Dynamics of a point particle

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
External Field ◽  
Conservation Law ◽  
Short Range ◽  
Reference Frames ◽  
World Line ◽  
Inertial Mass ◽  
Momentum Conservation ◽  
Point Particle ◽  
Mass Energy ◽  
Internal Forces

This chapter attributes an inertial ‘mass–energy’ to particles. It also distinguishes between the action of an external field and of long-range and short-range internal forces, which is useful for establishing the laws of dynamics of an interacting body—that is, the equations determining its world line. The chapter also presents the 4-momentum conservation law for massive particles and light particles in inertial reference frames. It then gives some examples which illustrate the role played by this law in collisions. Finally, the chapter illustrates the conservation law by the Compton experiment, that is, the collision of a light corpuscle with a particle, and the concept of the quantum of action that can be derived from it.

The kinematics of a point particle

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Internal Structure ◽  
Proper Time ◽  
World Line ◽  
Point Particle ◽  
Material Point ◽  
Spatial Extent ◽  
Geometric Representation ◽  
Mathematical Result ◽  
Point Particles ◽  
The World

This chapter discusses the kinematics of point particles undergoing any type of motion. It introduces the concept of proper time—the geometric representation of the time measured by an accelerated clock. It also describes a world line, which represents the motion of a material point or point particle P, that is, an object whose spatial extent and internal structure can be ignored. The chapter then considers the interpretation of the curvilinear abscissa, which by definition measures the length of the world line L representing the motion of the point particle P. Next, the chapter discusses a mathematical result popularized by Paul Langevin in the 1920s, the so-called ‘Langevin twins’ which revealed a paradoxical result. Finally, the transformation of velocities and accelerations is discussed.

THE APPROACH TO PARAMAGNETIC SATURATION

1962 ◽  
Vol 40 (12) ◽  
pp. 1693-1702 ◽  
Author(s):  
Richard Stevenson
Keyword(s):  
External Field ◽  
Magnetic Moment ◽  
Short Range ◽  
Short Range Order ◽  
Field Method ◽  
Order Parameters ◽  
Range Order ◽  
Molecular Field ◽  
Paramagnetic Materials ◽  
High Fields

The process of paramagnetic saturation in real substances is considered by means of the molecular field method and by Smart's elaboration of the Oguchi method. The magnetic moment and short-range order parameters are calculated as a function of the external field. Some qualitative rules are obtained which describe general tendencies toward saturation. The possibility arises that paramagnetic materials in high fields may change into a state of greater stability by altering their exchange couplings.

scholarly journals Numerical investigations of stainless steel melt motions on the surface of uranium dioxide

2019 ◽  
Vol 196 ◽  
pp. 00005 ◽  
Author(s):  
Eduard V. Usov ◽  
Pavel D. Lobanov ◽  
Ilya A. Klimonov ◽  
Alexander E. Kutlimetov ◽  
Anton A. Butov ◽  
...  
Keyword(s):  
Stainless Steel ◽  
Uranium Dioxide ◽  
Momentum Conservation ◽  
Mass Energy ◽  
Numerical Investigations ◽  
Fuel Rod ◽  
The Core ◽  
Fuel Pin ◽  
Energy And Momentum ◽  
Coolant Velocity

The paper contains the results of numerical simulation of stainless steel melt motions on the surface of uranium dioxide. The investigations are performed for purposes of understanding of the fuel rod behavior during the core disruptive accident in the fast reactors. The systems of mass, energy and momentum conservation equations are solved to simulate melt motion on the surface of the fuel pin. Heat transfer and friction between melt and pin's surface and melt and coolant flow are taken into consideration. The dependences of mass of the melt and the features of the melt motion on coolant velocity and contact angle between melt and surface of the fuel rod are presented.

scholarly journals THE SUPERLUMINAL NEUTRINOS FROM DEFORMED LORENTZ INVARIANCE

2012 ◽  
Vol 27 (33) ◽  
pp. 1250196 ◽  
Author(s):  
YUNJIE HUO ◽  
TIANJUN LI ◽  
YI LIAO ◽  
DIMITRI V. NANOPOULOS ◽  
YONGHUI QI ◽  
...  
Keyword(s):  
Energy Conservation ◽  
Conservation Laws ◽  
Conservation Law ◽  
Lorentz Invariance ◽  
Momentum Conservation ◽  
Neutrino Energy ◽  
Dispersion Relations ◽  
Energy And Momentum ◽  
Energy Conservation Law ◽  
Neutrino Momentum

We study two superluminal neutrino scenarios where [Formula: see text] is a constant. To be consistent with the OPERA, Borexino and ICARUS experiments and with the SN1987a observations, we assume that δvν on the Earth is about three-order larger than that on the interstellar scale. To explain the theoretical challenges from the Bremsstrahlung effects and pion decays, we consider the deformed Lorentz invariance, and show that the superluminal neutrino dispersion relations can be realized properly while the modifications to the dispersion relations of the other Standard Model particles can be negligible. In addition, we propose the deformed energy and momentum conservation laws for a generic physical process. In Scenario I the momentum conservation law is preserved while the energy conservation law is deformed. In Scenario II the energy conservation law is preserved while the momentum conservation law is deformed. We present the energy and momentum conservation laws in terms of neutrino momentum in Scenario I and in terms of neutrino energy in Scenario II. In such formats, the energy and momentum conservation laws are exactly the same as those in the traditional quantum field theory with Lorentz symmetry. Thus, all the above theoretical challenges can be automatically solved. We show explicitly that the Bremsstrahlung processes are forbidden and there is no problem for pion decays.

scholarly journals An attempt to geometrize electromagnetism

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 848-853
Author(s):  
XiuLin Huang ◽  
Yan Xu ◽  
ChengZhi Liu
Keyword(s):  
Reference Frames ◽  
World Line ◽  
Equation Of Motion ◽  
Unified Theory ◽  
Mass Ratio ◽  
Classical Electromagnetism ◽  
Lorentz Covariance ◽  
Flat Spacetime ◽  
Lorentz Equation ◽  
Equivalent Equation

AbstractThis study investigates the curved worldline of a charged particle accelerated by an electromagnetic field in flat spacetime. A new metric, which dependes on the charge-to-mass ratio and electromagnetic potential, is proposed to describe the curve characteristic of the world-line. The main result of this paper is that an equivalent equation of the Lorentz equation of motion is put forward based on a 4-dimensional Riemannian manifold defined by the metric. Using the Ricci rotation coefficients, the equivalent equation is self-consistently constructed. Additionally, the Lorentz equation of motion in the non-inertial reference frames is studied with the local Lorentz covariance of the equivalent equation. The model attempts to geometrize classical electromagnetism in the absence of the other interactions, and it is conducive to the establishment of the unified theory between electromagnetism and gravitation.

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