Solid Solutions

1993 ◽  
Author(s):  
Greg M. Anderson ◽  
David A. Crerar
Keyword(s):  
Activity Coefficient ◽  
Practical Interest ◽  
Physical Models ◽  
Ideal Solution ◽  
Ideal Behavior ◽  
Real Solutions ◽  
Ideal Solutions ◽  
Molecular Forces ◽  
Definition Of ◽  
Mixed Component

Real solutions of practical interest to Earth scientists do not behave ideally, although some do come fairly close. The problem of course lies in the stringent and unrealistic physical models we have prescribed for ideal solutions. The molecules of a gas do interact with each other, molecular forces within mixed component liquids really are non-uniform, and the different ions substituting for each other in solids are never exactly alike. So why bother defining an ideal solution in the first place if real systems do not behave that way? In fact, the ideal solution is a very useful artifice. It is something simple against which the behaviour of real solutions can be measured and compared. Our most fundamental definition of an ideal solution was With this as our reference, we can define a non-ideal solution as one for which the activity coefficient of each component i differs from unity The activity coefficient is the single quantity that expresses all deviations from non-ideality for each component of a solution. As we shall see, parameters other than the activity coefficient itself are frequently used to describe non-ideal behavior, but these could, if we wished, be related back to (15.1). Note that we say ⋎i, ≠1.0 in general; there are times when ⋎i = 1.0 for specific conditions (one set of T, P, Xi, etc.) even in highly non-ideal systems. This is just coincidental and certainly does not mean that the system is ideal at that particular point—the activity coefficient would have to be unity under all possible conditions for that to be the case.

Reactions in solution

2018 ◽  
Author(s):  
Dennis Sherwood ◽  
Paul Dalby
Keyword(s):  
Phase Equilibria ◽  
Gas Phase ◽  
First Principles ◽  
Unique Feature ◽  
Life Sciences ◽  
Equilibrium Mixture ◽  
Second Law ◽  
Ideal Solution ◽  
Coupled Reactions ◽  
Definition Of

Another key chapter, examining reactions in solution. Starting with the definition of an ideal solution, and then introducing Raoult’s law and Henry’s law, this chapter then draws on the results of Chapter 14 (gas phase equilibria) to derive the corresponding results for equilibria in an ideal solution. A unique feature of this chapter is the analysis of coupled reactions, once again using first principles to show how the coupling of an endergonic reaction to a suitable exergonic reaction results in an equilibrium mixture in which the products of the endergonic reaction are present in much higher quantity. This demonstrates how coupled reactions can cause entropy-reducing events to take place without breaking the Second Law, so setting the scene for the future chapters on applications of thermodynamics to the life sciences, especially chapter 24 on bioenergetics.

scholarly journals Human Capital as an Object of Accounting in the Knowledge Economy

2019 ◽  
Vol 71 ◽  
pp. 05003
Author(s):  
O. Kogut
Keyword(s):  
Economic Growth ◽  
Human Capital ◽  
Economic Development ◽  
Knowledge Economy ◽  
Practical Interest ◽  
Main Role ◽  
Independent Factor ◽  
Modern Economy ◽  
Productive Factor ◽  
Definition Of

The modern economy is called the economy of effective human capital, which emphasizes its main role in the development of the economy and society as a productive factor. Human capital is becoming the most important factor in the country's economic growth, the foundation of sustainable economic development. The article considers approaches to the definition of the concept and theoretical content of the category of human capital, its importance for the development of areas of science and practice. It is revealed that human capital is a necessary independent factor determining economic growth. The necessity of reflecting human capital in the system of accounting and reporting of firms is substantiated. The main problems of recognition of this most important factor of production are revealed, the directions of their further solution are determined. The scientific and practical necessity of introducing a new object of accounting and analysis of human capital is substantiated. The article contains information and conclusions that are of practical interest to firms.

scholarly journals Folding Flat Crease Patterns With Thick Materials

2016 ◽  
Vol 8 (3) ◽  
Author(s):  
Jason S. Ku ◽  
Erik D. Demaine
Keyword(s):  
Numerical Simulations ◽  
Mechanical Engineering ◽  
Practical Interest ◽  
Physical Models ◽  
Maximum Thickness ◽  
Material Thickness ◽  
Folded Structure

Modeling folding surfaces with nonzero thickness is of practical interest for mechanical engineering. There are many existing approaches that account for material thickness in folding applications. We propose a new systematic and broadly applicable algorithm to transform certain flat-foldable crease patterns into new crease patterns with similar folded structure but with a facet-separated folded state. We provide conditions on input crease patterns for the algorithm to produce a thickened crease pattern avoiding local self-intersection, and provide bounds for the maximum thickness that the algorithm can produce for a given input. We demonstrate these results in parameterized numerical simulations and physical models.

BRITTLE/DUCTILE ASSESSMENT OF HYBRID REINFORCED CONCRETE BEAMS CONTAINING STEEL REBAR AND FIBERS

2017 ◽  
Vol 4 (1) ◽  
Author(s):  
Alessandro P. Fantilli ◽  
Andrea Gorino ◽  
Bernardino Chiaia
Keyword(s):  
Reinforced Concrete ◽  
Volume Fraction ◽  
Practical Interest ◽  
Design Procedure ◽  
Fiber Reinforced Concrete ◽  
Reinforced Concrete Beams ◽  
Minimum Reinforcement ◽  
Steel Rebar ◽  
Definition Of ◽  
Hybrid Reinforcement

Many structures, such as precast and cast-in-situ tunnel linings, are nowadays realized with Hybrid Reinforced Concrete (HRC), where a combination of continuous steel rebar and discrete fibers is used to reinforce the cementitious matrix. Hence, the definition of a minimum amount of hybrid reinforcement (i.e., rebar and fibers), which prevents the brittle failure, is of practical interest. For predicting the brittle/ductile response of HRC beams in bending, a theoretical model is introduced and presented in this paper. It is based on the flexural response of both Lightly Reinforced Concrete (LRC) and Fiber-Reinforced Concrete (FRC) beams, separately analyzed. The numerical results of the model, and some experimental data as well, show that the minimum reinforcement of HRC beams can be determined with a new design procedure. It requires the definition of the ductility index (DI), which is proportional to the difference between ultimate and effective cracking load. As DI linearly increases with the amount of rebar and fibers, the minimum reinforcement in HRC members can be found when DI is equal to zero. In addition, the minimum hybrid reinforcement can be defined with a suitable linear combination of the minimum area of rebar and the minimum fiber volume fraction, related to LRC and FRC beams, respectively.

scholarly journals Generic Lightlike Submanifolds of an Indefinite Cosymplectic Manifold

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Dae Ho Jin ◽  
Jae Won Lee
Keyword(s):  
General Relativity ◽  
Black Hole ◽  
Physical Models ◽  
Hole Theory ◽  
Cosymplectic Manifold ◽  
Definition Of ◽  
Lightlike Submanifolds ◽  
Lightlike Hypersurfaces ◽  
Killing Horizons

Lightlike geometry has its applications in general relativity, particularly in black hole theory. Indeed, it is known that lightlike hypersurfaces are examples of physical models of Killing horizons in general relativity (Galloway, 2007). In this paper, we introduce the definition of generic lightlike submanifolds of an indefinite cosymplectic manifold. We investigate new results on a class of generic lightlike submanifolds of an indefinite cosymplectic manifold .

scholarly journals Social Dialects in Modern French Language

2020 ◽  
Author(s):  
Galina Bernetska
Keyword(s):  
Mass Media ◽  
Special Section ◽  
Practical Interest ◽  
Spoken Language ◽  
Point Of View ◽  
French Language ◽  
Semantic Features ◽  
Literary Language ◽  
Vertical Division ◽  
Definition Of

The article is a study of phonetic-morphological and semantic-stylistic features of argotic vocabulary in contemporary French language. The work is devoted to questions of structural-semantic and phonetic-morphological peculiarities of the argotic vocabulary in printed mass media. The conducted research has shown that the argotic vocabulary can be considered as a special lexical subsystem of spoken language, which is characterized by a steady tendency to penetrate into higher linguistic levels due to its phonetic-morphological and semantic features. The systematization of phonetic and semantic processes in the argotic dictionary is carried out. We have noticed that argot from a linguistic point of view is an expressive lexical subsystem of spoken language, which is characterized by a large expressive potential and rapid changes in vocabulary and penetrates into higher levels of the French language. From the point of view of modern linguistics, the French language can be viewed in vertical and horizontal sections. Horizontal division is caused by the existence of the dialectal partition of the French language. The vertical division is explained by the existence of social groups that use one or another sociolect. Analyzing the evolution of the definition of argot, we can assume that in its development argot passed the long way from the language taboo to the special lexical subsystem of the literary-spoken language. We have noticed that it is important to distinguish argot and spoken language. In spite of the both scientific and practical interest in the spoken language problem and the emergence of numerous studies that led to the creation of colloquialism as a special section of linguistics, a number of aspects of spoken language (approaches to its identification, differentiation of spoken language and related phenomena) remain insufficiently highlighted. The spoken language (vernacular), according to modern linguistic assertions, occupies an intermediate position between the spoken-literary language, dialects and sociolects. We have noticed that the democratization of the norms of the literary language led to the emergence of a literary-colloquial form of spoken language. Such a combination of literary and spoken language is caused by the nature of social development. Key words: argot; slang; French language; dialect; argotheistic vocabulary; non-normative variant elements; semantics; phonetics; morphology; mass media.

Optimal Synthesis of Topology for Compliant Mechanisms

2019 ◽  
Author(s):  
Antonio Caputi ◽  
Davide Russo
Keyword(s):  
Mechanical Response ◽  
Compliant Mechanisms ◽  
Design Tool ◽  
Physical Models ◽  
Synthesis Of Mechanisms ◽  
Response Set ◽  
Synthesis Tool ◽  
General Schema ◽  
Definition Of

Abstract The aim of the present work is disclosing a model suitable to provide a new tool for the synthesis of mechanisms and structures. Firstly, a framework will be introduced for the representation of a particular class of mechanisms: compliant mechanisms. For this purpose, the constitutive elements and the relations between the elements are organized in a taxonomy, similar to the ones used for the definition of ontologies. Ontologies have been taken as inspiration for the construction of the general schema for two main reasons: the first one is the need of consistency in the physical models, in order to obtain reliable results. The second reason is that one of the main features of ontologies is modularity, which means that they may be reused, and implemented for the creation of widest classifications. In the proposed framework, mechanisms result from the combination of the constitutive elements, according to a certain topology. The topologies are generated taking in account the defined feasible relations between elements. Once the mechanisms are defined, their behavior, in terms of mechanical response, is calculated and implemented in the schema as well. Finally, a classification of the evaluated mechanisms is provided, correlating the mechanical behavior of the mechanisms to the topological arrangement of their elements, or, in other words, their geometry. This classification may be synthetized in a table which may be query setting the mechanical response (set of deformation allowed or denied as response of a set of generalized forces). The result of the query is the indication of the topology of the mechanism that fits the mechanical response best. The proposed table is a design tool actually, suggesting the constructive form to the designer starting from a functional requirement. Moreover, considering the table of topologies and the physical model with which it was generated, they constitute a synthesis tool for that class of mechanisms, and, ultimately, a topology, and size optimization tool.

Finding the Shape of a Flexible Blade for Free-Form Layered Manufacturing of Plastic Foam Objects

1998 ◽  
Author(s):  
Imre Horváth ◽  
Joris S. M. Vergeest ◽  
Imre Juhász
Keyword(s):  
Order Approximation ◽  
Geometric Model ◽  
Cost Effective ◽  
Soft Materials ◽  
Layered Manufacturing ◽  
Physical Models ◽  
Free Form ◽  
Plastic Foams ◽  
Physically Based ◽  
Definition Of

Abstract The need for rapid, cost-effective and finish-less manufacturing of large sized, sculptured, physical models from various soft materials is increasing in several fields. For objects fabricated from plastic foams an advantageous approach is free-form, thick-layered manufacturing. Although it is technologically demanding, to achieve the best results (a) computer definition of the geometry has to be accurate, (b) the geometric model has to be directly sliced, (c) higher order approximation of the nominal shape is necessary, and (d) a quasi-free-form working out of the front surfaces of the layers is needed. The authors have developed the mathematical and/or technological fundamentals and process of free-form cutting based on heated flexible blades. The shape and the relative positions of the flexible blade are controlled continually as needed by the normal curvatures of the front faces of the layers. The paper elaborates on the computation methods for physically-based and geometrically-based modeling of flexible blades. The algorithms for approximating curve generation and curve matching are also presented. The paper extends to some of the most important aspects of the global thick-layered fabrication process.

Mean-Field Theories

2005 ◽  
Author(s):  
Eldred H. Chimowitz
Keyword(s):  
Ising Model ◽  
Critical Behavior ◽  
Degrees Of Freedom ◽  
Lattice Structure ◽  
Practical Interest ◽  
Universality Class ◽  
Physical Models ◽  
3 Dimensional ◽  
Interaction Terms ◽  
Basic Ideas

The most widely used analytic models for representing thermodynamic behavior in supercritical ßuids are of the mean-Þeld variety. In addition to the practical interest in studying this topic, this class of models is also the conceptual starting point for any microscopic discourse on critical phenomena. In this chapter we take up the basic ideas behind this approach, studying different physical models, showing how their mean-Þeld approximations can be constructed as well as investigating their critical behavior. A useful conceptual model for understanding mean-Þeld ideas is the Ising model whose properties we consider in some detail, especially its mean-Þeld approximation. The Ising model has the advantage of belonging to the same critical universality class as so-called simple fluids, deÞned as ßuids with short-range intermolecular potentials. Most supercritical ßuid solvent systems of practical interest fall within this class; hence results developed using the Ising model have important implications for understanding the critical behavior of this entire universality class. While we discuss universality and related ideas in more detail in subsequent chapters, sufÞce it to say here that the Ising system belongs to arguably the most important critical universality class from a process engineering standpoint. In its simplest form, the Ising model considers N spins arranged on a lattice structure (of 1, 2, or 3 dimensions) with each spin able to adopt one of two (up or down) orientations in its lattice position. A speciÞc state of the system is determined by a given conÞguration of all the spins. The model can be made more complex by considering additional degrees of freedom to the spin orientations. For example, the Heisenberg model considers a 3-dimensional lattice with the spin orientation at each lattice site described by a 3-dimensional vector quantity. All that is required to facilitate the use of statistical mechanics with this model is the deÞnition of the Hamiltonian (the systemÕs energy function) associated with a particular lattice state υ. This Hamiltonian usually consists of spinÐspin interaction terms, as well as a term representing the presence of a magnetic Þeld, which serves to orient the spins in its direction.

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