scholarly journals Symplectic gauge-invariant reformulation of a free-particle system on toric geometry

2021 ◽  
Vol 135 (1) ◽  
pp. 11002
Author(s):  
Anjali S ◽  
Saurabh Gupta
Keyword(s):  
Particle System ◽  
Free Particle ◽  
Toric Geometry ◽  
Gauge Invariant

scholarly journals BRST SYMMETRIES IN FREE PARTICLE SYSTEM ON TORIC GEOMETRY

2005 ◽  
Vol 20 (21) ◽  
pp. 1577-1588 ◽  
Author(s):  
SOON-TAE HONG
Keyword(s):  
Energy Spectrum ◽  
Particle System ◽  
Free Particle ◽  
Particle Dynamics ◽  
Toric Geometry ◽  
Symplectic Structures

We study a free particle system residing on a torus to investigate its Becci–Rouet–Stora–Tyutin symmetries associated with its Stückelberg coordinates, ghosts and anti-ghosts. By exploiting zeibein frame on the toric geometry, we evaluate energy spectrum of the system to describe the particle dynamics. We also investigate symplectic structures involved in the free particle system on the torus.

On the Volume Fraction Effects of Inertial Colliding Particles in Homogeneous Isotropic Turbulence

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
Martin Ernst ◽  
Martin Sommerfeld
Keyword(s):  
Fluid Flow ◽  
Particle Motion ◽  
Isotropic Turbulence ◽  
Volume Fraction ◽  
Particle System ◽  
Free Particle ◽  
Particle Diameter ◽  
Homogeneous Isotropic Turbulence ◽  
Particle Collisions ◽  
Carrier Fluid

Abstract The main objective of the present study is the investigation of volume fraction effects on the collision statistics of nonsettling inertial particles in a granular medium as well as suspended in an unsteady homogeneous isotropic turbulent flow. For this purpose, different studies with mono-disperse Lagrangian point-particles having different Stokes numbers are considered in which the volume fraction of the dispersed phase is varied between 0.001 and 0.01. The fluid behavior is computed using a three-dimensional Lattice-Boltzmann method. The carrier-fluid turbulence is maintained at Taylor microscale Reynolds number 65.26 by applying a spectral forcing scheme. The Lagrangian particle tracking is based on considering the drag force only and a deterministic model is applied for collision detection. The influence of the particle phase on the fluid flow is neglected at this stage. The particle size is maintained at a constant value for all Stokes numbers so that the ratio of particle diameter to Kolmogorov length scale is fixed at 0.58. The variation of the particle Stokes number was realized by modifying the solids density. The observed particle Reynolds and Stokes numbers are in between [1.07, 2.61] and [0.34, 9.79], respectively. In the present simulations, the fluid flow and the particle motion including particle-particle collisions are based on different temporal discretization. Hence, an adaptive time stepping scheme is introduced. The particle motion as well as the occurrence of inter-particle collisions is characterized among others by Lagrangian correlation functions, the velocity angles between colliding particles and the collision frequencies. Initially, a fluid-free particle system is simulated and compared with the principles of the kinetic theory to validate the implemented deterministic collision model. Moreover, a selection of results obtained for homogeneous isotropic turbulence is compared with in literature available DNS and LES results as well. According to the performed simulations, the collision rate of particles with large Stokes numbers strongly depends on the adopted volume fraction, whereas for particles with small Stokes numbers the influence of particle volume fraction is less pronounced.

A NEW GEOMETRICAL FRAMEWORK FOR THE DE BROGLIE–BOHM QUANTUM THEORY

2013 ◽  
Vol 10 (03) ◽  
pp. 1250096 ◽  
Author(s):  
D. J. HURLEY ◽  
M. A. VANDYCK
Keyword(s):  
Quantum Theory ◽  
Bound States ◽  
Particle System ◽  
Zeeman Effect ◽  
Free Particle ◽  
Physical Space ◽  
Quantization Condition ◽  
Curvilinear Coordinates ◽  
Dimensional Manifold ◽  
De Broglie Bohm

A geometrical framework for the de Broglie–Bohm quantum theory is presented, in which the trajectories of an N-particle system are interpretable as the integral curves of a particular vector field defined on a 3N-dimensional manifold [Formula: see text] constructed from physical space M. It is mathematically valid even when M is curved. If M is flat, the usual theory is recovered and automatically expressed in whatever curvilinear coordinates one may wish to choose. The general construction is illustrated by the case of a free particle moving on the surface of a sphere. (A modified Bohr quantization condition for angular momentum is obtained, with a first correction proportional to the curvature.) The Zeeman effect and some bound states on the sphere are also considered.

scholarly journals NONLOCALITY AND ELLIPTICITY IN A GAUGE-INVARIANT QUANTIZATION

2000 ◽  
Vol 15 (03) ◽  
pp. 449-460 ◽  
Author(s):  
GIAMPIERO ESPOSITO ◽  
COSIMO STORNAIOLO
Keyword(s):  
Boundary Conditions ◽  
Mixed Boundary ◽  
Free Particle ◽  
Nonlocal Boundary ◽  
Mixed Boundary Conditions ◽  
Nonlocal Boundary Conditions ◽  
Two Dimensions ◽  
Boundary Operator ◽  
Positive Order ◽  
Gauge Invariant

The quantum theory of a free particle in two dimensions with nonlocal boundary conditions on a circle is known to lead to surface and bulk states. Such a scheme is here generalized to the quantized Maxwell field, subject to mixed boundary conditions. If the Robin sector is modified by the addition of a pseudo-differential boundary operator, gauge-invariant boundary conditions are obtained at the price of dealing with gauge-field and ghost operators which become pseudo-differential. A good elliptic theory is then obtained if the kernel occurring in the boundary operator obeys certain summability conditions, and it leads to a peculiar form of the asymptotic expansion of the symbol. The cases of ghost operator of negative and positive order are studied within this framework.

Real-time meshless deformation based on particle system and shape matching

2009 ◽  
Vol 28 (12) ◽  
pp. 3007-3009
Author(s):  
Wang-gen WAN ◽  
Ji-cheng LIN ◽  
Xiao-qing YU ◽  
Huan DING ◽  
Xiao-hui TAN
Keyword(s):  
Real Time ◽  
Shape Matching ◽  
Particle System
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