Analisa Kestabilan dan Solusi Pendekatan Pada Persamaan Van der Pol

Abstrak: Di dalam tulisan ini disajikan analisa kestabilan, diselidiki eksistensi dan kestabilan limit cycle, dan ditentukan solusi pendekatan dengan menggunakan metode multiple scale dari persamaan Van der Pol. Penelitian ini dilakukan dalam tiga tahapan metode. Pertama, menganalisa perilaku dinamik persamaan Van der Pol di sekitar ekuilibrium, meliputi transformasi persamaan ke sistem persamaan, analisa kestabilan persamaan melalui linearisasi, dan analisa kemungkinan terjadinya bifukasi pada persamaan. Kedua, membuktikan eksistensi dan kestabilan limit cycle dari persamaan Van der Pol dengan menggunakan teorema Lienard. Ketiga, menentukan solusi pendekatan dari persamaan Van der Pol dengan menggunakan metode multiple scale. Hasil penelitian adalah, berdasarkan variasi nilai parameter kekuatan redaman, daerah kestabilan dari persamaan Van der Pol terbagi menjadi tiga. Untuk parameter kekuatan redaman bernilai positif mengakibatkan ekuilibrium tidak stabil, dan sebaliknya, untuk parameter kekuatan redaman bernilai negatif mengakibatkan ekuilibrium stabil asimtotik, serta tanpa kekuatan redaman mengakibatkan ekuilibrium stabil. Pada kondisi tanpa kekuatan redaman, persamaan Van der Pol memiliki solusi periodik dan mengalami bifurkasi hopf. Selain itu, dengan menggunakan teorema Lienard dapat dibuktikan bahwa solusi periodik dari persamaan Van der Pol berupa limit cycle yang stabil. Pada akhirnya, dengan menggunakan metode multiple scale dan memberikan variasi nilai amplitudo awal dapat ditunjukkan bahwa solusi persamaan Van der Pol konvergen ke solusi periodik dengan periode dua. Abstract: In this paper, the stability analysis is given, the existence and stability of the limit cycle are investigated, and the approach solution is determined using the multiple scale method of the Van der Pol equation. This research was conducted in three stages of method. First, analyzing the dynamic behavior of the equation around the equilibrium, including the transformation of equations into a system of equations, analysis of the stability of equations through linearization, and analysis of the possibility of bifurcation of the equations. Second, the existence and stability of the limit cycle of the equation are proved using the Lienard theorem. Third, the approach solution of the Van der Pol equation is determined using the multiple scale method. Our results, based on variations in the values of the damping strength parameters, the stability region of the Van der Pol equation is divided into three types. For the positive value, it is resulting in unstable equilibrium, and contrary, for the negative value, it is resulting in asymptotic stable equilibrium, and without the damping force, it is resulting in stable equilibrium. In conditions without damping force, the Van der Pol equation has a periodic solution and has hopf bifurcation. In addition, by using the Lienard theorem, it is proven that the periodic solution is a stable limit cycle. Finally, by using the multiple scale method with varying the initial amplitude values, it is shown that the solution of the Van der Pol equation is converge to a periodic solution with a period of two

NASA SBIR abstracts of 1991 phase 1 projects

The objectives of 301 projects placed under contract by the Small Business Innovation Research (SBIR) program of the National Aeronautics and Space Administration (NASA) are described. These projects were selected competitively from among proposals submitted to NASA in response to the 1991 SBIR Program Solicitation. The basic document consists of edited, non-proprietary abstracts of the winning proposals submitted by small businesses. The abstracts are presented under the 15 technical topics within which Phase 1 proposals were solicited. Each project was assigned a sequential identifying number from 001 to 301, in order of its appearance in the body of the report. Appendixes to provide additional information about the SBIR program and permit cross-reference of the 1991 Phase 1 projects by company name, location by state, principal investigator, NASA Field Center responsible for management of each project, and NASA contract number are included

Systems Analysis in Forestry and Forest Industries

The purpose of this book is to present a variety of articles revealing the state of the art of applications of systems analysis techniques to problems of the forest sector. Such applications cover a vast range of issues in forestry and the forest industry. They include the dynamics of the forest ecosystem, optimal forest management, the roundwood market, forest industrial strategy, regional and national forest sector policy as well as international trade in forest products. Forest industrial applications at mill level, such as optimal paper trimming, cutting, and production scheduling, are however, excluded

Applying Bayesian Growth Modeling In Machine Learning For Longitudinal Data

There has been increasing interest in the use of Bayesian growth modeling in machine learning environment to answer the questions relating to the patterns of change in trends of social and human behavior in longitudinal data. It is well understood that machine learning works properly with “big data,” because large sample sizes offer machines the better opportunity to “learn” the pattern/structure of data from a training data set to predict the performance in an unseen testing data set. Unfortunately, not all researchers have access to large samples and there is a lack of methodological research addressing the utility of using machine learning with longitudinal data based on small sample size. Additionally, there is limited methodological research conducted around moderation effect that priors have on other data conditions. Therefore, the purpose of the current study was to understand: (a) the interactive relationship between priors and sample sizes in longitudinal predictive modeling, (b) the interactive relationship between priors and number of waves of data, and (c) the interactive relationship between priors and the proportion of cases in the two levels of a dichotomous time-invariant predictor for Bayesian growth modeling in a machine learning environment. Monte Carlo simulation was adopted to answer assess the above aspects and data were generated based on alumni donation data from a university in the mid-Atlantic region where model parameters were set to mimic “real life” data as closely as possible. Results from the study show that although all main and interaction effects are statistically significant, only main effect of sample size, wave of data, and interaction between waves of data and sample sizes show meaningful effect size. Additionally, given the condition of prior of the study, informative priors did not show any higher prediction accuracy compared to non-informative priors. The reason behind indifferent between choices of informative and non-informative prior associated with model complexity, competition between strong informative and weakly informative prior. This study was one of the first known study to examine Bayesian estimation in the context of machine learning. Results of the current study suggest that capitalizing on the advantages offered jointly by these two modeling approaches shows promise. Although much is still unknown and in need of investigation regarding the conditions under which a combination of Bayesian modeling and machine learning affects prediction accuracy, the current dissertation provides a first step in that direction

Design, Simulation, Manufacturing: The Innovation Exchange

The content of this book is based on the 3rd International Conference on Design, Simulation, Manufacturing: The Innovation Exchange (DSMIE-2020), held on June 9-12, 2020, in Kharkiv, Ukraine. This book reports on topics at the interface between manufacturing, materials, mechanical, and chemical engineering, with a special emphasis on design, simulation, and manufacturing issues. Specifically, it covers the development of computer-aided technologies for product design, the implementation of smart manufacturing systems and Industry 4.0 strategies, topics in technological assurance, numerical simulation, and experimental studies of cutting, milling, grinding, pressing, and profiling processes, as well as the development and implementation of advanced materials. It covers recent developments in the mechanics of solids and structures, numerical simulation of coupled problems, including wearing, compression, detonation, and collision, chemical process technology, including ultrasonic technology, capillary rising process, pneumatic classification, membrane electrolysis, and absorption process. Further, it reports on developments in the field of heat and mass transfer, energyefficient technologies, and industrial ecology. The book provides academics and professionals with extensive information on trends, technologies, challenges, and practice-oriented experience in the areas mentioned above

Computable General Equilibrium Modeling for Regional Analysis

Partial equilibrium analysis illustrates results for one market at a time. However, there often exist market interactions and thus market feedbacks. Pricing outcomes in one market usually have effects in other markets, and these effects, in turn, create ripples throughout the economy, perhaps even to the extent of affecting the price-quantity equilibrium in the original market. To represent this complex set of economic relationships, it is necessary to go beyond partial equilibrium analysis and construct a model that permits viewing many markets simultaneously. This Web Book provides an introduction to and overview of the general equilibrium modeling framework in the context of regional analysis.https://researchrepository.wvu.edu/rri-web-book/1023/thumbnail.jp

Inductive Pattern Formation

With the extended computational limits of algorithmic recursion, scientific investigation is transitioning away from computationally decidable problems and beginning to address computationally undecidable complexity. The analysis of deductive inference in structure-property models are yielding to the synthesis of inductive inference in process-structure simulations. Process-structure modeling has examined external order parameters of inductive pattern formation, but investigation of the internal order parameters of self-organization have been hampered by the lack of a mathematical formalism with the ability to quantitatively define a specific configuration of points. This investigation addressed this issue of quantitative synthesis. Local space was developed by the Poincare inflation of a set of points to construct neighborhood intersections, defining topological distance and introducing situated Boolean topology as a local replacement for point-set topology. Parallel development of the local semi-metric topological space, the local semi-metric probability space, and the local metric space of a set of points provides a triangulation of connectivity measures to define the quantitative architectural identity of a configuration and structure independent axes of a structural configuration space. The recursive sequence of intersections constructs a probabilistic discrete spacetime model of interacting fields to define the internal order parameters of self-organization, with order parameters external to the configuration modeled by adjusting the morphological parameters of individual neighborhoods and the interplay of excitatory and inhibitory point sets. The evolutionary trajectory of a configuration maps the development of specific hierarchical structure that is emergent from a specific set of initial conditions, with nested boundaries signaling the nonlinear properties of local causative configurations. This exploration of architectural configuration space concluded with initial process-structure-property models of deductive and inductive inference spaces. In the computationally undecidable problem of human niche construction, an adaptive-inductive pattern formation model with predictive control organized the bipartite recursion between an information structure and its physical expression as hierarchical ensembles of artificial neural network-like structures. The union of architectural identity and bipartite recursion generates a predictive structural model of an evolutionary design process, offering an alternative to the limitations of cognitive descriptive modeling. The low computational complexity of these models enable them to be embedded in physical constructions to create the artificial life forms of a real-time autonomously adaptive human habitat

The identification of potential diagnostic biomarkers amd disease mechanisms in lysosomal storage disorders

Fabry disease (FD) is an X-linked lysosomal storage disorder caused by a deficiency of the enzyme alpha-galactosidase A. The resultant progressive intracellular accumulation of the glycosphingolipids globotriaosylceramide (Gb3) and globotriaosylsphingosine (lyso-Gb3) are the source of a variety of clinical consequences. Biomarkers capable of detecting FD at an early stage of disease progression and that enable monitoring of response to treatment are required urgently. Using label-free quantitative proteomics two potential biomarkers, proactivator polypeptide and ganglioside GM2 activator protein, were identified in the urine of paediatric FD patients. An ultra-performance liquid chromatography-tandem mass spectrometry assay was then developed for validation purposes. Subsequently a second, larger multiplexed assay was developed to identify biomarkers capable of detecting and monitoring pre-symptomatic kidney disease in those patients most at risk. A complementary metabolomic approach was also used to identify and evaluate new Gb3-related biomarkers in the plasma of FD patients. This aspect of the study revealed five novel Gb3-related biomarkers as well as existing Gb3-related analogues and isoforms providing a metabolic profile in these patients. Potential disease mechanisms involved in FD were investigated by studying the interactions between proteins and those molecules involved in the glycosphingolipid pathway, with particular interest to Gb3. A number of mitochondrial proteins were found to interact with Gb3 resulting in the investigation of the effect of glycosphingolipids and their deacylated counterparts on ATP synthase activity. Increasing concentrations of Gb3 and lyso-Gb3 were shown to increase ATP synthase activity. Subsequently the activities of the enzymes preceding ATP synthase, the mitochondrial respiratory chain enzymes, were investigated in a Fabry mouse model. In this aspect of the study complex II/III activity was found to be significantly decreased in kidney tissues. Finally, assessment of pain thresholds in mice has demonstrated significant increases in sensitivity to applied mechanical stimuli following exposure to Gb3 and lyso-Gb3