Correspondence Principle Research Articles

Unconventional Look at the Diameters of Quantum Systems: Could the Characteristic Atomic Radius Be Interpreted as a Reactivity Measure?

Decoding of atomic and ionic radii of transition metals in terms of energy response against changes in electron number and external potential variation has been considered. Energy as a functional of electron density by means of its derivatives is linked to response density and the electron detachment process. Employing charge sensitivity analysis and the electronegativity equalization principle, we interpret the electronic structure transformations (electron-following/preceding perspectives) into atomic diameters. Additionally, qualitative associations described within hard/soft acid/base theory and the approximate correlations of respective conceptual density functional theory reactivity descriptors were considered to meet postulates of the correspondence principle, giving the characteristic radius the attribute of latent variable related to quantum mechanical observables. By means of local density approximation, an insight from statistical analysis of frontier electron density complements the picture of...

An approach for modeling non-ageing linear viscoelastic composites with general periodicity

The present work deals with the modeling of non-ageing linear viscoelastic composite materials and quasi-periodic microstructure. The stratified functions and the curvilinear coordinates play an important role in the design of different geometrical shapes. The main objective focuses on the application of two-scales Asymptotic Homogenization Method (AHM) to obtain the overall behavior of the viscoelastic composite materials. Although the whole process is based on the analysis of laminated configurations, a multi-step homogenization scheme to estimate the effective properties of a structure reinforced with long rectangular fibers and wavy effects is used. The associated local problems, the homogenized problem and the analytical expressions for the effective coefficients are obtained by using the correspondence principle and the Laplace-Carson transform. Also, the interconnection between the effective relaxation modulus and the effective creep compliance is performed. Finally, the inversion to the original temporal space is calculated. Some comparisons between the proposed approach and Finite Elements Method (FEM) results are displayed.

Short-Term and Long-Term Mechanical Models of Wellbores Considering Cement Consolidation and Formation Creep

Summary With oil and gas wells extending deeper and deeper, downhole conditions become increasingly complicated, and thus increasingly sophisticated wellbore models are needed. Current wellbore models usually neglect the coupling effect in the cement–consolidation process and do not sufficiently consider the whole operation process of the wellbore. To overcome these shortcomings, short–term and long–term mechanical wellbore models while considering the relevant stages in wellbore life are built. In the short–term model, wellbore–operation stages include casing running, cement displacement, and cement consolidation. The governing equation of cement consolidation while considering the coupling effect between cement hardening and volume change is presented. In the long–term model, the governing equation of formation creep while considering prestresses and initial strains is given. The elastic/viscoelastic–correspondence principle and stress–superposition method are used to simplify the derivation. Next, the effects of relevant factors on short–term and long–term wellbore stresses are analyzed. The results show that wellbore stresses caused by cement consolidation will be underestimated when the coupling effects are neglected. The most vulnerable positions for wellbore failure are on different cylinder elements under different wellbore stages. Wellbore properties, short–term stresses, and formation creep greatly affect wellbore mechanical behaviors. Therefore, the new model provides an important basis for wellbore–failure prediction and optimal design.

Valley Hall phases in kagome lattices

We report the finding of the analogous valley Hall effect in phononic systems arising from mirror symmetry breaking, in addition to spatial inversion symmetry breaking. We study topological phases of plates and spring-mass models in Kagome and modified Kagome arrangements. By breaking the inversion symmetry it is well known that a defined valley Chern number arises. We also show that effectively, breaking the mirror symmetry leads to the same topological invariant. Based on the bulk-edge correspondence principle, protected edge states appear at interfaces between two lattices of different valley Chern numbers. By means a plane wave expansion method and the multiple scattering theory for periodic and finite systems respectively, we computed the Berry curvature, the band inversion, mode shapes and edge modes in plate systems. We also find that appropriate multi-point excitations in finite system gives rise to propagating waves along a one-way path only.

Prediction of dynamic modulus of asphalt mixture using micromechanical method with radial distribution functions

Inter-particle interaction is one of the major reinforcement mechanisms for aggregates in asphalt mixture, which is a classic example of high-volume fraction particulate composites. This paper introduced the modified Ju-Chen (J-C) micromechanical method based on two types of radial distribution assumptions for inclusions in the matrix, namely the uniform distribution and Percus–Yevick (P–Y) distribution. A two-step approach was proposed and the elastic–viscoelastic correspondence principle was used to predict the effective dynamic modulus of asphalt mixture at different frequencies. The prediction results show that the uniform distribution and P–Y distribution based J-C method could generate the upper and lower bounds of dynamic modulus for asphalt mixture, respectively. As compared to the measured dynamic modulus at different temperatures and loading frequencies, the modified J-C method showed better prediction accuracy as compared to two traditional micromechanical models based on single inclusion configuration, Mori–Tanaka (M–T) and differential scheme effective medium models. The J-C method assuming P–Y distribution provided better accuracy at the low frequencies; while the J-C method assuming the uniform distribution only had good accuracy at the high frequencies. The study findings indicate that dynamic modulus of asphalt mixture can be predicted based on laboratory tests conducted at the fine aggregate mix level and the void ratio and the gradation of coarse aggregate using appropriate micromechanics methods.

Modulus Predicting of Viscoelastic Composite Material and Numerical Method of Inverse Laplace Transform

It is studied about the modulus prediction of viscoelastic composite material and numerical method of inverse Laplace transform. According to elastic-viscoelastic correspondence principle, using Laplace transform, the effective modulus of composite materials is achieved by M-T method in the image domain. Then using inverse Laplace transform, the variation rule of modulus with the time and inclusion fraction would be obtained in the time domain.

A continuum damage model for transverse cracking in UD composites of linear viscoelastic behaviour

A damage model for linear viscoelastic unidirectional (UD) composites undergoing transverse matrix cracking is proposed. The damage representation for the corresponding elastic UD composite with an array of dispersed matrix cracks was derived from Li’s work based on continuum damage mechanics (CDM). The elastic-viscoelastic correspondence principle (CP) was used to obtain the damage representation for corresponding linear viscoelastic UD composites in the Laplace domain, and re-expressed in the time domain by taking the inverse Laplace transformation. A damage evolution law was constructed using the Weibull distribution of defects which will develop into cracks as a result of deformation. The time-temperature superposition principle (TTSP) approach has been incorporated into this model. Applications of this damage model are described in detail, and the predictions are compared with experimental data.

Schrödinger Correspondence Applied to Crystals.

In 1926, E. Schrödinger showed that the mean position and mean momentum of the displaced ground state in a harmonic oscillator obey the equations of motion of the classical oscillator. This Schrödinger Correspondence Principle, extended to an N-dimensional harmonic oscillator, is an intuitive and powerful way to approach many aspects of harmonic solids by converting the quantum-mechanical problems to the classical ones. For the application of the correspondence principle, the concepts of the phonon and its pseudomomentum are clarified, and the importance of taking into account the center-of-mass momentum is explained. Also, the concept of the antiphonon is introduced through the examples of physical processes in a line and a ring of atoms. With the correspondence principle, the quantum behavior of harmonic solids under a Mössbauer-like kick is analyzed classically, and the simulation verified the formation of an antiphonon.

Multi-dimensional consolidation analysis of transversely isotropic viscoelastic saturated soils

Based on the extended precise integration method, we investigate the multi-dimensional consolidation problem of transversely isotropic viscoelastic saturated soils. Firstly, we introduce extended precise integration solutions of multi-dimensional such as axisymmetric and three-dimensional Biot's consolidation. Then the Merchant model is applied to simulate the viscoelasticity of soils. Through the elastic-viscoelastic correspondence principle, the corresponding conversion between elastic parameters and viscoelastic parameters is achieved in the Laplace transformed domain. Finally, by a numerical inversion we obtain the solution of axisymmetric and three-dimensional consolidation of viscoelastic transversely isotropic saturated soils. Two numerical examples are conducted to verify this proposed method. Furthermore, several examples are presented to study the effect of viscoelasticity on the consolidation behavior of transversely isotropic viscoelastic saturated soils.

Modification of Numerical Inversion of Laplace Transform in Solving Problems of Poroviscoelasticity via BEM

The present paper is dedicated to numerical solving of three dimensional boundary-value problems in poroviscoelastic formulation. The poroviscoelastic formulation is treated as a combination of Biot’s theory of poroelasticity and elastic-viscoelastic correspondence principle. Kelvin-Voigt model and Standard linear solid model are employed in order to describe viscoelastic media properties. Boundary element method and boundary integral equation method are applied to obtain Laplace domain solution of boundary-value problem. Modified Durbin’s algorithm of numerical inversion of Laplace transform is used to perform solutions in time domain. Research is also dedicated to development of numerical modelling technique based on Boundary Element Method (BEM) in Laplace domain for solution of three dimensional transient poroviscoelastic problems. A problem of the three-dimensional poroviscoelastic prismatic solid clamped at one end, and subjected to uniaxial and uniform impact loading at another is considered. Viscosity parameter influence on dynamic responses of displacements and tractions is studied.

INNOVATION IN TOURISM: THEORETICAL ASPECT

The main strategic priorities of tourism development in Ukraine for the period till 2026 are determined. They are: creating a competitive national tourist product on the basis of systematic marketing activities; providing economic, social, environmental and innovative usage of existing tourism potential; creation of tourist information centers during fairs, festivals and exhibitions; improving the quality of tourism infrastructure; improving the information infrastructure of tourism services; ensuring the correspondence of the price and quality of tourist products, organization the high-quality training system of tourism business specialists.The general characteristics of tourist activities are provided in article. The main factors which inhibits the development of tourism business in the present conditions are determined (th e absence of an integrated system of state tourism management in the regions; the imperfection of the regulatory framework, the lack of methodological, organizational, informational and material support of the state; the investment lack in the development of tourism; the lack of tourism development facilities in the countryside; the insufficient provision of tourism industry by highly skilled specialists; the reduction of hotel industry enterprises; the lack of innovative projects and researches on the promising types of tourism development; the ineffective usage of recreational resources and the need for their saving; the insufficient level of information infrastructure development, the lack of state support for the promotion of a national tourist product etc.).The various scientists’ views on the definition of the term "innovation in tourism" are considered. The features of innovations in tourism are formulated and the principles of their application are defined (the principle of the science, the principle of the systemicity, the principle of the innovations correspondence to the needs of tourists, the principle of the positivity of the results, the principle of conformity of innovation activity to the society development level, the principle of connectivity and security).

Deformation regularities of carbon fiber reinforced plastic under time variable loading

The effect of strain rate on the stress-strain deformation process of unidirectional composites was investigated. As taking into account the influence of structural and technological factors, engineering methods of identification for mechanical characteristics were created. Descripting the mechanical properties of a laminate for a given structure was usually carried out based on the regularities of its constituent layers. The analysis of the viscoelastic properties of composite materials showed that along with the manifestation of rheological properties, a physical nonlinearity was observed, which may be a consequence of shear stresses. This paper is devoted to the development of a phenomenological model of the hereditary type, which makes it possible to evaluate the anisotropy of the rheological properties of a unidirectional composite by the results of tests over a wide range of strain rates. To obtain the constitutive equations, we used the relations of the anisotropic theory of elasticity, the Volterra correspondence principle and the algebra of resolvent operators, which simplify the transformation of the equations. To derive the constitutive equations for the layer, it was assumed that the dependence of the properties on time in the reinforcement direction can be neglected. In the direction perpendicular to the reinforcement, hereditary-elastic behaviour was assumed. The comparison of calculated data and experimental results was presented.

The Magical Horizontal Force Muscle? A Preliminary Study Examining the "Force-Vector" Theory.

The force-vector theory contends that horizontal exercises are more specific to horizontal sports skills. In this context, the focus is on horizontal force production relative to the global coordinate frame. However, according to the principle of dynamic correspondence, the direction of force relative to the athlete is more important, and thus the basis for the force-vector theory is flawed. The purpose of this study was therefore to test the force-vector theory. According to the force-vector theory, hip thrust is a horizontally loaded exercise, and so hip thrust training would be expected to create greater improvements in horizontal jump performance than vertical jump performance. Eleven collegiate female athletes aged 18–24 years completed a 14-week hip thrust training programme. Pre and post testing was used to measure the following: vertical squat jump, vertical countermovement jump, horizontal squat jump, horizontal countermovement jump and hip thrust 3 repetition maximum (3RM). Subjects improved their 3 repetition maximum hip thrust performance by 33.0% (d = 1.399, p < 0.001, η2 = 0.784) and their vertical and horizontal jump performance (improvements ranged from 5.4–7.7%; d = 0.371–0.477, p = 0.004, η2 = 0.585). However, there were no differences in the magnitude of the improvement between horizontal and vertical jumping (p = 0.561, η2 = 0.035). The results of this study are contrary to the predictions of the force-vector theory. Furthermore, this paper concludes with an analysis of the force-vector theory, presenting the mechanical inconsistencies in the theory. Coaches should use the well established principle of dynamic correspondence in order to assess the mechanical similarity of exercises to sports skills.

Replacement relations for a viscoelastic material containing multiple inhomogeneities

Classical replacement relations provide a connection between elastic properties of a porous material and the same material with fluid or solid infill of the porous space. We derive such relations for the case when both skeleton and infill materials are viscoelastic. For this goal, we use formalism of compliance/stiffness contribution tensors that lead to replacement relations for anisotropic elastic materials that, in the case of isotropy, coincide with classical Gassmann equation (Gassmann, 1951). We rewrite these relations using creep and relaxation contribution tensors that describe effect of individual inhomogeneities on the overall viscoelastic properties of a heterogeneous material. Explicit analytical expressions are obtained using elastic-viscoelastic correspondence principle and Laplace transform. It becomes possible when viscoelastic properties are expressed in terms of fraction-exponential operators of Scott Blair–Rabotnov. Results are obtained in closed explicit form.

Quantum Economics, Newtonian Economics, and Law

Just as Newtonian mechanics breaks down when we look at the constituent pieces of our universe—subatomic particles—neoclassical economics breaks down when we look at the constituent pieces of our society—individual people. At the scale of subatomic particles, quantum mechanics provides new foundations for understanding the physical world; at the scale of individual decisionmaking, behavioral economics promises new foundations for understanding the social, economic, and legal worlds. As this Article explains, this analogy between Newtonian and quantum physics, on the one hand, and neoclassical and behavioral economics, on the other hand, has much to reveal about law and economics. With the help of numerous examples of key finding in behavioral law and economics, I take three principles from quantum mechanics (the uncertainty principle, the correspondence principle, and the quantum principle) and show how analogous principles in economics help illuminate the future trajectory of law and economics. I then seek to accelerate this trajectory by proposing an agenda for strengthening behavioral law and economics through a stronger grounding in theory, and specifically a “quantum” theory of decisionmaking. Along the way, the analysis leads me to challenge some common misconceptions about law and economics: behavioral and neoclassical approaches to law and economics are not rivals, but partners; simplistic and artificial assumptions about human behavior remain a problem in law and economics, but most acutely in behavioral law and economics; and the notion that neoclassical economics promotes a deregulatory agenda and behavioral economics promotes a pro-regulatory agenda is, as often as not, exactly backwards.

Static and dynamic effective thickness in five-layered glass plates

In the last years, the effective thickness concept has been used to calculate deflections, stresses and modal parameters in laminated glass beams and plates, which consists of using a monolithic element with equivalent bending properties to a laminated element, i.e. the thickness of the equivalent monolithic model is time and temperature dependent because the interlayers show a viscoelastic behavior. Multi-layered laminated glass panels are those with at least three monolithic glass layers and two viscoelastic interlayers which are commonly used in floors, roofs and other applications where a high level of security is required. In this paper, a static deflection effective stiffness for a laminated glass plate consisting of three glass layers and two polymeric interlayers is derived. This static effective thickness is then extended to the frequency domain using the correspondence principle. The models are validated by static experimental tests and operational modal tests carried out on a rectangular multi-layered laminated glass plate pinned supported at the four corners.

ИССЛЕДОВАНИЕ ВЛИЯНИЯ ПРЕДВАРИТЕЛЬНОГО СОСТОЯНИЯ НА МЕХАНИЧЕСКИЕ СВОЙСТВА ВЯЗКОУПРУГИХ ТЕЛ

We present a new general statement of the problem on steady-state oscillations of a non-uniform viscoelastic body, taking into account the residual stress-strain state. To derive it, we use the theory of complex modules and the correspondence principle which makes it possible to write down the problem for viscoelastic bodies in the same form as the corresponding elasticity problems by replacing the elastic characteristics with the complex functions of vibration frequency. To describe the viscoelastic behavior, we employ a three-parameter model of the standard viscoelastic body consisting of instantaneous and long-term modules, as well as relaxation time. On the basis of the statement proposed, we consider the model problems on vibrations of inhomogeneous viscoelastic rods and pipes taking into account the presence of both pre-stress and residual strain. Within the problem for the viscoelastic rod, we analyze the longitudinal oscillations and consider the pre-stress and residual strain as functions of the longitudinal coordinate. Regarding the problem for the viscoelastic pipe, we consider the plane stress-strain state and assume that the oscillations are excited by the radial load; the mechanical properties of the cylinder and the residual stress-strain state depend on the radial coordinate. The numerical solutions in both cases are based on the shooting method. For both models problems under study, we present and observe the results of the comparative analysis of the effect of pre-stress and residual deformations on the amplitude-frequency characteristics (AFC), based on the computational experiments. We also provide the analysis of such an influence of each factor on the most sensitive frequencies values. The study conducted shows that for both rod and pipe the residual strain fields have a significantly greater effect on the AFC than the pre-stress fields do. This conclusion correlates with the results obtained previously for elastic bodies.

The energy-based method for effective dynamic properties of viscoelastic composite

Abstract The evolution of viscoelastic composite materials and their practical applications, necessitates the accurate modeling of their viscoelastic characteristics, for which the correspondence principle and energy method are widely used. The energy method for viscoelastic composite materials assumes the zero phase difference among the components of strain at a point, which may affect the accurate prediction of loss factor for high damping composite materials where the phase differences are significant. This work is to present re-formulation of energy method considering these phase differences and to extend it for the computation of effective properties of viscoelastic composites. The computed properties using Finite element method (FEM) with present formulation are observed to be more accurate than the earlier energy formulation with respect to correspondence principle.

Paul Samuelson’s Ways to Macroeconomic Dynamics

Samuelson kept optimization-based problems separated from macroeconomic dynamics in his Foundations, where dynamics were defined in terms of difference and differential equations. Despite some criticism of his “correspondence principle” of stability analysis by D.F. Gordon, D. Patinkin and others, it was only in the 1970s that Samuelson’s separation was effectively challenged, particularly by R. Lucas. After the Foundations, Samuelson developed dynamic optimization models, sometimes featuring representative agents, but he did not extend that to the study of macroeconomic fluctuations. Neither did he accept market clearing inter-temporal maximization as a solution to the microfoundations problem that beset his models of macroeconomic dynamics. His last contribution to macro dynamics was his 1988 nonlinear non-optimizing business cycle model. Eventually, he disentangled his 1965 “efficient market hypothesis” from rational expectations and claimed that the former should form one of the pillars of macroeconomic dynamics, together with imperfectly competitive markets for goods and labour.

Integer part independent polynomial averages and applications along primes

Exploiting the equidistribution properties of polynomial sequences, following the methods developed by Leibman (Pointwise Convergence of ergodic averages for polynomial sequences of translations on a nilmanifold. Ergodic Theory Dynam. Systems, 25 (2005) no. 1, 201-213) and Frantzikinakis (Multiple recurrence and convergence for Hardy field sequences of polynomial growth. Journal d'Analyse Mathematique, 112 (2010), 79-135 and Equidistribution of sparse sequences on nilmanifolds. Journal d'Analyse Mathematique, 109 (2009), 353-395) we show that the ergodic averages with iterates given by the integer part of real-valued strongly independent polynomials, converge in the mean to the right-expected limit. These results have, via Furstenberg's correspondence principle, immediate combinatorial applications while combining these results with methods from The polynomial multidimensional Szemeredi theorem along shifted primes. Israel J. Math., 194 (2013), no. 1, 331-348 and Closest integer polynomial multiple recurrence along shifted primes. Ergodic Theory Dynam. Systems, 1-20. doi:10.1017/etds.2016.40 we get the respective right limits and combinatorial results for multiple averages for a single sequence as well as for several sequences along prime numbers.