ON A HIERARCHY OF APPROXIMATE MODELS FOR FLOWS OF INCOMPRESSIBLE FLUIDS THROUGH POROUS SOLIDS

2007 ◽  
Vol 17 (02) ◽  
pp. 215-252 ◽  
Author(s):  
K. R. RAJAGOPAL
Keyword(s):  
Mathematical Models ◽  
Mixture Theory ◽  
Incompressible Fluids ◽  
Porous Solids ◽  
Approximate Models ◽  
Made In

The celebrated equations due to Fick and Darcy are approximations that can be obtained systematically on the basis of numerous assumptions within the context of mixture theory; the equations however not having been developed in such a manner by Fick or Darcy. Relaxing the assumptions made in deriving these equations via mixture theory selectively leads to a hierarchy of mathematical models and it can be shown that popular models due to Brinkman, Biot and many others can be obtained via various approximations. It is shown that a variety of other generalizations are possible in addition to those that are currently in favor, and these might be appropriate for describing interesting technological applications.

General Solutions to Nurses Travel in Linear and Circular Nursing Units

1974 ◽  
Vol 18 (2) ◽  
pp. 134-134
Author(s):  
Stanley Lippert
Keyword(s):  
Mathematical Models ◽  
Nursing Staff ◽  
General Solutions ◽  
Room Size ◽  
Number Of Patients ◽  
Internal Arrangement ◽  
Objective Determination ◽  
Made In

The hospital literature of the 1960's contains about a dozen reports or articles pertaining to the relative merits of circular vs. conventional (chiefly linear corridors flanked by patient rooms on both sides). The claims included items other than nurses travel, for example, patient visibility to nursing staff, subjective impressions, and building costs. This article is concerned only with general but quantitative comparisons of these two classes of nursing units with respect to nurses travel. Mathematical models have been developed which permit practically instant evaluation of nursing units where all patient rooms are for a single occupant or where all rooms are for two occupants. The model reflects changes in room size and internal arrangement. Examination of the architect's preliminary sketches permits the determination of superior ority of one layout over another in terms of travel. The fact that this is but one of hundreds of determinations to be made in hospital designs does not diminish its importance. The literature contains various claims to “efficiency” based on no objective criteria. The model provides a simple and objective determination of nurses travel, for any number of patients typically visited and for any pattern of randomness or orderliness in their assignments.

Mathematical Modeling of a Biomass Steam Gasifier—A Modified Equilibrium Approach

2018 ◽  
Vol 140 (4) ◽  
Author(s):  
Thomas Gröbl ◽  
Heimo Walter
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Models ◽  
Present Article ◽  
Equilibrium Model ◽  
Conversion Process ◽  
Thermochemical Conversion ◽  
Equilibrium Models ◽  
Gasification Process ◽  
Equilibrium Approach ◽  
Made In

A large potential is contributed to the energetic utilization of biomass, whereby thermochemical gasification seems to be especially interesting. In order to contribute to a better understanding of the thermochemical conversion process in the gasifier, mathematical models are used. An intensive effort is made in development of mathematical models describing the gasification process and a large number of models, considerably differing in their degree of simplification, and their applications are reported in literature. In the present article, a brief review of models applied, mainly focused on equilibrium models, is provided and a robust and flexible modified stoichiometric equilibrium model, for modeling a novel gasifier, is presented.

Observations of the Earth's magnetic field made in Edinburgh from 1670 to the present day

1994 ◽  
Vol 85 (4) ◽  
pp. 239-252 ◽  
Author(s):  
D. R. Barraclough
Keyword(s):  
Magnetic Field ◽  
Mathematical Models ◽  
Secular Variation ◽  
Geomagnetic Field ◽  
Upper Atmosphere ◽  
The Difference ◽  
Time Changes ◽  
Relative Measurements ◽  
Magnetic North ◽  
Made In

AbstractMagnetic observations made at the same site give valuable information about the time changes (the secular variation) of the geomagnetic field. This paper gives details of all known measurements of the geomagnetic field in and around Edinburgh since the earliest observation of magnetic declination (the difference between true and magnetic north) by George Sinclair in 1670. Early observations of the strength of the field were only relative measurements. Approximate conversion factors are derived to enable these data to be expressed in modern absolute units (nanoteslas). Observed values of declination, inclination and the horizontal intensity of the geomagnetic field are plotted and compared with values computed from mathematical models of the field covering the interval 1690 to 1990, inclusive. The earlier observations were not corrected for the effects of the rapidly varying magnetic fields caused by electric currents in the upper atmosphere. The consequences of this are estimated.

scholarly journals OIL SLICK FATE IN A REGION OF STRONG TIDAL CURRENTS

1974 ◽  
Vol 1 (14) ◽  
pp. 130
Author(s):  
G. Drapeau ◽  
W. Harrison ◽  
W. Bien ◽  
P. Leinonen
Keyword(s):  
Remote Sensing ◽  
Mathematical Models ◽  
Oil Spill ◽  
Field Measurements ◽  
Tidal Currents ◽  
Lawrence Estuary ◽  
Oil Slick ◽  
Scale Models ◽  
St Lawrence Estuary ◽  
Made In

This study examines the drifting, spreading and aging of small slicks of crude oil in the middle St. Lawrence Estuary. This region was chosen because it is well documented with field measurements, hydraulic scale models, and mathematical models; and also because it is becoming a strategic area for the development of supertanker ports for 300,000 and possibly 500,000 ton tankers. Two controlled releases of Venezuelan crude (370 and 800 litres) were made in November 1972, as ice began to form in the St. Lawrence Estuary. The experiments were supported by the Canada Centre for Remote Sensing which carried out extensive airborne monitoring. The results indicate that it is impossible either to recover or to disperse small spills of oil in this region of strong tidal currents. Models also predict slick motion poorly. The alternative is to construct slick-drift roses that will indicate areas of expected beaching and assist in deployment of oil-spill clean-up technology.

scholarly journals Analytical models of decision-making theory in digital transport logistics

2021 ◽  
Vol 2061 (1) ◽  
pp. 012129
Author(s):  
A Terentyev ◽  
M Karelina ◽  
E Karelina
Keyword(s):  
Mathematical Models ◽  
Analytical Models ◽  
Transport Systems ◽  
Large Set ◽  
Mathematical Methods ◽  
Large Databases ◽  
Information And Communication ◽  
High Level ◽  
High Degree ◽  
Made In

Abstract The active introduction of information and communication (digital) technologies into the modern reality of transport systems operation requires the development of modeling methods for the creation of software that allows to do the following: determine the formal efficiency of decisions made in digital transport systems (DTS); process large volumes of DTS data; perform analysis of DTS functioning environment using artificial intelligence algorithms, analytical analogues of neural networks, etc. A digital transport system, being a complex system, is determined by a large set of formalized indicators (database) and requires finding effective solutions for a sufficiently large number of criteria or signs of effectiveness. Obtaining reliable solutions in multi-criteria information situations causes difficulties, which are objective. In most cases modern mathematical models artificially reduce multi-criteria information situations to single-criteria categories. This approach, based on the use of integral criteria, has a fundamental disadvantage - the use of integral criteria to obtain estimates of the efficiency of actions or processes in complex systems is characterized by a high level of subjectivism. In this case, the obtained solution may be acceptable, but not an objective result. Therefore, it is necessary to develop mathematical models for solving multi-criteria problems applicable to the solution of problems in complex transport systems, allowing one to operate in the environment of large databases for operational reconfiguration of a management system in conditions of uncertainty and/or possible counteraction of the external environment. The article presents the results of development of mathematical methods of modeling, which allow us to construct algorithms for solving optimization tasks, formulated as multi-criteria models and in the presence of a high degree of uncertainty in the interaction of the system with the environment.

scholarly journals Modernization of grinding machines of grain cleaning machines

2018 ◽  
Vol 224 ◽  
pp. 05009 ◽  
Author(s):  
Aleksey Dorokhov ◽  
Victor Khamyev ◽  
Kirill Lepeshkin
Keyword(s):  
Mathematical Models ◽  
Seed Treatment ◽  
Experimental Studies ◽  
Polymeric Materials ◽  
New Type ◽  
Grinding Machines ◽  
And Performance ◽  
Made In

As a result of the analysis of developed earlier mathematical models of the process of seeds purification on a two-tier lattice mill of polymeric materials the possibility of significant improvement in the quality of seed treatment and performance at the same quality at the expense of more rational technological schemes and modernization of the sieve camp’s were revealed. Constructive changes were made in the lattice mill with using a new type of polymer sieves. Result of this experimental studies confirm the identified possibility of intensification of the process of seed cleaning - completeness of waste allocation increased from 0,653 to 0.75, i.e. 15 %, performance for the same quality of cleaning have increased by 24%.

scholarly journals Development and Testing of a Block Hydrocyclone

Processes ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 1577
Author(s):  
Alexandr Repko ◽  
Milan Sága ◽  
Boris Sentyakov ◽  
Vladislav Sviatskii
Keyword(s):  
Experimental Data ◽  
Experimental Study ◽  
Reynolds Number ◽  
Mathematical Models ◽  
High Strength ◽  
Fluid Consumption ◽  
Fluid Filtration ◽  
Fluid Movement ◽  
First Time ◽  
Made In

The study aimed to theoretically substantiate the efficiency of liquid purification and obtain corroborating experimental data for a hydrocyclone, consisting of several blocks. Mathematical models of the process of hydrodynamic fluid filtration were developed with the use of screw swirlers. The obtained mathematical models characterize all the main processes of fluid movement in various zones of the functioning of the hydrocyclone. Formulas for calculating the structures of hydrocyclone blocks are included. A block for swirling the flow of the liquid to be cleaned has been made in the form of a three-way screw. For the first time, wear-resistant and high-strength plastic ZEDEX ZX-324 has been used as a material. An experimental study was conducted and the change in the Reynolds number and the coefficient of fluid consumption was shown, using different constructions of the three-way screw. The research results confirmed the correctness and sufficiency of mathematical models for the development and production of block hydrocyclones.

scholarly journals A Comparison of Unsteady Wave Propagation for Various Snowpack Properties

1983 ◽  
Vol 4 ◽  
pp. 30-36 ◽  
Author(s):  
R. L. Brown
Keyword(s):  
Wave Attenuation ◽  
Mixture Theory ◽  
Material Behavior ◽  
Governing Equations ◽  
Continuity Equations ◽  
Snow Properties ◽  
Order Of Magnitude ◽  
Snowpack Properties ◽  
Constitutive Formulation ◽  
Made In

The manner in which inelastic Shockwaves propagate through snow is evaluated. The volumetric material behavior of snow is represented as an inelastic rate sensitive relationship. The constitutive equation has incorporated into it such crystalline properties as grain size, bond length, bond radius, pore size, and average number of bonds per grain. As a consequence, this constitutive formulation can be used to describe how Shockwave behavior is affected by different physical properties. The governing equations, i.e. the momentum and continuity equations, are solved by integrating them to put these equations in terms of jumps in pressure, density, and particle velocity.Results are obtained for a wide variety of snow properties. First, the effect of density is evaluated by considering densities ranging from 150 to 300 kg m−3. Then the effect of intergranular bonding is considered by varying the bond radius/grain radius ratio from 0.15 to 0.40. Finally, the Shockwave frequency is varied parametrically to determine the effect of these parameters on wave attenuation rates.The results are then compared to experimental data. The theoretical results are shown to agree well with the test data. The degree of intergranular bonding was also found to have a very significant effect on attenuation rates.Finally the importance of the air phase on the propagation of Shockwaves in snow is investigated. The governing equations for each phase are developed by using a mixture theory formulation. An order of magnitude analysis is made in order to assess the importance of the air phase on attenuation rates.

scholarly journals Development And Research Of The Press Operating Mechanism, Made In The Form Of The Wedge-Joint Mechanism With A Curving Wedge For Separation Operations

2021 ◽  
Author(s):  
Sergii G. Karnaukh ◽  
Nataly V. Chosta ◽  
Oleg E. Markov ◽  
Volodymyr V. Kukhar
Keyword(s):  
Mathematical Models ◽  
Elastic Deformation ◽  
Experimental Studies ◽  
Dynamic Force ◽  
Separation Processes ◽  
The Press ◽  
Deformation Force ◽  
Joint Mechanism ◽  
Lower Height ◽  
Made In

Abstract The applicability of a wedge-joint mechanism with a curving wedge in presses for the implementation of metal forming separation processes was substantiated. The paper states the fact, that the wedge-joint mechanism graph of the deformation force change is the closest to the technological typical graph of the force change during separation. At the same time, the wedge-joint mechanism with a curving wedge has a lower height of the parts in comparison with the traditional crank mechanisms, which provides less elastic deformation and press dynamics. The use of the additional wedge mechanism in a press with the wedge-joint mechanism with a curving wedge to ensure the approximation motion is proved. This makes it possible to reduce the energy consumption for elastic deformation and further reduce the dynamic force. The mathematical models of the wedge-joint mechanism with a curving wedge, presented in the form of a two-slide link mechanism, were developed, allowing to perform its structural, kinematic and dynamic analysis. Based on the analysis of the proposed mathematical models, dependencies were identified and a procedure for calculating the geometric, kinematic and power parameters of wedge-joint mechanisms with a curving wedge for separation processes was developed. Comparison of the kinematic and dynamic analyzes results carried out by analytical and graphic-analytical methods confirms the reliability of estimates, since their discrepancy is not more than 2.5%. Experimental studies have confirmed the adequacy of mathematical models. The error between the calculated and measured values ​​of the forces on the slide does not exceed 10%.

Recent Advances in Modelling Crop Response to Temperature

1989 ◽  
Vol 18 (2) ◽  
pp. 54-57 ◽  
Author(s):  
C. D. Vincent
Keyword(s):  
Mathematical Models ◽  
Soil Temperature ◽  
Real Life ◽  
Crop Response ◽  
Recent Advances ◽  
Response To Temperature ◽  
Made In

Mathematical models to predict the effect of altering various parameters in real-life situations are now widely used. The complexity of the factors that control the growth of crops makes such modelling very difficult in the context of agriculture, but nevertheless some useful results have been obtained. This article reviews the progress that has been made in predicting the effect of air and soil temperature on the growth of plants.

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