14 Multi-Compartmental System with Stochastic Input�Mathematical Formulation by the ito Calculus and its Application to Health Physics

2015 ◽  
pp. 156-165
Author(s):  
Shinobu Tatsunami ◽  
Nagasumi Yago ◽  
Nobuo Fukuda
Keyword(s):  
Mathematical Formulation ◽  
Compartmental System ◽  
Health Physics ◽  
Itô Calculus ◽  
Stochastic Input

A numerical method for fitting compartmental models directly to tracer data

1977 ◽  
Vol 233 (1) ◽  
pp. R1-R7 ◽  
Author(s):  
H. A. Feldman
Keyword(s):  
Computer Program ◽  
Exchange Rates ◽  
Numerical Method ◽  
Time Course ◽  
Bolus Injection ◽  
Mathematical Formulation ◽  
Compartmental Models ◽  
Compartmental System ◽  
Exponential Functions ◽  
Tracer Activity

A numerical method is presented for obtaining the exchange rates of a metabolic compartmental system, working directly from the time course of tracer activity and excretion after bolus injection. The conventional mathematical formulation of this problem, in terms of sums of exponential functions, is bypassed, enabling implementation of the method in a short computer program. An important by-product of the method is a set of variance-covariance estimates for the fitted parameters. The method is tested on "classic" data, both simulated and real. Its capabilities and limitations are demonstrated, and the strategy of its effective application is discussed.

Discussion of the Oblique Rotator Model Cases Of 108 Aqr and x Serp.

1976 ◽  
Vol 32 ◽  
pp. 577-588
Author(s):  
C. Mégessier ◽  
V. Khokhlova ◽  
T. Ryabchikova
Keyword(s):  
Mathematical Formulation ◽  
The Other ◽  
Rotator Model ◽  
Oblique Rotator ◽  
First Results

My talk will be on the oblique rotator model which was first proposed by Stibbs (1950), and since received success and further developments. I shall present two different attempts at describing a star according to this model and the first results obtained in the framework of a Russian-French collaboration in order to test the precision of the two methods. The aim is to give the best possible representation of the element distributions on the Ap stellar surfaces. The first method is the mathematical formulation proposed by Deutsch (1958-1970) and applied by Deutsch (1958) to HD 125248, by Pyper (1969) to α2CVn and by Mégessier (1975) to 108 Aqr. The other one was proposed by Khokhlova (1974) and used by her group.

Burgers fluid flow in perspective of Buongiorno’s model with improved heat and mass flux theory for stretching cylinder

2020 ◽  
Vol 92 (3) ◽  
pp. 31101
Author(s):  
Zahoor Iqbal ◽  
Masood Khan ◽  
Awais Ahmed
Keyword(s):  
Diffusion Process ◽  
Mathematical Formulation ◽  
Thermal Relaxation ◽  
Mass Diffusion ◽  
Stretching Cylinder ◽  
Discussion Section ◽  
Buongiorno’S Model ◽  
Homotopy Analysis ◽  
Burgers Fluid ◽  
Diffusion Phenomena

In this study, an effort is made to model the thermal conduction and mass diffusion phenomena in perspective of Buongiorno’s model and Cattaneo-Christov theory for 2D flow of magnetized Burgers nanofluid due to stretching cylinder. Moreover, the impacts of Joule heating and heat source are also included to investigate the heat flow mechanism. Additionally, mass diffusion process in flow of nanofluid is examined by employing the influence of chemical reaction. Mathematical modelling of momentum, heat and mass diffusion equations is carried out in mathematical formulation section of the manuscript. Homotopy analysis method (HAM) in Wolfram Mathematica is utilized to analyze the effects of physical dimensionless constants on flow, temperature and solutal distributions of Burgers nanofluid. Graphical results are depicted and physically justified in results and discussion section. At the end of the manuscript the section of closing remarks is also included to highlight the main findings of this study. It is revealed that an escalation in thermal relaxation time constant leads to ascend the temperature curves of nanofluid. Additionally, depreciation is assessed in mass diffusion process due to escalating amount of thermophoretic force constant.

INFLUENCE OF FLOW SWIRLING ON COMBUSTION OF ALUMINUM POWDER AEROSUSPENSION IN A CHAMBER WITH EXTENSION

2020 ◽  
Author(s):  
A. Yu. Krainov ◽  
◽  
K. M. Moiseeva ◽  
V. A. Poryazov ◽  
◽  
...  
Keyword(s):  
Dynamic Model ◽  
Aluminum Powder ◽  
Swirling Flow ◽  
Numerical Study ◽  
Mathematical Formulation ◽  
Expansion Chamber ◽  
Flow Swirling ◽  
Air Suspension

A numerical study of combustion of the aluminum-air suspension in the swirling flow in the expansion chamber has been performed. The physical and mathematical formulation of the problem is based on the dynamic model of the multiphase reacting media.

scholarly journals Lean Maturity Assessment in ETO Scenario

2021 ◽  
Vol 11 (9) ◽  
pp. 3833
Author(s):  
Mariastella Chiera ◽  
Francesco Lupi ◽  
Andrea Rossi ◽  
Michele Lanzetta
Keyword(s):  
Lean Manufacturing ◽  
Mathematical Formulation ◽  
Assessment Model ◽  
Assessment Framework ◽  
Lean Product Development ◽  
Lean Assessment ◽  
Assessment And Monitoring ◽  
Mission Management ◽  
Engineer To Order ◽  
Manufacturing Organization

The obligatory path towards a lean manufacturing organization requires assessment and monitoring. However, a lean assessment framework is not yet available for the engineer to order (ETO) scenario. This work explored ten lean ETO maturity principles—identified from the literature—that take insight from three formally defined sets (Toyota Way, lean construction, and lean product development principles). A practical assessment model was proposed based on the evaluation of ten lean ETO objective criteria (four with mathematical formulation) and was validated on a real industrial case. A problem-solving tool, including a new lean tool, called the Problem Focus Matrix (PFM), was also presented; this tool was aimed toward development of an integrated framework that would include the organization mission, management, and continuous improvement.

scholarly journals Plane Wave Imaging through Interfaces

Sensors ◽  
2021 ◽  
Vol 21 (15) ◽  
pp. 4967
Author(s):  
Guillermo Cosarinsky ◽  
Jorge F. Cruza ◽  
Jorge Camacho
Keyword(s):  
Image Quality ◽  
Plane Wave ◽  
Phased Array ◽  
Mathematical Formulation ◽  
Non Destructive Testing ◽  
Arbitrary Geometry ◽  
Destructive Testing ◽  
Wave Imaging ◽  
Imaging Strategy ◽  
Non Destructive

Plane Wave Imaging (PWI) has been recently proposed for fast ultrasound inspections in the Non-Destructive-Testing (NDT) field. By using a single (or a reduced number) of plane wave emissions and parallel beamforming in reception, frame rates of hundreds to thousands of images per second can be achieved without significant image quality losses with regard to the Total Focusing Method (TFM) or Phased Array (PA). This work addresses the problem of applying PWI in the presence of arbitrarily shaped interfaces, which is a common problem in NDT. First, the mathematical formulation for generating a plane wave inside a component of arbitrary geometry is given, and the characteristics of the resultant acoustic field are analyzed by simulation, showing plane wavefronts with non-uniform amplitude. Then, an imaging strategy is proposed, accounting for this amplitude effect. Finally, the proposed method is experimentally validated, and its application limits are discussed.

scholarly journals Mathematical Formulation and Analytic Solutions for Uncertainty Analysis in Probabilistic Safety Assessment of Nuclear Power Plants

Energies ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 929
Author(s):  
Gyun Seob Song ◽  
Man Cheol Kim
Keyword(s):  
Monte Carlo ◽  
Uncertainty Analysis ◽  
Probability Density ◽  
Nuclear Power ◽  
Safety Assessment ◽  
Power Plants ◽  
Mathematical Formulation ◽  
Analytic Solutions ◽  
Probabilistic Safety Assessment ◽  
Probabilistic Safety

Monte Carlo simulations are widely used for uncertainty analysis in the probabilistic safety assessment of nuclear power plants. Despite many advantages, such as its general applicability, a Monte Carlo simulation has inherent limitations as a simulation-based approach. This study provides a mathematical formulation and analytic solutions for the uncertainty analysis in a probabilistic safety assessment (PSA). Starting from the definitions of variables, mathematical equations are derived for synthesizing probability density functions for logical AND, logical OR, and logical OR with rare event approximation of two independent events. The equations can be applied consecutively when there exist more than two events. For fail-to-run failures, the probability density function for the unavailability has the same probability distribution as the probability density function (PDF) for the failure rate under specified conditions. The effectiveness of the analytic solutions is demonstrated by applying them to an example system. The resultant probability density functions are in good agreement with the Monte Carlo simulation results, which are in fact approximations for those from the analytic solutions, with errors less than 12.6%. Important theoretical aspects are examined with the analytic solutions such as the validity of the use of a right-unbounded distribution to describe the uncertainty in the unavailability/probability. The analytic solutions for uncertainty analysis can serve as a basis for all other methods, providing deeper insights into uncertainty analyses in probabilistic safety assessment.

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