scholarly journals Dendrogramic Representation of Data: CHSH Violation vs. Nonergodicity

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 971
Author(s):  
Oded Shor ◽  
Felix Benninger ◽  
Andrei Khrennikov
Keyword(s):  
Experimental Data ◽  
Clustering Algorithms ◽  
Realistic Model ◽  
Minkowski Geometry ◽  
Ultrametric Spaces ◽  
Chsh Inequality ◽  
Classical Quantum ◽  
Basic Features ◽  
Totally Disconnected ◽  
Explicate Order

This paper is devoted to the foundational problems of dendrogramic holographic theory (DH theory). We used the ontic–epistemic (implicate–explicate order) methodology. The epistemic counterpart is based on the representation of data by dendrograms constructed with hierarchic clustering algorithms. The ontic universe is described as a p-adic tree; it is zero-dimensional, totally disconnected, disordered, and bounded (in p-adic ultrametric spaces). Classical–quantum interrelations lose their sharpness; generally, simple dendrograms are “more quantum” than complex ones. We used the CHSH inequality as a measure of quantum-likeness. We demonstrate that it can be violated by classical experimental data represented by dendrograms. The seed of this violation is neither nonlocality nor a rejection of realism, but the nonergodicity of dendrogramic time series. Generally, the violation of ergodicity is one of the basic features of DH theory. The dendrogramic representation leads to the local realistic model that violates the CHSH inequality. We also considered DH theory for Minkowski geometry and monitored the dependence of CHSH violation and nonergodicity on geometry, as well as a Lorentz transformation of data.

scholarly journals Dendrogramic Representation of Data: CHSH-Violation vs. Nonergodicity

2021 ◽  
Author(s):  
Oded Shor ◽  
Andrei Khrennikov ◽  
Felix Benninger
Keyword(s):  
Experimental Data ◽  
Time Series ◽  
Lorentz Transformation ◽  
Clustering Algorithms ◽  
Chsh Inequality ◽  
Classical Quantum ◽  
Basic Features ◽  
Totally Disconnected ◽  
Explicate Order

This paper is devoted to the foundational problems of dendrogramic holographic theory (DH-theory). We use the ontic-epistemic (implicate-explicate order) methodology. The epistemic counterpart is based on representation of data by dendrograms constructed with hierarchic clustering algorithms. The ontic Universe is described as the p-adic tree; it is zero dimensional, totally disconnected, disordered, and bounded (in p-adic ultrametric). Interrelation classical-quantum loses its sharpness; generally simple dendrograms are ``more quantum’’ than complex one. We use the CHSH-inequality as a measure of quantum(-likeness). We demonstrate that it can be violated by classical experimental data represented by dendrograms. The seed of this violation is neither nonlocality nor rejection of realism. This is nonergodicity of dendrogramic time series. Generally, violation of ergodicity is one of the basic features of DH-theory. We also consider DH-theory for Minkovski geometry and monitor the dependence of CHSH-violation and nonergodicity on geometry as well as a Lorentz transformation of data.

scholarly journals Representation of the Universe as a Dendrogramic Hologram Endowed With Relational Interpretation

2021 ◽  
Author(s):  
Andrei Khrennikov ◽  
Oded Shor ◽  
Felix Benninger
Keyword(s):  
Quantum Physics ◽  
Dimensional Space ◽  
Bell Inequality ◽  
Order Structure ◽  
Implicate Order ◽  
Classical Quantum ◽  
The Universe ◽  
Physical Quantities ◽  
Totally Disconnected ◽  
Explicate Order

proposal for a fundamental theory is described in which classical and quantum physics as a representation of the universe as a gigantic dendrogram are unified. The latter is the explicate order structure corresponding to the purely number-theoretical implicate order structure given by p-adic numbers. This number field was zero-dimensional, totally disconnected, and disordered. Physical systems (such as electrons, photons) are sub-dendrograms of the universal dendrogram. Measurement process is described as interactions among dendrograms; in particular, quantum measurement problems can be resolved using this process. The theory is realistic, but realism is expressed via the the Leibnitz principle of the Identity of Indiscernible. The classical-quantum interplay is based on the degree of indistinguishability between dendrograms (in which the ergodicity assumption is removed). Depending on this degree, some physical quantities behave more or less in a quantum manner (versus classic manner). Ideologically, our theory is very close to Smolin’s dynamics of difference and Rovelli’s relational quantum mechanics. The presence of classical behavior in nature implies a finiteness of the Universe-dendrogram. (Infinite Universe is considered to be purely quantum.) Reconstruction of events in a four-dimensional space type is based on the holographic principle. Our model reproduces Bell-type correlations in the dendrogramic framework. By adjusting dendrogram complexity, violation of the Bell inequality can be made larger or smaller.

The nucleon–nucleon interaction. II. Pseudoscalar mesons

1976 ◽  
Vol 54 (3) ◽  
pp. 333-341
Author(s):  
A. Z. Capri ◽  
D. Menon ◽  
R. Teshima
Keyword(s):  
Experimental Data ◽  
Realistic Model ◽  
Nucleon Nucleon ◽  
Nucleon Interaction ◽  
Scalar Mesons ◽  
Pseudoscalar Mesons ◽  
Spin Singlet ◽  
Nucleon Nucleon Interaction ◽  
Isospin Triplet

An earlier paper examined the role of scalar mesons in the nucleon–nucleon interaction. A more realistic model, with pseudoscalar mesons, is studied here. Unlike previous treatments of this problem, this approach seems to yield more repulsion than would be required to reproduce experimental data. Calculations are performed on the spin singlet, isospin triplet state; a brief discussion of the deuteron channel and the resulting potentials is also included.

Dendrodendritic Inhibition and Simulated Odor Responses in a Detailed Olfactory Bulb Network Model

2003 ◽  
Vol 90 (3) ◽  
pp. 1921-1935 ◽  
Author(s):  
Andrew P. Davison ◽  
Jianfeng Feng ◽  
David Brown
Keyword(s):  
Experimental Data ◽  
Spatial Distribution ◽  
Olfactory Bulb ◽  
Time Course ◽  
Granule Cells ◽  
Temporal Structure ◽  
Network Connectivity ◽  
Realistic Model ◽  
Mitral Cells ◽  
Dendrodendritic Synapses

In the olfactory bulb, both the spatial distribution and the temporal structure of neuronal activity appear to be important for processing odor information, but it is currently impossible to measure both of these simultaneously with high resolution and in all layers of the bulb. We have developed a biologically realistic model of the mammalian olfactory bulb, incorporating the mitral and granule cells and the dendrodendritic synapses between them, which allows us to observe the network behavior in detail. The cell models were based on previously published work. The attributes of the synapses were obtained from the literature. The pattern of synaptic connections was based on the limited experimental data in the literature on the statistics of connections between neurons in the bulb. The results of simulation experiments with electrical stimulation agree closely in most details with published experimental data. This gives confidence that the model is capturing features of network interactions in the real olfactory bulb. The model predicts that the time course of dendrodendritic inhibition is dependent on the network connectivity as well as on the intrinsic parameters of the synapses. In response to simulated odor stimulation, strongly activated mitral cells tend to suppress neighboring cells, the mitral cells readily synchronize their firing, and increasing the stimulus intensity increases the degree of synchronization. Preliminary experiments suggest that slow temporal changes in the degree of synchronization are more useful in distinguishing between very similar odorants than is the spatial distribution of mean firing rate.

scholarly journals Improved VIV Response Prediction Using Adaptive Parameters and Data Clustering

2020 ◽  
Vol 8 (2) ◽  
pp. 127
Author(s):  
Jie Wu ◽  
Decao Yin ◽  
Halvor Lie ◽  
Signe Riemer-Sørensen ◽  
Svein Sævik ◽  
...  
Keyword(s):  
Experimental Data ◽  
Data Clustering ◽  
Prediction Accuracy ◽  
Clustering Algorithms ◽  
Field Measurements ◽  
Response Prediction ◽  
Response Characteristics ◽  
Hydrodynamic Parameters ◽  
Adaptive Parameters ◽  
Using Data

Slender marine structures such as deep-water riser systems are continuously exposed to currents, leading to vortex-induced vibrations (VIV) of the structure. This may result in amplified drag loads and fast accumulation of fatigue damage. Consequently, accurate prediction of VIV responses is of great importance for the safe design and operation of marine risers. Model tests with elastic pipes have shown that VIV responses are influenced by many structural and hydrodynamic parameters, which have not been fully modelled in present frequency domain VIV prediction tools. Traditionally, predictions have been computed using a single set of hydrodynamic parameters, often leading to inconsistent prediction accuracy when compared with observed field measurements and experimental data. Hence, it is necessary to implement a high safety factor of 10–20 in the riser design, which increases development costs and adds extra constraints in the field operation. One way to compensate for the simplifications in the mathematical prediction model is to apply adaptive parameters to describe different riser responses. The objective of this work is to demonstrate a new method to improve the prediction consistency and accuracy by applying adaptive hydrodynamic parameters. In the present work, a four-step approach has been proposed: First, the measured VIV response will be analysed to identify key parameters to represent the response characteristics. These parameters will be grouped by using data clustering algorithms. Secondly, optimal hydrodynamic parameters will be identified for each data group by optimisation against measured data. Thirdly, the VIV response using the obtained parameters will be calculated and the prediction accuracy evaluated. Last but not least, classification algorithms will be applied to determine the correct hydrodynamic parameters to be used for new cases. An iteration of the previous steps may be needed if the prediction accuracy of the new case is not satisfactory. This concept has been demonstrated with examples from experimental data.

Computer Simulations of Airflow Field Around a Cube: Comparisons of LES and RANS Models

2010 ◽  
Author(s):  
Behtash Tavakoli ◽  
Goodarz Ahmadi
Keyword(s):  
Experimental Data ◽  
Computational Models ◽  
Transport Model ◽  
Separated Flow ◽  
Realistic Model ◽  
Navier Stokes ◽  
Reynolds Stress Transport Model ◽  
Rans Models ◽  
Airflow Field ◽  
Computationally Intensive

Simulations of flow field around wall mounted square cylinders have been used extensively for validation of computational models in the literature. In this paper the airflow fields around a square cylinder were simulated using the Reynolds Averaged Navier-Stokes (RANS) models as well as the Large Eddy Simulations (LES). Particular attention was given to the case with Reynolds number of 80,000 for which the experimental data of Hussein and Matinuzzi [1] are available. The nature of the 3D wakes behind the cube as well as the vortices in front and at the back of the cube were investigated. The simulation results were compared with the experimental data and the accuracy of different models were studied. While the LES better captured the features of this separated flow, it is computationally intensive. The Reynolds Stress Transport Model (RSTM) did not properly predict some features of this separated flow, but is comparatively more economical. The accuracy of RSTM for predicting the turbulence features of separated flows was discussed, and its application for the flow around a realistic model of a building was pointed out.

scholarly journals Bistability of buoyancy-driven exchange flows in vertical tubes

2018 ◽  
Vol 850 ◽  
pp. 525-550 ◽  
Author(s):  
Jenny Suckale ◽  
Zhipeng Qin ◽  
Davide Picchi ◽  
Tobias Keller ◽  
Ilenia Battiato
Keyword(s):  
Experimental Data ◽  
Annular Flow ◽  
Laboratory Experiments ◽  
Classical Problem ◽  
Data Interpretation ◽  
Analytical Models ◽  
Natural Systems ◽  
Exchange Flows ◽  
Basic Features ◽  
Vertical Tubes

Buoyancy-driven exchange flows are common to a variety of natural and engineering systems, ranging from persistently active volcanoes to counterflows in oceanic straits. Laboratory experiments of exchange flows have been used as surrogates to elucidate the basic features of such flows. The resulting data have been analysed and interpreted mostly through core–annular flow solutions, the most common flow configuration at finite viscosity contrasts. These models have been successful in fitting experimental data, but less effective at explaining the variability observed in natural systems. In this paper, we demonstrate that some of the variability observed in laboratory experiments and natural systems is a consequence of the inherent bistability of core–annular flow. Using a core–annular solution to the classical problem of buoyancy-driven exchange flows in vertical tubes, we identify two mathematically valid solutions at steady state: a solution with fast flow in a thin core and a solution with relatively slow flow in a thick core. The theoretical existence of two solutions, however, does not necessarily imply that the system is bistable in the sense that flow switching may occur. Through direct numerical simulations, we confirm the hypothesis that core–annular flow in vertical tubes is inherently bistable. Our simulations suggest that the bistability of core–annular flow is linked to the boundary conditions of the domain, which implies that is not possible to predict the realized flow field from the material parameters of the fluids and the tube geometry alone. Our finding that buoyancy-driven exchange flows are inherently bistable systems is consistent with previous experimental data, but is in contrast to the underlying hypothesis of previous analytical models that the solution is unique and can be identified by maximizing the flux or extremizing the dissipation in the system. Our results have important implications for data interpretation by analytical models and may also have interesting ramifications for understanding volcanic degassing.

scholarly journals Covid-19: Why Herd Immunity was not Approached Anywhere? Ultrametric Diffusion Modeling of Virus Spread in Hierarchically Clustered Population

2021 ◽  
Author(s):  
Andrei Khrennikov
Keyword(s):  
Herd Immunity ◽  
Disease Spread ◽  
The Novel ◽  
Virus Spread ◽  
Ultrametric Spaces ◽  
The Social ◽  
Standard Models ◽  
Models Of Disease ◽  
Basic Features ◽  
Novel Model

In spite of numerous predictions, the natural herd immunity for covid-19 visru had not been approahed anywhere in the world. Thus, the traditional mathematical models of disease spread demonstrated their inability to describe adequately the covid-19 pandemic. In author's works, the novel model of the disease spread was developed. This model reflects the basic features of the covid-19 pandemic: a) the social clustering character of virus spread, b) . Social clustering is mathematically modelled with ultrametric spaces having the treelike geometry encoding hierarchy of the regulation constraints. The virus spread is described by ultrametric diffusion or random walk on the hierarchic energy landscape. In contrast to the standard models which are characterized by the exponential decrease of the probability to become infected - at the stage of approaching of the herd immunity, the ultrametric model is characterized by the power law. Moreover, the model gives the possibility to quantify the influence of restriction measures up to the lockdown. Our main result is that the play with restrictions, including lockdowns, is counterproductive and leads to the essential slowdown of approaching the herd immunity or even makes this impossible.

scholarly journals On Carrier Diffusion in Nanostructures for Nanomedicine

2019 ◽  
Author(s):  
Paolo Di Sia
Keyword(s):  
Experimental Data ◽  
Time Domain ◽  
Domain Model ◽  
Analytical Modelling ◽  
Relativistic Case ◽  
Carrier Diffusion ◽  
Bulk Solids ◽  
Potential Applications ◽  
Classical Quantum ◽  
Analytical Time

Nanometer-sized particles have optical, magnetic, chemical and structural propertiessetting them apart from bulk solids, with fruitful potential applications in nanomedicine. Carrier diffusion at the nanoscale plays a very important role in the dynamics of the processes taking place at this scale. Advances in analytical modelling allow a detailed study of carrier diffusion in the classical, quantum and relativistic case. Important results and previsions come by a promising analytical “time-domain” model for classical and quantum-relativistic transport in nano systems, called DS model; it is demonstrating high generality and very good fitting with available experimental data of literature.

ELASTIC SCATTERING OF 28Si–27Al IN A REALISTIC OPTICAL POTENTIAL

1996 ◽  
Vol 05 (03) ◽  
pp. 533-541 ◽  
Author(s):  
M. RASHDAN
Keyword(s):  
Experimental Data ◽  
Elastic Scattering ◽  
Cross Section ◽  
Cross Sections ◽  
Differential Cross ◽  
Optical Potential ◽  
Realistic Model ◽  
Entire Energy Range ◽  
Entire Energy ◽  
Soft Core Potential

Within a realistic model for the optical potential between nuclei based on the solution of the Bethe-Goldstone equation with the Reid soft-core potential, the differential cross-sections of the 28 Si –27 Al system, recently measured at energies around the Coulomb barrier, are calculated. The experimental data are well-reproduced over the entire energy range without any adjustable parameters to fit the cross-section.

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