scholarly journals Time-Dependent Lagrangian Energy Systems on Supermanifolds with Graph Bundles

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Cansel Aycan ◽  
Simge Şimşek
Keyword(s):  
Graph Theory ◽  
Mechanical Energy ◽  
Energy System ◽  
Geometric Interpretation ◽  
Time Dependent ◽  
Jet Bundles ◽  
Graph Manifold ◽  
Body And Soul ◽  
Energy Equations ◽  
Graph Bundle

The aim of this article is firstly to improve time-dependent Lagrangian energy equations using the super jet bundles on supermanifolds. Later, we adapted this study to the graph bundle. Thus, we created a graph bundle by examining the graph manifold structure in superspace. The geometric structures obtained for the mechanical energy system with superbundle coordinates were reexamined with the graph bundle coordinates. Thus, we were able to calculate the energy that occurs during the motion of a particle when we examine this motion with graph points. The supercoordinates on the superbundle structure of supermanifolds have been given for body and soul and also even and odd dimensions. We have given the geometric interpretation of this property in coordinates for the movement on graph points. Lagrangian energy equations have been applied to the presented example, and the advantage of examining the movement with graph points was presented. In this article, we will use the graph theory to determine the optimal motion, velocity, and energy of the particle, due to graph points. This study showed a physical application and interpretation of supervelocity and supertime dimensions in super-Lagrangian energy equations utilizing graph theory.

A time-dependent model for high-pressure discharges in narrow ablative capillaries

1993 ◽  
Vol 50 (1) ◽  
pp. 51-70 ◽  
Author(s):  
D. Zoler ◽  
S. Cuperman ◽  
J. Ashkenazy ◽  
M. Caner ◽  
Z. Kaplan
Keyword(s):  
High Pressure ◽  
Equation Of State ◽  
Time Dependent ◽  
Dimensional Model ◽  
Plasma Sources ◽  
One Dimensional ◽  
Space And Time ◽  
Dependent Model ◽  
Energy Equations ◽  
Time Dependent Model

A time-dependent quasi-one-dimensional model is developed for studying high- pressure discharges in ablative capillaries used, for example, as plasma sources in electrothermal launchers. The main features of the model are (i) consideration of ablation effects in each of the continuity, momentum and energy equations; (ii) use of a non-ideal equation of state; and (iii) consideration of space- and time-dependent ionization.

scholarly journals On known and less known relations of Leonhard Euler with Poland

2016 ◽  
Vol 15 ◽  
pp. 75-110
Author(s):  
Roman Sznajder ◽  
Keyword(s):  
Graph Theory ◽  
18Th Century ◽  
Mathematical Community ◽  
Geometric Interpretation ◽  
European Countries ◽  
Complex Numbers ◽  
And Topology ◽  
Bridge Problem ◽  
Leonhard Euler ◽  
The City

In this work we focus on research contacts of Leonhard Euler with Polish scientists of his era, mainly with those from the city of Gdańsk (then Gedanum, Danzig). L. Euler was the most prolific mathematician of all times, the most outstanding mathematician of the 18th century, and one of the best ever. The complete edition of his manuscripts is still in process (Kleinert 2015; Kleinert, Mattmüller 2007). Euler’s contacts with French, German, Russian, and Swiss scientists have been widely known, while relations with Poland, then one of the largest European countries, are still in oblivion. Euler visited Poland only once, in June of 1766, on his way back from Berlin to St. Petersburg. He was hosted for ten days in Warsaw by Stanisław II August Poniatowski, the last king of Poland. Many Polish scientists were introduced to Euler, not only from mathematical circles, but also astronomers and geographers. The correspondence of Euler with Gdańsk scientists and officials, including Carl L. Ehler, Heinrich Kühn and Nathanael M. von Wolf, originated already in the mid-1730s. We highlight the relations of L. Euler with H. Kühn, a professor of mathematics at the Danzig Academic Gymnasium and arguably the best Polish mathematician of his era. It was H. Kühn from whom Euler learned about the Königsberg Bridge Problem; hence one can argue that the beginning of the graph theory and topology of the plane originated in Gdańsk. In addition, H. Kühn was the first mathematician who proposed a geometric interpretation of complex numbers, the theme very much appreciated by Euler. Findings included in this paper are either unknown or little known to a general mathematical community.

Characteristics of Fully Developed Flow and Heat Transfer in Channels With Varying Wall Geometry

2013 ◽  
Vol 136 (2) ◽  
Author(s):  
Abhishek G. Ramgadia ◽  
Arun K. Saha
Keyword(s):  
Heat Transfer ◽  
Time Dependent ◽  
Navier Stokes ◽  
Fully Developed Flow ◽  
Flow And Heat Transfer ◽  
Collocated Grid ◽  
Wall Profile ◽  
Energy Equations ◽  
Volume Method ◽  
Wall Geometry

Present study focuses on numerical investigation of fully developed flow and heat transfer through three channels having sine-shaped, triangle-shaped, and arc-shaped wall profiles. All computations are performed at Reynolds number of 600. Finite volume method on collocated grid is used to solve the time-dependent Navier–Stokes and energy equations in primitive variable form. For all the geometries considered in the study, the ratios Hmin/Hmax and L/a are kept fixed to 0.4 and 8.0, respectively. The thermal performances of all the three wall configurations are assessed using integral parameters as well as instantaneous, time-averaged and fluctuating flow fields. The geometry with the sinusoidal-shaped wall profile is found to produce the best thermal properties as compared to the triangle-shaped and the arc-shaped profiles though the obtained heat transfer is the highest for the arc-shaped geometry.

Theoretical Investigation in Thermoelastohydrodynamic Lubrication With Non-Newtonian Lubricants Under Heavy Load Change

2004 ◽  
Author(s):  
Mongkol Mongkolwongrojn ◽  
Kasame Thammakosol
Keyword(s):  
Initial Conditions ◽  
Solid Lubricants ◽  
Solid Particles ◽  
Time Dependent ◽  
Line Contact ◽  
Heavy Load ◽  
Steady State Condition ◽  
Load Change ◽  
Load Function ◽  
Energy Equations

The time-dependent thermal compressible elastohydrodynamic (EHD) lubrication of sliding line contact has been developed to investigate the effect of a sudden load change. The time-dependent modified Reynolds equation with non-Newtonian fluids has been formulated using power law’s model. In this study, the non-Newtonian dilatant fluids for liquids-solid lubricants have been purposed experimentally using the common solid particles namely, Molybdenum disulfide (MoS2) and Polytetrafluoroethylene (PTFE). The simultaneous systems of modified Reynolds and elasticity and energy equations with initial conditions were solved numerically using multigrid multilevel technique. The performance characteristics of the thermoelastohydrodynamic under line contact were presented with varying time for the pressure distribution, temperature distribution and oil film thickness. The transient response of the line contact between two surfaces was simulated under a heavy step load function. The coefficients of friction were also presented in this work at steady state condition with varying particle concentration. This simulation showed a significant effect of liquid-solid on thermoelastohydrodynamic (TEHD) lubrication under heavy load conditions.

Effects of a Single Bump or Dent in Time Dependent Thermal Line EHD Lubrication

1994 ◽  
Vol 116 (1) ◽  
pp. 9-20 ◽  
Author(s):  
Farshid Sadeghi ◽  
Kyung-Hoon Kim
Keyword(s):  
Film Thickness ◽  
Elastohydrodynamic Lubrication ◽  
Transient Behavior ◽  
Time Dependent ◽  
Line Contact ◽  
Temperature Distributions ◽  
Ehd Lubrication ◽  
Pure Rolling ◽  
Energy Equations ◽  
Thermal Line

A time-dependent thermal compressible elastohydrodynamic lubrication of line contact model has been developed to investigate the effects of a single bump or dent in heavily loaded rolling/sliding contacts. The results illustrate the transient behavior of the film thickness, pressure and temperature distributions as a bump or a dent travels through the contact. The multigrid multilevel technique was used to simultaneously solve the discretized time dependent Reynolds, elasticity and energy equations. The effects of various loads and speeds have been investigated. Results are presented for the nondimensional loads of W = 1.3 × 10−4, 2.3 × 10−4 and nondimensional speeds ranging from U = 1 × 10−11 to U = 10−10 under pure rolling and rolling/sliding conditions.

Outpatient Hysteroscopic Polypectomy: Bipolar Energy System (Versapoint®) versus Mechanical Energy System (TRUCLEAR System®) - Preliminary Results

2015 ◽  
Vol 80 (1) ◽  
pp. 3-9 ◽  
Author(s):  
Jennifer Rovira Pampalona ◽  
Maria Degollada Bastos ◽  
Gemma Mancebo Moreno ◽  
Esther Ratia Garcia ◽  
Andrea Buron Pust ◽  
...  
Keyword(s):  
Mechanical Energy ◽  
Energy System ◽  
Preliminary Results ◽  
Bipolar Energy

Expanding of Fire-Ball and Subsequent Shock Wave Propagation by Explosives Detonation in Underwater

2011 ◽  
Author(s):  
Ho-Young Kwak ◽  
Ki-Moon Kang ◽  
Ilgon Ko
Keyword(s):  
Shock Wave ◽  
Pressure Wave ◽  
Similarity Solutions ◽  
Time Dependent ◽  
Uniform Density ◽  
Pressure Waves ◽  
Shock Wave Generation ◽  
Sudden Release ◽  
Energy Equations ◽  
Spherical Shock

A well known problem in hydrodynamics involves the sudden release of explosion energy, concentrated in a finite volume, to surroundings with uniform density. However, only similarity solutions which have no detailed information on the behavior of the fire-ball are available on this problem. In this study, we obtain a set of analytical solutions for the time dependent radius of expanding fire-ball after explosives detonation by solving continuity, Euler and energy equations with a “polytope” assumption for the fire-ball center. Subsequent spherical shock waves developed from the fire-ball in underwater are obtained by Kirkwood-Bethe hypothesis with Tait’s equation of state for water. The pressure waves emanating from the oscillating bubble in underwater, which has a notably different time scale from the shock wave generation, are obtained using the Rayleigh equation. The calculated results of period and the maximum radius of bubble developed from the fire-ball and the pressure wave from the oscillating bubble are similar to those observed.

Mechanical Analysis of a Solar-Powered Solid State Engine

1985 ◽  
Vol 9 (3) ◽  
pp. 137-141 ◽  
Author(s):  
H. Tobushi ◽  
J.R. Gahoon
Keyword(s):  
Solid State ◽  
Solar Energy ◽  
Photovoltaic Effect ◽  
Mechanical Energy ◽  
Energy System ◽  
Mechanical Analysis ◽  
Total Efficiency ◽  
Nitinol Wire ◽  
Higher Power ◽  
Solar Powered

The mechanical principle of a solar-powered solid state engine utilizing the shape-memory effect is analyzed. The performance of a differential pulley Nitinol engine is discussed and it is calculated that a small, solar-powered differential pulley Nitinol engine could produce up to 15W with a single Nitinol wire, A higher power solar Nitinol engine producing up to 15 kW is possible by using larger Nitinol wire, and over 1 MW may be expected by applying the higher power engine system. The size of the solar energy collector needed to generate mechanical energy via a Nitinol engine is estimated to be about 0.02 m2/W and the total efficiency of the engine predicted to be about 4%, The overall efficiency and economics of a solar-powered Nitinol engine should be in the same order as that of solar energy system utilizing the photovoltaic effect.

Geometric interpretation of fractional-order derivative

2016 ◽  
Vol 19 (5) ◽  
Author(s):  
Vasily E. Tarasov
Keyword(s):  
Differential Geometry ◽  
Fractional Order ◽  
Infinite Series ◽  
Fractional Derivatives ◽  
Geometric Interpretation ◽  
Order Derivative ◽  
Jet Bundles ◽  
Fractional Order Derivative ◽  
Integer Order ◽  
Derivatives Of

AbstractA new geometric interpretation of the Riemann-Liouville and Caputo derivatives of non-integer orders is proposed. The suggested geometric interpretation of the fractional derivatives is based on modern differential geometry and the geometry of jet bundles. We formulate a geometric interpretation of the fractional-order derivatives by using the concept of the infinite jets of functions. For this interpretation, we use a representation of the fractional-order derivatives by infinite series with integer-order derivatives. We demonstrate that the derivatives of non-integer orders connected with infinite jets of special type. The suggested infinite jets are considered as a reconstruction from standard jets with respect to order.

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