Static Systems: Probabilistic Input Uncertainty

2022 ◽  
pp. 54-90
1975 ◽  
Vol 26 ◽  
pp. 395-407
Author(s):  
S. Henriksen

The first question to be answered, in seeking coordinate systems for geodynamics, is: what is geodynamics? The answer is, of course, that geodynamics is that part of geophysics which is concerned with movements of the Earth, as opposed to geostatics which is the physics of the stationary Earth. But as far as we know, there is no stationary Earth – epur sic monere. So geodynamics is actually coextensive with geophysics, and coordinate systems suitable for the one should be suitable for the other. At the present time, there are not many coordinate systems, if any, that can be identified with a static Earth. Certainly the only coordinate of aeronomic (atmospheric) interest is the height, and this is usually either as geodynamic height or as pressure. In oceanology, the most important coordinate is depth, and this, like heights in the atmosphere, is expressed as metric depth from mean sea level, as geodynamic depth, or as pressure. Only for the earth do we find “static” systems in use, ana even here there is real question as to whether the systems are dynamic or static. So it would seem that our answer to the question, of what kind, of coordinate systems are we seeking, must be that we are looking for the same systems as are used in geophysics, and these systems are dynamic in nature already – that is, their definition involvestime.


In a recent paper Synge (1952) reformulated in current standard notation the basic principles of the theory of relativity of A. N. Whitehead and investigated the gravitational properties of a spherically symmetrical static distribution of matter. He applied this theory to the solar field and verified the result previously indicated by Whitehead (1922) that the theory is in good agreement with the local tests satisfied by Einstein’s general theory of relativity. The present paper extends the theory of Whitehead to non-static systems whose velocity and density distributions possess complete spherical symmetry about a spatial origin in a Galilean frame of reference. In particular, a uniformly expanding homogeneous world-model is constructed which differs significantly both from Milne’s model and that of special relativity. The motion of free particles and photons in this model is investigated and a formula for the law of red-shifts is derived.


Author(s):  
Baligh El Hefni ◽  
Daniel Bouskela
Keyword(s):  

2021 ◽  
Vol 4 (2) ◽  
Author(s):  
Selma Franca ◽  
Fabian Hassler ◽  
Ion Cosma Fulga

We show that scattering from the boundary of static, higher-order topological insulators (HOTIs) can be used to simulate the behavior of (time-periodic) Floquet topological insulators. We consider D-dimensional HOTIs with gapless corner states which are weakly probed by external waves in a scattering setup. We find that the unitary reflection matrix describing back-scattering from the boundary of the HOTI is topologically equivalent to a (D-1)-dimensional nontrivial Floquet operator. To characterize the topology of the reflection matrix, we introduce the concept of `nested' scattering matrices. Our results provide a route to engineer topological Floquet systems in the lab without the need for external driving. As benefit, the topological system does not suffer from decoherence and heating.


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