scholarly journals Proof Formalism General Quantum Density Commutator Matrix Physics

2021 ◽  
Author(s):  
Rajan Iyer
Keyword(s):  
Analytic Solutions ◽  
Inner Product ◽  
Hamiltonian Mechanics ◽  
Algebraic Equations ◽  
Level System ◽  
Scale Level ◽  
Outer Product ◽  
Macro Scale ◽  
Matrix Properties ◽  
General Derivation

Formalism proofing general derivation, applying matrix properties operations, showing fundamental relationships with inner product to outer product has been advanced here. This general proof formalism has direct application with physics to quantify quantum density at micro scale level to time commutator at macro scale level. System of operator algebraic equations have been rigorously derived to obtain analytic solutions which are physically acceptable. Extended physics application will include metricizing towards unitarization to achieve gaging Hamiltonian mechanics to electromagnetic gravitational strong theory, towards grand unifying physics atomistic to astrophysics or vice versa via quantum relativistic general physics thereby patching to classical physics fields energy.

scholarly journals Proof Formalism General Quantum Density Commutator Matrix Physics

2021 ◽  
Vol 5 (2) ◽  
pp. 1-5
Author(s):  
Iyer R
Keyword(s):  
Analytic Solutions ◽  
Inner Product ◽  
Hamiltonian Mechanics ◽  
Algebraic Equations ◽  
Level System ◽  
Scale Level ◽  
Outer Product ◽  
Macro Scale ◽  
Matrix Properties ◽  
General Derivation

Formalism proofing general derivation, applying matrix properties operations, showing fundamental relationships with inner product to outer product has been advanced here. This general proof formalism has direct application with physics to quantify quantum density at micro scale level to time commutator at macro scale level. System of operator algebraic equations has been rigorously derived to obtain analytic solutions which are physically acceptable. Extended physics application will include metricizing towards unitarization to achieve gaging Hamiltonian mechanics to electromagnetic gravitational strong theory, towards grand unifying physics atomistic to astrophysics or vice versa via quantum relativistic general physics thereby patching to classical physics fields energy.

scholarly journals Comparative Assessment of the Built-Up Area Expansion Based on Corine Land Cover and Landsat Datasets: A Case Study of a Post-Socialist City

2020 ◽  
Vol 12 (13) ◽  
pp. 2137 ◽  
Author(s):  
Ilinca-Valentina Stoica ◽  
Marina Vîrghileanu ◽  
Daniela Zamfir ◽  
Bogdan-Andrei Mihai ◽  
Ionuț Săvulescu
Keyword(s):  
Land Cover ◽  
Urban Expansion ◽  
Ground Truth ◽  
Cost Effective ◽  
Planning System ◽  
The European Union ◽  
Scale Level ◽  
Corine Land Cover ◽  
Macro Scale ◽  
Area Expansion

Monitoring uncontained built-up area expansion remains a complex challenge for the development and implementation of a sustainable planning system. In this regard, proper planning requires accurate monitoring tools and up-to-date information on rapid territorial transformations. The purpose of the study was to assess built-up area expansion, comparing two freely available and widely used datasets, respectively, Corine Land Cover and Landsat, to each other, as well as the ground truth, with the goal of identifying the most cost-effective and reliable tool. The analysis was based on the largest post-socialist city in the European Union, the capital of Romania, Bucharest, and its neighboring Ilfov County, from 1990 to 2018. This study generally represents a new approach to measuring the process of urban expansion, offering insights about the strengths and limitations of the two datasets through a multi-level territorial perspective. The results point out discrepancies between the datasets, both at the macro-scale level and at the administrative unit’s level. On the macro-scale level, despite the noticeable differences, the two datasets revealed the spatiotemporal magnitude of the expansion of the built-up area and can be a useful tool for supporting the decision-making process. On the smaller territorial scale, detailed comparative analyses through five case-studies were conducted, indicating that, if used alone, limitations on the information that can be derived from the datasets would lead to inaccuracies, thus significantly limiting their potential to be used in the development of enforceable regulation in urban planning.

scholarly journals Analytic solutions for a three-level system in a time-dependent field

2011 ◽  
Vol 240 (6) ◽  
pp. 542-545 ◽  
Author(s):  
Jan Naudts ◽  
Winny O’Kelly de Galway
Keyword(s):  
Analytic Solutions ◽  
Time Dependent ◽  
Level System ◽  
Dependent Field

Scattering of Anti-Plane SH-Wave by the Semi-Cylindrical Gap with Multiple Shallow-Buried Inclusions in Elastic Semi-Space

2012 ◽  
Vol 569 ◽  
pp. 78-81
Author(s):  
Hong Liang Li ◽  
Jing Guo ◽  
Li Ming Cai
Keyword(s):  
Displacement Field ◽  
Ground Surface ◽  
Analytic Solutions ◽  
Polar Coordinate System ◽  
Algebraic Equations ◽  
Sh Wave ◽  
Dynamic Stress Concentration Factor ◽  
Polar Coordinate ◽  
Cylindrical Inclusions ◽  
Plane Sh Wave

Semi-cylindrical gap and Multiple circular inclusions exists widely in natural media, composite materials and modern municipal construction. The scattering field produced by semi-cylindrical gap and multiple circular inclusions determines the dynamic stress concentration factor around the gap and circular inclusions, and therefore determines whether the material is damaged or not. These problems are complicated. It is hard to obtain analytic solutions except for several simple conditions. In this paper, the solution of displacement field for elastic semi-space with semi-cylindrical gap and multiple cylindrical inclusions by anti-plane SH-wave is constructed. In complex plane, considering the symmetry of SH-wave scattering , the displacement field aroused by the anti-plane SH-wave and the scattering displacement field impacted by the gap and the cylindrical inclusions comprised of Fourier-Bessel series with undetermined coefficients which satisfies the stress-free condition on the ground surface are constructed. Through applying the method of multi-polar coordinate system, the equations with unknown coefficients can be obtained by using the displacement and stress condition around the edge of the gap and cylindrical inclusions. According to orthogonality condition for trigonometric function, these equations can be reduced to a series of algebraic equations. Then the value of the unknown coefficients can be obtained by solving these algebraic equations. The total wave displacement field is the superposition of the displacement field aroused by the anti-plane SH-wave and the scattering displacement field. By using the expressions, an example is provided to show the effect of the change of relative location of the cylindrical inclusions.

NOISE ATTENUATION ON COMMON‐DEPTH‐POINT SEISMIC RECORDS BY A SEMIDETERMINISTIC APPROACH

Geophysics ◽  
1968 ◽  
Vol 33 (5) ◽  
pp. 723-733 ◽  
Author(s):  
John C. Robinson
Keyword(s):  
Frequency Domain ◽  
Random Noise ◽  
Analytic Solutions ◽  
Harmonic Spectrum ◽  
Algebraic Equations ◽  
Coherent Noise ◽  
Common Depth Point ◽  
Seismic Records ◽  
Point Data ◽  
The Time Domain

A simple seismic record synthesis for common‐depth‐point data was examined for analytic representation in terms of its harmonic spectrum. This frequency‐domain investigation revealed that the primary‐reflection signal can be completely recovered in the absence of random noise, or it can be better recovered in the presence of random noise than normal stacking affords, especially, if the coherent‐noise‐to‐random‐noise ratio is high. The success of this technique is founded upon the principle that difference equations in the time domain become algebraic equations in the frequency domain. The technique is partially “probabilistic” because analytic solutions for the primary‐reflection signal are stacked for further attenuation of noise. The constituents of the seismic records, after static and normal‐moveout corrections, are: identical, coincident, primary‐reflection signal; identical, time‐shifted coherent noise; and random noise. The coherent‐noise time shifts must be determined for application of the semideterministic technique; methods are discussed in the Data Processing section.

scholarly journals Study of interaction of C+ ion beam with a Si pitch grating on a macro-scale level

2012 ◽  
Vol 293 ◽  
pp. 11-15 ◽  
Author(s):  
Andreas Mutzke ◽  
Ivan Bizyukov ◽  
Hagen Langhuth ◽  
Matej Mayer ◽  
Karl Krieger ◽  
...  
Keyword(s):  
Ion Beam ◽  
Scale Level ◽  
Macro Scale

scholarly journals Enhancing a Junior Level Materials Lab with SEM Iimages

2011 ◽  
Author(s):  
Aezeden Mohamed ◽  
Ron Britton
Keyword(s):  
Aluminum Alloy ◽  
Fracture Surface ◽  
Alloy Steel ◽  
Team Work ◽  
Scale Level ◽  
Sem Images ◽  
Aluminum Alloy 6061 ◽  
Self Confidence ◽  
Macro Scale ◽  
Alloy 6061

Lab courses can enhance a student's communicationskills, provide opportunities to practice team work, and raise self-confidence early in their university experience, as well as impart valuable technical knowledge. Students ran impact Charpy tests on alloy steel 1045, and aluminum alloy 6061 as a function of temperature, and then analyzed and investigated by unaided eye the fracture surface in the two alloys at the macro-scale level. In this paper, micro-scale level investigation by the scanning electron microscopy (SEM) images introduced for the first time in this context to enhanced junior level materials lab. Keywords: Students: SEM images: alloy steel 1045; aluminum alloy 6061; fracture surface

Calculation of Nonlifting Potential Flow About Arbitrary Three-Dimensional Bodies

1964 ◽  
Vol 8 (04) ◽  
pp. 22-44 ◽  
Author(s):  
John L. Hess ◽  
A. M. O. Smith
Keyword(s):  
Body Surface ◽  
Potential Flow ◽  
Fluid Velocity ◽  
Normal Component ◽  
Three Dimensional ◽  
Analytic Solutions ◽  
The Body ◽  
Algebraic Equations ◽  
Source Density ◽  
Linear Algebraic Equations

A general method is described for calculating, with the aid of an electronic computer, the incompressible potential flow about arbitrary, nonlifting, three-dimensional bodies. The method utilizes a source density distribution on the surface of the body and solves for the distribution necessary to make the normal component of fluid velocity zero on the boundary. Plane quadrilateral surface elements are used to approximate the body surface, and the integral equation for the source density is replaced by a set of linear algebraic equations for the values of the source density on the quadrilateral elements. When this set of equations has been solved, the flow velocity both on and off the body surface is calculated. After the basic ideas and equations have been derived end discussed, the accuracy of the method is exhibited by means of comparisons with analytic solutions, and its usefulness is shown by comparing calculated pressure distributions with experimental data. Some of the design problems to which the method has been applied are also presented, to indicate the variety of flow situations that can be calculated by this approach.

The Effect of Thermal Waves on Heat Transfer Enhancement in Nanofluid Suspensions

2008 ◽  
Author(s):  
Johnathan J. Vadasz
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Heat Conduction ◽  
Heat Transfer Enhancement ◽  
Hyperbolic Heat Conduction ◽  
Thermal Waves ◽  
Transfer Enhancement ◽  
Scale Level ◽  
Macro Scale ◽  
Wave Effects

The spectacular heat transfer enhancement revealed experimentally in nanofluids suspensions is being investigated theoretically at the macro-scale level aiming at explaining the possible mechanisms that lead to such impressive experimental results. In particular, the anticipation that thermal wave effects via hyperbolic heat conduction could have been the source of the excessively improved effective thermal conductivity of the suspension is shown to be impossible.

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