Correspondence Principle Research Articles

Prediction and Measurement of the Damping Ratios of Laminated Polymer Composite Plates.

Laminated composites materials are mostly used in dynamically loaded structures. The design of these structures with finite element packages is focused on vibrations, elastic deformations and failure control. Damping is often neglected because of its assumed secondary importance and also because of dearth of information on relevant material properties. This trend is prone to change as it is now realised that damping plays an increasingly important role in vibration comfort, noise radiation and crash simulations. This paper shows in a first step how to identify the orthotropic elastic and damping properties of single layer fibre-reinforced composite material sheets using a new extended version of the Resonalyser procedure. The procedure is based on the elastic-viscoelastic correspondence principle and uses a mixed numerical experimental method. In a subsequent step, the complex laminate stiffness values are computed using the identified single layer material properties. To validate this approach, the modal damping ratios of arbitrary laminated plates of different materials at several resonance frequencies are predicted and experimentally verified.

Trajectory Interpretation of Correspondence Principle: Solution of Nodal Issue

The correspondence principle states that the quantum system will approach to the classical system in high quantum numbers. Indeed, the average of the probability density distribution reflects a classical-like distribution. However, the likelihood of finding a particle at node of the wave function is zero. This condition is recognized as the nodal issue. In this paper, we propose a solution for this issue by means of complex quantum random trajectories which are obtained by solving the stochastic differential equation under the optimal guidance law. It turns out that point set A which is collected by the intersections of complex random trajectories and the real axis can present the quantum mechanical compatible distribution of the quantum harmonic oscillator system. Meanwhile, the projections of complex quantum random trajectories on the real axis form point set B that gives a distribution without appearance of nodes. Moreover, point set B can represent the classical compatible distribution in high quantum numbers. Furthermore, the statistical distribution of point set B is verified by the solution of the Fokker-Planck equation.

Boundary element method for contact between multiple rigid punches and anisotropic viscoelastic foundation

In this paper both of the elastic-viscoelastic correspondence principle and time stepping method, which can convert viscoelasticity to elasticity, are employed to the boundary element method (BEM) to solve the contact problems between multiple rigid punches and anisotropic viscoelastic foundation. The one based upon the correspondence principle has the restriction on time-invariant boundaries, and hence can only be applied to the cases of complete indentation whose contact region as well as contact status are time-independent. The other based upon the time stepping method is processed step-by-step in time domain, and its boundary conditions may vary in each time step, and hence can be applied to both complete and incomplete indentations. Both methods are valid for the frictionless or frictional contact surface, the punches can be in equilibrium status or in quasi-static sliding condition, and the number of punches and the punch profiles are arbitrary. Benefited by the elastic system used for BEM, both methods hold the feature that no meshes are required on the rigid punches and holes/cracks. Through the iteration procedure and numerical examples presented in this study, we see that the one based upon time-stepping method is much more general and efficient than the other one.

Second-order topological insulator in a coinless discrete-time quantum walk

Higher-order topological insulators not only exhibit exotic bulk-boundary correspondence principle, but also have an important application in quantum computing. However, they have never been achieved in quantum walk. In this paper, we construct a two-dimensional coinless discrete-time quantum walk to simulate second-order topological insulator with zero-dimensional corner states. We show that both of the corner and edge states can be observed through the probability distribution of the walker after multi-step discrete-time quantum walks. Furthermore, we demonstrate the robustness of the topological corner states by introducing the static disorder. Finally, we propose a possible experimental implementation to realize this discrete-time quantum walk in a three-dimensional integrated photonic circuits. Our work offers a new route to explore exotic higher-order topological matters using discrete-time quantum walks.

Coupled Vibrations of Viscoelastic Three-Layer Composite Plates. 1. Formulation of the Problem

A mathematical model of damped vibrations of three-layer plates formed by two rigid anisotropic layers and a soft middle isotropic viscoelastic polymer layer is proposed in this paper. The model is based on the Hamilton’s variational principle, the refined theory of first-order plates, the model of complex modules, and the principle of elastic-viscoelastic correspondence in the linear theory of viscoelasticity. The frequency-temperature dependence of the elastic-dissipative characteristics is considered negligible for rigid layer materials; however, this dependence is taken into account for the viscoelastic polymer of the soft layer. By minimizing the Hamilton functional we reduce the problem of damped vibrations of anisotropic structures to the algebraic problem of complex eigenvalues. The Rietz method using the Legendre polynomials as coordinate functions is applied to form the system of algebraic equations. The real solutions are found. When determining the complex natural frequencies of the plate, real natural frequencies obtained are used as their initial values, and then the complex frequencies are calculated by the third-order iteration method. The results of the study of the convergence of the numerical solution are discussed. The estimation of reliability of the mathematical model and the numerical solution method obtained by comparing the calculated and the experimental values of natural frequencies and loss factors is presented.

Semianalytical Solution for Evaluating Viscoelastic Consolidation of Saturated Soils with Overlying Dry Layers

Saturated soils with overlying dry layers are frequently encountered in geotechnical engineering. In urban construction works, the underground water level is usually influenced by the extraction of water or complex fluid for industrial uses or oil exploitation tasks. The creep and consolidation behavior of saturated soils with overlying dry layers is drastically different from that of completely saturated soils. This paper presents an investigation on the creep and consolidation behavior of the layered saturated soils with overlying dry layers under the vertical load. With the aid of the Laplace–Hankel transform, typical viscoelastic models (e.g., the Kelvin, the Maxwell, or the standard linear solid model), and the correspondence principle, a semianalytical solution is presented for this investigation. Detailed comparisons between the present results with the published numerical and analytical results are given to confirm the solution, followed by an extensive parametric study examining the effect of types of viscoelastic models, thickness of the overlying layer, and viscosity. This paper aims to present a semianalytical solution to describe the time-dependent consolidation of layered saturated soils with the overlying layer accurately and to provide useful implications for foundation design on those soils.

Edge probes of topological order

According to the bulk-edge correspondence principle, the physics of the gapless edge in the quantum Hall effect determines the topological order in the gapped bulk. As the bulk is less accessible, the last two decades saw the emergence of several experimental techniques that invoke the study of the compressible edge. We review the properties of the edge, and describe several experimental techniques that include shot noise and thermal noise measurements, interferometry, and energy (thermal) transport at the edge. We pay special attention to the filling factor 5/2 in the first excited Landau level (in two-dimensional electron gas in GaAs), where experimental evidence of a non-Abelian topological order was found. A brief discussion is devoted to recent interferometry experiments that uncovered unexpected physics in the integer quantum Hall effect. The article also addresses the theory of edge states, for systems with Abelian and non-Abelian topological orders.

Fractional non-axisymmetric consolidation of stratified cross-anisotropic visco-poroelastic media

This paper investigates the fractional non-axisymmetric consolidation of stratified cross-anisotropic visco-poroelastic media. Firstly, based on the Laplace–Hankel transform, the ordinary differential equations of cross-anisotropic poroelastic media are derived, which are extended to those of fractional visco-poroelastic media by introducing the fractional Merchant model and the elastic-viscoelastic correspondence principle. Then, the extended equations are solved by the extended precise integration method (PIM), and the proposed theory is compared with the results reported in the references. Finally, selected numerical examples are performed to investigate the effects of the order of fractional derivative, viscoelasticity, cross-anisotropy and stratification on the non-axisymmetric consolidation.

Dudas en torno a la negociación de los planes de igualdad: la respuesta de los tribunales

Resumen. No son pocos los problemas interpretativos que surgen a la hora de encarar la negociación colectiva de un plan de igualdad. Las primeras dudas pueden surgir ya al consti­tuir la mesa negociadora, especialmente cuando existan centros de trabajo con representación legal de los trabajadores y otros sin ella, pudiendo verse afectado el principio de correspon­dencia. También genera dudas el alcance que debe darse a la exigencia legal de que sea en la mesa de negociación donde se elabore el diagnóstico de igualdad, o si la obligación de negociar el plan exige alcanzar un acuerdo o es una mera obligación de medios, o las consecuencias que pueden derivarse de incumplir las medidas del plan o los compromisos de información durante la fase de seguimiento del plan. Estas y otras cuestiones interpretativas resultan muy trascendentes ya que pueden dar lugar a la declaración de nulidad del plan de igualdad e in­cluso a condenas de cuantías indemnizatorias por la vulneración del derecho constitucional de libertad sindical y de apremios pecuniarios. Los tribunales han ido dado respuesta a estas du­das, dotando así de mayor seguridad jurídica al proceso negociador de los planes de igualdad.

Study on Mechanical Behavior of Viscoelastic Polymer

Due to the energy loss in deformation process, the mechanical problems of polymer materials can not keep the energy conservation, and a series of calculation methods of elasticity can not be directly applied. In this paper, we find that the differential stress-strain relationship can be transformed into algebraic equation form according to the correspondence principle. That is, in the Laplace space, the viscoelastic problem maintains the conservation.

Paul Samuelson’s ways to macroeconomic dynamics

Samuelson kept optimisation-based problems separated from macroeconomic dynamics in his Foundations, where dynamics was 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. E. Lucas. After the Foundations, Samuelson developed dynamic optimisation 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 maximisation as a solution to the micro-foundations problem that beset his models of macroeconomic dynamics. His 1988 nonlinear non-optimising business cycle model was his last contribution to dynamics. Eventually, Samuelson disentangled his 1965 “efficient market hypothesis” of financial economics 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.

Viscous-viscoelastic correspondence principle for Brownian motion.

Motivated by the classical expressions of the mean-square displacement and the velocity autocorrelation function of Brownian particles either suspended in a Newtonian viscous fluid or trapped in a harmonic potential, we show that for all timescales the mean-square displacement of Brownian microspheres with mass m and radius R suspended in any linear, isotropic viscoelastic material is identical to the creep compliance of a linear mechanical network that is a parallel connection of the linear viscoelastic material with an inerter with distributed inertance m_{R}=m/6πR. The synthesis of this mechanical network leads to the statement of a viscous-viscoelastic correspondence principle for Brownian motion which simplifies appreciably the calculations of the mean-square displacement and the velocity autocorrelation function of Brownian particles suspended in viscoelastic materials where inertia effects are non-negligible at longer timescales. The viscous-viscoelastic correspondence principle established in this paper by introducing the concept of the inerter is equivalent to the viscous-viscoelastic analogy adopted by Mason and Weitz [T. G. Mason and D. A. Weitz, Phys. Rev. Lett. 74, 1250 (1995)10.1103/PhysRevLett.74.1250].

Asymptotic and numerical homogenization methods applied to fibrous viscoelastic composites using Prony’s series

The paper focuses on the evaluation of the effective properties of linear viscoelastic composites with a periodic structure, containing long cylindrical fibers of circular cross-section and for two different cell arrangements: square and hexagonal unit cells. For this purpose, we use the two-scale asymptotic homogenization method (AHM) and a numerical homogenization method (NHM). Based on the correspondence principle, the local functions and the relaxation overall properties are obtained in explicit form by the AHM using the Prony series. Additionally, the NHM is established for a three-dimensional representative cell, and the problem is solved under appropriate boundary conditions, by using the Finite Element Method. The numerical results obtained by the AHM and NHM are compared and verified with other theoretical approaches. The comparisons show a good agreement and a benchmark for further experimental and theoretical investigations.

Convolutional neural networks explain tuning properties of anterior, but not middle, face-processing areas in macaque inferotemporal cortex

Recent computational studies have emphasized layer-wise quantitative similarity between convolutional neural networks (CNNs) and the primate visual ventral stream. However, whether such similarity holds for the face-selective areas, a subsystem of the higher visual cortex, is not clear. Here, we extensively investigate whether CNNs exhibit tuning properties as previously observed in different macaque face areas. While simulating four past experiments on a variety of CNN models, we sought for the model layer that quantitatively matches the multiple tuning properties of each face area. Our results show that higher model layers explain reasonably well the properties of anterior areas, while no layer simultaneously explains the properties of middle areas, consistently across the model variation. Thus, some similarity may exist between CNNs and the primate face-processing system in the near-goal representation, but much less clearly in the intermediate stages, thus requiring alternative modeling such as non-layer-wise correspondence or different computational principles.

A macro–micro viscoelastic-plastic constitutive model for saturated frozen soil

A macro–micro creep constitutive model of viscoelastic-plastic deformation characteristics for three-phase saturated frozen soils is derived in this paper based on micromechanics, considering the influences of ice content and temperature. First, creep tests of saturated frozen soils are performed, and the mechanism of creep deformation is discussed from a micro perspective. Then, the micro-scale and macro-scale information are connected by establishing a relationship between the macroscopic strain energy rate and strain energy rate of the ice particles, soil matrix, and unfrozen water. The viscoelastic stress tensor for the three phases of materials is derived using the visoelastic correspondence principle and the micromechanics method. Thus, the macro-micro viscoelastic constitutive model for saturated frozen soils is obtained. Based on this analysis, the viscoelastic-plastic constitutive model is further considered for the viscoplastic properties of the soil matrix and ice particles. In addition, the corresponding relationship between viscoplastic and viscoelastic is established based on the “equivalent” method. Therefore, the macro-micro creep constitutive model of viscoelastic-plastic deformation characteristics for three-phase saturated frozen soils is finally derived. The model parameters are determined based on the creep tests of frozen soils and the model is verified using creep test results for saturated frozen soil. It is also determined that the proposed model can illustrate the influence of temperature and ice content on the creep of saturated frozen soils.

Early Interculturation, Late Interculturation – Does It Make a Difference in Our Memories?

Abstract Our research is in the perspective of intercultural psychology and addresses the question of memories an intercultural situation leaves for individuals who experience it during their life. More precisely, it is through the autobiographical memory that our research analyzes the articulation between identity and memory processes in relation to a life experience in an intercultural situation, whether it is a life in a multicultural environment, a migration towards a new cultural environment, a plurality of cultural affiliations or many other configurations that the present world is filled with and for which the cultures contact is put in the foreground. The autobiographical memory retains representations of our past and plays a fundamental role in building a sense of identity and continuity of existence. Our article presents results from an analysis based on the life stories of 5 elderly subjects who had intercultural experiences. It would seem that early intercultural experience directs life discourse towards a principle of coherence in autobiographical memory, emphasizing what the participant was rather than what he achieved. On the other hand, Late intercultural experience orients it to a correspondence principle in autobiographical memory, attaching to actions and temporality of life experience and highlighting achievements rather than individuals self perception.

METHODOLOGY FOR MODELING MACROECONOMIC LIMITATIONS OF SCIENTIFIC AND TECHNOLOGICAL PROGRESS

The subject of this article is the methodology of macroeconomic modeling of scientific and technological progress from the point of view, which is an alternative to the modern paradigm of unlimited potential for economic efficiency.The research is based on the general scientific method of transition from simple to complex. As a starting point, the general laws of scientific and technical progress are selected, independent of individual economic factors. The analysis of long-term economic dynamics is based on the model of limited scientific and technological progress (LSTP-model), first proposed in this article. During the simulation, it is shown that even with infinite resources directed to the R&D sector, the rate of STP has its limit. In this connection, the conclusion is formulated that not only the volume and quality of resources in the R&D sector, but also the duration of their use are important for technological development.The methodology used in the article implements the general scientific principle of correspondence. It is shown that: 1) the classical models of unlimited STP are the limiting case of one of the proposed equations; 2) traditional production functions proved to be the limiting case of the proposed production function with restrictions on maximum product efficiency and minimum efficiency of production factors.A feature of the study is a multivariate approach - consideration and comparative analysis of possible macroeconomic functions and equations of dynamics. Based on this approach, functions and equations were determined that describe the unevenness of economic development, fluctuations in the rate of growth of efficiency, and endogenous waves of STP. It is shown that the new indicators (the potential for increasing efficiency, the sufficiency index of the STP factor) and the functions made up of them allow us to adequately analyze the increasingly complex aspects of scientific and technological progress. A function of exogenous dynamics reflecting the exogenous effect on STP is proposed. An analysis of this function made it possible to adequately describe the historical dynamics of various economic systems that differ in the balance of positive and negative exogenous factors.The general laws of STP are modeled using complex (including implicit) functions. Depending on the specifics of the process under study, complex functions of higher orders can be applied. From a mathematical point of view, the presented equations of dynamics are classified as ordinary autonomous first-order differential equations. Such a mathematical apparatus made it possible to demonstrate the need to observe the general scientific principle of the homogeneity of time. It is shown that limited scientific and technological progress can be described using the utility function.

Improved damping in sandwich beams through the inclusion of dispersed graphite particles within the viscoelastic core

In this work, the passive damping in a sandwich beam is investigated for the inclusion of dispersed graphite particles within the viscoelastic core. The effective material properties of the viscoelastic particulate composite (VEPC) are estimated using a differential scheme and the elastic–viscoelastic correspondence principle. The corresponding results reveal increased effective storage moduli and decreased effective loss factor of a viscoelastic medium for the inclusion of graphite particles. As it implies both the possibilities of augmentation and deterioration of passive damping in the sandwich beam, the subsequent study is carried out on the variation of damping characteristics of the sandwich beam especially for different volume fractions of inclusion. It is found that the passive damping in the sandwich beam increases significantly for the inclusion of graphite particles within the viscoelastic core, and also an optimal volume fraction of inclusion corresponding to the maximum damping in the sandwich beam appears. Further study on the optimal utilization of VEPC patches within the core of the sandwich beam reveals a minimal change of weight of the overall beam for the replacement of patches of conventional viscoelastic material by VEPC patches while this replacement yields a remarkable improvement of passive damping in the sandwich beam.

Improved pseudo three-dimensional model for hydraulic fractures under stress contrast

The conventional pseudo three-dimensional (P3D) model is improved to consistently account for arbitrary stress contrast when simulating hydraulic fractures in a rock stratum. The improvement is based on proper combining the model by Khristianovich-Geertsma-de Klerk (KGD), generalized to a medium with stress contrast, and the original P3D model. We suggest the correspondence principle, which establishes a correspondence between the two models in terms of physical quantities present in each of them. These are: (i) the positions of fracture tips, and (ii) the fluid volumes above and below the injection point. When these quantities are same for the both models, it may be expected that the speeds of height growth, not present in the original P3D model, may be equated to those of the KGD model, which includes these speeds in its formulation. This approach is applicable in all the cases when the solution to a KGD problem uniquely defines the speeds of fracture tips via their positions and fluid volumes below (above) a tip.The comparison of fracture footprints, obtained by the method suggested, with published truly 3D solutions for cases with strong stress contrast, has shown good agreement. This confirms that the P3D model, complemented with the correspondence principle, provides acceptable results for the height growth. A simple approach to meet the correspondence principle is suggested and successfully tested. Examples demonstrate abilities of the improved model for simplified modeling of HF in a layered stratum with stress contrast. The model developed serves also to establish conditions, under which the P3D modeling is relevant.

Physical Violations of the Bulk-Edge Correspondence in Topological Electromagnetics.

In this Letter, we discuss two general classes of apparent violations of the bulk-edge correspondence principle for continuous topological photonic materials, associated with the asymptotic behavior of the surface modes for diverging wave numbers. Considering a nonreciprocal plasma as a model system, we show that the inclusion of spatial dispersion (e.g., hydrodynamic nonlocality) formally restores the bulk-edge correspondence by avoiding an unphysical response at large wave numbers. Most importantly, however, our findings show that, for the considered cases, the correspondence principle is physically violated for all practical purposes, as a result of the unavoidable attenuation of highly confined modes even if all materials are assumed perfect, with zero intrinsic bulk losses, due to confinement-induced Landau damping or nonlocality-induced radiation leakage. Our work helps clarifying the subtle and rich topological wave physics of continuous media.