scholarly journals Noether’s theorem in statistical mechanics

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Sophie Hermann ◽  
Matthias Schmidt
Keyword(s):  
Rotational Symmetry ◽  
Center Of Mass ◽  
Functional Differentiation ◽  
Mass Motion ◽  
Brownian Particles ◽  
Standard Application ◽  
Temporal Coupling ◽  
Spatio Temporal ◽  
Many Body Systems ◽  
External Forces

AbstractNoether’s calculus of invariant variations yields exact identities from functional symmetries. The standard application to an action integral allows to identify conservation laws. Here we rather consider generating functionals, such as the free energy and the power functional, for equilibrium and driven many-body systems. Translational and rotational symmetry operations yield mechanical laws. These global identities express vanishing of total internal and total external forces and torques. We show that functional differentiation then leads to hierarchies of local sum rules that interrelate density correlators as well as static and time direct correlation functions, including memory. For anisotropic particles, orbital and spin motion become systematically coupled. The theory allows us to shed new light on the spatio-temporal coupling of correlations in complex systems. As applications we consider active Brownian particles, where the theory clarifies the role of interfacial forces in motility-induced phase separation. For active sedimentation, the center-of-mass motion is constrained by an internal Noether sum rule.

NUCLEON IN NUCLEAR MEDIUM

2009 ◽  
Vol 18 (05n06) ◽  
pp. 1166-1175
Author(s):  
SHASHIKANT C. PHATAK
Keyword(s):  
Standard Procedure ◽  
Center Of Mass ◽  
Critical Density ◽  
Magnetic Interaction ◽  
Nuclear Medium ◽  
Mass Motion ◽  
Field Equations ◽  
Dielectric Model ◽  
Chiral Color Dielectric Model

The behavior of a nucleon in nuclear medium is discussed in Chiral Color Dielectric Model. It is assumed that the nucleons in nuclear medium produces a background dielectric field and the quark and dielectric field equations are solved self consistantly in presence of the dielectric field. A nucleon in nuclear medium is then constructed by means of standard procedure followed in chiral bag models. The corrections due to center of mass motion, color magnetic interaction and meson interaction are included. The calculations show that the nucleon becomes bigger in the medium but its mass does not change much. It is found that beyond a certian density, bound solutions in which quarks are bound in self-generated dielectric field are not possible. Thus, the calculations indicate that there is a critical density beyond which the matter consists of deconfined quarks.

De watervoorziening op de zandgronden

2019 ◽  
Vol 4 (2) ◽  
pp. 74-88
Author(s):  
BERT GROENEWOUDT
Keyword(s):  
Drinking Water ◽  
The Netherlands ◽  
Water Supply ◽  
Rural Areas ◽  
Functional Differentiation ◽  
16Th Century ◽  
14Th Century ◽  
Local Topography ◽  
Spatio Temporal ◽  
Settlement Landscape

Water supply in the sandy dry lands (the Netherlands). Spatio-temporal developments Wells as water facilities were standard elements of the Dutch settlement landscape only since the Roman period. At the same time (drinking) water facilities became largely detached from the local topography. The position of a well within a settlement became determined by that of its associated house, and its position relative to the house became more or less fixed. This reflects the functional and social subdivision of the farmhouse into two distinct sections: ‘front’ and ‘back’. Communal water facilities (socially important as well) seem to have been associated with nucleated settlement, and they always existed alongside private facilities. Communal (public) wells first appeared in towns around the 13th or 14th century, but in rural areas probably not until the 16th century. In different periods there is evidence for the expression of social and functional differentiation.

Spontaneous emission in a standing-wave cavity: Classical center-of-mass motion

1992 ◽  
Vol 46 (11) ◽  
pp. 7162-7178 ◽  
Author(s):  
W. Ren ◽  
J. D. Cresser ◽  
H. J. Carmichael
Keyword(s):  
Standing Wave ◽  
Spontaneous Emission ◽  
Center Of Mass ◽  
Mass Motion

Background Subtraction and Object Tracking via Key Frame-Based Rotational Symmetry Dynamic Texture

2018 ◽  
pp. 1431-1460
Author(s):  
Jeyabharathi D ◽  
Dejey D
Keyword(s):  
Object Tracking ◽  
Video Processing ◽  
Background Subtraction ◽  
Rotational Symmetry ◽  
Dynamic Texture ◽  
Statistical Parameters ◽  
Key Frame ◽  
Moving Average Model ◽  
Benchmark Datasets ◽  
Spatio Temporal

Developing universal methods for background subtraction and object tracking is one of the critical and hardest challenges in many video processing and computer-vision applications. To achieve superior foreground detection quality across unconstrained scenarios, a novel Two Layer Rotational Symmetry Dynamic Texture (RSDT) model is proposed, which avoids illumination variations by using two layers of spatio temporal patches. Spatio temporal patches describe both motion and appearance parameters in a video sequence. The concept of key frame is used to avoid redundant samples. Auto Regressive Integrated Moving Average model (ARIMA) (Hyndman & Rob, 2015) estimates the statistical parameters from the subspace. Uniform Local Derivative Pattern (LDP) (Zhang et al., 2010) acts as a feature for tracking objects in a video. Extensive experimental evaluations on a wide range of benchmark datasets validate the efficiency of RSDT compared to Center Symmetric Spatio Temporal Local Ternary Pattern (CS-STLTP) (Lin et al., 2015) for unconstrained video analytics.

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