposed formulation of the Kalman filter relies on principles of optimization and convex duality to obtain a stable quadratic form. It allows for performance and stability efficiency by minimizing the estimation error with the manipulation of a single scalar variable. Secondly, the proposed Kalman filter formulation is embedded into the Ex-KRLS-KF algorithm, an extension of the Ex-KRLS, to further improve its tracking performance. For this purpose, the state model of the proposed Ex-KRLS-KF variant is constructed in the original state space, while the hidden state is then estimated using the proposed Kalman filter formulation. The standard KRLS algorithm learns the measurement model used in hidden state estimation. We show through a comprehensive set of computer experiments that the proposed hybrid algorithm has more flexible state and noise models than competing alternative algorithms. We evaluate the proposed algorithm in two benchmarking tasks (nonlinear Rayleigh multipath channel tracking and Lorenz system modeling) and compare its performance with those provided by the state-of-the-art algorithms.

Ductile failure as a constitutive instability in porous plastic solids

A criterion for ductile rupture is derived using Rice’s theory for macroscopic strain localization, and a constitutive relation for porous plastic solids that accounts for inhomogeneous yielding at the mesoscale. At the microscopic scale, it is assumed that failure occurs by void coalescence along a band of voids. An approximate, parameter-free closed form expression for the failure criterion is derived as a function of a single scalar damage variable –the porosity– and the macroscopic stress state, characterized by the stress triaxiality and Lode parameters. For practical applications, an uncoupled approach is developed whereby the failure criterion is supplemented with a damage-free plasticity model and a loading path dependent damage evolution law. The predictive capabilities of the approach are illustrated by comparisons with finite element cell model studies. In particular, the influence of strain hardening is investigated in some detail.

High Frame Rate Video Reconstruction Based on an Event Camera.

Event-based cameras measure intensity changes (called 'events') with microsecond accuracy under high-speed motion and challenging lighting conditions. With the 'active pixel sensor' (APS), the 'Dynamic and Active-pixel Vision Sensor' (DAVIS) allows the simultaneous output of intensity frames and events. However, the output images are captured at a relatively low frame rate and often suffer from motion blur. A blurred image can be regarded as the integral of a sequence of latent images, while events indicate changes between the latent images. Thus, we are able to model the blur-generation process by associating event data to a latent sharp image. Based on the abundant event data alongside a low frame rate, easily blurred images, we propose a simple yet effective approach to reconstruct high-quality and high frame rate sharp videos. Starting with a single blurred frame and its event data from DAVIS, we propose the Event-based Double Integral (EDI) model and solve it by adding regularization terms. Then, we extend it to multiple Event-based Double Integral (mEDI) model to get more smooth results based on multiple images and their events. Furthermore, we provide a new and more efficient solver to minimize the proposed energy model. By optimizing the energy function, we achieve significant improvements in removing blur and the reconstruction of a high temporal resolution video. The video generation is based on solving a simple non-convex optimization problem in a single scalar variable. Experimental results on both synthetic and real datasets demonstrate the superiority of our mEDI model and optimization method compared to the state-of-the-art.

Modeling and Characterization of Resistor Elements for Neuromorphic Systems

Physical structures changing their resistance in operation can serve as a basis for making elements of neural networks (synapses, neurons, etc.). The processes inducing changes of resistance are rather complicated and cannot be described readily. To demonstrate the potential of this sort of variable resistors it is possible to substitute a complex physical system by a simple mathematical model reproducing the important behavioral characteristics of the actual system. A simple resistor element whose state is defined by a single scalar variable is taken as a model unit. Equations responsible for changes of the state variable are determined. Different functions and parameters that can enter these equations are discussed. Combinations of such elements and conventional electronic components are considered. Measurement methods for variable resistors are investigated. Experimental data are used to determine characteristics of a particular type of variable resistor, metal-insulator-metal structures with amorphous titanium dioxide as insulator. Specific sets of functions defining the “voltage-current” experiment-resembling behavior of a resistor element are presented.

An enriched Bouc-Wen model with damage

This paper presents an enriched hysteresis model with damage relying on the Bouc-Wen formulation, in which a single scalar variable is introduced to reproduce effects of strength and stiffness degradation emerging for damaging materials. First, some acknowledged limits of the original Bouc-Wen model are discussed, focusing on its thermodynamic admissibility and compatibility with Drucker's plasticity postulate, and highlighting the effects of the parameters β and γ. Then, a reformulated expression of the dissipated energy is presented, which is consistent from the thermodynamic point of view. This formulation is extended to the case of degrading Bouc-Wen models. Uniaxial validation analyses are proposed, together with some considerations on the physical and thermodynamic admissibility of the model.The effect of pinching is also introduced by means of the arrangement in parallel of a non-dissipative Bouc-Wen and a degrading (damaging) device, resulting in a varied set of hysteresis shapes.Finally, the proposed model is adopted to analyse the cyclic response of masonry structural elements under in-plane horizontal loads. Within the framework of equivalent frame formulation, masonry panels are modelled by an elastic beam arranged in series with nonlinear flexural hinges lumped at the ends and a shear link, whose constitutive relationships are described by means of the enriched hysteretic model with damage.

Phase-response analysis of synchronization for periodic flows

We apply phase-reduction analysis to examine synchronization properties of periodic fluid flows. The dynamics of unsteady flows is described in terms of the phase dynamics, reducing the high-dimensional fluid flow to its single scalar phase variable. We characterize the phase response to impulse perturbations, which can in turn quantify the influence of periodic perturbations on the unsteady flow. These insights from phase-based analysis uncover the condition for synchronization. In the present work, we study as an example the influence of periodic external forcing on an unsteady cylinder wake. The condition for synchronization is identified and agrees closely with results from direct numerical simulations. Moreover, the analysis reveals the optimal forcing direction for synchronization. Phase-response analysis holds potential to uncover lock-on characteristics for a range of periodic flows.

Adaptive filtering method for magnetic anomaly detection

Magnetic anomaly detection (MAD) is a technique applied in searching, localizing, and even tracking (if the target is moving) a ferromagnetic target of interest. Due to the complexity of the ambient magnetic field, almost all of the detection methods need a filter to be a preprocessing procedure. A typical way is passing the measured signal through a fixed frequency band that contains the frequency of the target signal. However, the target signal’s frequency is mostly determined by the movement velocity of the magnetometer and the distance from magnetometer to target. Namely, in different cases, the targets’ frequencies are different. We analyze the target model and represent the target signal with a single scalar variable. Through projecting the three-dimensional space into a two-dimensional plane, we lastly transform the target signal into a superposition of three sinusoids. Based on it, we propose a method to estimate the frequency band adaptively. Furthermore, we present an adaptive filtering method based on wavelet transform and take some simulation tests to prove that the proposed method has better performance compared with traditional filters.

Symbolic conditioning of arrays in probabilistic programs

Probabilistic programming systems make machine learning more modular by automating inference . Recent work by Shan and Ramsey makes inference more modular by automating conditioning . Their technique uses a symbolic program transformation that treats conditioning generally via the measure-theoretic notion of disintegration . This technique, however, is limited to conditioning a single scalar variable. As a step towards modular inference for realistic machine learning applications, we have extended the disintegration algorithm to symbolically condition arrays in probabilistic programs. The extended algorithm implements lifted disintegration , where repetition is treated symbolically and without unrolling loops. The technique uses a language of index variables for tracking expressions at various array levels. We find that the method works well for arbitrarily-sized arrays of independent random choices, with the conditioning step taking time linear in the number of indices needed to select an element.

On the Use of Summary Comorbidity Measures for Prognosis and Survival Treatment Effect Estimation.

Prognostic scores have been proposed as outcome based confounder adjustment scores akin to propensity scores. However, prognostic scores have not been widely used in the substantive literature. Instead, comorbidity scores, which are limited versions of prognostic scores, have been used extensively by clinical and health services researchers. A comorbidity is an existing disease an individual has in addition to a primary condition of interest, such as cancer. Comorbidity scores are used to reduce the dimension of a vector of comorbidity variables into a single scalar variable. Such scores are often added to regression models with other non-comorbidity variables such as age and sex, both for analyzing prognosis and for confounder adjustment when analyzing treatment effects. Despite their widespread use, the properties of and conditions under which comorbidity scores are valid dimension reduction tools in statistical models is largely unknown. In this article, we show that under relatively standard assumptions, comorbidity scores can have equal prognostic and confounder-adjustment abilities as the individual comorbidity variables, but that biases can occur if there are additional effects, such as interactions, of covariates beyond that captured by the comorbidity score. Simulations were performed to illustrate empirical properties and a data example using breast cancer data from the SEER Medicare Database demonstrates the application of these results.

On the link between martian total ozone and potential vorticity

We demonstrate for the first time that total ozone in the martian atmosphere is highly correlated with the dynamical tracer, potential vorticity, under certain conditions. The degree of correlation is investigated using a Mars global circulation model including a photochemical model. Potential vorticity is the quantity of choice to explore the dynamical nature of polar vortices because it contains information on winds and temperature in a single scalar variable. The correlation is found to display a distinct seasonal variation, with a strong positive correlation in both northern and southern winter at poleward latitudes in the northern and southern hemisphere respectively.The identified strong correlation implies variations in polar total ozone during winter are predominantly controlled by dynamical processes in these spatio-temporal regions. The weak correlation in northern and southern summer is due to the dominance of photochemical reactions resulting from extended exposure to sunlight. The total ozone/potential vorticity correlation is slightly weaker in southern winter due to topographical variations and the preference for ozone to accumulate in Hellas basin. In northern winter, total ozone can be used to track the polar vortex edge.The ozone/potential vorticity ratio is calculated for both northern and southern winter on Mars for the first time. Using the strong correlation in total ozone and potential vorticity in northern winter inside the polar vortex, it is shown that potential vorticity can be used as a proxy to deduce the distribution of total ozone where satellites cannot observe for the majority of northern winter. Where total ozone observations are available on the fringes of northern winter at poleward latitudes, the strong relationship of total ozone and potential vorticity implies that total ozone anomalies in the surf zone of the northern polar vortex can potentially be used to determine the origin of potential vorticity filaments.

Analysis, Adaptive Control and Synchronization of a Novel 4-D Hyperchaotic Hyperjerk System via Backstepping Control Method

AbstractA hyperjerk system is a dynamical system, which is modelled by annth order ordinary differential equation withn≥ 4 describing the time evolution of a single scalar variable. Equivalently, using a chain of integrators, a hyperjerk system can be modelled as a system ofnfirst order ordinary differential equations withn≥ 4. In this research work, a 4-D novel hyperchaotic hyperjerk system with two nonlinearities has been proposed, and its qualitative properties have been detailed. The novel hyperjerk system has a unique equilibrium at the origin, which is a saddle-focus and unstable. The Lyapunov exponents of the novel hyperjerk system are obtained asL1= 0.14219,L2= 0.04605,L3= 0 andL4= −1.39267. The Kaplan-Yorke dimension of the novel hyperjerk system is obtained asDKY= 3.1348. Next, an adaptive controller is designed via backstepping control method to stabilize the novel hyperjerk chaotic system with three unknown parameters. Moreover, an adaptive controller is designed via backstepping control method to achieve global synchronization of the identical novel hyperjerk systems with three unknown parameters. MATLAB simulations are shown to illustrate all the main results derived in this research work on a novel hyperjerk system.

Analysis, adaptive control and synchronization of a novel 4-D hyperchaotic hyperjerk system and its SPICE implementation

Abstract A hyperjerk system is a dynamical system, which is modelled by an nth order ordinary differential equation with n ⩾ 4 describing the time evolution of a single scalar variable. Equivalently, using a chain of integrators, a hyperjerk system can be modelled as a system of n first order ordinary differential equations with n ⩾ 4. In this research work, a 4-D novel hyperchaotic hyperjerk system has been proposed, and its qualitative properties have been detailed. The Lyapunov exponents of the novel hyperjerk system are obtained as L1 = 0.1448, L2 = 0.0328, L3 = 0 and L4 = −1.1294. The Kaplan-Yorke dimension of the novel hyperjerk system is obtained as DKY= 3.1573. Next, an adaptive backstepping controller is designed to stabilize the novel hyperjerk chaotic system with three unknown parameters. Moreover, an adaptive backstepping controller is designed to achieve global hyperchaos synchronization of the identical novel hyperjerk systems with three unknown parameters. Finally, an electronic circuit realization of the novel jerk chaotic system using SPICE is presented in detail to confirm the feasibility of the theoretical hyperjerk model.

A New Chaotic Jerk Circuit

Much recent interest has been given to simple chaotic oscillators based on jerk equations that involve a third-time derivative of a single scalar variable. The simplest such equation has yet to be electronically implemented. This paper describes a particularly elegant circuit whose operation is accurately described by a simple variant of that equation in which the requisite nonlinearity is provided by a single diode and for which the analysis is particularly straightforward.

Isotropic continuum damage mechanics for concrete under cyclic loading: Stiffness recovery, inelastic strains and frictional sliding

A three dimensional set of constitutive equations for modelling quasi-brittle materials such as concrete is presented. It is formulated within the framework of irreversible processes thermodynamics in order to fulfill physical consistency. A single scalar damage variable has been introduced in order to take into account nonlinearities due to micro-cracking. The sliding influence and the partial stiffness recovery have been considered for cyclic loadings. Related numerical aspects are presented. Both plain and reinforced concrete structures are computed up to failure in order to show the efficiency and the robustness of the proposed model. Numerical results are both quantitatively and qualitatively compared to experimental data and highlight good agreement. The proposed constitutive equations seem accurate and robust enough for computing large scale structure subject not only to monotonic loadings but also to cyclic ones.

Online maintenance policy for a deteriorating system with random change of mode

Most of maintenance policies proposed in the literature for gradually deteriorating systems, consider a stationary deterioration process. This paper is an attempt to take into account stochastically deteriorating systems which are subject to a sudden change in their degradation process. A technical device subject to gradual degradation is considered. It is assumed that the level of degradation can be resumed by a single scalar variable. An online maintenance decision rule is proposed, which makes it possible to take into account in real time the online information available on the operating mode of the system as well as its actual deterioration level. We show the efficiency of considering online decision rules for maintenance with respect to traditional maintenance policies based on a static alarm threshold. Numerical simulations are given, to assess and optimize the performance of the maintained system from its asymptotic unavailability point of view. It is compared to the results obtained with classical control-limit maintenance policies.

Chaotic hyperjerk systems

A hyperjerk system is a dynamical system governed by an nth order ordinary differential equation with n > 3 describing the time evolution of a single scalar variable. Such systems are surprisingly general and are prototypical examples of complex dynamical systems in a high-dimensional phase space. This paper describes a numerical study of a simple subclass of such systems and shows that they provide a means to extend the extensive study of chaotic systems with n =3 . We present some simple chaotic hyperjerks of 4th and 5th order. Two cases are examined that are apparently the simplest possible chaotic flows for n = 4, together with several hyperchaotic cases for n = 4 and 5. 2005 Elsevier Ltd. All rights reserved.

An Introduction to Linear and Nonlinear Finite Element Analysis: A Computational Approach

9R1. An Introduction to Linear and Nonlinear Finite Element Analysis: A Computational Approach. - Edited by PK Kythe and Dongming Wei (Dept of Math, Univ of New Orleans, New Orleans LA 70148-0001). Birkhauser, Boston. 2004. 445 pp. ISBN 0-8176-4308-7. $79.95.Reviewed by M Okrouhlik (Dept of Solids, Inst of Thermomech, Acad of Sci, Dolejskova 5, 182 00 Prague 8, Czech Republic).The book is intended as a textbook for undergraduate and graduate students from engineering, geophysics, and applied mathematics. Very broad spectrum of engineering problems is covered—the examples are taken from structural, mechanical, electrical, and chemical fields. Generally, the book deals with linear and nonlinear problems in radiation, heat transfer, mechanics of elastic and plastic media, continuum mechanics, non-Newtonian fluid flows, and electromagnetics. The book is composed of 14 chapters, 6 appendices, a bibliography, and subject index. Chapter 1 deals with weak variational formulation of a boundary value problem, Galerkin and Rayleigh-Ritz weighted residual methods. Chapter 2 presents one-dimensional local and global interpolation functions. Chapter 3 explains the Galerkin method and applies it to a one-dimensional second-order equation using liner and quadratic elements. Chapter 4 treats one-dimensional fourth-order equation (beam). Chapter 5 introduces linear triangular and bilinear four-node rectangular elements. Chapter 6 is devoted to two-dimensional problems with a single scalar variable. Stiffness matrix and load vector are derived. In Chapter 7 the two-dimensional boundary value problems as heat exchange, torsion, and seepage are treated. Chapter 8 deals with axisymmetric linear and nonlinear heat transfer problems in solid and fluids. Chapter 9 is devoted to transient problems and numerical time integration. Chapter 10 treats nonlinear problems in one dimension—radiation heat transfer, stress in elastoplastic bars, non-Newtonian fluid flow in between parallel plates, and turbulent flows in tubes. For the numerical solution the Newton method, the method of the steepest descent and conjugate gradient methods are used. Chapter 11 presents the steady-state problems of plane elasticity. Linear triangular and bilinear rectangular elements are treated; stiffness matrices and load vectors are derived. Assembling is clearly described but implementation considerations are not considered. Chapter 12 introduces the penalty method. It is applied to the treatment of both Newtonian and power law non-Newtonian Stokes flow. Chapter 13 deals with vibration analysis—elastic rods, Euler beams, and in-plane vibration of an elastic plate are treated. The last chapter contains the computer codes in Mathematica, Matlab, and Fortran. They form a vivid complement to selected problems appearing in the book. Results of computer runs are presented in the tabular form. There are six appendices, labeled A to G, in the book. They contain useful complementary information and are subsequently devoted to overview of classical integration formulas, evaluation of stiffness matrices for triangular and rectangular elements for a chosen geometry, time-step marching algorithms (forward and backward difference schemes, Cranck-Nicolson formulas, Newmark method, etc). Also the concept of isoparametric elements is briefly explained, Green identities are shown and Gauss quadrature formulas are derived. In the last appendix the classical minimization methods (method of the steepest gradient and conjugate gradient method) are presented. There are 87 examples and 148 exercises and 152 figures in the book. Solving the problems both SI and imperial units are used. The finite element analysis is clearly presented with rigorous mathematical treatment of its background and accompanied by numerous examples. Finite element methodology is covered briefly being saliently combined with a proper computer implementation. Programs and subroutines written in Fortran, Matlab, and Mathematica, treating the examples presented in the book, form a consistent part of the book. The book is carefully edited and printed. The only misprint I found is on p. 403 where there is a missing zero term in a matrix. From the reviewer’s point of view the book has high educational value stemming from the fact that a very large spectrum of engineering topics is covered. As such the book might well be a good purchase both for university libraries and individuals.