Force-Field Analysis: Incorporating Critical Thinking in Goal Setting
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Measurement of the Speed of Gravity
Measurement of the Speed of Gravity Yin Zhu Agriculture Department of Hubei Province, Wuhan, China Abstract From the Liénard-Wiechert potential in both the gravitational field and the electromagnetic field, it is shown that the speed of propagation of the gravitational field (waves) can be tested by comparing the measured speed of gravitational force with the measured speed of Coulomb force. PACS: 04.20.Cv; 04.30.Nk; 04.80.Cc Fomalont and Kopeikin [1] in 2002 claimed that to 20% accuracy they confirmed that the speed of gravity is equal to the speed of light in vacuum. Their work was immediately contradicted by Will [2] and other several physicists. [3-7] Fomalont and Kopeikin [1] accepted that their measurement is not sufficiently accurate to detect terms of order , which can experimentally distinguish Kopeikin interpretation from Will interpretation. Fomalont et al [8] reported their measurements in 2009 and claimed that these measurements are more accurate than the 2002 VLBA experiment [1], but did not point out whether the terms of order have been detected. Within the post-Newtonian framework, several metric theories have studied the radiation and propagation of gravitational waves. [9] For example, in the Rosen bi-metric theory, [10] the difference between the speed of gravity and the speed of light could be tested by comparing the arrival times of a gravitational wave and an electromagnetic wave from the same event: a supernova. Hulse and Taylor [11] showed the indirect evidence for gravitational radiation. However, the gravitational waves themselves have not yet been detected directly. [12] In electrodynamics the speed of electromagnetic waves appears in Maxwell equations as c = √휇0휀0, no such constant appears in any theory of gravity. -
Classical Mechanics
Classical Mechanics Hyoungsoon Choi Spring, 2014 Contents 1 Introduction4 1.1 Kinematics and Kinetics . .5 1.2 Kinematics: Watching Wallace and Gromit ............6 1.3 Inertia and Inertial Frame . .8 2 Newton's Laws of Motion 10 2.1 The First Law: The Law of Inertia . 10 2.2 The Second Law: The Equation of Motion . 11 2.3 The Third Law: The Law of Action and Reaction . 12 3 Laws of Conservation 14 3.1 Conservation of Momentum . 14 3.2 Conservation of Angular Momentum . 15 3.3 Conservation of Energy . 17 3.3.1 Kinetic energy . 17 3.3.2 Potential energy . 18 3.3.3 Mechanical energy conservation . 19 4 Solving Equation of Motions 20 4.1 Force-Free Motion . 21 4.2 Constant Force Motion . 22 4.2.1 Constant force motion in one dimension . 22 4.2.2 Constant force motion in two dimensions . 23 4.3 Varying Force Motion . 25 4.3.1 Drag force . 25 4.3.2 Harmonic oscillator . 29 5 Lagrangian Mechanics 30 5.1 Configuration Space . 30 5.2 Lagrangian Equations of Motion . 32 5.3 Generalized Coordinates . 34 5.4 Lagrangian Mechanics . 36 5.5 D'Alembert's Principle . 37 5.6 Conjugate Variables . 39 1 CONTENTS 2 6 Hamiltonian Mechanics 40 6.1 Legendre Transformation: From Lagrangian to Hamiltonian . 40 6.2 Hamilton's Equations . 41 6.3 Configuration Space and Phase Space . 43 6.4 Hamiltonian and Energy . 45 7 Central Force Motion 47 7.1 Conservation Laws in Central Force Field . 47 7.2 The Path Equation . -
FORCE FIELDS for PROTEIN SIMULATIONS by JAY W. PONDER
FORCE FIELDS FOR PROTEIN SIMULATIONS By JAY W. PONDER* AND DAVIDA. CASEt *Department of Biochemistry and Molecular Biophysics, Washington University School of Medicine, 51. Louis, Missouri 63110, and tDepartment of Molecular Biology, The Scripps Research Institute, La Jolla, California 92037 I. Introduction. ...... .... ... .. ... .... .. .. ........ .. .... .... ........ ........ ..... .... 27 II. Protein Force Fields, 1980 to the Present.............................................. 30 A. The Am.ber Force Fields.............................................................. 30 B. The CHARMM Force Fields ..., ......... 35 C. The OPLS Force Fields............................................................... 38 D. Other Protein Force Fields ....... 39 E. Comparisons Am.ong Protein Force Fields ,... 41 III. Beyond Fixed Atomic Point-Charge Electrostatics.................................... 45 A. Limitations of Fixed Atomic Point-Charges ........ 46 B. Flexible Models for Static Charge Distributions.................................. 48 C. Including Environmental Effects via Polarization................................ 50 D. Consistent Treatment of Electrostatics............................................. 52 E. Current Status of Polarizable Force Fields........................................ 57 IV. Modeling the Solvent Environment .... 62 A. Explicit Water Models ....... 62 B. Continuum Solvent Models.......................................................... 64 C. Molecular Dynamics Simulations with the Generalized Born Model........ -
FORCE FIELDS and CRYSTAL STRUCTURE PREDICTION Contents
FORCE FIELDS AND CRYSTAL STRUCTURE PREDICTION Bouke P. van Eijck ([email protected]) Utrecht University (Retired) Department of Crystal and Structural Chemistry Padualaan 8, 3584 CH Utrecht, The Netherlands Originally written in 2003 Update blind tests 2017 Contents 1 Introduction 2 2 Lattice Energy 2 2.1 Polarcrystals .............................. 4 2.2 ConvergenceAcceleration . 5 2.3 EnergyMinimization .......................... 6 3 Temperature effects 8 3.1 LatticeVibrations............................ 8 4 Prediction of Crystal Structures 9 4.1 Stage1:generationofpossiblestructures . .... 9 4.2 Stage2:selectionoftherightstructure(s) . ..... 11 4.3 Blindtests................................ 14 4.4 Beyondempiricalforcefields. 15 4.5 Conclusions............................... 17 4.6 Update2017............................... 17 1 1 Introduction Everybody who looks at a crystal structure marvels how Nature finds a way to pack complex molecules into space-filling patterns. The question arises: can we understand such packings without doing experiments? This is a great challenge to theoretical chemistry. Most work in this direction uses the concept of a force field. This is just the po- tential energy of a collection of atoms as a function of their coordinates. In principle, this energy can be calculated by quantumchemical methods for a free molecule; even for an entire crystal computations are beginning to be feasible. But for nearly all work a parameterized functional form for the energy is necessary. An ab initio force field is derived from the abovementioned calculations on small model systems, which can hopefully be generalized to other related substances. This is a relatively new devel- opment, and most force fields are empirical: they have been developed to reproduce observed properties as well as possible. There exists a number of more or less time- honored force fields: MM3, CHARMM, AMBER, GROMOS, OPLS, DREIDING.. -
1 Multiscale Modeling of Electrochemical Systems Jonathan E
j1 1 Multiscale Modeling of Electrochemical Systems Jonathan E. Mueller, Donato Fantauzzi, and Timo Jacob 1.1 Introduction As one of the classic branches of physical chemistry, electrochemistry enjoys a long history. Its relevance and vitality remain unabated as it not only finds numerous applications in traditional industries, but also provides the scientific impetus for a plethora of emerging technologies. Nevertheless, in spite of its venerability and the ubiquity of its applications, many of the fundamental processes, underlying some of the most basic electrochemical phenomena, are only now being brought to light. Electrochemistry is concerned with the interconversion of electrical and chemical energy. This interconversion is facilitated by transferring an electron between two species involved in a chemical reaction, such that the chemical energy associated with the chemical reaction is converted into the electrical energy associated with transferring the electron from one species to the other. Taking advantage of the electrical energy associated with this electron transfer for experimental or techno- logical purposes requires separating the complementary oxidation and reduction reactions of which every electron transfer is composed. Thus, an electrochemical system includes an electron conducting phase (a metal or semiconductor), an ion conducting phase (typically an electrolyte, with a selectively permeable barrier to provide the requisite chemical separation), and the interfaces between these phases at which the oxidation and reduction reactions take place. Thus, the fundamental properties of an electrochemical system are the electric potentials across each phase and interface, the charge transport rates across the conducting phases, and the chemical concentrations and reaction rates at the oxidation and reduction interfaces. -
Some Potential/Force Fields for Particle Systems
Some Potential/Force Fields for Particle Systems D.A. Forsyth, largely lifted from Steve Rotenberg Independent particles • Force on particle does not depend on other particles • Attractive for obvious reasons • Simple gravity • Drag • Attractors/repellors Uniform Gravity A very simple, useful force is the uniform gravity field: It assumes that we are near the surface of a planet with a huge enough mass that we can treat it as infinite As we don’t apply any equal and opposite forces to anything, it appears that we are breaking Newton’s third law, however we can assume that we are exchanging forces with the infinite mass, but having no relevant affect on it Aerodynamic Drag Aerodynamic interactions are actually very complex and difficult to model accurately A reasonable simplification it to describe the total aerodynamic drag force on an object using: Where ρ is the density of the air (or water…), cd is the coefficient of drag for the object, a is the cross sectional area of the object, and e is a unit vector in the opposite direction of the velocity Aerodynamic Drag Like gravity, the aerodynamic drag force appears to violate Newton’s Third Law, as we are applying a force to a particle but no equal and opposite force to anything else We can justify this by saying that the particle is actually applying a force onto the surrounding air, but we will assume that the resulting motion is just damped out by the viscosity of the air Force Fields We can also define any arbitrary force field that we want. -
Designing Force Field Engines Solomon BT* Xodus One Foundation, 815 N Sherman Street, Denver, Colorado, USA
ISSN: 2319-9822 Designing Force Field Engines Solomon BT* Xodus One Foundation, 815 N Sherman Street, Denver, Colorado, USA *Corresponding author: Solomon BT, Xodus One Foundation, 815 N Sherman Street, Denver, Colorado, USA, Tel: 310- 666-3553; E-mail: [email protected] Received: September 11, 2017; Accepted: October 20, 2017; Published: October 24, 2017 Abstract The main objective of this paper is to present sample conceptual propulsion engines that researchers can tinker with to gain a better engineering understanding of how to research propulsion that is based on gravity modification. A Non- Inertia (Ni) Field is the spatial gradient of real or latent velocities. These velocities are real in mechanical structures, and latent in gravitational and electromagnetic field. These velocities have corresponding time dilations, and thus g=τc2 is the mathematical formula to calculate acceleration. It was verified that gravitational, electromagnetic and mechanical accelerations are present when a Ni Field is present. For example, a gravitational field is a spatial gradient of latent velocities along the field’s radii. g=τc2 is the mathematical expression of Hooft’s assertion that “absence of matter no longer guarantees local flatness”, and the new gravity modification based propulsion equation for force field engines. To achieve Force Field based propulsion, a discussion of the latest findings with the problems in theoretical physics and warp drives is presented. Solomon showed that four criteria need to be present when designing force field engines (i) the spatial gradient of velocities, (ii) asymmetrical non-cancelling fields, (iii) vectoring, or the ability to change field direction and (iv) modulation, the ability to alter the field strength. -
Motion in a Central Force Field
Motion in a Central Force Field We now study the properties of a particle of (constant) mass moving in a particular type of force field, a central force field. Central forces are very important in physics and engineering. For example, the gravitational force of attraction between two point masses is a central force. The Coulomb force of attraction and repulsion between charged particles is a central force. Because of their importance they deserve special consideration. We begin by giving a precise definition of central force, or central force field. Central Forces: The Definition. Suppose that a force acting on a particle of mass has the properties that: • the force is always directed from toward, or away, from a fixed point O, • the magnitude of the force only depends on the distance from O. Forces having these properties are called central forces. The particle is said to move in a central force field. The point O is referred to as the center of force. Mathematically, is a central force if and only if: (1) where is a unit vector in the direction of . If , the force is said to be attractive towards O. If , the force is said to be repulsive from O. We give a geometrical illustration in Fig. 1. Properties of a Particle Moving under the Influence of a Central Force. If a particle moves in a central force field then the following properties hold: 1. The path of the particle must be a plane curve, i.e., it must lie in a plane. 2. The angular momentum of the particle is conserved, i.e., it is constant in time. -
18 Electric Charge and Electric Field
CHAPTER 18 | ELECTRIC CHARGE AND ELECTRIC FIELD 627 18 ELECTRIC CHARGE AND ELECTRIC FIELD Figure 18.1 Static electricity from this plastic slide causes the child’s hair to stand on end. The sliding motion stripped electrons away from the child’s body, leaving an excess of positive charges, which repel each other along each strand of hair. (credit: Ken Bosma/Wikimedia Commons) Learning Objectives 18.1. Static Electricity and Charge: Conservation of Charge • Define electric charge, and describe how the two types of charge interact. • Describe three common situations that generate static electricity. • State the law of conservation of charge. 18.2. Conductors and Insulators • Define conductor and insulator, explain the difference, and give examples of each. • Describe three methods for charging an object. • Explain what happens to an electric force as you move farther from the source. • Define polarization. 18.3. Coulomb’s Law • State Coulomb’s law in terms of how the electrostatic force changes with the distance between two objects. • Calculate the electrostatic force between two charged point forces, such as electrons or protons. • Compare the electrostatic force to the gravitational attraction for a proton and an electron; for a human and the Earth. 18.4. Electric Field: Concept of a Field Revisited • Describe a force field and calculate the strength of an electric field due to a point charge. • Calculate the force exerted on a test charge by an electric field. • Explain the relationship between electrical force (F) on a test charge and electrical field strength (E). 18.5. Electric Field Lines: Multiple Charges • Calculate the total force (magnitude and direction) exerted on a test charge from more than one charge • Describe an electric field diagram of a positive point charge; of a negative point charge with twice the magnitude of positive charge • Draw the electric field lines between two points of the same charge; between two points of opposite charge. -
An Electron Force Field for Simulating Large Scale Excited Electron Dynamics
An electron force ¯eld for simulating large scale excited electron dynamics Thesis by Julius T. Su In Partial Ful¯llment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 2007 (Defended April 12, 2007) ii °c 2007 Julius T. Su All rights Reserved iii Acknowledgements I dedicate this thesis to my parents. I thank them for teaching me early, teaching me well, and indulging and nurturing my curiosity about the world until it became self-sustaining. My brother Jonathan and sisters Judy and Jessica have always been there for me as well, and we have had a good journey together. It has been a pleasure to work for my advisor, Prof. Bill Goddard, who attacks scienti¯c problems with great enthusiasm, open-mindedness, and a formidable arse- nal of ideas and approaches. His way of getting to the root of things and identifying the key experiment that needs to be done is as reflexive for him as breathing. I appreciate that Bill gave me the freedom to work on many di®erent projects, and his level of expertise and broad range of interests was such that he provided good insights on every one of them. The stimulus behind the electron force ¯eld and this thesis was the ideas presented in his Nature of the Chemical Bond course { he talked about electrons moving around and \pooching", changing in size and becoming orthogonal to each other, and his level of enthusiasm motivated me to develop a simulation of these events happening. I also had the privilege to work with Prof. -
Machine Learning Transferable Physics-Based Force Fields Using Graph Convolutional Neural Networks
Machine Learning Transferable Physics-Based Force Fields using Graph Convolutional Neural Networks by William H. Harris B.S. Chemical Engineering, B.S. Physics North Carolina State University, 2016 SUBMITTED TO THE DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN MATERIALS SCIENCE AND ENGINEERING AT THE MASSACHUSETTS INSTITUTE OF TECHNOLOGY SEPTEMBER 2020 © 2020 Massachusetts Institute of Technology. All rights reserved. Signature of Author: ____________________________________________________________ Department of Materials Science and Engineering August 6, 2020 Certified by: __________________________________________________________________ Rafael Gomez-Bombarelli Assistant Professor of Materials Science and Engineering Thesis Supervisor Accepted by: __________________________________________________________________ Frances Ross Professor of Materials Science and Engineering Chair, Departmental Committee on Graduate Studies 1 Machine Learning Transferable Physics-Based Force Fields using Graph Convolutional Neural Networks by William H. Harris Submitted to the Department of Materials Science and Engineering on August 6, 2020 in Partial Fulfillment of the Requirements for the Degree of Master of Science in Materials Science and Engineering ABSTRACT Molecular dynamics and Monte Carlo methods allow the properties of a system to be determined from its potential energy surface (PES). In the domain of crystalline materials, the PES is needed for electronic structure calculations, critical for modeling semiconductors, optical, and energy- storage materials. While first principles techniques can be used to obtain the PES to high accuracy, their computational complexity limits applications to small systems and short timescales. In practice, the PES must be approximated using a computationally cheaper functional form. Classical force field (CFF) approaches simply define the PES as a sum over independent energy contributions. -
Force Field Development Phase II: Relaxation of Physics-Based Criteria… Or Inclusion of More Rigorous Physics Into the Representation of Molecular Energetics
Journal of Computer-Aided Molecular Design https://doi.org/10.1007/s10822-018-0134-x PERSPECTIVE Force field development phase II: Relaxation of physics-based criteria… or inclusion of more rigorous physics into the representation of molecular energetics A. T. Hagler1,2 Received: 5 March 2018 / Accepted: 18 July 2018 © Springer Nature Switzerland AG 2018 Abstract In the previous paper, we reviewed the origins of energy based calculations, and the early science of FF development. The initial efforts spanning the period from roughly the early 1970s to the mid to late 1990s saw the development of methodolo- gies and philosophies of the derivation of FFs. The use of Cartesian coordinates, derivation of the H-bond potential, different functional forms including diagonal quadratic expressions, coupled valence FFs, functional form of combination rules, and out of plane angles, were all investigated in this period. The use of conformational energetics, vibrational frequencies, crystal structure and energetics, liquid properties, and ab initio data were all described to one degree or another in deriving and vali- dating both the FF functional forms and force constants. Here we discuss the advances made since in improving the rigor and robustness of these initial FFs. The inability of the simple quadratic diagonal FF to accurately describe biomolecular energetics over a large domain of molecular structure, and intermolecular configurations, was pointed out in numerous studies. Two main approaches have been taken to overcome this problem. The first involves the introduction of error functions, either exploit- ing torsion terms or introducing explicit 2-D error correction grids. The results and remaining challenges of these functional forms is examined.