scholarly journals Thermophysical Investigation of Oldroyd-B Fluid with Functional Effects of Permeability: Memory Effect Study Using Non-Singular Kernel Derivative Approach

2021 ◽  
Vol 5 (3) ◽  
pp. 124 ◽  
Author(s):  
Muhammad Bilal Riaz ◽  
Jan Awrejcewicz ◽  
Aziz-Ur Rehman ◽  
Ali Akgül
Keyword(s):  
Heat Emission ◽  
Effect Study ◽  
Relative Increase ◽  
Fractional Models ◽  
Established Fact ◽  
Mathematical Techniques ◽  
Definition Of ◽  
Energy And Momentum ◽  
Thermophysical Investigation ◽  
Graphical Illustration

It is well established fact that the functional effects, such as relaxation and retardation of materials, can be measured for magnetized permeability based on relative increase or decrease during magnetization. In this context, a mathematical model is formulated based on slippage and non-slippage assumptions for Oldroyd-B fluid with magnetized permeability. An innovative definition of Caputo-Fabrizio time fractional derivative is implemented to hypothesize the constitutive energy and momentum equations. The exact solutions of presented problem, are determined by using mathematical techniques, namely Laplace transform with slipping boundary conditions have been invoked to tackle governing equations of velocity and temperature. The Nusselt number and limiting solutions have also been persuaded to estimate the heat emission rate through physical interpretation. In order to provide the validation of the problem, the absence of retardation time parameter led the investigated solutions with good agreement in literature. Additionally, comprehensively scrutinize the dynamics of the considered problem with parametric analysis is accomplished, the graphical illustration is depicted for slipping and non-slipping solutions for temperature and velocity. A comparative studies between fractional and non-fractional models describes that the fractional model elucidate the memory effects more efficiently.

The bouncing ball and the Grünwald-Letnikov definition of fractional derivative

2021 ◽  
Vol 24 (4) ◽  
pp. 1003-1014
Author(s):  
J. A. Tenreiro Machado
Keyword(s):  
Fractional Calculus ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Restitution Coefficient ◽  
Classical Physics ◽  
Bouncing Ball ◽  
Mechanical Experiment ◽  
Fractional Models ◽  
Definition Of

Abstract This paper proposes a conceptual experiment embedding the model of a bouncing ball and the Grünwald-Letnikov (GL) formulation for derivative of fractional order. The impacts of the ball with the surface are modeled by means of a restitution coefficient related to the coefficients of the GL fractional derivative. The results are straightforward to interpret under the light of the classical physics. The mechanical experiment leads to a physical perspective and allows a straightforward visualization. This strategy provides not only a motivational introduction to students of the fractional calculus, but also triggers possible discussion with regard to the use of fractional models in mechanics.

Assessment of Certainty of Ventilation Processes Mathematical Modeling

2015 ◽  
Vol 725-726 ◽  
pp. 1255-1260
Author(s):  
Tamara Daciuk ◽  
Vera Ulyasheva
Keyword(s):  
Mathematical Modeling ◽  
Turbulent Flows ◽  
Turbulence Models ◽  
Field Measurements ◽  
Heat Emission ◽  
Emission Sources ◽  
Wide Range ◽  
Calculation Results ◽  
Definition Of ◽  
Semiempirical Models

Numerical experiment has been successfully used during recent 10-15 years to solve a wide range of thermal and hydrogasodynamic tasks. Application of mathematical modeling used to design the ventilation systems for production premises characterized by heat emission may be considered to be an effective method to obtain reasonable solutions. Results of calculation performed with numerical solution of ventilation tasks depend on turbulence model selection. Currently a large number of different turbulence models used to calculate turbulent flows are known. Testing and definition of applicability limits for semiempirical models of turbulence should be considered to be a preliminary stage of calculation. This article presents results of test calculations pertaining to thermal air process modeling in premises characterized by presence of heat emission sources performed with employment of different models of turbulence. Besides, analysis of calculation results and comparison with field measurements data are presented.

scholarly journals The Total Energy and Momentum Stored in a Particle

2017 ◽  
Vol 9 (2) ◽  
pp. 65
Author(s):  
Eyal Brodet
Keyword(s):  
Total Energy ◽  
Special Relativity ◽  
Decay Time ◽  
Rest Mass ◽  
Minimum Time ◽  
Mass Energy ◽  
Light Velocity ◽  
Extra Energy ◽  
Definition Of ◽  
Energy And Momentum

In this paper we reconsider the conventional expressions given by special relativity to the energy and momentum of a particle. In the current framework, the particle's energy and momentum are computed using the particle's rest mass, M and rest mass time, t_m=h/M c^2  where t_m has the same time unit as conventionally used for the light velocity c. Therefore it is currently assumed that this definition of time describes the total kinetic and mass energy of a particle as given by special relativity. In this paper we will reexamine the above assumption and suggest describing the particle's energy as a function of its own particular decay time and not with respect to its rest mass time unit. Moreover we will argue that this rest mass time unit currently used is in fact the minimum time unit defined for a particle and that the particle may have more energy stored with in it. Experimental ways to search for this extra energy stored in particles such as electrons and photons are presented.

Output error MISO system identification using fractional models

2021 ◽  
Vol 24 (5) ◽  
pp. 1601-1618
Author(s):  
Abir Mayoufi ◽  
Stéphane Victor ◽  
Manel Chetoui ◽  
Rachid Malti ◽  
Mohamed Aoun
Keyword(s):  
System Identification ◽  
Optimization Algorithm ◽  
Simulation Analysis ◽  
Good Efficiency ◽  
Output Error ◽  
Single Output ◽  
Multiple Input ◽  
Fractional Models ◽  
Definition Of ◽  
Initialization Procedure

Abstract This paper deals with system identification for continuous-time multiple-input single-output (MISO) fractional differentiation models. An output error optimization algorithm is proposed for estimating all parameters, namely the coefficients and the differentiation orders. Given the high number of parameters to be estimated, the output error method can converge to a local minimum. Therefore, an initialization procedure is proposed to help the convergence to the optimum by using three variants of the algorithm. Moreover, a new definition of structured-commensurability (or S-commensurability) has been introduced to cope with the differentiation order estimation. First, a global S-commensurate order is estimated for all subsystems. Then, local S-commensurate orders are estimated (one for each subsystem). Finally the S-commensurability constraint being released, all differentiation orders are further adjusted. Estimating a global S-commensurate order greatly reduces the number of parameters and helps initializing the second variant, where local S-commensurate orders are estimated which, in turn, are used as a good initial hit for the last variant. It is known that such an initialization procedure progressively increases the number of parameters and provides good efficiency of the optimization algorithm. Monte Carlo simulation analysis are provided to evaluate the performances of this algorithm.

Computer Simulations

2019 ◽  
pp. 9-20
Author(s):  
Paul Humphreys
Keyword(s):  
Computer Simulation ◽  
Numerical Methods ◽  
Computer Simulations ◽  
Scientific Progress ◽  
Computational Science ◽  
Working Definition ◽  
Mathematical Techniques ◽  
Definition Of ◽  
Special Case ◽  
Numerical Treatments

The need to solve analytically intractable models has led to the rise of a new kind of science, computational science, of which computer simulations are a special case. It is noted that the development of novel mathematical techniques often drives scientific progress and that even relatively simple models require numerical treatments. A working definition of a computer simulation is given and the relation of simulations to numerical methods is explored. Examples where computational methods are unavoidable are provided. Some epistemological consequences for philosophy of science are suggested and the need to take into account what is possible in practice is emphasized.

scholarly journals Optimization of Radiators, Underfloor and Ceiling Heater Towards the Definition of a Reference Ideal Heater for Energy Efficient Buildings

2018 ◽  
Vol 8 (12) ◽  
pp. 2477 ◽  
Author(s):  
Andrea Ferrantelli ◽  
Karl-Villem Võsa ◽  
Jarek Kurnitski
Keyword(s):  
Energy Efficient ◽  
Heat Emission ◽  
Optimized Design ◽  
Maximum Heat ◽  
Operative Temperature ◽  
Energy Efficient Buildings ◽  
Building Enclosures ◽  
Analytical Formulas ◽  
The One ◽  
Definition Of

Heat emitters, as the primary devices used in space heating, cover a fundamental role in the energy efficient use of buildings. In the search for an optimized design, heating devices should be compared with a benchmark emitter with maximum heat emission efficiency. However, such an ideal heater still needs to be defined. In this paper we perform an analysis of heat transfer in a European reference room, considering surface effects of thermal radiation and computing the induced operative temperature (op.t.) both analytically and numerically. Our ideal heater is the one determining the highest op.t. By means of functional optimization, we analyse trends such as the variation of operative temperature with radiator panel dimensions, finding optimal configurations. To make our definitions as general as possible, we address panel radiators, convectors, underfloor (UFH) and ceiling heater. We obtain analytical formulas for the operative temperature induced by panel radiators and identify the 10-type as our ideal radiator, while the UFH provides the best performance overall. Regarding specifically UFH and ceiling heaters, we find optimal sizes providing maximum op.t. The analytical method and qualitative results reported in this paper can be generalized and adopted in most studies concerning the efficiency of different heat emitter types in building enclosures.

Discovering News Frames

2020 ◽  
pp. 702-721
Author(s):  
Loretta H. Cheeks ◽  
Tracy L. Stepien ◽  
Dara M. Wald ◽  
Ashraf Gaffar
Keyword(s):  
Machine Learning ◽  
Data Mining ◽  
Online News ◽  
Machine Learning Algorithms ◽  
News Frames ◽  
Water Insecurity ◽  
News Content ◽  
Making Sense ◽  
Mathematical Techniques ◽  
Definition Of

The Internet is a major source of online news content. Current efforts to evaluate online news content including text, storyline, and sources is limited by the use of small-scale manual techniques that are time consuming and dependent on human judgments. This article explores the use of machine learning algorithms and mathematical techniques for Internet-scale data mining and semantic discovery of news content that will enable researchers to mine, analyze, and visualize large-scale datasets. This research has the potential to inform the integration and application of data mining to address real-world socio-environmental issues, including water insecurity in the Southwestern United States. This paper establishes a formal definition of framing and proposes an approach for the discovery of distinct patterns that characterize prominent frames. The authors' experimental evaluation shows the proposed process is an effective approach for advancing semi-supervised machine learning and may assist in advancing tools for making sense of unstructured text.

Chronic Kidney Disease

2016 ◽  
pp. 565-570
Author(s):  
Carrie A. Schinstock
Keyword(s):  
Chronic Kidney Disease ◽  
Acute Kidney Injury ◽  
Renal Failure ◽  
Acute Renal Failure ◽  
Kidney Disease ◽  
Kidney Injury ◽  
Relative Increase ◽  
Absolute Increase ◽  
Definition Of ◽  
Stage 1

The term acute kidney injury (AKI) has replaced acute renal failure in contemporary medical literature. AKI denotes a rapid deterioration of kidney function within hours to weeks, resulting in the accumulation of nitrogenous metabolites in addition to fluid, electrolyte, and acid-base imbalances. The definition of AKI was refined to a 3-stage definition, with criteria for stage 1 as follows: 1) an absolute increase in serum creatinine (SCr) by at least 0.3 mg/dL from baseline within 48 hours; or 2) a relative increase in SCr to at least 1.5 times baseline within the past 7 days; or 3) urine output decreased to less than 0.5 mL/kg/h for 6 hours.

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