Dimensional analysis revisited

2001 ◽  
Vol 215 (11) ◽  
pp. 1365-1375 ◽  
Author(s):  
R Butterfield
Keyword(s):  
Dimensional Analysis ◽  
Specific Problem ◽  
Sufficient Conditions ◽  
Optimal Number ◽  
Physical Knowledge ◽  
Dimensionless Groups ◽  
New Knowledge ◽  
Complete Set ◽  
Pi Theorem ◽  
Necessary And Sufficient

Dimensionless groups, the output of a successful dimensional analysis, are usually developed via Buckingham's pi theorem. Because this theorem provides a necessary but not sufficient condition for a solution, such a dimensional analysis may, on occasion, appear to fail. The paper presents the necessary and sufficient conditions in a simple form and builds on them to demonstrate how new physical knowledge can augment a ‘primitive’ set of dimensions to arrive at an optimal number of dimensionless groups. The formulation is used to elucidate the historical Rayleigh-Ria-bouchinsky controversy and a related thermomechanical problem is analysed to demonstrate the complete ‘new knowledge’ algorithm. Mathematica code is appended which incorporates these ideas and generates the complete set of admissible dimensionless groups for any specific problem.

scholarly journals Characterizations of variational convergence of bifunctions defined on products of two sets

2020 ◽  
Vol 3 (SI3) ◽  
pp. First
Author(s):  
Diem Thi Hong Huynh
Keyword(s):  
Basic Property ◽  
Specific Problem ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Variational Convergence ◽  
Product Spaces ◽  
The Third ◽  
Left And Right ◽  
Definition Of ◽  
Necessary And Sufficient

We present definitions of types of variational convergence of finite-valued bifunctions defined on rectangular domains and establish characterizations of these convergences. In the introduction, we present the origins of the research on variational convergence and then we lead to the specific problem of this paper. The content of the paper consists of 3 parts: variational convergance of fucntion; variational convergance of bifunction; and characterizations of variational convergence of bifunction, this part is the main results of this paper. In section 2, we presented the definition of epi convergence and presented a basic property problem that will be used to extend and develop the next two sections. In section 3, we start to present a new definition, the definition of convergence epi / hypo, minsup and maxinf. To clearly understand of these new definitions we have provided comments (remarks) and some examples which reader can check these definitions. The above contents serve the main result of this paper will apply in part 4. Now, we will explain more detail for this part as follows. Firstly, variational convergence of bifunctions is characterized by the epi- and hypo-convergence of related unifunctions, which are slices sup- and inf-projections. The second characterization expresses the equivalence of variational convergence of bifunctions and the same convergence of the so-called proper bifunctions defined on the whole product spaces. In the third one, the geometric reformulation, we establish explicitly the interval of all the limits by computing formulae of the left- and right-end limit bifunctions, and this is necessary and sufficient conditions of the sequence bifunctions to attain epi / hypo, minsup and maxinf convergence.

Exact regions of oscillation for a neutral differential equation

2000 ◽  
Vol 130 (2) ◽  
pp. 277-286
Author(s):  
S. S. Cheng ◽  
Y. Z. Lin
Keyword(s):  
Differential Equation ◽  
Sufficient Conditions ◽  
Neutral Differential Equation ◽  
Necessary And Sufficient Conditions ◽  
All Solutions ◽  
Constant Coefficients ◽  
Complete Set ◽  
Necessary And Sufficient

This paper is concerned with a neutral differential equation with four constant coefficients, one delay and one advancement. By means of the theory of envelopes, we consider all possible values of the parameters involved in the equation and obtain a complete set of necessary and sufficient conditions for all solutions to be oscillatory.

Similarity and Invariance in Scaled Bilateral Telemanipulation

1999 ◽  
Vol 121 (1) ◽  
pp. 79-87 ◽  
Author(s):  
Michael Goldfarb
Keyword(s):  
Dimensional Analysis ◽  
Physical Environment ◽  
Degrees Of Freedom ◽  
Sufficient Conditions ◽  
Nonlinear Effects ◽  
Dynamic Similarity ◽  
Physical Environments ◽  
Force Scaling ◽  
Necessary And Sufficient ◽  
Selection Of

This paper addresses the issue of dynamic similarity and intensive property invariance in scaled bilateral manipulation, and offers a design methodology based on these considerations. The methodology incorporates dimensional analysis techniques to define a set of necessary and sufficient conditions to preserve the dynamic similarity of any physical environment. These techniques are utilized to demonstrate that any combination of kinematic and force scaling in a bilateral manipulator control structure will preserve the dynamic similarity of any physical environment. Any combination of kinematic and force scaling, however, will not in general maintain intensive property invariance between the original and scaled physical environments, and thus will result in lost information. As such, the dimensional analysis methods are further utilized to form the basis of a constrained optimization problem that enables selection of a force scaling factor that minimizes the intensive distortion of the environment. The proposed formulation is applicable to any physical environment, including those that are nonlinear and contain multiple degrees of freedom. Further, the formulation does not require an exact environmental model, provided the parameters that influence the environment are known. The proposed techniques are particularly relevant to bilateral manipulation of a microscopic environment (i.e., macro-micro bilateral manipulation), since such environments are difficult to model exactly and are largely influenced by nonlinear effects.

Hydrology without Dimensions

2021 ◽  
Author(s):  
Amilcare Porporato
Keyword(s):  
Dimension Reduction ◽  
Dimensional Analysis ◽  
Landscape Evolution ◽  
Nonlinear Models ◽  
Soil Formation ◽  
Self Similarity ◽  
Weathering Rates ◽  
Dimensionless Groups ◽  
Pi Theorem ◽  
Budyko’S Curve

<div> </div><div> <div> <div>Dimensional analysis offers an ideal playground to tackle complex hydrological problems. The powerful dimension reduction, in terms of governing dimensionless groups, afforded by the PI-theorem and the related self-similarity arguments is especially fruitful in case of nonlinear models and complex datasets. After briefly reviewing these main concepts, in this lecture I will present several applications ranging from hydrologic partitioning (Budyko's curve) and stochastic ecohydrology, to global weathering rates and soil formation, as well as landscape evolution and channelization. Since Copernicus-dot-org asks me to add at least 25 words to the abstract, I would like to thank the colleagues who supported my nomination for the Dalton medal and my many collaborators.</div> </div> </div>

Hydrology without Dimensions

2020 ◽  
Author(s):  
Amilcare Porporato
Keyword(s):  
Dimension Reduction ◽  
Dimensional Analysis ◽  
Landscape Evolution ◽  
Nonlinear Models ◽  
Soil Formation ◽  
Self Similarity ◽  
Weathering Rates ◽  
Dimensionless Groups ◽  
Pi Theorem ◽  
S Curve

<p>Dimensional analysis offers an ideal playground to tackle complex hydrological problems. The powerful dimension reduction, in terms of governing dimensionless groups, afforded by PI-theorem and related self-similarity arguments is especially fruitful in case of nonlinear models and complex datasets. After briefly reviewing these main concepts, in this lecture I will present several applications ranging from hydrologic partitioning (Budyko’s curve) and stochastic ecohydrology, to global weathering rates and soil formation, as well as landscape evolution and channelization. Since Copernicus-dot-org asks me to add at least 25 words to the abstract, I would like to thank the colleagues who supported my nomination and my many collaborators.</p><p> </p><p> </p>

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

Budgeting in Socio-economic Development Strategies (Raising a Problem)

2008 ◽  
pp. 134-151
Author(s):  
A. Shastitko ◽  
M. Ovchinnikov
Keyword(s):  
Economic Policy ◽  
Economic Development ◽  
Social Change ◽  
Eastern Europe ◽  
Statistical Data ◽  
Sufficient Conditions ◽  
Transitional Period ◽  
Socio Economic Development ◽  
Necessary And Sufficient ◽  
Economic Development Strategies

The article proposes an approach to the analysis of social change and contributes to the clarification of concepts of economic policy. It deals in particular with the notion of "change of system". The author considers positive and normative aspects of the analysis of capitalist and socialist systems. The necessary and sufficient conditions for the system to be changed are introduced, their fulfillment is discussed drawing upon the historical and statistical data. The article describes both economic and political peculiarities of the transitional period in different countries, especially in Eastern Europe.

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