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We establish two-term spectral asymptotics for the operator of linear elasticity with mixed boundary conditions on a smooth compact Riemannian manifold of arbitrary dimension. We illustrate our results by explicit examples in dimension two and three, thus verifying our general formulae both analytically and numerically.
In Chapter 4, we bring more sophistication to our demand curve analysis with a lengthy description of elasticity, a discussion of lagged-demand and network goods, and a dialogue on concerns about demand theory.
Elastin function is to endow vertebrate tissues with elasticity so that they can adapt to local mechanical constraints. The hydrophobicity and insolubility of the mature elastin polymer have hampered studies of its molecular organisation and structure-elasticity relationships. Nevertheless, a growing number of studies from a broad range of disciplines have provided invaluable insights, and several structural models of elastin have been proposed. However, many questions remain regarding how the primary sequence of elastin (and the soluble precursor tropoelastin) governs the molecular structure, its organisation into a polymeric network, and the mechanical properties of the resulting material. The elasticity of elastin is known to be largely entropic in origin, a property that is understood to arise from both its disordered molecular structure and its hydrophobic character. Despite a high degree of hydrophobicity, elastin does not form compact, water-excluding domains and remains highly disordered. However, elastin contains both stable and labile secondary structure elements. Current models of elastin structure and function are drawn from data collected on tropoelastin and on elastin-like peptides (ELPs) but at the tissue level, elasticity is only achieved after polymerisation of the mature elastin. In tissues, the reticulation of tropoelastin chains in water defines the polymer elastin that bears elasticity. Similarly, ELPs require polymerisation to become elastic. There is considerable interest in elastin especially in the biomaterials and cosmetic fields where ELPs are widely used. This review aims to provide an up-to-date survey of/perspective on current knowledge about the interplay between elastin structure, solvation, and entropic elasticity.
Chapter 3 develops the fundamentals of demand analysis through the lens of demand for medical care. The chapter discusses how to read and use demand curves and why demand for health is not commonly used (there is no direct market for health). Then various demand elasticities are covered: price elasticity of demand, income elasticity of demand, and cross-price elasticity of demand. Each elasticity is developed along with examples specific to the market for medical care and health decision-making. The chapter also develops important tools for using demand curves: how to think through demand shifters, Engel curves, how to calculate consumer surplus, and how to aggregate from individual to market demand. The end of chapter supplement walks through how to calculate elasticities.
Three typical elastic problems, including beam bending, truss extension and compression, and two-rings collision are simulated with smoothed particle hydrodynamics (SPH) using Lagrangian and Eulerian algorithms. A contact-force model for elastic collisions and equation of state for pressure arising in colliding elastic bodies are also analytically derived. Numerical validations, on using the corresponding theoretical models, are carried out for the beam bending, truss extension and compression simulations. Numerical instabilities caused by largely deformed particle configurations in finite/large elastic deformations are analysed. The numerical experiments show that the algorithms handle small deformations well, but only the Lagrangian algorithm can handle large elastic deformations. The numerical results obtained from the Lagrangian algorithm also show a good agreement with the theoretical values.
Louis Pasteur is considered by many to be one of the most influential scientists in history, with his interests spanning from chemistry to biology to immunology. This type of wandering isn’t uncommon during a scientist’s career, which is often driven by curiosity and a willingness to explore new fields. But how feasible is it to incentivize or force scientists to change their research pursuits, a concept known as elasticity, thus changing the direction of biomedical discoveries? How much would it take to divert a modern Pasteur away from his own natural scientific interests? Chapter 14 explores the costs associated with incentivizing a scientist to pursue new research directions, the extent to which the pharmaceutical industry is elastic, and how we can more generally steer pursuits towards areas society deems important.
The crystal structure of ice is described, together with the concepts of elasticity and dissipation. The growth of ice on earth is analysed, including the effect of salinity on ice freezing. This leads to definitions of ice types on earth, and to definitions of first year and multiyear ice, as well as icebergs.
This chapter presents a comprehensive review of vague language studies from a pragmatic perspective. An utterance is vague when it conveys unspecific meaning. For example, “Many friends attended her birthday party,” how many is many? 20, 100 or 200? Our interpretation of “many” may vary from individual to individual, from context to context. Vague language is fluid, stretchable, and strategic. It consists of various types, including approximators, vague quantifiers, placeholder words, vague category identifiers, general terms, intensifiers, softeners, and epistemic stance markers. This chapter serves as a guide for understanding the characteristics of vague language. The discussion involves the conceptual frameworks and features of vague language, which are illustrated by examples and research drawn from intercultural corpora. This chapter reviews the theorization of vague language, its linguistic categories and pragmatic functions, vague language use in intercultural communication, and includes suggestions for future research. Vague language plays a crucial role in intercultural communication and its pragmatic functions, such as mitigation, politeness, and self-protection, form an important part of the strategic moves used in effective language interactions. This chapter provides an important contribution to the field of intercultural pragmatics.
The findings of this study can be explained by elasticity theory, frame theory, pragmeme theory and integrated pragmatics. For example, they show how language users carry out, adjust and adapt to the pragmeme of delivering online health information using EL in different and shifting contexts. This study supports the conceptualisations of these theories and more importantly it further develops elasticity theory through adopting enriched perspectives of pragmatics as well as metapragmatics.
The general definition of elasticity is given, and as a special case the linear elasticity with Hooke’s law, is presented together with its derivation on the basis of the Cayley–Hamilton theorem. Some applications of elasticity theory in soil mechanics are presented.
In discrete choice models the relationships between the independent variables and the choice probabilities are nonlinear, depending on both the value of the particular independent variable being interpreted and the values of the other independent variables. Thus, interpreting the magnitude of the effects (the “substantive effects”) of the independent variables on choice behavior requires the use of additional interpretative techniques. Three common techniques for interpretation are described here: first differences, marginal effects and elasticities, and odds ratios. Concepts related to these techniques are also discussed, as well as methods to account for estimation uncertainty. Interpretation of binary logits, ordered logits, multinomial and conditional logits, and mixed discrete choice models such as mixed multinomial logits and random effects logits for panel data are covered in detail. The techniques discussed here are general, and can be applied to other models with discrete dependent variables which are not specifically described here.
This topic examines the nature of factors that affect what people buy and how much. These factors can be categorised into controllable and uncontrollable by managers. The first category relates to internal factors to the firm and involves the marketing mix. The second category relates to external factors in the business environment. A mathematical framework of analysis is required to quantify the effects of the different variables. This involves the use of demand functions or equations, which are often in a linear or power form. The linear form entails the coefficients of explanatory variables representing the marginal effects of those variables. The power form entails the coefficients or powers of the variables representing elasticities. There is a discussion of the factors determining various elasticities and their interpretation. The importance of elasticities in economic analysis is explained, in terms of managerial decision making and forecasting. The focus is on the application of concepts in demand theory to real-life situations, and the performance of the necessary calculations to make decisions and forecasts. Many solved problems are presented as an aid to this process.
Condensation and faithful separation of the genome are crucial for the cellular life cycle. During chromosome segregation, mechanical forces generated by the mitotic spindle pull apart the sister chromatids. The mechanical nature of this process has motivated a lot of research interest into the mechanical properties of mitotic chromosomes. Although their fundamental mechanical characteristics are known, it still remains unclear how these characteristics emerge from the structure of the mitotic chromosome. Recent advances in genomics, computational and super-resolution microscopy techniques have greatly promoted our understanding of the chromosomal structure and have motivated us to review the mechanical characteristics of chromosomes in light of the current structural insights. In this review, we will first introduce the current understanding of the chromosomal structure, before reviewing characteristic mechanical properties such as the Young's modulus and the bending modulus of mitotic chromosomes. Then we will address the approaches used to relate mechanical properties to the structure of chromosomes and we will also discuss how mechanical characterization can aid in elucidating their structure. Finally, future challenges, recent developments and emergent questions in this research field will be discussed.
The second chapter deals with the fundamental of continuum mechanics. It describes stresses and strains in a continuum. This is followed by fundamental laws of mechanics and constitutive relations. Elasticity and Hooke's law are described. Next, the chapter describes poroelasticity as well as poroplasticity, followed by fracture mechanics. Finally, rock physics models as applied to pore pressure detection are described.
This chapter provides the economic framework and context in which entertainment and media businesses operate. Covers hours of work, growth rates, population effects, productivity, price effects, industry structures, valuation variables, and basic economic concepts.
Chapter 6 covers the internal energy E, which is the first term in the free energy, F = E – TS. The internal energy originates from the quantum mechanics of chemical bonds between atoms. The bond between two atoms in a diatomic molecule is developed first to illustrate concepts of bonding, antibonding, electronegativity, covalency, and ionicity. The translational symmetry of crystals brings a new quantum number, k, for delocalized electrons. This k-vector is used to explain the concept of energy bands by extending the ideas of molecular bonding and antibonding to electron states spread over many atoms. An even simpler model of a gas of free electrons is also developed for electrons in metals. Fermi surfaces of metals are described. The strength of bonding depends on the distance between atoms. The interatomic potential of a chemical bond gives rise to elastic constants that characterize how a bulk material responds to small deformations. Chapter 6 ends with a discussion of the elastic energy generated when a particle of a new phase forms inside a parent phase, and the two phases differ in specific volume.
An intensive overview of the fundamentals and physical principles on which seismic methods are based. It provides the necessary related geophysical background to understand seismic data and, hence, the reader will obtain a more clear understanding of how to properly process the data in order to ultimately obtain better seismic images that are used for accurate interpretation.With various examples, this includes the theory of elasticity, the wave equation, the types of seismic waves, single-layer reflector models, seismic events, etc.
Based on class-tested material, this concise yet comprehensive treatment of the fundamentals of solid mechanics is ideal for those taking single-semester courses on the subject. It provides interdisciplinary coverage of the key topics, combining solid mechanics with structural design applications, mechanical behavior of materials, and the finite element method. Part I covers basic theory, including the analysis of stress and strain, Hooke's law, and the formulation of boundary-value problems in Cartesian and cylindrical coordinates. Part II covers applications, from solving boundary-value problems, to energy methods and failure criteria, two-dimensional plane stress and strain problems, antiplane shear, contact problems, and much more. With a wealth of solved examples, assigned exercises, and 130 homework problems, and a solutions manual available online, this is ideal for senior undergraduates studying solid mechanics, and graduates taking introductory courses in solid mechanics and theory of elasticity, across aerospace, civil and mechanical engineering, and materials science.
The Law and Economics literature details how information can be generated from legal rules drawn from both private and public spheres; designing legal rules to become more effective in creating useful information to improve both private and public decision making. We examined the market-based tool known as marketable emission permits or as tradable permits. The ability to sell permits does provide incentives if holders of permits can find greener solutions at prices attractive enough to sell off their permits. Pigou advocated for placing taxes on activities that led to negative externalities; that by carefully adding tax costs to the activity so that the marginal costs could become accurate, fully reflective of the externalities. Coase’s analysis of transaction costs complicates the question of against whom should the taxes be levied. Taxing activities that could give rise to environmental injuries must carefully understand the relative elasticities of demand to ensure that the tax will actually fall on the correct party and thus create the correct incentives. In conclusion, we found that market-based instruments worked best alongside more traditional forms of public regulation, that market-based instruments are not robustly implemented as a stand-alone alternative to traditional forms of public regulation.
In this study, continuous contact problem in the functionally graded (FG) layer loaded with two rigid flat blocks resting on the elastic semi-infinite plane was analyzed by the finite element method. The two-dimensional numerical model of the FG layer was made with the software added to the ANSYS program. This software can be adapted to all contact problem types by making minor changes. The accuracy check of the program was performed by comparing with the analytical solution of the problem by homogeneous layer and its solution by the finite element method. So, fast and practical solutions can be obtained by the developed finite element method on many applications such as; automotive, aviation and space industry applications. The comparisons made showed that the proposed solution gave good results at acceptable levels. In the problem, it was thought that all surfaces were frictionless. The external loads P and Q were transmitted to the FG layer via two flat rigid blocks. Normal stresses between the FG layer and the elastic plane, initial separation loads, initial separation distances and contact stresses under the blocks were investigated for various dimensionless quantities.