Hamilton Description of Plasmas and Other Models of Matter: Structure and Applications I
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Modeling the Physics of RRAM Defects
Modeling the physics of RRAM defects A model simulating RRAM defects on a macroscopic physical level T. Hol Modeling the physics of RRAM defects A model simulating RRAM defects on a macroscopic physical level by T. Hol to obtain the degree of Master of Science at the Delft University of Technology, to be defended publicly on Friday August 28, 2020 at 13:00. Student number: 4295528 Project duration: September 1, 2019 – August 28, 2020 Thesis committee: Prof. dr. ir. S. Hamdioui TU Delft, supervisor Dr. Ir. R. Ishihara TU Delft Dr. Ir. S. Vollebregt TU Delft Dr. Ir. M. Taouil TU Delft Ir. M. Fieback TU Delft, supervisor An electronic version of this thesis is available at https://repository.tudelft.nl/. Abstract Resistive RAM, or RRAM, is one of the emerging non-volatile memory (NVM) technologies, which could be used in the near future to fill the gap in the memory hierarchy between dynamic RAM (DRAM) and Flash, or even completely replace Flash. RRAM operates faster than Flash, but is still non-volatile, which enables it to be used in a dense 3D NVM array. It is also a suitable candidate for computation-in-memory, neuromorphic computing and reconfigurable computing. However, the show stopping problem of RRAM is that it suffers from unique defects, which is the reason why RRAM is still not widely commercially adopted. These defects differ from those that appear in CMOS technology, due to the arbitrary nature of the forming process. They can not be detected by conventional tests and cause defective devices to go unnoticed. -
Kinematics, Kinetics, Dynamics, Inertia Kinematics Is a Branch of Classical
Course: PGPathshala-Biophysics Paper 1:Foundations of Bio-Physics Module 22: Kinematics, kinetics, dynamics, inertia Kinematics is a branch of classical mechanics in physics in which one learns about the properties of motion such as position, velocity, acceleration, etc. of bodies or particles without considering the causes or the driving forces behindthem. Since in kinematics, we are interested in study of pure motion only, we generally ignore the dimensions, shapes or sizes of objects under study and hence treat them like point objects. On the other hand, kinetics deals with physics of the states of the system, causes of motion or the driving forces and reactions of the system. In a particular state, namely, the equilibrium state of the system under study, the systems can either be at rest or moving with a time-dependent velocity. The kinetics of the prior, i.e., of a system at rest is studied in statics. Similarly, the kinetics of the later, i.e., of a body moving with a velocity is called dynamics. Introduction Classical mechanics describes the area of physics most familiar to us that of the motion of macroscopic objects, from football to planets and car race to falling from space. NASCAR engineers are great fanatics of this branch of physics because they have to determine performance of cars before races. Geologists use kinematics, a subarea of classical mechanics, to study ‘tectonic-plate’ motion. Even medical researchers require this physics to map the blood flow through a patient when diagnosing partially closed artery. And so on. These are just a few of the examples which are more than enough to tell us about the importance of the science of motion. -
1 the Basic Set-Up 2 Poisson Brackets
MATHEMATICS 7302 (Analytical Dynamics) YEAR 2016–2017, TERM 2 HANDOUT #12: THE HAMILTONIAN APPROACH TO MECHANICS These notes are intended to be read as a supplement to the handout from Gregory, Classical Mechanics, Chapter 14. 1 The basic set-up I assume that you have already studied Gregory, Sections 14.1–14.4. The following is intended only as a succinct summary. We are considering a system whose equations of motion are written in Hamiltonian form. This means that: 1. The phase space of the system is parametrized by canonical coordinates q =(q1,...,qn) and p =(p1,...,pn). 2. We are given a Hamiltonian function H(q, p, t). 3. The dynamics of the system is given by Hamilton’s equations of motion ∂H q˙i = (1a) ∂pi ∂H p˙i = − (1b) ∂qi for i =1,...,n. In these notes we will consider some deeper aspects of Hamiltonian dynamics. 2 Poisson brackets Let us start by considering an arbitrary function f(q, p, t). Then its time evolution is given by n df ∂f ∂f ∂f = q˙ + p˙ + (2a) dt ∂q i ∂p i ∂t i=1 i i X n ∂f ∂H ∂f ∂H ∂f = − + (2b) ∂q ∂p ∂p ∂q ∂t i=1 i i i i X 1 where the first equality used the definition of total time derivative together with the chain rule, and the second equality used Hamilton’s equations of motion. The formula (2b) suggests that we make a more general definition. Let f(q, p, t) and g(q, p, t) be any two functions; we then define their Poisson bracket {f,g} to be n def ∂f ∂g ∂f ∂g {f,g} = − . -
Model CIB-L Inertia Base Frame
KINETICS® Inertia Base Frame Model CIB-L Description Application Model CIB-L inertia base frames, when filled with KINETICSTM CIB-L inertia base frames are specifically concrete, meet all specifications for inertia bases, designed and engineered to receive poured concrete, and when supported by proper KINETICSTM vibration for use in supporting mechanical equipment requiring isolators, provide the ultimate in equipment isolation, a reinforced concrete inertia base. support, anchorage, and vibration amplitude control. Inertia bases are used to support mechanical KINETICSTM CIB-L inertia base frames incorporate a equipment, reduce equipment vibration, provide for unique structural design which integrates perimeter attachment of vibration isolators, prevent differential channels, isolator support brackets, reinforcing rods, movement between driving and driven members, anchor bolts and concrete fill into a controlled load reduce rocking by lowering equipment center of transfer system, utilizing steel in tension and concrete gravity, reduce motion of equipment during start-up in compression, resulting in high strength and stiff- and shut-down, act to reduce reaction movement due ness with minimum steel frame weight. Completed to operating loads on equipment, and act as a noise inertia bases using model CIB-L frames are stronger barrier. and stiffer than standard inertia base frames using heavier steel members. Typical uses for KINETICSTM inertia base frames, with poured concrete and supported by KINETICSTM Standard CIB-L inertia base frames -
KINETICS Tool of ANSA for Multi Body Dynamics
physics on screen KINETICS tool of ANSA for Multi Body Dynamics Introduction During product manufacturing processes it is important for engineers to have an overview of their design prototypes’ motion behavior to understand how moving bodies interact with respect to each other. Addressing this, the KINETICS tool has been incorporated in ANSA as a Multi-Body Dynamics (MBD) solution. Through its use, engineers can perform motion analysis to study and analyze the dynamics of mechanical systems that change their response with respect to time. Through the KINETICS tool ANSA offers multiple capabilities that are accomplished by the functionality presented below. Model definition Multi-body models can be defined on any CAD data or on existing FE models. Users can either define their Multi-body models manually from scratch or choose to automatically convert an existing FE model setup (e.g. ABAQUS, LSDYNA) to a Multi- body model. Contact Modeling The accuracy and robustness of contact modeling are very important in MBD simulations. The implementation of algorithms based on the non-smooth dynamics theory of unilateral contacts allows users to study contact incidents providing accurate solutions that the ordinary regularized methodologies cannot offer. Furthermore, the selection between different friction types maximizes the realism in the model behavior. Image 1: A Seat-dummy FE model converted to a multibody model Image 2: A Bouncing of a piston inside a cylinder BETA CAE Systems International AG D4 Business Village Luzern, Platz 4 T +41 415453650 [email protected] CH-6039 Root D4, Switzerland F +41 415453651 www.beta-cae.com Configurator In many cases, engineers need to manipulate mechanisms under the influence of joints, forces and contacts and save them in different positions. -
Fundamentals of Biomechanics Duane Knudson
Fundamentals of Biomechanics Duane Knudson Fundamentals of Biomechanics Second Edition Duane Knudson Department of Kinesiology California State University at Chico First & Normal Street Chico, CA 95929-0330 USA [email protected] Library of Congress Control Number: 2007925371 ISBN 978-0-387-49311-4 e-ISBN 978-0-387-49312-1 Printed on acid-free paper. © 2007 Springer Science+Business Media, LLC All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. 987654321 springer.com Contents Preface ix NINE FUNDAMENTALS OF BIOMECHANICS 29 Principles and Laws 29 Acknowledgments xi Nine Principles for Application of Biomechanics 30 QUALITATIVE ANALYSIS 35 PART I SUMMARY 36 INTRODUCTION REVIEW QUESTIONS 36 CHAPTER 1 KEY TERMS 37 INTRODUCTION TO BIOMECHANICS SUGGESTED READING 37 OF UMAN OVEMENT H M WEB LINKS 37 WHAT IS BIOMECHANICS?3 PART II WHY STUDY BIOMECHANICS?5 BIOLOGICAL/STRUCTURAL BASES -
Chapter 12. Kinetics of Particles: Newton's Second
Chapter 12. Kinetics of Particles: Newton’s Second Law Introduction Newton’s Second Law of Motion Linear Momentum of a Particle Systems of Units Equations of Motion Dynamic Equilibrium Angular Momentum of a Particle Equations of Motion in Radial & Transverse Components Conservation of Angular Momentum Newton’s Law of Gravitation Trajectory of a Particle Under a Central Force Application to Space Mechanics Kepler’s Laws of Planetary Motion Kinetics of Particles We must analyze all of the forces acting on the racecar in order to design a good track As a centrifuge reaches high velocities, the arm will experience very large forces that must be considered in design. Introduction Σ=Fam 12.1 Newton’s Second Law of Motion • If the resultant force acting on a particle is not zero, the particle will have an acceleration proportional to the magnitude of resultant and in the direction of the resultant. • Must be expressed with respect to a Newtonian (or inertial) frame of reference, i.e., one that is not accelerating or rotating. • This form of the equation is for a constant mass system 12.1 B Linear Momentum of a Particle • Replacing the acceleration by the derivative of the velocity yields dv ∑ Fm= dt d dL =(mv) = dt dt L = linear momentum of the particle • Linear Momentum Conservation Principle: If the resultant force on a particle is zero, the linear momentum of the particle remains constant in both magnitude and direction. 12.1C Systems of Units • Of the units for the four primary dimensions (force, mass, length, and time), three may be chosen arbitrarily. -
Basics of Physics Course II: Kinetics | 1
Basics of Physics Course II: Kinetics | 1 This chapter gives you an overview of all the basic physics that are important in biomechanics. The aim is to give you an introduction to the physics of biomechanics and maybe to awaken your fascination for physics. The topics mass, momentum, force and torque are covered. In order to illustrate the physical laws in a practical way, there is one example from physics and one from biomechanics for each topic area. Have fun! 1. Mass 2. Momentum 3. Conservation of Momentum 4. Force 5. Torque 1.Mass In physics, mass M is a property of a body. Its unit is kilogram [kg] . Example Physics Example Biomechanics 2. Momentum In physics, the momentum p describes the state of motion of a body. Its unit is kilogram times meter per second [\frac{kg * m}{s}] The momentum combines the mass with the velocity. The momentum is described by the following formula: p = M * v Here p is the momentum, M the mass and v the velocity of the body. © 2020 | The Biomechanist | All rights reserved Basics of Physics Course II: Kinetics | 2 Sometimes the formula sign for the impulse is also written like this: \vec{p} . This is because the momentum is a vectorial quantity and therefore has a size and a direction. For the sake of simplicity we write only p . Example Physics 3. conservation of momentum Let us assume that a billiard ball rolls over a billiard table at a constant speed and then hits a second ball that is lighter than the first ball. -
Canonical Coordinates on Lie Groups and the Baker Campbell Hausdorff Formula
Utah State University DigitalCommons@USU All Graduate Theses and Dissertations Graduate Studies 8-2018 Canonical Coordinates on Lie Groups and the Baker Campbell Hausdorff Formula Nicholas Graner Utah State University Follow this and additional works at: https://digitalcommons.usu.edu/etd Part of the Mathematics Commons Recommended Citation Graner, Nicholas, "Canonical Coordinates on Lie Groups and the Baker Campbell Hausdorff Formula" (2018). All Graduate Theses and Dissertations. 7232. https://digitalcommons.usu.edu/etd/7232 This Thesis is brought to you for free and open access by the Graduate Studies at DigitalCommons@USU. It has been accepted for inclusion in All Graduate Theses and Dissertations by an authorized administrator of DigitalCommons@USU. For more information, please contact [email protected]. CANONICAL COORDINATES ON LIE GROUPS AND THE BAKER CAMPBELL HAUSDORFF FORMULA by Nicholas Graner A thesis submitted in partial fulfillment of the requirements for the degree of MASTERS OF SCIENCE in Mathematics Approved: Mark Fels, Ph.D. Charles Torre, Ph.D. Major Professor Committee Member Ian Anderson, Ph.D. Mark R. McLellan, Ph.D. Committee Member Vice President for Research and Dean of the School for Graduate Studies UTAH STATE UNIVERSITY Logan,Utah 2018 ii Copyright © Nicholas Graner 2018 All Rights Reserved iii ABSTRACT Canonical Coordinates on Lie Groups and the Baker Campbell Hausdorff Formula by Nicholas Graner, Master of Science Utah State University, 2018 Major Professor: Mark Fels Department: Mathematics and Statistics Lie's third theorem states that for any finite dimensional Lie algebra g over the real numbers, there is a simply connected Lie group G which has g as its Lie algebra. -
Hamiltonian Dynamics Lecture 1
Hamiltonian Dynamics Lecture 1 David Kelliher RAL November 12, 2019 David Kelliher (RAL) Hamiltonian Dynamics November 12, 2019 1 / 59 Bibliography The Variational Principles of Mechanics - Lanczos Classical Mechanics - Goldstein, Poole and Safko A Student's Guide to Lagrangians and Hamiltonians - Hamill Classical Mechanics, The Theoretical Minimum - Susskind and Hrabovsky Theory and Design of Charged Particle Beams - Reiser Accelerator Physics - Lee Particle Accelerator Physics II - Wiedemann Mathematical Methods in the Physical Sciences - Boas Beam Dynamics in High Energy Particle Accelerators - Wolski David Kelliher (RAL) Hamiltonian Dynamics November 12, 2019 2 / 59 Content Lecture 1 Comparison of Newtonian, Lagrangian and Hamiltonian approaches. Hamilton's equations, symplecticity, integrability, chaos. Canonical transformations, the Hamilton-Jacobi equation, Poisson brackets. Lecture 2 The \accelerator" Hamiltonian. Dynamic maps, symplectic integrators. Integrable Hamiltonian. David Kelliher (RAL) Hamiltonian Dynamics November 12, 2019 3 / 59 Configuration space The state of the system at a time q 3 t can be given by the value of the t2 n generalised coordinates qi . This can be represented by a point in an n dimensional space which is called “configuration space" (the system t1 is said to have n degrees of free- q2 dom). The motion of the system as a whole is then characterised by the line this system point maps out in q1 configuration space. David Kelliher (RAL) Hamiltonian Dynamics November 12, 2019 4 / 59 Newtonian Mechanics The equation of motion of a particle of mass m subject to a force F is d (mr_) = F(r; r_; t) (1) dt In Newtonian mechanics, the dynamics of the system are defined by the force F, which in general is a function of position r, velocity r_ and time t. -
Kinematics and Kinetics of Elite Windmill Softball Pitching
Kinematics and Kinetics of Elite Windmill Softball Pitching Sherry L. Werner,*† PhD, Deryk G. Jones,‡ MD, John A. Guido, Jr,† MHS, PT, SCS, ATC, CSCS, and Michael E. Brunet,† MD From the †Tulane Institute of Sports Medicine, New Orleans, Louisiana, and the ‡Sports Medicine Section, Ochsner Clinic Foundation, New Orleans, Louisiana Background: A significant number of time-loss injuries to the upper extremity in elite windmill softball pitchers has been docu- mented. The number of outings and pitches thrown in 1 week for a softball pitcher is typically far in excess of those seen in baseball pitchers. Shoulder stress in professional baseball pitching has been reported to be high and has been linked to pitch- ing injuries. Shoulder distraction has not been studied in an elite softball pitching population. Hypothesis: The stresses on the throwing shoulder of elite windmill pitchers are similar to those found for professional baseball pitchers. Study Design: Descriptive laboratory study. Methods: Three-dimensional, high-speed (120 Hz) video data were collected on rise balls from 24 elite softball pitchers during the 1996 Olympic Games. Kinematic parameters related to pitching mechanics and resultant kinetics on the throwing shoulder were calculated. Multiple linear regression analysis was used to relate shoulder stress and pitching mechanics. Results: Shoulder distraction stress averaged 80% of body weight for the Olympic pitchers. Sixty-nine percent of the variabil- ity in shoulder distraction can be explained by a combination of 7 parameters related to pitching mechanics. Conclusion: Excessive distraction stress at the throwing shoulder is similar to that found in baseball pitchers, which suggests that windmill softball pitchers are at risk for overuse injuries. -
Fractional Poisson Process in Terms of Alpha-Stable Densities
FRACTIONAL POISSON PROCESS IN TERMS OF ALPHA-STABLE DENSITIES by DEXTER ODCHIGUE CAHOY Submitted in partial fulfillment of the requirements For the degree of Doctor of Philosophy Dissertation Advisor: Dr. Wojbor A. Woyczynski Department of Statistics CASE WESTERN RESERVE UNIVERSITY August 2007 CASE WESTERN RESERVE UNIVERSITY SCHOOL OF GRADUATE STUDIES We hereby approve the dissertation of DEXTER ODCHIGUE CAHOY candidate for the Doctor of Philosophy degree * Committee Chair: Dr. Wojbor A. Woyczynski Dissertation Advisor Professor Department of Statistics Committee: Dr. Joe M. Sedransk Professor Department of Statistics Committee: Dr. David Gurarie Professor Department of Mathematics Committee: Dr. Matthew J. Sobel Professor Department of Operations August 2007 *We also certify that written approval has been obtained for any proprietary material contained therein. Table of Contents Table of Contents . iii List of Tables . v List of Figures . vi Acknowledgment . viii Abstract . ix 1 Motivation and Introduction 1 1.1 Motivation . 1 1.2 Poisson Distribution . 2 1.3 Poisson Process . 4 1.4 α-stable Distribution . 8 1.4.1 Parameter Estimation . 10 1.5 Outline of The Remaining Chapters . 14 2 Generalizations of the Standard Poisson Process 16 2.1 Standard Poisson Process . 16 2.2 Standard Fractional Generalization I . 19 2.3 Standard Fractional Generalization II . 26 2.4 Non-Standard Fractional Generalization . 27 2.5 Fractional Compound Poisson Process . 28 2.6 Alternative Fractional Generalization . 29 3 Fractional Poisson Process 32 3.1 Some Known Properties of fPp . 32 3.2 Asymptotic Behavior of the Waiting Time Density . 35 3.3 Simulation of Waiting Time . 38 3.4 The Limiting Scaled nth Arrival Time Distribution .