9 Linear momentum and collisions

This work derives and applies a method for the investigation of numerical accuracy in computational fluid dynamics. The method is used to investigate discretization errors in computations of swirling flow in water turbines. The work focuses on the conservation of a subset of the angular momentum equations that is particularly important to swirling flow in water turbines. The method is based on the fact that the discretized angular momentum equations are not necessarily conserved when the discretized linear momentum equations are solved. However, the method can be used to investigate the effect of discretization on any equation that should be conserved in the correct solution, and the application is not limited to water turbines. Computations made for two Kaplan water turbine runners and a simplified geometry of one of the Kaplan runner ducts are investigated to highlight the general and simple applicability of the method.

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Imaging of spatial many-body wave functions via linear momentum measurements

Physical Chemistry Chemical Physics ◽

10.1039/c3cp53300j ◽

2014 ◽

Vol 16 (2) ◽

pp. 453-457 ◽

Cited By ~ 10

Author(s):

Peer C. Fechner ◽

Hanspeter Helm

Keyword(s):

Body Wave ◽

Linear Momentum ◽

Wave Functions ◽

Many Body

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Diffusion and dissipation by linear momentum in spherical environment

International Journal of Modern Physics B ◽

10.1142/s0217979214500775 ◽

2014 ◽

Vol 28 (11) ◽

pp. 1450077

Author(s):

Werner Scheid ◽

Aurelian Isar ◽

Aurel Sandulescu

Keyword(s):

Potential Energy ◽

Density Matrix ◽

Finite Number ◽

Bessel Functions ◽

Open Quantum System ◽

Equation Of Motion ◽

Linear Momentum ◽

Spherical Space ◽

Infinite Energy ◽

Infinite Wall

An open quantum system is studied consisting of a particle moving in a spherical space with an infinite wall. With the theory of Lindblad the system is described by a density matrix which gets affected by operators with diffusive and dissipative properties depending on the linear momentum and density matrix only. It is shown that an infinite number of basis states leads to an infinite energy because of the infinite unsteadiness of the potential energy at the infinite wall. Therefore only a solution with a finite number of basis states can be performed. A slight approximation is introduced into the equation of motion in order that the trace of the density matrix remains constant in time. The equation of motion is solved by the method of searching eigenvalues. As a side-product two sums over the zeros of spherical Bessel functions are found.

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Lifshitz hydrodynamics at generic z from a moving black brane

Journal of High Energy Physics ◽

10.1007/jhep07(2021)197 ◽

2021 ◽

Vol 2021 (7) ◽

Author(s):

Aruna Rajagopal ◽

Larus Thorlacius

Keyword(s):

Field Theory ◽

Steady State ◽

Critical Exponent ◽

Stress Tensor ◽

Perfect Fluid ◽

Scale Invariance ◽

Linear Momentum ◽

Black Brane ◽

Dilaton Gravity ◽

Non Equilibrium

Abstract A Lifshitz black brane at generic dynamical critical exponent z > 1, with non-zero linear momentum along the boundary, provides a holographic dual description of a non-equilibrium steady state in a quantum critical fluid, with Lifshitz scale invariance but without boost symmetry. We consider moving Lifshitz branes in Einstein-Maxwell-Dilaton gravity and obtain the non-relativistic stress tensor complex of the dual field theory via a suitable holographic renormalisation procedure. The resulting black brane hydrodynamics and thermodynamics are a concrete holographic realization of a Lifshitz perfect fluid with a generic dynamical critical exponent.

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Propagation Characteristics of Vortex Beam Using Visualization Analysis in Free Space

Journal of Nanoelectronics and Optoelectronics ◽

10.1166/jno.2021.2990 ◽

2021 ◽

Vol 16 (5) ◽

pp. 838-843

Author(s):

Yan Zhang ◽

Minru Hao ◽

Min Shao ◽

Yunzhe Zhang

Keyword(s):

Optical Communication ◽

Free Space ◽

Simulation Analysis ◽

Propagation Distance ◽

Momentum Density ◽

Linear Momentum ◽

Propagation Characteristics ◽

Transverse Profile ◽

Vortex Beams ◽

Topological Charges

We theoretically analyze the linear momentum density and orbital angular momentum (OAM) propagation characteristics of Gaussian vortex beams in free space, and perform detailed numerical simulation analysis of the linear momentum density and OAM propagation characteristics. Further, we study the variation of the propagation characteristics with different topological charges. In addition, we also analyzed the position of momentum in the transverse profile, where the momentum density of the spot will be broadened with propagation distance. This study can provide guidance for using vortex beams in optical communication and manipulation.

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