Search results for: non-stationary dynamics

Authors: Chad Brown

Abstract:

This paper establishes general conditions for the convergence rates of nonparametric sieve estimators with dependent data. We present two key results: one for nonstationary data and another for stationary mixing data. Previous theoretical results often lack practical applicability to deep neural networks (DNNs). Using these conditions, we derive convergence rates for DNN sieve estimators in nonparametric regression settings with both nonstationary and stationary mixing data. The DNN architectures considered adhere to current industry standards, featuring fully connected feedforward networks with rectified linear unit activation functions, unbounded weights, and a width and depth that grows with sample size.

Keywords: sieve extremum estimates, nonparametric estimation, deep learning, neural networks, rectified linear unit, nonstationary processes

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Authors: Yiyuan Tao

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Under the impact of global warming together with the intensification of human activities, the hydrological regimes may be altered, and the traditional stationary assumption was no longer satisfied. However, most of the current design standards of water infrastructures were still based on the hypothesis of stationarity, which may inevitably result in severe biases. Many critical impacts of climate on ecosystems, society, and the economy are controlled by extreme events rather than mean values. Therefore, it is of great significance to identify the non-stationarity of precipitation extremes and model the precipitation extremes in a nonstationary framework. The Wei River Basin (WRB), located in a continental monsoon climate zone in China, is selected as a case study in this study. Six extreme precipitation indices were employed to investigate the changing patterns and stationarity of precipitation extremes in the WRB. To identify if precipitation extremes are stationary, the Mann-Kendall trend test and the Pettitt test, which is used to examine the occurrence of abrupt changes are adopted in this study. Extreme precipitation indices series are fitted with non-stationary distributions that selected from six widely used distribution functions: Gumbel, lognormal, Weibull, gamma, generalized gamma and exponential distributions by means of the time-varying moments model generalized additive models for location, scale and shape (GAMLSS), where the distribution parameters are defined as a function of time. The results indicate that: (1) the trends were not significant for the whole WRB, but significant positive/negative trends were still observed in some stations, abrupt changes for consecutive wet days (CWD) mainly occurred in 1985, and the assumption of stationarity is invalid for some stations; (2) for these nonstationary extreme precipitation indices series with significant positive/negative trends, the GAMLSS models are able to capture well the temporal variations of the indices, and perform better than the stationary model. Finally, the differences between the quantiles of nonstationary and stationary models are analyzed, which highlight the importance of nonstationary modeling of precipitation extremes in the WRB.

Keywords: extreme precipitation, GAMLSSS, non-stationary, Wei River Basin

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Authors: C. Slim

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Traditional techniques for analyzing time series are based on the notion of stationarity of phenomena under study, but in reality most economic and financial series do not verify this hypothesis, which implies the implementation of specific tools for the detection of such behavior. In this paper, we study nonstationary non-seasonal time series tests in a non-exhaustive manner. We formalize the problem of nonstationary processes with numerical simulations and take stock of their statistical characteristics. The theoretical aspects of some of the most common unit root tests will be discussed. We detail the specification of the tests, showing the advantages and disadvantages of each. The empirical study focuses on the application of these tests to the exchange rate (USD/TND) and the Consumer Price Index (CPI) in Tunisia, in order to compare the Power of these tests with the characteristics of the series.

Keywords: stationarity, unit root tests, economic time series, ADF tests

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Authors: Filimonova Alexanra

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Inviscid incompressible fluid flows are considered. The object of the study is a vortex parquet – a structure consisting of distributed vortex spots of different directions, occupying the entire plane. The main attention is paid to the study of advection processes of passive particles in the corresponding velocity field. The dynamics of the vortex structures is considered in a rectangular region under the assumption that periodic boundary conditions are imposed on the stream function. Numerical algorithms are based on the solution of the initial-boundary value problem for nonstationary Euler equations in terms of vorticity and stream function. For this, the spectral-vortex meshless method is used. It is based on the approximation of the stream function by the Fourier series cut and the approximation of the vorticity field by the least-squares method from its values in marker particles. A vortex configuration, consisting of four vortex patches is investigated. Results of a numerical study of the dynamics and interaction of the structure are presented. The influence of the patch radius and the relative position of positively and negatively directed patches on the processes of interaction and mixing is studied. The obtained results correspond to the following possible scenarios: the initial configuration does not change over time; the initial configuration forms a new structure, which is maintained for longer times; the initial configuration returns to its initial state after a certain period of time. The processes of mass transfer of vorticity by liquid particles on a plane were calculated and analyzed. The results of a numerical analysis of the particles dynamics and trajectories on the entire plane and the field of local Lyapunov exponents are presented.

Keywords: ideal fluid, meshless methods, vortex structures in liquids, vortex parquet.

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Authors: Olivier Delage, Hassan Bencherif, Alain Bourdier

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Signal decomposition approaches represent an important step in time series analysis, providing useful knowledge and insight into the data and underlying dynamics characteristics while also facilitating tasks such as noise removal and feature extraction. As most of observational time series are nonlinear and nonstationary, resulting of several physical processes interaction at different time scales, experimental time series have fluctuations at all time scales and requires the development of specific signal decomposition techniques. Most commonly used techniques are data driven, enabling to obtain well-behaved signal components without making any prior-assumptions on input data. Among the most popular time series decomposition techniques, most cited in the literature, are the empirical mode decomposition and its variants, the empirical wavelet transform and singular spectrum analysis. With increasing popularity and utility of these methods in wide ranging applications, it is imperative to gain a good understanding and insight into the operation of these algorithms. In this work, we describe all of the techniques mentioned above as well as their ability to denoise signals, to capture trends, to identify components corresponding to the physical processes involved in the evolution of the observed system and deduce the dimensionality of the underlying dynamics. Results obtained with all of these methods on experimental total ozone columns and rainfall time series will be discussed and compared

Keywords: denoising, empirical mode decomposition, singular spectrum analysis, time series, underlying dynamics, wavelet analysis

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Authors: Andrew Clark

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McCauley, Bassler, and Gunaratne show that integration I(d) processes as used in economics and finance do not necessarily produce stationary increments, which are required to determine causality in both the short term and the long term. This paper follows their lead and shows I(d) aluminum cash and futures log prices at daily and weekly intervals do not have stationary increments, which means prior causality studies using I(d) processes need to be re-examined. Wavelets based on undifferenced cash and futures log prices do have stationary increments and are used along with transfer entropy (versus cointegration) to measure causality. Wavelets exhibit causality at most daily time scales out to 1 year, and weekly time scales out to 1 year and more. To determine stationarity, localized stationary wavelets are used. LSWs have the benefit, versus other means of testing for stationarity, of using multiple hypothesis tests to determine stationarity. As informational flows exist between cash and futures at daily and weekly intervals, the aluminum market is efficient. Therefore, hedges used by producers and consumers of aluminum need not have a big concern in terms of the underestimation of hedge ratios. Questions about arbitrage given efficiency are addressed in the paper.

Keywords: transfer entropy, nonstationary increments, wavelets, localized stationary wavelets, localized stationary wavelets

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Authors: Joseph Thomas Eghwerido, Julian I. Mbegbu

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In modelling environment processes, we apply multidisciplinary knowledge to explain, explore and predict the Earth's response to natural human-induced environmental changes. Thus, the analysis of spatial-time ecological and environmental studies, the spatial parameters of interest are always heterogeneous. This often negates the assumption of stationarity. Hence, the dispersion of the transportation of atmospheric pollutants, landscape or topographic effect, weather patterns depends on a good estimate of spatial covariance. The generalized linear mixed model, although linear in the expected value parameters, its likelihood varies nonlinearly as a function of the covariance parameters. As a consequence, computing estimates for a linear mixed model requires the iterative solution of a system of simultaneous nonlinear equations. In other to predict the variables at unsampled locations, we need to know the estimate of the present sampled variables. The geostatistical methods for solving this spatial problem assume covariance stationarity (locally defined covariance) and uniform in space; which is not apparently valid because spatial processes often exhibit nonstationary covariance. Hence, they have globally defined covariance. We shall consider different existing methods of solutions of spatial covariance of a space-time processes at unsampled locations. This stationary covariance changes with locations for multiple time set with some asymptotic properties.

Keywords: parametric, nonstationary, Kernel, Kriging

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Authors: Lifar M. S., Tereshchenko A. A., Bulgakov A. N., Guda S. A., Guda A. A., Soldatov A. V.

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Metal nanoparticles are widely used as heterogeneous catalysts to activate adsorbed molecules and reduce the energy barrier of the reaction. Reaction product yield depends on the interplay between elementary processes - adsorption, activation, reaction, and desorption. These processes, in turn, depend on the inlet feed concentrations, temperature, and pressure. At stationary conditions, the active surface sites may be poisoned by reaction byproducts or blocked by thermodynamically adsorbed gaseous reagents. Thus, the yield of reaction products can significantly drop. On the contrary, the dynamic control accounts for the changes in the surface properties and adjusts reaction parameters accordingly. Therefore dynamic control may be more efficient than stationary control. In this work, a reinforcement learning algorithm has been applied to control the simulation of CO oxidation on a catalyst. The policy gradient algorithm is learned to maximize the CO₂ production rate based on the CO and O₂ flows at a given time step. Nonstationary solutions were found for the regime with surface deactivation. The maximal product yield was achieved for periodic variations of the gas flows, ensuring a balance between available adsorption sites and the concentration of activated intermediates. This methodology opens a perspective for the optimization of catalytic reactions under nonstationary conditions.

Keywords: artificial intelligence, catalyst, co oxidation, reinforcement learning, dynamic control

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Authors: Jorge Lopez

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In this work, we introduce fractional calculus in order to study the dynamics of a damped multistory building with some symmetry. Initially we make a review of the dynamics of a free and damped multistory building. Then we introduce those concepts of fractional calculus that will be involved in our study. It has been noticed that fractional calculus provides models with less parameters than those based on classical calculus. In particular, a damped classical oscilator is more naturally described by using fractional derivatives. Accordingly, we model our multistory building as a set of coupled fractional oscillators and compare its dynamics with the results coming from traditional methods.

Keywords: coupled oscillators, fractional calculus, fractional oscillator, structural dynamics

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Authors: Ali Oveysi Sarabi

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In this paper, controller design for the attitude and altitude dynamics of an outdoor quadrotor, which is constructed with low cost actuators and drivers, is aimed. Before designing the controller, the quadrotor is modeled mathematically in Matlab-Simulink environment. To control attitude dynamics, linear quadratic regulator (LQR) based controllers are designed, simulated and applied to the system. Two different proportional-integral-derivative action (PID) controllers are designed to control yaw and altitude dynamics. During the implementation of the designed controllers, different test setups are used. Designed controllers are implemented and tuned on the real system using xPC Target. Tests show that these basic control structures are successful to control the attitude and altitude dynamics.

Keywords: helicopter balance, flight dynamics, autonomous landing, control robotics

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Authors: Liliia N. Butymova, Vladimir Ya Modorskii

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To ensure the gas transmittal GCU's efficient operation, leakages through the labyrinth packings (LP) should be minimized. Leakages can be minimized by decreasing the LP gap, which in turn depends on thermal processes and possible rotor vibrations and is designed to ensure absence of mechanical contact. Vibration mitigation allows to minimize the LP gap. It is advantageous to research influence of processes in the dynamic gas-structure system on LP vibrations. This paper considers influence of rotor vibrations on LP gas dynamics and influence of the latter on the rotor structure within the FSI unidirectional dynamical coupled problem. Dependences of nonstationary parameters of gas-dynamic process in LP on rotor vibrations under various gas speeds and pressures, shaft rotation speeds and vibration amplitudes, and working medium features were studied. The programmed multi-processor ANSYS CFX was chosen as a numerical computation tool. The problem was solved using PNRPU high-capacity computer complex. Deformed shaft vibrations are replaced with an unyielding profile that moves in the fixed annulus "up-and-down" according to set harmonic rule. This solves a nonstationary gas-dynamic problem and determines time dependence of total gas-dynamic force value influencing the shaft. Pressure increase from 0.1 to 10 MPa causes growth of gas-dynamic force oscillation amplitude and frequency. The phase shift angle between gas-dynamic force oscillations and those of shaft displacement decreases from 3π/4 to π/2. Damping constant has maximum value under 1 MPa pressure in the gap. Increase of shaft oscillation frequency from 50 to 150 Hz under P=10 MPa causes growth of gas-dynamic force oscillation amplitude. Damping constant has maximum value at 50 Hz equaling 1.012. Increase of shaft vibration amplitude from 20 to 80 µm under P=10 MPa causes the rise of gas-dynamic force amplitude up to 20 times. Damping constant increases from 0.092 to 0.251. Calculations for various working substances (methane, perfect gas, air at 25 ˚С) prove the minimum gas-dynamic force persistent oscillating amplitude under P=0.1 MPa being observed in methane, and maximum in the air. Frequency remains almost unchanged and the phase shift in the air changes from 3π/4 to π/2. Calculations for various working substances (methane, perfect gas, air at 25 ˚С) prove the maximum gas-dynamic force oscillating amplitude under P=10 MPa being observed in methane, and minimum in the air. Air demonstrates surging. Increase of leakage speed from 0 to 20 m/s through LP under P=0.1 MPa causes the gas-dynamic force oscillating amplitude to decrease by 3 orders and oscillation frequency and the phase shift to increase 2 times and stabilize. Increase of leakage speed from 0 to 20 m/s in LP under P=1 MPa causes gas-dynamic force oscillating amplitude to decrease by almost 4 orders. The phase shift angle increases from π/72 to π/2. Oscillations become persistent. Flow rate proved to influence greatly on pressure oscillations amplitude and a phase shift angle. Work medium influence depends on operation conditions. At pressure growth, vibrations are mostly affected in methane (of working substances list considered), and at pressure decrease, in the air at 25 ˚С.

Keywords: aeroelasticity, labyrinth packings, oscillation phase shift, vibration

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Authors: Sathish Kumar Jayaraj

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The study of urban traffic dynamics, underpinned by the principles of fluid dynamics, offers a distinct perspective to comprehend and enhance the efficiency of traffic flow within bustling cityscapes. Leveraging the concept of the Traffic Flow Factor (TFF) as an analog to the Reynolds number, this research delves into the intricate interplay between traffic density, velocity, and road category, drawing compelling parallels to fluid dynamics phenomena. By introducing the notion of Vehicle Shearing Resistance (VSR) as an analogy to dynamic viscosity, the study sheds light on the multifaceted influence of traffic regulations, lane management, and road infrastructure on the smoothness and resilience of traffic flow. The TFF equation serves as a comprehensive metric for quantifying traffic dynamics, enabling the identification of congestion hotspots, the optimization of traffic signal timings, and the formulation of data-driven traffic management strategies. The study underscores the critical significance of integrating fluid dynamics principles into the domain of urban traffic management, fostering sustainable transportation practices, and paving the way for a more seamless and resilient urban mobility ecosystem.

Keywords: traffic flow factor (TFF), urban traffic dynamics, fluid dynamics principles, vehicle shearing resistance (VSR), traffic congestion management, sustainable urban mobility

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Authors: Anca Radulescu, Danae Evans

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The relationship between a network’s hardwiring and its emergent dynamics are central to neuroscience. We study the principles of this correspondence in a canonical setup (in which network nodes exhibit well-studied complex quadratic dynamics), then test their universality in biological networks. By extending methods from discrete dynamics, we study the effects of network connectivity on temporal patterns, encapsulating long-term behavior into the rich topology of network Mandelbrot sets. Then elements of fractal geometry can be used to predict and classify network behavior.

Keywords: canonical model, complex dynamics, dynamic networks, fractals, Mandelbrot set, network connectivity

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Authors: Tukeaban Hasanova, Jamila Imamalieva

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By the operational method, the problem on two-dimensional wave propagation in elastic medium excited by the round cylinder is solved. An analytical solution responding to instantaneous application of speed to the inclusion at its subsequent change is constructed. The two-dimensional problem on wave propagation in an elastic medium is considered.

Keywords: cylinder, inclusion, wave, elastic medium, speed

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Authors: D. He, Y. Pang, G. Lodewijks

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Belt conveyors play an important role in continuous dry bulk material transport, especially at the mining industry. Speed control is expected to reduce the energy consumption of belt conveyors. Transient operation is the operation of increasing or decreasing conveyor speed for speed control. According to literature review, current research rarely takes the conveyor dynamics in transient operation into account. However, in belt conveyor speed control, the conveyor dynamic behaviors are significantly important since the poor dynamics might result in risks. In this paper, the potential risks in transient operation will be analyzed. An existing finite element model will be applied to build a conveyor model, and simulations will be carried out to analyze the conveyor dynamics. In order to realize the soft speed regulation, Harrison’s sinusoid acceleration profile will be applied, and Lodewijks estimator will be built to approximate the required acceleration time. A long inclined belt conveyor will be studied with two major simulations. The conveyor dynamics will be given.

Keywords: belt conveyor , speed control, transient operation, dynamics

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Authors: K. Pandey

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The present study is a functional analysis of the relationship between castes which indicates the dynamics of the caste structure in the rural setting. The researcher has tried to show both the cooperation and competition on important ceremonial and social occasions. The real India exists in the villages, so we need to know about their solidarity and also what the village life is and has been shaping into. We need to emphasize a microcosmic study of Indian rural life. Furthermore, caste integration is an acute problem country faces today. To resolve this we are required to know the dynamics of behavior of the people of different castes and for the study of the caste dynamics a study of caste relations are needed. The present study is an attempt in this direction.

Keywords: hierarchial groups, jajmani system, functional dependence, commensalities

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Authors: K. Manmi, Q. X. Wang

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This paper investigates microbubble dynamics subject to ultrasound in a weakly viscous fluid near a rigid boundary. The phenomenon is simulated using a boundary integral method. The weak viscous effects are incorporated into the model through the normal stress balance across the bubble surface. The model agrees well with the Rayleigh-Plesset equation for a spherical bubble for several cycles. The effects of the fluid viscosity in the bubble dynamics are analyzed, including jet development, centroid movement and bubble volume.

Keywords: microbubble dynamics, bubble jetting, viscous effect, boundary integral method

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Authors: Ramdas Sonawane, Mahaveer Gadiya

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The control problem associated with nuclear dynamics is represented by nonlinear integro-differential equation with additive controls. To control chain reaction, certain amount of neutrons is added into (or withdrawn out of) chamber as and when required. It is not realistic. So, we can think of controlling the reactor dynamics by bilinear control, which enters the system as coefficient of state. In this paper, we study the approximate and exact controllability of parabolic integro-differential equation controlled by bilinear control with non-homogeneous boundary conditions in bounded domain. We prove the existence of control and propose an explicit control strategy.

Keywords: approximate control, exact control, bilinear control, nuclear dynamics, integro-differential equations

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Authors: Mohammad A. Bani-Khaled

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In this work we use the Discrete Proper Orthogonal Decomposition transform to characterize the properties of coupled dynamics in thin-walled beams by exploiting numerical simulations obtained from finite element simulations. The outcomes of the will improve our understanding of the linear and nonlinear coupled behavior of thin-walled beams structures. Thin-walled beams have widespread usage in modern engineering application in both large scale structures (aeronautical structures), as well as in nano-structures (nano-tubes). Therefore, detailed knowledge in regard to the properties of coupled vibrations and buckling in these structures are of great interest in the research community. Due to the geometric complexity in the overall structure and in particular in the cross-sections it is necessary to involve computational mechanics to numerically simulate the dynamics. In using numerical computational techniques, it is not necessary to over simplify a model in order to solve the equations of motions. Computational dynamics methods produce databases of controlled resolution in time and space. These numerical databases contain information on the properties of the coupled dynamics. In order to extract the system dynamic properties and strength of coupling among the various fields of the motion, processing techniques are required. Time- Proper Orthogonal Decomposition transform is a powerful tool for processing databases for the dynamics. It will be used to study the coupled dynamics of thin-walled basic structures. These structures are ideal to form a basis for a systematic study of coupled dynamics in structures of complex geometry.

Keywords: coupled dynamics, geometric complexity, proper orthogonal decomposition (POD), thin walled beams

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Authors: Pardeep Bishnoi, Mayank Srivastava, Mrityunjay Kumar Sinha

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This article represents the numerical investigation of the pressure and velocity field variation of the dynamics of pendant drop formation through a capillary tube. Numerical simulations are executed using volume of fluid (VOF) method in the computational fluid dynamics (CFD). In this problem, Non Newtonian fluid is considered as dispersed fluid whereas air is considered as a continuous fluid. Pressure contours at various time steps expose that pressure varies nearly hydrostatically at each step of the dynamics of drop formation. A result also shows the pressure variation of the liquid droplet during free fall in the computational domain. The evacuation of the fluid from the necking region is also shown by the contour of the velocity field. The role of surface tension in the Pressure contour of the dynamics of drop formation is also studied.

Keywords: pressure contour, surface tension, volume of fluid, velocity field

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Authors: Meziane Belkacem

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We aim at converting the original 3D Lorenz-Haken equations, which describe laser dynamics –in terms of self-pulsing and chaos- into 2-second-order differential equations, out of which we extract the so far missing mathematics and corroborations with respect to nonlinear interactions. Leaning on basic trigonometry, we pull out important outcomes; a fundamental result attributes chaos to forbidden periodic solutions inside some precisely delimited region of the control parameter space that governs the bewildering dynamics.

Keywords: Physics, optics, nonlinear dynamics, chaos

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Authors: Iwan Setiawan, Bobby Eka Gunara, Katshuhiro Nakamura

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The theory to accelerate system on quantum dynamics has been constructed to get the desired wave function on shorter time. This theory is developed on adiabatic quantum dynamics which any regulation is done on wave function that satisfies Schrödinger equation. We show accelerated manipulation of WFs with the use of a parameter-dependent in asymmetric double-well potential and also when it’s influenced by electromagnetic fields.

Keywords: driving potential, Adiabatic Quantum Dynamics, regulation, electromagnetic field

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Authors: Christian Angerer, Markus Lienkamp

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Electric vehicles offer a high variety of possible drivetrain topologies with up to 4 motors. Multi-motor-designs can have several advantages regarding traction, vehicle dynamics, safety and even efficiency. With a rising number of motors, the whole drivetrain becomes more complex. All permutations of gearings, drivetrain-layouts, motor-types and –sizes lead up in a very large solution space. Single elements of this solution space can be analyzed by simulation methods. In addition to longitudinal vehicle behavior, which most optimization-approaches are restricted to, also lateral dynamics are important for vehicle dynamics, stability and efficiency. In order to compete large solution spaces and to find an optimal result, genetic algorithm based optimization is state-of-the-art. As lateral dynamics simulation is way more CPU-intensive, optimization takes much more time than in case of longitudinal-only simulation. Therefore, this paper shows an approach how to create meta-models from a 14-degree of freedom vehicle model in order to enable a numerically efficient drivetrain-layout optimization process under consideration of lateral dynamics. Different meta-modelling approaches such as neural networks or DoE are implemented and comparatively discussed.

Keywords: driving dynamics, drivetrain layout, genetic optimization, meta-modeling, lateral dynamicx

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Authors: Boguslaw Schreyer

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In this paper, a general dynamical model is derived using the Lagrange formalism. The two masses: sprang and unsprang are included in a six-degree of freedom model for a sprung mass. The unsprung mass is included and shown only in a simplified model, although its equations have also been derived by an author. The simplified equations, more suitable for the computer model of robot’s dynamics are also shown.

Keywords: dynamics, mobile, robot, wheeled mobile robots

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Authors: Christopher I. Ifeacho, Adeleke Omolade

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The paper examines the relationship between energy price dynamics and green growth in Sub Sahara African Countries. The quest for adopting green energy in order to improve green growth that can engender sustainability and stability has received more attention from researchers in recent times. This study uses a panel autoregressive distributed lag approach to investigate this relationship. Findings from the result showed that energy price dynamics and exchange rates have more short-run significant impacts on green growth in individual countries rather than the pooled result. Furthermore, the long-run result confirmed that inflation and capital have a significant long-run relationship with green growth. The causality test result revealed the existence of a bi-directional relationship between green growth and energy price dynamics. The study recommends caution in a currency devaluation and improvement in renewable energy production in the Sub Sahara Africa in order to achieve sustainable green growth.

Keywords: green growth, energy price dynamics, Sub Saharan Africa, relationship

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Authors: Takashi Shimizu, Tomoaki Hashimoto

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Recently, crystal growth technologies have made progress by the requirement for the high quality of crystal materials. To control the crystal growth dynamics actively by external forces is useuful for reducing composition non-uniformity. In this study, a control method based on model predictive control using thermal inputs is proposed for crystal growth dynamics of semiconductor materials. The control system of crystal growth dynamics considered here is governed by the continuity, momentum, energy, and mass transport equations. To establish the control method for such thermal fluid systems, we adopt model predictive control known as a kind of optimal feedback control in which the control performance over a finite future is optimized with a performance index that has a moving initial time and terminal time. The objective of this study is to establish a model predictive control method for crystal growth dynamics of semiconductor materials.

Keywords: model predictive control, optimal control, process control, crystal growth

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Authors: Luong A. Nguyen, Elihu Deneke, Thomas L. Harman

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This paper describes a multibody dynamics algorithm formulated for parallel implementation on multiprocessor computing platforms using the divide-and-conquer approach. The system of interest is a general topology of rigid and elastic articulated bodies with or without loops. The algorithm is an extension of Featherstone’s divide and conquer approach to include the flexible-body dynamics formulation. The equations of motion, configured for the International Space Station (ISS) with its robotic manipulator arm as a system of articulated flexible bodies, are implemented in separate computer processors. The performance of this divide-and-conquer algorithm implementation in multiple processors is compared with an existing method implemented on a single processor.

Keywords: multibody dynamics, multiple processors, multithreading, divide-and-conquer algorithm, computational efficiency, flexible body dynamics

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Authors: Khaled I. Nawafleh

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In this work, we apply the method of Hamilton-Jacobi to obtain solutions of Hamiltonian systems in classical mechanics with two certain structures: the first structure plays a central role in the theory of time-dependent Hamiltonians, whilst the second is used to treat classical Hamiltonians, including dissipation terms. It is proved that the generalization of problems from the calculus of variation methods in the nonstationary case can be obtained naturally in Hamilton-Jacobi formalism. Then, another expression of geometry of the Hamilton Jacobi equation is retrieved for Hamiltonians with time-dependent and frictional terms. Both approaches shall be applied to many physical examples.

Keywords: Hamilton-Jacobi, time dependent lagrangians, dissipative systems, variational principle

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Authors: Wataru Nakamura, Tomoaki Hashimoto, Liang-Kuang Chen

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This paper provides a state estimation method for automatic control systems of nonlinear vehicle dynamics. A nonlinear tire model is employed to represent the realistic behavior of a vehicle. In general, all the state variables of control systems are not precisedly known, because those variables are observed through output sensors and limited parts of them might be only measurable. Hence, automatic control systems must incorporate some type of state estimation. It is needed to establish a state estimation method for nonlinear vehicle dynamics with restricted measurable state variables. For this purpose, unscented Kalman filter method is applied in this study for estimating the state variables of nonlinear vehicle dynamics. The objective of this paper is to propose a state estimation method using unscented Kalman filter for nonlinear vehicle dynamics. The effectiveness of the proposed method is verified by numerical simulations.

Keywords: state estimation, control systems, observer systems, nonlinear systems

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Authors: Tai-Young Park, Yangjin Park

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Introduction: This study analyzed a family therapy case involving a female client in her thirties with panic disorder (PD) in South Korea. We identified five stages of the psychological process in the development of PD and examined external situations, family dynamics, and psychological experiences at each stage. Method: The client, mother, sister, and husband participated in therapy. Researchers analyzed the transcripts, notes, and video recordings of the therapy sessions. A thematic analysis was used to examine the data and display our findings using a network. Results: The developmental process of PD was as follows: (1) formation of anxiety, (2) sheltered life, (3) crisis, (4) loss of safe haven, and (5) inner breakdown. Conclusion: The family dynamics that developed as a result of coping with external situations in each stage contributed to clients’ psychological experiences. These psychological experiences triggered anxiety, which led to the development of PD. Moreover, this study empirically suggests that family dynamics can be associated with a person’s internal experiences that could lead to PD. Our findings highlight the significance of functional family dynamics and coping patterns when facing difficult external situations or crises.

Keywords: developmental process, family therapy, panic disorder, psychological dynamics

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