Paradoxical Chaos-Like Chattering in the Bouncing Ball System

2018 ◽  
Author(s):  
Kilian Schindler ◽  
Remco I. Leine
Keyword(s):  
Detailed Analysis ◽  
Critical Value ◽  
Forward Dynamics ◽  
Bouncing Ball ◽  
Relative Acceleration ◽  
Self Similar ◽  
Simulation Results

This paper reports and investigates paradoxical simulation results of the bouncing ball system. Chaos-like motion of the bouncing ball system with intermittent chattering (Zeno behaviour) is observed in simulations if the relative acceleration of the table exceeds a critical value. However, one can show that this is theoretically impossible. A detailed analysis is given by looking at the backward and forward dynamics of grazing solutions. It is shown in detail that a self-similar structure appears if the relative acceleration of the table exceeds the critical value.

The Martyrdom of Polycarp in Church Slavonic: An Evidence of the Academic Menologion

2013 ◽  
Vol 67 (4) ◽  
pp. 393-406
Author(s):  
Taras Khomych
Keyword(s):  
Detailed Analysis ◽  
Present Article ◽  
Critical Value

Abstract This contribution deals with a significant gap in the studia Polycarpiana. It focuses, in particular, on a Church Slavonic translation of the Martyrdom of Polycarp, one of the earliest of Christian martyria. This versional evidence has not been published until now and, consequently, not taken into account by any of the previous editions of the Martyrdom. The present article offers a collation and a detailed analysis of the earliest available copy of the translation. Eventually it shows that the Slavonic version may provide an independent (from the extant Greek manuscripts) testimony to the text of the Martyrdom and as such is of significant text-critical value.

scholarly journals Launch Velocities in Successful Golf Putting: An Analytical Analysis

2017 ◽  
Vol 5 (2) ◽  
pp. 24
Author(s):  
John F. Mahoney ◽  
Daniel P. Connaughton
Keyword(s):  
Critical Value ◽  
Theoretical Studies ◽  
Newtonian Mechanics ◽  
Ambient Conditions ◽  
Analytical Analysis ◽  
Bouncing Ball ◽  
Golf Putting ◽  
A Value ◽  
Special Case

Background: This study is concerned with the special case of a putted ball intersecting a standard golf hole at its diameter. The velocity of the ball at the initial rim of the hole is termed the launch velocity and depending upon its value the ball may either be captured or it may escape capture by jumping over the hole. The critical value of the launch velocity (V) is such that lesser values result in capture while greater values produce escape. Purpose: Since the value of the V entered prominently in some theoretical studies of putting, the aim of the current study is to provide an original re-evaluation of V and to contrast our results with existing results. Method: This analytical analysis relies on trigonometry in conjunction with Newtonian mechanics and the mathematics of projectiles. The results of a recent study into the mathematics of a bouncing ball which included the notions of restitution and friction were also employed in the analysis. Results: If bouncing and slipping do not occur when the ball hits the far rim of the hole our analysis produces a value of V of 1.356 m/s. When bouncing and slipping are present we find that V is at least 1.609 m/s but increases beyond this value as slipping and friction become greater. Useful relations which relate the dynamics and geometry of the ball to V are provided. Conclusion: Since ambient conditions may influence the extent of bounce and slippage we conjecture that the value of V is not unique.

Analysis and Optimization of a Series-Elastic Actuator for Jumping in Robots With Articulated Legs

2008 ◽  
Author(s):  
Simon Curran ◽  
David E. Orin ◽  
Brian T. Knox ◽  
James P. Schmiedeler
Keyword(s):  
Detailed Analysis ◽  
Design Equation ◽  
Motor Speed ◽  
Complex Dynamic ◽  
Analytical Design ◽  
Series Elastic Actuator ◽  
Simulation Results ◽  
The Moment ◽  
Elastic Elements ◽  
Series Elastic

This paper presents the analysis and optimization of a series-elastic actuator (SEA) for jumping with an articulated leg. Analytical and simulation results are validated with experimental results from a prototype leg. Similar to the series-elastic elements in muscles, an SEA decouples the dynamic limitations of a DC actuator from the joint, allowing larger liftoff velocities than with a directly driven joint. Detailed analysis of the complex dynamic SEA response during the thrust phase yields insights into its performance. The maximum impulse occurs when the motor speed is approximately half the no-load speed at the moment of peak motor torque. This proposed criterion is used to develop a simple analytical design equation for an optimal SEA.

scholarly journals PAMTRA 1.0: A Passive and Active Microwave radiative TRAnsfer tool for simulating radiometer and radar measurements of the cloudy atmosphere

2020 ◽  
Author(s):  
Mario Mech ◽  
Maximilian Maahn ◽  
Stefan Kneifel ◽  
Davide Ori ◽  
Emiliano Orlandi ◽  
...  
Keyword(s):  
Radiative Transfer ◽  
Forward Model ◽  
Doppler Spectrum ◽  
Brightness Temperatures ◽  
Cloudy Atmosphere ◽  
Radar Measurements ◽  
Self Similar ◽  
Atmospheric State ◽  
Simulation Results

Abstract. Forward models are a key tool to generate synthetic observations given the knowledge of the atmospheric state. In this way they are an integral part of inversion algorithms that aim to retrieve geophysical variables from observations or in data assimilation. Their application for the exploitation of the full information content of remote sensing observations becomes increasingly important when these are used to evaluate the performance of cloud resolving models (CRMs). Herein, CRMs profiles or fields provide the input to the forward model whose simulation results are subsequently compared to the observations. This paper introduces the freely available comprehensive microwave forward model PAMTRA (Passive and Active Microwave TRAnsfer), demonstrates its capabilities to simulate passive and active measurements across the microwave spectral region for up- and downward looking geometries, and illustrates how the forward simulations can be used to evaluate CRMs and to interpret measurements to improve our understanding of cloud processes. PAMTRA is unique as it treats passive and active radiative transfer (RT) in a consistent way with the passive forward model providing up- and down-welling polarized brightness temperatures and radiances for arbitrary observation angles. The active part is capable of simulating the full radar Doppler spectrum and its moments. PAMTRA is designed to be flexible with respect to instrument specifications, interfaces to many different formats of in- and output type, especially CRMs, spanning the range from bin-resolved microphysical output to one- and two-moment schemes, and to in situ measured hydrometeor properties. A specific highlight is the incorporation of the self-similar Rayleigh--Gans Approximation (SSRGA) both for active and passive applications which becomes especially important for the investigation of frozen hydrometeors.

The Performance Analysis of CDMA Traffic Access Self-Similar Equalization Protocol

2014 ◽  
Vol 490-491 ◽  
pp. 1205-1208
Author(s):  
Liang Zheng ◽  
Bin Yan
Keyword(s):  
Performance Analysis ◽  
Power Law ◽  
Performance Optimization ◽  
Random Access ◽  
Data Traffic ◽  
Similar Model ◽  
Network Load ◽  
Self Similar ◽  
Simulation Results ◽  
Access Technique

The random access technique has a bigger influence to the performance optimization of CDMA data traffic. A CDMA random access technique based on self-similar model and its performance analysis are put forward in this paper. The simulation results indicate that the access performance of CDMA data traffic based on self-similar model is attenuated by power law, related to such parameters as fractal coefficient H and network load G. The CDMA traffic access self-similar equalization protocol (TASEP) is put forward and it can improve the access performance of CDMA data traffic distinctly.

Numerical Simulation of MEMS Stirling Cooler

2010 ◽  
Vol 44-47 ◽  
pp. 924-928
Author(s):  
Wen Song ◽  
Xian Zhou Wang ◽  
Lei Yue ◽  
Zhi Guo Zhang
Keyword(s):  
Numerical Method ◽  
Detailed Analysis ◽  
Design Parameters ◽  
Gas Flows ◽  
Design Code ◽  
Manufacture Process ◽  
Engine Design ◽  
Micro Channels ◽  
Mems Device ◽  
Simulation Results

The heat transfer and the fluid dynamics characteristics of subsonic gas flows through micro-channels are examined using numerical method. Detailed analysis on the Stirling MEMS device has been examined for the feasibility of the performance. The 1-D Stirling engine design code was utilized to provide basic information to meet the design parameters and criteria. Furthermore a 2-D CFD code has been used to perform a detailed analysis. The simulation results show that the numerical method used here could be used for the prediction of MEMS performance before experimental test and manufacture process start.

Dynamic Behavior and Simulation of Nanoparticle Sliding During Nanoprobe-Based Positioning

2004 ◽  
Author(s):  
Afshin Tafazzoli ◽  
Metin Sitti
Keyword(s):  
Atomic Force Microscope ◽  
Dynamic Behavior ◽  
Dynamic Simulation ◽  
Silicon Substrate ◽  
Critical Value ◽  
Gold Particles ◽  
Atomic Force ◽  
Simulation Results

In this paper, the behavior of nanoparticles, manipulated by an atomic force microscope nanoprobe, is investigated. Manipulation by pushing, pulling or picking nanoparticles can result in rolling, sliding, sticking, or rotation behavior. The dynamic simulation of the nanoparticle manipulation, using atomic force microscope (AFM), is performed. According to the dynamics of the system, the AFM pushing force increases to the critical value required for nanoparticle motion. Nanoparticle positioning is designed based on when the nanoparticle is stopped by the AFM in order to move on the substrate. Simulation results for gold particles on a silicon substrate showed that sliding on the substrate is dominant in nanoscales.

Research on Mechanical Balance of the Beam-Pumper

2013 ◽  
Vol 706-708 ◽  
pp. 1529-1532
Author(s):  
Ling Wang ◽  
Hu Ping An ◽  
Fu Yan Qi ◽  
Tian Xing Yang
Keyword(s):  
Detailed Analysis ◽  
Balance Method ◽  
Motor Power ◽  
Beam Balance ◽  
Simulation Results

The detailed analysis of mechanical balance based on beam-pumper is put forward to reduce the motor power, and save consumption. It has discussed something about the analysis of the crack balance, the walking beam balance and the composite balance. Finally, MATLAB M-file editor are used to compile the applications. The simulation results show that the program of the optimal mechanical balance method is feasible.

Calibration of Constraint Promotion Does Not Help with Learning Variation in Stochastic Optimality Theory

2020 ◽  
Vol 51 (1) ◽  
pp. 97-123
Author(s):  
Giorgio Magri ◽  
Benjamin Storme
Keyword(s):  
Detailed Analysis ◽  
Optimality Theory ◽  
Learning Algorithm ◽  
Test Cases ◽  
Ranking Algorithm ◽  
Gradual Learning Algorithm ◽  
Simulation Results ◽  
Stochastic Optimality

The Calibrated Error-Driven Ranking Algorithm (CEDRA; Magri 2012 ) is shown to fail on two test cases of phonologically conditioned variation from Boersma and Hayes 2001 . The failure of the CEDRA raises a serious unsolved challenge for learnability research in stochastic Optimality Theory, because the CEDRA itself was proposed to repair a learnability problem ( Pater 2008 ) encountered by the original Gradual Learning Algorithm. This result is supported by both simulation results and a detailed analysis whereby a few constraints and a few candidates at a time are recursively “peeled off” until we are left with a “core” small enough that the behavior of the learner is easy to interpret.

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