Nonlinear Aspects Research Articles

Aeroelastic Optimization with an Economical Transonic Flutter Constraint Using Navier–Stokes Aerodynamics

Structural optimization with a flutter constraint for a vehicle designed to fly in the transonic regime is a particularly difficult task. In this speed range, the flutter boundary is very sensitive to aerodynamic nonlinearities, typically requiring high-fidelity Navier–Stokes simulations. However, the repeated application of unsteady computational fluid dynamics to guide an aeroelastic optimization process is very computationally expensive. This expense has motivated the development of methods that incorporate aspects of the aerodynamic nonlinearity, classical tools of flutter analysis, and more recent methods of optimization. Although it is possible to use doublet-lattice method aerodynamics, this paper focuses on the use of an unsteady high-fidelity aerodynamic reduced-order model combined with successive transformations that allows for an economical way of using high-fidelity aerodynamics in the optimization process. This approach is applied to the common research model wing structural design. The high-fidelity aerodynamics produces a heavier wing than that optimized with doublet-lattice aerodynamics. It is found that the optimized lower wing skin thickness distribution using high-fidelity aerodynamics differs significantly from that using doublet-lattice aerodynamics.

Exponential density transition based self-focusing of Gaussian laser beam in collisional plasma

In this work, nonlinear aspects of a high intensity Gaussian laser beam propagating in plasma having upward density ramp of tangent and exponential profiles are studied. We have employed the nonlinearity in dielectric function of plasma due to nonuniform heating of carriers along the wavefront of the laser beam which is important in collisional plasmas. The differential equation governing the dimensionless beam width parameter is achieved by using Wentzel–Kramers–Brillouin (WKB) and paraxial approximations and solved it numerically by using Runge-Kutta fourth order method. Effect of exponential density ramp profile on self-focusing is systematically carried out and compared with tangent density ramp profile. It is found that exponential plasma density ramp causes the laser beam to become more focused than tangent density ramp over several Rayleigh length and gives reasonably interesting results.

Modelling and design of a two axis small scale solar tracking system for an ecological small scale house model

Nowadays power generation is one of the greatest challenges of humanity in the framework of Sustainable Development. For example, as it is globally accepted sun tracking systems allows improvement of solar panel power ratio. In order to illustrate this concept, this paper presents the design and a behaviour modelling of a two axis small scale system for future didactical applications. The principle of tracking is described. Mathematical description is done and a mixed SPICE modelling of the system, including geometrical, optical, electronic linear and non-linear aspects is built. Simulations results are analysed. Practical mechanical and electronic designs are detailed, before conclusion. This small scale solar tracking system is now installed in a eco-friendly small scale house model.

Vibration Study in Human-Car Seat System: Overview and a Novel Simulation Technique

This paper will propose a complete solution with a novel simulation set up to get the final vibration data of seated human body inside an automobile structure without carrying out measurement tests. Furthermore, it will improve the existing technology in assessing the dynamic interaction between the human body and a car seat subjected to different conditions and establish a clear idea about the vibration effects, vibration transmissibility, damping, variable stiffness, natural frequencies, modal analysis, random vibration, harmonic aspects, mode superposition, response spectrum, transient effects etc. The research will provide a novel solution of the entire system rather than focussing only on a very specific portion of the system, thus, trying to close the gap in present technological areas and omitting the time consuming and expensive testing methods in the modern industries. This research will contribute a cutting edge landmark by providing a simulation model to predict final vibration level inside the human body and car seat to avoid the time consuming and expensive testing methods. It will help better understanding the impact and estimation of the vibration level inside the car seat and occupant human body. The non-linear dynamic aspects and efforts will be made to understand, characterize and optimize the level of vibration by establishing a computational simulations model of the car seat and the occupant to match the experimental results. Some technologies have been achieved to judge the dynamic interaction between the human body and a car seat, though such technologies cover only either vibration effects or dynamics or measurement techniques or small portion of the car and human body without considering all the real life factors like pre-stressed bodies, variable stiffness, equivalent stiffness and damping factors based on the behaviour of the human muscles, bones and postures. So, efforts will be made to establish numerical and simulation models for the non-linear bio-dynamics of the seated human body, polyurethane foam cushions, dynamic contacts between the human body and the seat, occupant under the real life car motion, vibration testing of the car seat and finally, to provide a comprehensive solution to judge the vibration levels, which eventually will lead the various industries to avoid the time consuming and expensive testing methods.

ANALYTIC OVERLOOK OF THE METHODOLOGY OF SYNERGETICS IN POSTNONCLASSICAL SCIENCE

Purpose. This article reveals the main definitions of synergetics and methods that are being used in synergetic research. The differences-characteristics of classical, nonclassical, and postnonclassical science and their schematic illustration are described. There are criteria, by which the main methodological principles of synergetics are being chosen. The reasons that have caused an appearance of synergetics and its methodological apparatus and the framework of this apparatus are considered. The special aspects of nonlinearity of complicated systems, in our opinion, include the economic ones. Methodology. Such foreign and domestic scientists as Wiener N. (2003), Thom R. (1975, 1996), Prigogine I., Stengers I. (1986), Zang V.B. (1999), and Arnold V. (2004) have used methodological apparatus of synergetics in modern science. Methodologically synergetics is open for those new conceptions that are being formed in certain disciplines. Methodological principles of synergetics that cause the “colostral” principles are nonlinearity, nonclosure, and instability. The main principle – the rule of nonlinearity is a contravention of the principle of the super offer in the certain phenomenon (process): the result of adding the impacts on the system is not the adding these impacts’ results. The causes’ results cannot be added. This means that the result of adding the causes does not equal to the union of causes’ results. Results. For the synergy concept, the idea is typical that we see everything at once: the whole and its parts. It combines holism and elementarizm that are continuing each other. Synergetics, in fact, integrates deterministic and probabilistic styles of scientific thinking. Synergetics is the general theory of self-organization. It formulates the general principles of self-organization, valid for all levels of matter. A specific feature of the synergetic approach is to move from the study of simple to complex, from closed to open, from linear to nonlinear, from consideration of equilibrium and near-equilibrium processes to delocalization and instability, to the study of what happens far from equilibrium. Practical implications. The synergetic approach has a great advantage over others. Unlike cybernetics and systems engineering, research which focused on maintaining and preserving the existing state of dynamic equilibrium or order system, synergy, as logical extensions, studying systems in their dynamics and development. Accordingly, if the cybernetics principle operates mainly negative feedback aimed at the preservation of order in the system, synergistic implemented the principle of positive feedback, whereby the changes that occur in the system, not extinguished, and accumulate and amplified. Value/originality. As a result of the interaction of elements of the environment come to coordinated, cooperative behaviour, resulting in spontaneous, a new order, structure or dynamic mode.

Precompensation and System Parameters Estimation for Low-Cost Nonlinear Tera-Hertz Transmitters in the Presence of I/Q Imbalance

Tera-Hertz (THz) transmission can offer several attractive applications, yet developing low-cost energy-efficient THz devices is at an early stage. The most promising low-cost THz transmitter architecture in the literature is the so-called frequency-multiplier-last architecture. However, it is incapable of transmitting quadrature amplitude modulation (QAM) due to the architecture's inherent nonlinear distortions. We study such nonlinear THz communication systems by incorporating the nonlinearity aspects of the low-cost THz devices and the inphase and quadrature (I/Q) imbalance effect into the signal model. Then, we propose a precompensation scheme to compensate the nonlinearity and I/Q imbalance effects, thus enabling the QAM-capable frequency-multiplier-last architecture for THz systems. The proposed precompensation scheme requires the knowledge of the system parameters. To estimate the system parameters, we propose a maximum-likelihood estimator and its practical implementation via an alternating estimation algorithm. We also derive closed-form expressions for the Cramér-Rao lower bounds (CRLBs) of the system parameters estimation, and design the pilot sequence used in estimating the system parameters. Numerical results show that the proposed precompensation schemes overcome the prominent problems experienced in the existing THz systems, namely severe nonlinear distortions of the modulation symbols as well as spectral spreading and/or large spectrum sidelobes, and mitigate the I/Q imbalance effect.

Non-Linear First-Harmonic Balance to Compute the Electrochemical Impedance of Butler-Volmer Equation

The Butler-Volmer equation is commonly used to describe heterogeneous reaction mechanisms (e.g., charge transfer) involved on electrochemical systems. Under the application of an oscillatory exciting potential, the frequency response (i.e., electrochemical impedance spectroscopy) of the net current on the electrode is extensively quantified to characterize the mechanisms involved in the reaction process. This work uses a first-harmonic balance method to compute the electrochemical impedance response of the Butler-Volmer equation under kinetic control and subjected to a simple mass transfer coefficient model. The proposed approach recovers some nonlinear aspects, such as the effects of sinusoidal potential amplitude in the electrochemical impedance. The results showed that the frequency response can be equivalently described by a series RC circuit, where the resistance is attributed to the charge transfer and the capacitance to the accumulation dynamics on the electrode surface. The effects of fractional-order kinetics and mass transport restrictions were also considered, leading to a behavior similar to a Randles equivalent circuit. A simple example with parameters of the electrochemical ferricyanide/ferrocyanide system was used to illustrate the findings.

Compressible Kolmogorov flow in strongly coupled dusty plasma using molecular dynamics and computational fluid dynamics. II. A comparative study

In this paper, we perform comparative studies of compressible Kolmogorov flow in the two-dimensional strongly coupled dusty plasma by means of atomistic or molecular dynamics (MD) and continuum or computational fluid dynamics (CFD) methods. Recently, using MD simulation, generation of molecular shear heat at the atomistic level is shown to reduce the average coupling strength of the system and destruct the vortical structures. To suppress the molecular heat, a novel method of a thermostat, namely, the configurational thermostat is introduced by which the microscale heat generated by the shear flow has shown to be thermostatted out efficiently without compromising the large scale vortex dynamics. While using a configurational thermostat, it has been found that the growth rate obtained from both the studies is the same with the marginal difference. To make the comparison with the continuum fluid model, we perform the same study using the generalised hydrodynamic model, wherein molecular shear heating phenomena is completely absent, however, viscous dissipation is there at the macroscale level. For this purpose, an Advanced Generalised SPECTral Code has been developed to study the linear and nonlinear aspects of the Kolmogorov flow in the incompressible and compressible limit for viscoelastic fluids. All the phenomenological parameters used in CFD simulations have been calculated from MD simulations. Code is benchmarked against the eigen value solver in the linear regime. Linear growth-rates calculated from the phenomenological fluid model is found to be close to that obtained from MD simulation for the same set of input parameters. The transition from laminar to turbulent flow has been found at a critical value of Reynolds number Rc in both the macroscopic (CFD) and microscopic (MD) simulation. Rc in MD is smaller than the one obtained by CFD simulation. In the nonlinear regime of CFD, the mode becomes unstable and vortex formation happens earlier than in MD. The peak vorticity value is better preserved in MD whereas in the CFD model, we find that the peak vorticity is dissipated relatively earlier.

Sustainability factors in dynamical systems modeling: Simulating the non-linear aspects of multiple equilibria

What is sustainability? Sustainability is a concept that can be defined in many ways depending upon a society's perception of current material needs and the actual material needs of future generations. Much of our ability to achieve sustainability entails developing indicators and measurements that will guide us to this goal. This paper suggests that we can strengthen the prediction of sustainability indicators by adopting a “multiple equilibria” approach for a more effective decision-making process in various sectors of the economy, in ecosystem protection, or in political arenas. There is an emerging need for further development of predictive mathematical models of system sustainability over economic growth models for sustainable resource measurement and management. The objective of this paper is to use computer modeling and differential equations to simulate the “multiple equilibria” of a 3 variable real world system. In our study, we tested the theoretical validity of “multiple equilibria” sustainability modeling through simulated measurements of precipitation and nitrogen runoff into a hypothetical lake. As a quantitative tool to model, the “multiple equilibria” techniques can have tremendous predictive power for business leaders, political decision makers, and environmental scientists, and assist in better management of ecological, economic, and material resources in short-term and long-term end-use scenarios.

Understanding everyday life and mental health recovery through CHIME

PurposeThe purpose of this paper is to understand how daily life reflects the recovery journeys of individuals with serious mental illness (SMI) living independently in the community.Design/methodology/approachThe go-along technique, which blends participant observation and interviewing, was used to gather data from 19 individuals with SMI living in supported housing. Data were analyzed through the CHIME framework of personal recovery, which includes social connectedness, hope and optimism, identity, meaning in life, and empowerment.FindingsApplying the CHIME framework to qualitative data reveals the multiple ways in which everyday experiences, within and beyond formal mental healthcare environments, shapes personal recovery processes.Research limitations/implicationsCombining novel methods and conceptual frameworks to lived experiences sharpens extant knowledge of the active and non-linear aspects to personal recovery. The role of the researcher must be critically considered when using go-along methods.Practical implicationsPractitioners working with this population should account for the role of socially supportive and financially accessible spaces and activities that support the daily work of recovery beyond the context of formal care and services.Originality/valueThis study utilizes an innovative method to illustrate the crucial role of daily and seemingly banal experiences in fostering or hindering personal recovery processes. It is also the one of the first studies to comprehensively apply the CHIME framework to qualitative data in order to understand the recovery journeys of individuals with SMI living in supported housing.

Exploiting Coherence in Nonlinear Spin-Superfluid Transport

We show how the interference between superfluid spin currents can endow spin circuits with coherent logic functionality. While the hydrodynamic aspects of the linear-response collective spin transport obviate interference features, we focus on the nonlinear regime, where the critical supercurrent is sensitive to the phase accumulated by the condensate in a loop geometry. We propose to control this phase by electrical gating that tunes the spin-condensate coherence length. The nonlinear aspects of the spin superfluidity thus naturally lend themselves to the construction of logic gates, uniquely exploiting the coherence of collective spin currents. Vice versa, this functionality can be used to reveal the fundamental properties of spin superfluids.

Kernel dynamic latent variable model for process monitoring with application to hot strip mill process

Dynamic models are preferred rather than static models in the process monitoring of modern manufacturing. Compared with static models, dynamic models can reflect not only correlations but also causality among measurements and manipulated variables. Linear dynamic models are very common due to the simplicity of representation and parameter estimation. However, because of natural nonlinearity of a dynamic process, it is ineffective to apply linear models within a long term and varying condition. Nonlinear dynamic models are hence desired under such a circumstance. In this paper, a kernel dynamic latent variable (KDLV) model is proposed to describe the nonlinearity between original measurements and dynamic latent variables. This model is an extension of dynamic latent variable model in the aspect of nonlinearity, and keeps all merits of it. In order to build such a model, a KDLV search algorithm is proposed to acquire key model parameters from data, then a KDLV modeling procedure is derived to complete the whole model. After the KDLV model is trained from data, corresponding detection strategy is also developed to perform fault detection. The KDLV based fault detection is applied to the monitoring of hot strip mill process and comparison study is also conducted on both DLV and DKPCA models.

Nonlinear dynamics of deformation bands in aluminum–magnesium alloy in the creep test

Various types of plastic instabilities that emerge in intermittent creep have been studied experimentally for AlMg6 aluminum–magnesium alloy. It has been shown that intermittent creep exhibits threshold dynamics. The deformation step on the creep curve of amplitude is ~1–6% and begins when the rate of the preceding continuous creep attains a certain critical value. In the course of evolution of the step, the strain rate varies in the interval that spans more than two orders of magnitude, and transitions occur between different dynamic regimes of type A and B characterized by different stress drop regularity levels in the force response. Nonlinear aspects of the deformation behavior of the alloy in the intermittent creep conditions are considered.

A pseudo-transient heat transfer simulation of a continuous casting process, employing the element-free Galerkin method

The present work has been conducted in order to develop a novel solution for the heat transfer problem during the continuous casting of steel billets and blooms, by using the element-free Galerkin method under a pseudo-transient moving cross-section slice approach. The transport laws, non-linear aspects and boundary conditions of the initial value problem have been specified. A detailed explanation concerning the characteristics inherent to the application of the element-free Galerkin method to this problem has also been provided. The feasibility and suitability of this novel approach has been verified by comparison with the numerical techniques proposed and the results reported by other researchers as well as an analytical solution of a simple 1-D alloy solidification problem. The results have revealed that this technique could be used successfully in the pseudo transient moving cross-section solution of the heat transfer problem involved in the continuous casting of blooms and square billets.

Effect of strain rate on bending and transmission characteristics of injection molded polyamide 66 spur gears

Polymer material exhibits time-dependent mechanical behavior due to its viscoelastic characteristics. Thus, unlike steel gears, polymer gears exhibit complex behavior when transmitting loads at various rotational speeds. In general, gear tooth surfaces exhibit complex stress due to their nonconformal geometry. Hence, the nonlinear material and nonlinear geometric aspects of polymer gear mesh prompted an investigation of the bending and transmission characteristics of injection molded polyamide 66 gears at various strain rate conditions. The injection molded tensile specimens made from the gear material were subjected to various rates of loading. The stress–strain performance at various rates of loading was evaluated and used to model linear and nonlinear gear materials for the numerical analysis. The numerical investigation was carried out on the steel–polyamide gear pair with the commercial finite element analysis tool ABAQUS® to predict the bending stress and static transmission error. The predicted static transmission error of the gear pair was compared with the experimental results obtained using an in-house developed gear test rig. The bending stress with the linear material models was higher than that of the nonlinear material models. An increase in bending stress with the strain rate was observed in the case of the nonlinear material models. The static transmission error predicted with the nonlinear material model at a higher strain rate was lower for both the single tooth contact and the double teeth contacts.

Probing the quantum vacuum with petawatt lasers

Due to the bosonic nature of the photon, increasing the peak intensity through a combination of raising the pulse energy and decreasing the pulse duration will pile up more and more photons within the same finite region of space. In the absence of material, this continues until the vacuum is stressed to the point of breakdown and virtual particles become real. The critical intensity where this occurs for electrons and positrons – the so-called Schwinger limit – is predicted to be ∼ 1029 W/cm2. At substantially lower intensities, however, nonlinear aspects of the quantum vacuum associated with polarization of the vacuum can be explored. These studies become viable at the petawatt level where 1023 W/cm2 and above can be reached. This is an era into which we are just embarking that will provide critical tests of QED and theories beyond the Standard Model of particle physics.

Analysis of Certain Aspects of Nonlinearity in Mental Processes within the Frame Work of Vedic Science

Attempts are made to highlight and quantify the nonlinearity through mathematical models that arise in the study of certain phenomena in human behavior and experiences. For this purpose, we employ a philosophical atom-like (patomic) model for the dynamics of inner and outer essences of life which in fact constitute the human Being in accordance with the tenets of Vedic science. In particular, the evolution of thoughts and of the so called ‘mindset’ function with respect to the meditation parameter (µ) is studied. The stability analysis of the underlying nonlinear equations is expected to provide the island of peace and pleasure out of the day-to-day actions performed by a person.

Low-Power Photothermal Self-Oscillation of Bimetallic Nanowires.

We investigate the nonlinear mechanics of a bimetallic, optically absorbing SiN-Nb nanowire in the presence of incident laser light and a reflecting Si mirror. Situated in a standing wave of optical intensity and subject to photothermal forces, the nanowire undergoes self-induced oscillations at low incident light thresholds of <1 μW due to engineered strong temperature-position (T-z) coupling. Along with inducing self-oscillation, laser light causes large changes to the mechanical resonant frequency ω0 and equilibrium position z0 that cannot be neglected. We present experimental results and a theoretical model for the motion under laser illumination. In the model, we solve the governing nonlinear differential equations by perturbative means to show that self-oscillation amplitude is set by the competing effects of direct T-z coupling and 2ω0 parametric excitation due to T-ω0 coupling. We then study the linearized equations of motion to show that the optimal thermal time constant τ for photothermal feedback is τ → ∞ rather than the previously reported ω0 τ = 1. Lastly, we demonstrate photothermal quality factor (Q) enhancement of driven motion as a means to counteract air damping. Understanding photothermal effects on nano- and micromechanical devices, as well as nonlinear aspects of optics-based motion detection, can enable new device applications as oscillators or other electronic elements with smaller device footprints and less stringent ambient vacuum requirements.

Nonlinear wave interaction with curved front seawalls

The hydrodynamic performance of three prevalent curved front seawalls along with a vertical seawall has been investigated in the Ursell number ranging from 8 to 16. Experiments have been conducted to measure dynamic pressure on these seawalls under the action of regular monochromatic waves. Two different numerical models have been used to analyse the measured data: An in house Smoothed Particle Hydrodynamics (SPH) particle based model and the commercial Computational Fluid Dynamics (CFD) package ANSYS- FLUENT®. The numerical simulation of peak dynamic pressures on the seawall front surface differs with the laboratory measurements by less than 10% while, the maximum velocity magnitude reveals differences of the order of 20–30% between SPH and FLUENT during overtopping of the wave. The comparison between these models shows that the performance of improved SPH models is similar to that of FLUENT, as long as the flow is laminar. The SPH solution contains several important nonlinear aspects also revealed in the experiments. The comparison of measured and simulated pressures along the curved front proves the capability of the SPH models in predicting the nature of run-up and overtopping, if occurs.

Radiation memory, boosted Schwarzschild spacetimes and supertranslations

We investigate gravitational radiation memory and its corresponding effect on the asymptotic symmetries of a body whose exterior is a boosted Schwarzschild spacetime. First, in the context of linearized theory, we consider such a Schwarzschild body which is initially at rest, then goes through a radiative stage and finally emerges as a boosted Schwarzschild body. We show that the proper retarded solution of the exterior Schwarzschild spacetime for this process can be described in terms of the ingoing Kerr–Schild form of the Schwarzschild metric for both the initial and final states. An outgoing Kerr–Schild or time symmetric metric does not give the proper solution. The special property of Kerr–Schild metrics that their linearized and nonlinear forms are identical allows us to extend this result to processes in the nonlinear regime. We then discuss how the nonlinear memory effect, and its associated supertranslation, affect angular momentum conservation. Our approach provides a new framework for studying nonlinear aspects of the memory effect.