Flow Map Processing by Space-Time Deformation

Weintend to use the description oftheelectron orbital trajectory in the de Broglie-Bohm (dBB) theory to assimilate to a geodesiccorresponding to the General Relativity (GR) and get from itphysicalconclusions. ThedBBapproachindicatesustheexistenceof a non-local quantumfield (correspondingwiththequantumpotential), anelectromagneticfield and a comparativelyveryweakgravitatoryfield, togetherwith a translationkineticenergyofelectron. Ifweadmitthatthosefields and kineticenergy can deformthespace time, according to Einstein'sfield equations (and to avoidtheviolationoftheequivalenceprinciple as well), we can madethehypothesisthatthegeodesicsof this space-time deformation coincide withtheorbitsbelonging to thedBBapproach (hypothesisthat is coherentwiththestabilityofmatter). Fromit, we deduce a general equation that relates thecomponentsofthemetric tensor. Thenwe find anappropriatemetric for it, bymodificationofanexactsolutionofEinstein'sfield equations, whichcorresponds to dust in cylindricalsymmetry. Thefoundmodelproofs to be in agreementwiththebasicphysicalfeaturesofthehydrogenquantum system, particularlywiththeindependenceoftheelectronkineticmomentum in relationwiththeorbit radius. Moreover, themodel can be done Minkowski-like for a macroscopicshortdistancewith a convenientelectionof a constant. According to this approach, theguiding function ofthewaveontheparticlecould be identifiedwiththedeformationsofthespace-time and thestabilityofmatterwould be easilyjustifiedbythe null accelerationcorresponding to a geodesicorbit.

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Data-Driven Model Reduction for Stochastic Burgers Equations

Entropy ◽

10.3390/e22121360 ◽

2020 ◽

Vol 22 (12) ◽

pp. 1360

Author(s):

Fei Lu

Keyword(s):

Energy Spectrum ◽

Space Time ◽

Time Step ◽

Burgers Equations ◽

Time Reduction ◽

Flow Map ◽

Invariant Densities ◽

Stability Limits ◽

Maximal Space ◽

Maximal Time

We present a class of efficient parametric closure models for 1D stochastic Burgers equations. Casting it as statistical learning of the flow map, we derive the parametric form by representing the unresolved high wavenumber Fourier modes as functionals of the resolved variable’s trajectory. The reduced models are nonlinear autoregression (NAR) time series models, with coefficients estimated from data by least squares. The NAR models can accurately reproduce the energy spectrum, the invariant densities, and the autocorrelations. Taking advantage of the simplicity of the NAR models, we investigate maximal space-time reduction. Reduction in space dimension is unlimited, and NAR models with two Fourier modes can perform well. The NAR model’s stability limits time reduction, with a maximal time step smaller than that of the K-mode Galerkin system. We report a potential criterion for optimal space-time reduction: the NAR models achieve minimal relative error in the energy spectrum at the time step, where the K-mode Galerkin system’s mean Courant–Friedrichs–Lewy (CFL) number agrees with that of the full model.

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Fluid Simulation with a Dense Space-Time Deformation via $$L_0$$ Gradient Minimization

Lecture Notes in Electrical Engineering - Frontier Computing ◽

10.1007/978-981-16-0115-6_12 ◽

2021 ◽

pp. 125-137

Author(s):

Kun Li ◽

Na Qi ◽

Qing Zhu

Keyword(s):

Space Time ◽

Fluid Simulation ◽

Time Deformation

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Hypermotion due to space-time deformation

International Journal of Modern Physics Conference Series ◽

10.1142/s2010194516601253 ◽

2016 ◽

Vol 41 ◽

pp. 1660125

Author(s):

Michael Fil’chenkov ◽

Yuri Laptev

Keyword(s):

Space Time ◽

Local Velocity ◽

Practical Realization ◽

Speed Of Light ◽

Time Deformation ◽

Superluminal Motion

A superluminal motion (hypermotion) via M. Alcubierre’s warp drive is considered. Parameters of the warp drive have been estimated. The equations of starship geodesics have been solved. The starship velocity have been shown to exceed the speed of light, with the local velocity relative to the deformed space-time being below it. Hawking’s radiation does not prove to affect the ship interior considerably. Difficulties related to a practical realization of the hypermotion are indicated.

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Huge Filaments as Regions of Space-Time Deformation

10.20944/preprints202005.0320.v1 ◽

2020 ◽

Author(s):

Irina Rozgacheva

Keyword(s):

Exact Solution ◽

Ideal Fluid ◽

Strain Tensor ◽

Space Time ◽

Local Region ◽

Time Deformation ◽

Christoffel Symbols ◽

Definition Of ◽

Anisotropic Deformation

Huge filaments with scales from several hundred megaparsecs to gigaparsecs are detected in the distribution of galaxies and clusters, quasars, gamma-bursters. The hypothesis on the nature of the huge filaments as regions of space-time deformation is proposed. An anisotropic deformation of the local region is described by the strain tensor, it depends on the velocities of matter. Galaxies get an extra velocity in the region, which leads to the formation of filamentary structures. The class of exact solution of the GR equations is constructed by introducing the special definition of the Christoffel symbols as function of the velocity of matter. With a definition of these symbols, the motion matter equation turns into identity. For the sake of simplicity, an ideal fluid is considered.

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Fluid Simulation with an L0 Based Optical Flow Deformation

Applied Sciences ◽

10.3390/app10186351 ◽

2020 ◽

Vol 10 (18) ◽

pp. 6351

Author(s):

Kun Li ◽

Na Qi ◽

Qing Zhu

Keyword(s):

Optical Flow ◽

Space Time ◽

Fluid Simulation ◽

Data Driven ◽

Deformation Model ◽

Deformation Method ◽

Time Deformation ◽

Flow Deformation ◽

Using Data ◽

Simulation Scheme

Fluid simulation can be automatically interpolated by using data-driven fluid simulations based on a space-time deformation. In this paper, we propose a novel data-driven fluid simulation scheme with the L0 based optical flow deformation method by matching two fluid surfaces rather than the L2 regularization. The L0 gradient smooth regularization can result in prominent structure of the fluid in a sparsity-control manner, thus the misalignment of the deformation can be suppressed. We adopt the objective function using an alternating minimization with a half-quadratic splitting for solving the L0 based optical flow deformation model. Experiment results demonstrate that our proposed method can generate more realistic fluid surface with the optimal space-time deformation under the L0 gradient smooth constraint than the L2 one, and outperform the state-of-the-art methods in terms of both objective and subjective quality.

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Data-driven Model Reduction for Stochastic Burgers Equations

10.20944/preprints202010.0076.v1 ◽

2020 ◽

Author(s):

Fei Lu

Keyword(s):

Energy Spectrum ◽

Space Time ◽

Time Step ◽

Burgers Equations ◽

Time Reduction ◽

Flow Map ◽

Invariant Densities ◽

Stability Limits ◽

Maximal Time ◽

Optimal Space

We present a class of efficient parametric closure models for 1D stochastic Burgers equations. Casting it as statistical learning of the flow map, we derive the parametric form by representing the unresolved high wavenumber Fourier modes as functionals of the resolved variables’ trajectory. The reduced models are nonlinear autoregression (NAR) time series models, with coefficients estimated from data by least squares. The NAR models can accurately reproduce the energy spectrum, the invariant densities, and the autocorrelations. Taking advantage of the simplicity of the NAR models, we investigate maximal and optimal space-time reduction. Reduction in space dimension is unlimited, and NAR models with two Fourier modes can perform well. The NAR model’s stability limits time reduction, with a maximal time step smaller than that of the K-mode Galerkin system. We report a potential criterion for optimal space-time reduction: the NAR models achieve minimal relative error in the energy spectrum at the time step where the K-mode Galerkin system’s mean CFL number agrees with the full model’s.

Download Full-text