scholarly journals Some Aspects of Lagrangian Dynamics of Turbulence

2017 ◽  
pp. 101-127
Author(s):  
Mickaël Bourgoin
Keyword(s):  
Lagrangian Dynamics

Center-of-mass variables in the relativistic Lagrangian dynamics of a system of particles

1994 ◽  
Vol 101 (3) ◽  
pp. 1443-1453 ◽  
Author(s):  
R. P. Gaida ◽  
V. I. Tretyak ◽  
Yu. G. Yaremko
Keyword(s):  
Center Of Mass ◽  
Lagrangian Dynamics ◽  
System Of Particles

scholarly journals Global weak solutions to the generalized mCH equation via characteristics

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Fanqin Zeng ◽  
Yu Gao ◽  
Xiaoping Xue
Keyword(s):  
Weak Solutions ◽  
Radon Measure ◽  
Measure Space ◽  
Blow Up ◽  
Space Time ◽  
Classical Solutions ◽  
Lagrangian Dynamics ◽  
Global Weak Solutions ◽  
Compactness Arguments ◽  
Mollification Method

<p style='text-indent:20px;'>In this paper, we study the generalized modified Camassa-Holm (gmCH) equation via characteristics. We first change the gmCH equation for unknowns <inline-formula><tex-math id="M1">\begin{document}$ (u,m) $\end{document}</tex-math></inline-formula> into its Lagrangian dynamics for characteristics <inline-formula><tex-math id="M2">\begin{document}$ X(\xi,t) $\end{document}</tex-math></inline-formula>, where <inline-formula><tex-math id="M3">\begin{document}$ \xi\in\mathbb{R} $\end{document}</tex-math></inline-formula> is the Lagrangian label. When <inline-formula><tex-math id="M4">\begin{document}$ X_\xi(\xi,t)&gt;0 $\end{document}</tex-math></inline-formula>, we use the solutions to the Lagrangian dynamics to recover the classical solutions with <inline-formula><tex-math id="M5">\begin{document}$ m(\cdot,t)\in C_0^k(\mathbb{R}) $\end{document}</tex-math></inline-formula> (<inline-formula><tex-math id="M6">\begin{document}$ k\in\mathbb{N},\; \; k\geq1 $\end{document}</tex-math></inline-formula>) to the gmCH equation. The classical solutions <inline-formula><tex-math id="M7">\begin{document}$ (u,m) $\end{document}</tex-math></inline-formula> to the gmCH equation will blow up if <inline-formula><tex-math id="M8">\begin{document}$ \inf_{\xi\in\mathbb{R}}X_\xi(\cdot,T_{\max}) = 0 $\end{document}</tex-math></inline-formula> for some <inline-formula><tex-math id="M9">\begin{document}$ T_{\max}&gt;0 $\end{document}</tex-math></inline-formula>. After the blow-up time <inline-formula><tex-math id="M10">\begin{document}$ T_{\max} $\end{document}</tex-math></inline-formula>, we use a double mollification method to mollify the Lagrangian dynamics and construct global weak solutions (with <inline-formula><tex-math id="M11">\begin{document}$ m $\end{document}</tex-math></inline-formula> in space-time Radon measure space) to the gmCH equation by some space-time BV compactness arguments.</p>

scholarly journals Lagrangian dynamics on matched pairs

2017 ◽  
Vol 111 ◽  
pp. 142-157 ◽  
Author(s):  
Oğul Esen ◽  
Serkan Sütlü
Keyword(s):  
Matched Pairs ◽  
Lagrangian Dynamics

Lagrangian Dynamics

1970 ◽  
Vol 38 (1) ◽  
pp. 115-116
Author(s):  
C. W. Kilminster ◽  
Ciaran Ryan
Keyword(s):  
Lagrangian Dynamics

LAGRANGIAN DYNAMICS

1974 ◽  
pp. 46-95
Author(s):  
RONALD A. MANN
Keyword(s):  
Lagrangian Dynamics

scholarly journals Lagrangian dynamics of the coupled field-medium state of light

2019 ◽  
Vol 21 (7) ◽  
pp. 073062 ◽  
Author(s):  
Mikko Partanen ◽  
Jukka Tulkki
Keyword(s):  
Lagrangian Dynamics ◽  
Coupled Field

scholarly journals Nature does not play Dice at the Planck scale

2020 ◽  
Vol 29 (14) ◽  
pp. 2043012
Author(s):  
Tejinder P. Singh
Keyword(s):  
Degrees Of Freedom ◽  
Large Scale ◽  
Planck Scale ◽  
Coarse Graining ◽  
Lagrangian Dynamics ◽  
Time Intervals ◽  
Spacetime Geometry ◽  
The Status ◽  
Planck Time ◽  
Matter Fields

We start from classical general relativity coupled to matter fields. Each configuration variable and its conjugate momentum, as also spacetime points are raised to the status of matrices [equivalently operators]. These matrices obey a deterministic Lagrangian dynamics at the Planck scale. By coarse-graining this matrix dynamics over time intervals much larger than Planck time, one derives quantum theory as a low energy emergent approximation. If a sufficiently large number of degrees of freedom get entangled, spontaneous localisation takes place, leading to the emergence of classical spacetime geometry and a classical universe. In our theory, dark energy is shown to be a large-scale quantum gravitational phenomenon. Quantum indeterminism is not fundamental, but results from our not probing physics at the Planck scale.

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