Correspondence Principle Research Articles

Interaction among neighbouring rectangular finite strike slip faults in a linear viscoelastic half space representing lithosphere-asthenosphere system

There are seismically active regions consisting of fault system with a number of neighbouring earthquake faults. A movement across any one of them may affect the nature of stress accumulation near the others. Mathematical models may be developed to study these interactions and the pattern of interseismic stresses during the aseismic period in between two consecutive seismic events. In this paper, the lithosphere-asthenosphere system is being represented by a linear viscoelastic half space. The material of the half space is expected to possess the properties of both Maxwell and Kelvin type materials. It is assumed that the system is under a steady shear stress generated by some tectonic phenomena. For obtaining the solution for displacement, strain and stresses from the resulting boundary value problem, Integral transform, Green’s function techenique and correspondence principle have been used. Appropriate estimates of the model parameters were used in carrying out the numerical computations for investigating the nature of interactions among the faults.

A novel kind of equations linking the quantum dynamics and the classical wave motions based on the catastrophe theory

Considering that the catastrophe theory could describe quantitatively any phase transition process, we adopt the folding and cusp catastrophe types as the potential functions in the Schrödinger equation to attempt to link the quantum dynamics and the classical wave motions. Thus, through the dimensionless analysis a novel kind of partial differential equations is derived out. When the scaling parameter of the novel equation is equal to the Planck's constant, this equation becomes a detailed time-independent Schrödinger equation, from which Bohr correspondence principle can be found. On the other hand, when the scaling parameter tends to zero, this equation could degenerate to the classical Helmholtz equation. Therefore, this novel kind of equations could describe quantitatively the variation process of the wave functions from the macroscopic level to the quantum size.

An ergodic correspondence principle, invariant means and applications

A theorem due to Hindman states that if E is a subset of ℕ with d*(E) > 0, where d* denotes the upper Banach density, then for any ε > 0 there exists N ∈ ℕ such that $$d^{\ast}(\cup_{i=1}^{N}(E-i))>1-\varepsilon$$ . Curiously, this result does not hold if one replaces the upper Banach density d* with the upper density $$\bar{d}$$ . Originally proved combinatorially, Hindman’s theorem allows for a quick and easy proof using an ergodic version of Furstenberg’s correspondence principle. In this paper, we establish a variant of the ergodic Furstenberg’s correspondence principle for general amenable (semi)-groups and obtain some new applications, which include a refinement and a generalization of Hindman’s theorem and a characterization of countable amenable minimally almost periodic groups.

On characteristic identification for prestressed human skin

In the paper, we present a model of skin in the form of viscoelastic layer-like structure that is inhomogeneous in thickness and consists in turn of three layers: subcutaneous fat, dermis and epidermis. We also assume the presence of an inhomogeneous uniaxial prestress in the skin layer arisen as a result of relaxation after the skin lifting (tightening) surgery procedure. We formulate the problem on the basis of the general problem statement on steady-state vibrations of an inhomogeneous body, taking into account the initial stress-strain state. Using the correspondence principle, the elastic moduli in the problem statement are replaced by complex analogs corresponding to the model of a standard viscoelastic body. The inverse problem is to determine the mechanical characteristics (complex analogs of the Lame parameters) and prestress using the data on the acoustic response for a periodic probing non-invasive effect on the layer surface. By using the Fourier transform in the longitudinal coordinate, we reduce the original problem to solving a number of simpler problems in transforms. Based on the combination of different loading modes, we present a two-stage scheme for identifying mechanical properties and prestress. Within this scheme, at the first stage, complex analogs of the Lame parameters are successively determined using the iterative approach and the Tikhonov regularization method. At the second stage, by using the functions found at the first stage, prestresses are determined using the proposed projection technique. We illustrate the approach developed to the considered skin integument problem by performing computational experiments showing the efficiency of the techniques proposed in the ranges corresponding to the real values of the sought-for parameters. Additionally, we provide some recommendations on the choice of frequency ranges for the best identification at each stage.

Репрезентация эталонов красоты человека в сравнительных оборотах русского языка

The article deals with the problems of representation of the standards of human beauty in the comparative turns of the Russian language [beautiful, as...]. When choosing beauty standards, a person is guided by cultural norms and stereotypes that exist in the socio-cultural space. Native speakers of the language and culture most often choose religious and mythological characters (god, angel, madonna, witch, devil) as standards. They belong not only to Slavic mythology, but also to ancient, Eastern, and Scandinavian (nymph, Apollo, Aphrodite, peri, guria, valkyrie). The standards of beauty also include the precedent proper names of literary heroes, actors, singers, historical figures (Agamemnon, Eugene Onegin, Brad Pitt, Lyubov Orlova, Liudmila Zykina, Chapaev, Cleopatra). Beauty standards are gender-oriented: there are separate standards of male beauty and standards of female beauty. When choosing standards, the principle of gender correspondence of the standard and the object of comparison is observed.

Mixed FEM for flexoelectric effect analyses in a viscoelastic material

The correspondence principle is applied to solve general 2-D electro-viscoelastic problems with the flexoelectric effect. Two competitive characteristics of strengthening and softening of micro-/nano-sized structures are considered for some advanced materials. Due to higher order derivatives of the primary solution parameters in the governing equations, the standard C0 continuous finite element method cannot be applied directly to analyze this problem. The mixed FEM (MFEM) is developed here to this end. The C0 continuous approximation is applied independently for displacements and strains; kinematic constraints between them are satisfied by a collocation method. The Stehfest’s inversion method is applied to obtain the final time-dependent solutions. Two example problems are presented to demonstrate the successful implementation of the collocation-MFEM, the first involves a cantilever beam for which analytical solution is available for verification; and the second, is a rectangular domain with an edge crack.

Topological lattice defects by groupoid methods and Kasparov’s KK-theory* *This work was supported by the National Science Foundation through the Grant DMR-1823800.

The bulk-boundary and a new bulk-defect correspondence principles are formulated using groupoid algebras. The new strategy relies on the observation that the groupoids of lattices with boundaries or defects display spaces of units with invariant accumulation manifolds, hence they can be naturally split into disjoint unions of open and closed invariant sub-sets. This leads to standard exact sequences of groupoid C*-algebras that can be used to associate a Kasparov element to a lattice defect and to formulate an extremely general bulk-defect correspondence principle. As an application, we establish a correspondence between topological defects of a two-dimensional square lattice and Kasparov’s group . Numerical examples of non-trivial bulk-defect correspondences are supplied.

Alternative approach to the quantization of the damped harmonic oscillator

In this paper, a new approach for constructing Lagrangians for driven and undriven linearly damped systems is proposed, by introducing a redefined time coordinate and an associated coordinate transformation to ensure that the resulting Lagrangian satisfies the Helmholtz conditions. The approach is applied to canonically quantize the damped harmonic oscillator and although it predicts an energy spectrum that decays at the same rate to previous models, unlike those approaches it recovers the classical critical damping condition, which determines transitions between energy eigenstates, and is therefore consistent with the correspondence principle. It is also demonstrated how to apply the procedure to a driven damped harmonic oscillator.

Specificity and incremental predictive validity of implicit attitudes: studies of a race-based phenotype

Four studies involving 2552 White American participants were conducted to investigate bias based on the race-based phenotype of hair texture. Specifically, we probed the existence and magnitude of bias in favor of Eurocentric (straight) over Afrocentric (curly) hair and its specificity in predicting responses to a legal decision involving the phenotype. Study 1 revealed an implicit preference, measured by an Implicit Association Test (IAT), favoring Eurocentric over Afrocentric hair texture among White Americans. This effect was not reducible to a Black/White implicit race attitude nor to mere perceptual preference favoring straight over curly hair. In Study 2, the phenotype (hair) IAT significantly and uniquely predicted expressions of support in response to an actual legal case that involved discrimination on the basis of Afrocentric hair texture. Beyond replicating this result, Studies 3 and 4 (the latter preregistered) provided further, and even more stringent, evidence for incremental predictive validity: in both studies, the phenotype IAT was associated with support for a Black plaintiff above and beyond the effects of two parallel explicit scales and, additionally, a race attitude IAT. Overall, these studies support the idea that race bias may be uniquely detected by examining implicit attitudes elicited by group-based phenotypicality, such as hair texture. Moreover, the present results inform theoretical investigations of the correspondence principle in the context of implicit social cognition: they suggest that tailoring IATs to index specific aspects of an attitude object (e.g., by decomposition of phenotypes) can improve prediction of intergroup behavior.

Viscoelastic normal indentation of nominally flat randomly rough contacts

Viscoelastic materials are receiving increasing attention in soft robots and pressure sensitive adhesives design, but also in passive damping techniques in automotive and aerospace industry. Here, by using the correspondence principle originally developed by Lee and Radok and further extended by Ting and Greenwood, we transform the elastic solutions of Persson for contact of nominally flat but randomly rough surfaces to viscoelastic indentation. As an example, the cases of step loading and of the response to a single cycle of harmonic loading are studied. For the latter, the effect of the loading frequency, of the ratio between the rubbery and the glassy moduli of the material, and of the mean normal load on the dissipated energy per cycle is studied in detail for a standard viscoelastic material. The results shown are significant for the engineering applications involving cyclic indentation of soft materials, such as in tire-road contact, seals, pick-and-place manipulators and grippers

A Graphical Approach to Understanding a Mechanism of Synchronicity by Mirror Archetype against the Background of the Psychic Correspondence Principle

A Graphical Approach to Understanding a Mechanism of Synchronicity by Mirror Archetype against the Background of the Psychic Correspondence Principle

Deciphering the Q-markers of nourishing kidney-yin of Cortex Phellodendri amurense from ZhibaiDihuang pill based on Chinmedomics strategy

BackgroundCortex Phellodendri amurensis (CPA) has high medicinal value in the treatment of kidney-yin deficiency diseases. However, due to the lack of research on the therapeutic material basis of CPA, the current quality control standard for CPA is defective, and the effect of the nourishing kidney-yin of CPA was limited. PurposeBased on the principle of correspondence between the syndrome and prescriptions, we studied the CPA in ZhibaiDihuang pill (ZBDH) to identify quality markers (Q-markers) of CPA in ZBDH for treating kidney-yin deficiency and seek the potential Q-markers of CPA under nourishing kidney-yin effect combined with the analysis of single CPA. MethodsTaking Chinmedomics as the core strategy, metabonomics analysis and effective component identification were performed by UPLC-MS. ResultsA total of 121 chemical components of ZBDH were identified, among which the contents of berberine, palmatine, jatrorrhizine and magnoflorine changed the most obviously with the addition of CPA. Forty-five components were identified in the blood in the markedly effective state, including berberine, palmatine, jatrorrhizine and magnoflorine. The therapeutic material basis of ZBDH in the treatment of kidney-yin deficiency was found, and 6 components were found to derive from CPA, including magnoflorine and jatrorrhizine. In addition, seventeen components were identified in the blood in the single CPA treatment, including berberine, palmatine, jatrorrhizine and magnoflorine. ConclusionsMagnoflorine and jatrorrhizine were the Q-markers of CPA for treating kidney-yin deficiency in the formula of ZBDH and they were also potential Q-markers of the nourishing kidney-yin of CPA.

On the consolidation and creep behaviour of layered viscoelastic gassy sediments

Gassy sediments are frequently encountered in engineering geology and geotechnical engineering. Gas bubbles contained in these sediments significantly change the engineering properties, and further influence the consolidation and creep process. The long term behaviour of gassy sediment is drastically different from that of saturated and unsaturated soils. This study presents an analytical solution for exploring such behaviour within layered viscoelastic gassy sediments under different type of load. An Analytical layer element method together with a Laplace-Hankel transform are employed to solve the governing equations, and the viscoelastic solution is then captured with the aid of the elastic-viscoelastic correspondence principle. Comparisons of the present solution with published semianalytical solutions and experimental results, for a single and double layered soils, are provided. Extensive parametric analyses were carried out to explore the effects of the soil skeleton model, fractional order, type of load, saturation degree and stratification characteristics on consolidation and creep processes. In the present model, the permeability is saturation degree- and porosity-dependent and the modulus of elasticity is time-dependent, which can simulate the long term behaviours of gassy sediments reasonably.

Investigation of corner states in second-order photonic topological insulator.

Recently, higher-order topological insulators have been investigated as a novel topological phase of matter that obey an extended topological bulk-boundary correspondence principle. In this paper, we study the influence of BNN interaction on photonic higher-order corner states. We find both next-nearest-neighbor (NNN) hopping and perfect electric conductor (PEC) boundaries can solely result in two kinds of corner states which are quite different from the traditional "zero-energy" state. To demonstrate this intuitively, we design a novel all-dielectric structure that can effectively shield the influence of NNN couplings while remain the effect of PEC boundaries, so that we can distinguish the contributions from NNN hopping and PEC boundaries. In addition, we also investigate the total contribution on corner states when NNN couplings and PEC boundaries coexist, and some interesting features are revealed. These findings may expand our understanding of the high-order corner modes in a more general framework.

Norm and human health

The concept of norms is common to biology and medicine. It represents the essence of any phenomenon. In medicine, human health is expressed through the category of norm. The basis of the construction of the norm (normology) should be based on the principle of correspondence of morphofunctional properties of the organism to the environment, and not their nature. And then indicators that reflect the stability of a living non-equilibrium system or the state of an adapted organism will characterize (normal) human health. The norm is always stable, otherwise it will not be the norm. The science of human health developed through analysis the decomposition of a complex whole into simple parts. In this case, the object disappeared as a whole, as a system with all its inherent features. The norm was derived from the fitness, balance of the body with the environment. Recently, it has become possible to consider a person as a system that is determined by the relationship of the whole and its parts (the golden ratio). In biology, the golden ratio manifests itself in many ways, from the structure of polypeptides to the human body. The study of a living organism as a system allowed us to establish the harmonic essence of its structure. The idea of the harmony of the world of systems is connected with the relations of "opposites" within the object. The "golden opposites" of healthy people are a kind of norm reference. What brings "opposites" to unity is harmony. Harmony is closely related to the golden ratio. Golden harmony is the basis of human health. Mathematical expression of harmony, symmetry a method of assessing (norm) human health. Deviations from the "golden" relations can be used in medicine as indicators (criteria) for the diagnosis of pathological disorders.

Dynamic prediction model for surface settlement of horizontal salt rock energy storage

In order to theoretically calculate the surface settlement of horizontal salt rock energy storage, the conformal mapping method in the complex variable function was adopted, and the superposition principle and viscoelastic correspondence principle were considered to derive a theoretical displacement formula. This formula can be used to calculate the radial displacement of the surrounding rock on the cross section of horizontal elliptical cylindrical salt rock storage at any time, and then the volume shrinkage of the storage can be obtained. Based on the assumption that the volume shrinkage during the long-term operation of the horizontal salt rock storage is proportional to the volume of the surface settlement trough, a compound power function was proposed to describe the surface settlement curve, and then a dynamic prediction model for the surface settlement of the horizontal salt rock storage was established. The numerical simulation results of surface settlement during the long-term operation of horizontal elliptical cylindrical salt rock storage were used to verify the rationality of the surface settlement model. The comparison shows that when the operation time is 0, the error between the settlement of the center point calculated from theoretical model and that from numerical simulation is 241.61%, and then the error gradually decreases with increasing time. When the operation time exceeded 3 years, the settlement at the center point and the surface settlement curves calculated from the theoretical model are all in good agreement with numerical simulation results, and the maximum error, occurs at the center point of surface, is only 8.11% when the operation time is 15 years.

Metoda VECD jako narzędzie do oceny trwałości zmęczeniowej konstrukcji nawierzchni

Postęp technologiczny i wprowadzenie do stosowania zaawansowanych materiałów o ponadstandardowych właściwościach, np. mieszanek mineralno-asfaltowych z lepiszczami wysokomodyfikowanymi polimerami HiMA (ang. highly modified asphalt), wymaga poszukiwania metody umożliwiającej kompleksowe uwzględnienie cech tych materiałów w obliczeniach. Jedną z takich metod może być metoda wykorzystująca model rozproszonego niszczenia w ośrodku lepkosprężystym (ang. viscoelastic continuum damage model, VECD). W artykule zaprezentowano metodologię opartą na modelu VECD oraz możliwości, jakie daje przy wymiarowaniu nawierzchni drogowych. Opisano poszczególne komponenty metody: analogię sprężysto-lepkosprężystą, mechanikę rozproszonego niszczenia i zasadę równoważności temperaturowo-czasowej z przyrostowym niszczeniem. Przedstawiono rów¬nież koncepcję uproszczonych obliczeń w metodzie S-VECD (ang. simplified viscoelastic continuum damage model). Artykuł zawiera opisy opracowanych kryteriów zniszczenia. Przybliżono również metody badań, które dostarczają danych wejściowych. W końcowej części artykułu przedstawiono przykładową analizę porównawczą z wykorzystaniem metody S-VECD dla konstrukcji z mieszankami mineralno-asfaltowymi z HiMA w warstwie podbudowy i mieszankami mineralno-asfaltowymi z HiMA we wszystkich warstwach.

Analytical solutions and boundary element analysis for holes and cracks in anisotropic viscoelastic solids via time-stepping method

In this study the time-stepping method, which can convert the problem of anisotropic viscoelasticity into two sets of elastic-like system, is employed for both analytical solutions and boundary element method (BEM) to solve the two-dimensional problems of holes and cracks in anisotropic viscoelastic solids. Based upon this method and the available solutions for the corresponding elastic problems, some analytical solutions for the two-dimensional problems of holes and cracks in anisotropic viscoelastic solids are presented, such as the one with an elliptical hole, a straight crack, two collinear cracks, or collinear periodic cracks under uniform load at infinity. We also present the fundamental solution for the problems with an elliptical hole, and use this solution to construct a special boundary element method (SBEM). Further extension of SBEM is made to develop the boundary-based finite element method (BFEM) to deal with the problems with multiple holes and cracks. The advantage of SBEM and BFEM is that no meshes are required on the boundaries of holes and cracks. To show the accuracy and efficiency of the proposed method, several representative examples are implemented and compared with those obtained by the finite element method and the elastic-viscoelastic correspondence principle. The results show that the solutions obtained by different methods are in well agreement with each other, and the ones obtained by the time-stepping method are around 3 to 36 times faster than the others depending on the problems and methods.

Characterization of viscoelastic properties of asphalt mixture at low temperatures using DC(T) creep test

This study presents a framework to identify the low-temperature viscoelastic properties of asphalt concrete using the disk-shaped compacted tension (DC(T)) creep test. Due to the DC(T) geometry, the stress–strain state in the DC(T) geometry is not simple, and a geometry coefficient is needed to characterize the relationship between the mechanical and geometrical properties. The geometry coefficient of DC(T) was calculated by invoking the correspondence principle in viscoelasticity. The DC(T) creep test was conducted on different asphalt mixtures comprised of various components and modifiers at three temperature levels of 0, −12, and −24 °C. The creep compliance function for each of these mixtures was modeled using a generalized Voigt-Kelvin spring-dashpot phenomenological representation. The numerical implementation of the generalized Voigt-Kelvin model was developed in the finite element code Abaqus via a user material subroutine (UMAT). Numerical simulations of DC(T) creep tests using the identified viscoelastic properties are presented, which indicate the capability of the proposed approach to characterize the low-temperature linear viscoelastic behavior of the investigated asphalt mixtures. To further validate the viscoelastic properties obtained from DC(T) test through different stress–strain states, numerical simulation results from an Indirect Tensile Creep Test were compared to experimental results. The close agreement found between the results of indirect tension creep tests and numerical simulations indicates the capability of the proposed approach for identification of viscoelastic properties of asphalt mixtures at low temperatures, which opens the door to avoid the intricate experimental setup and poor repeatability of the indirect tensile creep test at low temperatures.

Time-dependent model for unidirectional composite with a viscoelastic matrix

Modelling of time-dependent properties of unidirectional fiber reinforced plastics on the basis of structural mechanics of composite materials and mechanics of hereditary media has been proposed in this research. The constitutive equations of unidirectional fiber reinforced plastics have been obtained using the Volterra correspondence principle and the algebraic properties of resolvent operators. Modelling of viscoelastic properties of a unidirectional composite material on the basis of EDT-10 epoxy resin has been shown.