Analysis of the Hydrogen-Like Atom for Neuro-Oncology Based on Bloch’s NMR Flow Equation

2021 ◽  
pp. 219-246
Author(s):  
Michael O. Dada ◽  
Bamidele O. Awojoyogbe
Keyword(s):  
Flow Equation

Karakteristik aliran dua fase pada saluran ekspansi tiba-tiba

2018 ◽  
Vol 11 (1) ◽  
pp. 7
Author(s):  
Latif Ngudi Wibawanto ◽  
Budi Santoso ◽  
Wibawa Endra Juwana
Keyword(s):  
Standard Deviation ◽  
Flow Pattern ◽  
Flow Characteristic ◽  
Homogeneous Model ◽  
Flow Equation ◽  
Pressure Recovery ◽  
Sudden Expansion ◽  
Air Velocity ◽  
Model Flow ◽  
Two Phases

This research was conducted to find out the flow characteristic of two phases through the channel with sudden expansion in the form of change of flow pattern and pressure recovery. The test was carried out with variation of superficial velocity of water 0.2-1.3 m / s and superficial air velocity of 0.2-1.9 m / s resulting in pattern of three flow patterns ie bubble, plug, and slug. The expansion channel resulted in some changes to the flow pattern that originally plugs in the upstream channel into bubble in the downstream channel and the slug becomes plug. Pressure recovery experimental results compared with the homogeneous model flow equation and Wadle correlation, both correlations have predictions with standard deviation values of 0.32 and 0.43.

Algebraic Solution of the Horton-Izzard Turbulent Overland Flow Model of the Rising Hydrograph

1977 ◽  
Vol 8 (4) ◽  
pp. 249-256 ◽  
Author(s):  
Mohammad Akram Gill
Keyword(s):  
Differential Equation ◽  
Turbulent Flow ◽  
Flow Model ◽  
Overland Flow ◽  
Flow Equation ◽  
Algebraic Solution ◽  
Mixed Flow ◽  
Overland Flow Model

In the differential equation of the overland turbulent flow which was first postulated by Horton, Eq.(6), the value of c equals 5/3. For this value of c, the flow equation could not be integrated algebraically. Horton solved the equation for c = 2 and believed that his solution was valid for mixed flow. The flow equation with c = 5/3 is solved algebraically herein. It is shown elsewhere (Gill 1976) that the flow equation can indeed be integrated for any rational value of c.

A possible modification of groundwater flow equation using coordinate transformations

2014 ◽  
Vol 15 (2) ◽  
pp. 278-287 ◽  
Author(s):  
Abdon Atangana ◽  
Ernestine Alabaraoye
Keyword(s):  
Groundwater Flow ◽  
Prolate Spheroid ◽  
Flow Equation ◽  
Time Space ◽  
Adomian Decomposition ◽  
Iteration Methods ◽  
Groundwater Flow Equation ◽  
Factor Α ◽  
Modified Equation ◽  
Good Agreement

We described a groundwater model with prolate spheroid coordinates, and introduced a new parameter, namely τ the silhouette influence of the geometric under which the water flows. At first, we supposed that the silhouette influence approaches zero; under this assumption, the modified equation collapsed to the ordinary groundwater flow equation. We proposed an analytical solution to the standard version of groundwater as a function of time, space and uncertainty factor α. Our proposed solution was in good agreement with experimental data. We presented a good approximation to the exponential integral. We obtained an asymptotic special solution to the modified equation by means of the Adomian decomposition and variational iteration methods.

scholarly journals $$ T\overline{T} $$-like flows in non-linear electrodynamic theories and S-duality

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
H. Babaei-Aghbolagh ◽  
Komeil Babaei Velni ◽  
Davood Mahdavian Yekta ◽  
H. Mohammadzadeh
Keyword(s):  
Type Theory ◽  
Free Action ◽  
Momentum Tensor ◽  
Flow Equation ◽  
Supersymmetric Model ◽  
Deformation Problem ◽  
Dimensional Spacetime ◽  
Non Linear ◽  
The Relationship ◽  
Simple Integration

Abstract We investigate the $$ T\overline{T} $$ T T ¯ -like flows for non-linear electrodynamic theories in D(=2n)-dimensional spacetime. Our analysis is restricted to the deformation problem of the classical free action by employing the proposed $$ T\overline{T} $$ T T ¯ operator from a simple integration technique. We show that this flow equation is compatible with $$ T\overline{T} $$ T T ¯ deformation of a scalar field theory in D = 2 and of a non-linear Born-Infeld type theory in D = 4 dimensions. However, our computation discloses that this kind of $$ T\overline{T} $$ T T ¯ flow in higher dimensions is essentially different from deformation that has been derived from the AdS/CFT interpretations. Indeed, the gravity that may be exist as a holographic dual theory of this kind of effective Born-Infeld action is not necessarily an AdS space. As an illustrative investigation in D = 4, we shall also show that our construction for the $$ T\overline{T} $$ T T ¯ operator preserves the original SL(2, ℝ) symmetry of a non-supersymmetric Born-Infeld theory, as well as $$ \mathcal{N} $$ N = 2 supersymmetric model. It is shown that the corresponding SL(2, ℝ) invariant action fixes the relationship between the $$ T\overline{T} $$ T T ¯ operator and quadratic form of the energy-momentum tensor in D = 4.

scholarly journals Relating a Rate-Independent System and a Gradient System for the Case of One-Homogeneous Potentials

2021 ◽  
Author(s):  
Alexander Mielke
Keyword(s):  
Gradient Flow ◽  
Careful Analysis ◽  
Flow Equation ◽  
Uniqueness Result ◽  
Gradient System ◽  
Independent System ◽  
Exact Relation ◽  
Flow Equations ◽  
Total Variation Flow ◽  
Energetic Solutions

AbstractWe consider a non-negative and one-homogeneous energy functional $${{\mathcal {J}}}$$ J on a Hilbert space. The paper provides an exact relation between the solutions of the associated gradient-flow equations and the energetic solutions generated via the rate-independent system given in terms of the time-dependent functional $${{\mathcal {E}}}(t,u)= t {{\mathcal {J}}}(u)$$ E ( t , u ) = t J ( u ) and the norm as a dissipation distance. The relation between the two flows is given via a solution-dependent reparametrization of time that can be guessed from the homogeneities of energy and dissipations in the two equations. We provide several examples including the total-variation flow and show that equivalence of the two systems through a solution dependent reparametrization of the time. Making the relation mathematically rigorous includes a careful analysis of the jumps in energetic solutions which correspond to constant-speed intervals for the solutions of the gradient-flow equation. As a major result we obtain a non-trivial existence and uniqueness result for the energetic rate-independent system.

scholarly journals Modeling an Aquifer: Numerical Solution to the Groundwater Flow Equation

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
V. Vázquez-Báez ◽  
A. Rubio-Arellano ◽  
D. García-Toral ◽  
I. Rodríguez Mora
Keyword(s):  
Stationary Flow ◽  
Flow Equation ◽  
Computational Tool ◽  
Groundwater Dynamics ◽  
Isotropic Media ◽  
Groundwater Flow Equation ◽  
The Finite Difference Method ◽  
Anisotropic Soil ◽  
Constant Slope

We present a model of groundwater dynamics under stationary flow and, governed by Darcy’s law of water motion through porous media, we apply it to study a 2D aquifer with water table of constant slope comprised of a homogeneous and isotropic media; the more realistic case of an homogeneous anisotropic soil is also considered. Taking into account some geophysical parameters we develop a computational routine, in the Finite Difference Method, which solves the resulting elliptic partial equation, both in a homogeneous isotropic and in a homogeneous anisotropic media. After calibration of the numerical model, this routine is used to begin a study of the Ayamonte-Huelva aquifer in Spain, a modest analysis of the system is given, and we compute the average discharge vector as well as its root mean square as a first predictive approximation of the flux in this system, providing us a signal of the location of best exploitation; long term goal is to develop a complete computational tool for the analysis of groundwater dynamics.

Theory and Application of the Parallel-Plate Plastimeter. Part 2

1935 ◽  
Vol 8 (4) ◽  
pp. 587-596 ◽  
Author(s):  
J. R. Scott
Keyword(s):  
Plastic Flow ◽  
Parallel Plate ◽  
Plastic Material ◽  
Compressive Load ◽  
Flow Equation ◽  
Simple Type ◽  
Plastic Properties ◽  
Further Development ◽  
Rubber Stock ◽  
Existing Data

Abstract In Part I (loc. cit.) the behavior of a plastic material in the parallel-plate (Williams) plastimeter was studied, and an expression was deduced showing how the rate of decrease in thickness of the sample during compression depends on the volume of the sample, its plastic properties, the compressive load, and the thickness itself. Subsequently, observations were published which showed that the basic principle adopted in this study was incorrect in certain particulars. Peek (loc. cit.), using these observations as a basis, deduced a new expression for the rate of decrease in thickness, though this is too complex for convenient practical use, except in an approximate simplified form. It has now been shown that the expression deduced in Part I, in spite of the inaccurate basis used, is sufficiently near to the truth to render substantially correct the conclusions there stated concerning the plastic properties of unvulcanized rubber stocks. By adopting the more accurate basis used by Peek, moreover, expressions for the rate of decrease in thickness can be deduced for materials showing more complex types of plastic flow than that considered in Part I or by Peek; this had proved impossible by the method previously used. The expression obtained by Peek for the simple type of plastic flow, as well as those now deduced for the more complex types, can be expressed in a form that furnishes a simple and rapid method of examining and analyzing experimental results. As a result of the work described in this paper, it is thus possible to determine, from results obtained with the parallel-plate plastimeter, whether or not a material such as unvulcanized rubber stock exhibits any of the types of plastic flow represented in the general form by Equation 1, and, if so, to find the values of the plastic constants of the material. The procedure is similar to that described in Part I, and consists simply in comparing, by superposition, a set of standard curves drawn on transparent paper with the curve plotted from experimental data. This further development of the method of studying plastic properties by means of the parallel-plate plastimeter should greatly increase its utility as an instrument of research. It has not yet been possible to apply the new method to a systematic study of rubber stocks, but from an examination of existing data it appears that these stocks, tested at 90° C., agree approximately with various forms of the generalized plastic flow equation already referred to.

An Optimal Control Method Based on the Energy Flow Equation

2009 ◽  
Vol 17 (4) ◽  
pp. 866-875 ◽  
Author(s):  
N. Fukushima ◽  
M.S. Arslan ◽  
I. Hagiwara
Keyword(s):  
Optimal Control ◽  
Energy Flow ◽  
Control Method ◽  
Flow Equation ◽  
Optimal Control Method
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