Correspondence Principle Research Articles

СОВРЕМЕННЫЕ УГРОЗЫ УТРАТЫ ОБЩЕСТВЕННО-ИСТОРИЧЕСКИХ МОДЕЛЕЙ СИМВОЛИЧЕСКИХ ПРОГРАММ РОССИЙСКОГО МЫШЛЕНИЯ И СОЦИАЛЬНОГО ПОВЕДЕНИЯ В СОВРЕМЕННОЙ РОССИИ

The article is devoted to the analysis of modern threats to the loss of the cultural identity of Russian thinking and social behavior of Russians (in the broad sense of the word), as well as to the promotion of constructive measures aimed at protecting Russian cultural identity, primarily in the sphere of its "soft power", within the boundaries of which it will be necessary to form the level of a nationwide independent cultural stratum capable of pushing the “mass culture” of the West to the periphery of Russians' interest. Particular attention is paid to the position of the methodology of science, known as the "principle of correspondence", stating that the new is the heir and successor of the old, and not its denier, denoting the logic of the evolution of any activity and any tradition.

The Furstenberg–Sárközy theorem and asymptotic total ergodicity phenomena in modular rings

The Furstenberg–Sárközy theorem asserts that the difference set E−E of a subset E⊂N with positive upper density intersects the image set of any polynomial P∈Z[n] for which P(0)=0. Furstenberg's approach relies on a correspondence principle and a polynomial version of the Poincaré recurrence theorem, which is derived from the ergodic-theoretic result that for any measure-preserving system (X,B,μ,T) and set A∈B with μ(A)>0, one has c(A):=limN→∞⁡1N∑n=1Nμ(A∩T−P(n)A)>0. The limit c(A) will have its optimal value of μ(A)2 when T is totally ergodic. Motivated by the possibility of new combinatorial applications, we define the notion of asymptotic total ergodicity in the setting of modular rings Z/NZ. We show that a sequence of modular rings Z/NmZ,m∈N, is asymptotically totally ergodic if and only if lpf(Nm), the least prime factor of Nm, grows to infinity. From this fact, we derive some combinatorial consequences, for example the following. Fix δ∈(0,1] and a (not necessarily intersective) polynomial P∈Q[n] with deg⁡(P)>1 such that P(Z)⊆Z. For any integer N>1 with lpf(N) sufficiently large, for any subsets A and B of Z/NZ such that |A||B|≥δN2, one has Z/NZ=A+B+S, where S={P(n):1≤n≤N}⊂Z/NZ.

Topological charge Fano effect in multi-Weyl semimetals

We theoretically analyze the Fano interference in a single impurity multi-Weyl semimetal hybrid system and show the emergence of the topological charge Fano effect in the bulk local density of states. In multi-Weyl semimetals, the number of Fermi arcs at the system boundaries is determined by the topological charge $J$, a direct consequence of the "bulk-boundary" correspondence principle. Analogously, we find that $J$ also modulates the bulk Fano profile of the system with an embedded quantum impurity. Thus, by increasing $J$, the Fano lineshape evolves from resonant, typical for $J=1$ (single Weyl), towards antiresonant, extrapolating to the so-called hyper Weyl semimetals with $J\gg1$. Specially for the maximum case protected by the rotational symmetry $C_{2J=6}$, namely the $J=3$ (triple Weyl), which acquires asymmetric Fano profile, the Fano parameter absolute value is predicted to be $\tan(C_{2J=6})$, where $C_{2J}\equiv(360^{\circ}/2J)$ defines the rotational angle. Hence, the Fano discretization in the $J$ term introduces the topological charge Fano effect in multi-Weyl semimetals. We also suggest a transport device where we expect that the proposed Fano effect could be detected.

Effective thermo-viscoelastic behavior of short fiber reinforced thermo-rheologically simple polymers: An application to high temperature fiber reinforced additive manufacturing

This paper presents a procedure for the estimation of the effective thermo-viscoelastic behavior in fiber-reinforced polymer filaments used in high temperature fiber-reinforced additive manufacturing (HT-FRAM). The filament is an amorphous polymer matrix (PEI) reinforced with elastic short glass fibers treated as a single polymer composite (SPC) holding the assumption of thermo-rheologically simple matrix. Effective thermo-viscoelastic behavior is obtained by implementing mean-field homogenization schemes through the extension of the correspondence principle to continuous variations of temperature by using the time–temperature superposition principle and the internal time technique. The state of the fibers in the composite is described through the use of probability distribution functions. Explicit forms of the effective properties are obtained from an identification step, ensuring the same mathematical structure as the matrix behavior. The benchmark simulations are predictions of residual stress resulting from the cooling of the representative elementary volumes (REVs) characterizing the composite filament. The computation of the averaged stress in the benchmarking examples is achieved by solving numerically the stress–strain problem via the internal variables’ framework. Reference solutions are obtained from Fast Fourier Transform based full-field homogenization simulations. A comparative analysis is performed, showing the reliability of the proposed homogenization procedure to predict residual stress against extensive computations of the macroscopic behavior of a given microstructure.

Rotation symmetry-protected topological phases of fermions

We study classification of interacting fermionic symmetry-protected topological (SPT) phases with both rotation symmetry and Abelian internal symmetries in one, two, and three dimensions. By working out this classification, on the one hand, we demonstrate the recently proposed correspondence principle between crystalline topological phases and those with internal symmetries through explicit block-state constructions. We find that for the precise correspondence to hold it is necessary to change the central extension structure of the symmetry group by the $\mathbb{Z}_2$ fermion parity. On the other hand, we uncover new classes of intrinsically fermionic SPT phases that are only enabled by interactions, both in 2D and 3D with four-fold rotation. Moreover, several new instances of Lieb-Schultz-Mattis-type theorems for Majorana-type fermionic SPTs are obtained and we discuss their interpretations from the perspective of bulk-boundary correspondence.

Modeling of Imperfect Viscoelastic Interfaces in Composite Materials

The present work deals with hierarchical composites in three dimensions, whose constituents behave as non-aging linear viscoelastic materials. We model the influence that imperfect viscoelastic interfaces have on the macroscopic effective response of these structures. As an initial approach, the problem of two bodies in adhesion is studied and in particular the case of soft viscoelastic interface at zero-order is considered. We deduce the integral form of the viscoelastic interface by applying the matched asymptotic expansion method, the correspondence principle, and the Laplace–Carson transform. Then, by adapting the integral form previously obtained, we address a heterogeneous problem for periodic structures. Here, theoretical results obtained for perfect interfaces are extended to the formal viscoelastic counterpart of the spring-type imperfect interface model. Finally, we show the potential of the proposed approach by performing calculations of effective properties in heterogeneous structures with two- and three-scale geometrical configurations and imperfect viscoelastic interfaces.

Теоретические проблемы прагмастилистики. Часть 1

The author presents the theoretical basis for linguistic research, whose subject is the interaction of two disciplines: stylistics and pragmatics. In the first part of the article, the author provides a brief overview of the history and problem fields of both disciplines, emphasizing the fact that each of them has its own characteristics from conceptual and ontological points of view. In the second part, the author considers stylistics and pragmatics in the general semiotic model as two “dimensions” of linguistic signs. In addition to the three dimensions introduced by C. Morris, i.e., syntactics, semantics, and pragmatics, the author introduces stylistics as the relation (according to the principle of correspondence) of signs to their socio-cultural environment, i.e., their practical/instrumental context. The author distinguishes between two directions within the framework of pragmastylistic studies. The indicative aspect consists of the study of pragmatic characteristics of separate styles, in other words, in the description of the style employing the conceptual apparatus of pragmalinguistics (such concepts as illocutionary function, speech act, pragmatic strategy, pragmatic implication, pragmatic operator, etc.). The applicative aspect of pragmatic studies is the study in the use of stylistic means of language (i.e., stylistically marked lexical forms and their constructions) for the implementation of different types of speech acts.

Subsidence above gas storage in salt caverns predicted with viscoelastic theory

Based on the on-site monitoring data, the surface subsidence in the Jintan underground gas storage site has occurred continuously since the construction and operation of gas storage engineering. Therefore, the prediction of surface subsidence above gas storage in salt caverns is important to ensure the long-term safety of gas storage. Based on the mechanics theory, the formulas of elastic deformation of spherical and cylindrical caverns are derived. The Burgers viscoelastic model is used to describe the creep of rock salt. The viscoelastic analytical solution of the cavern deformation is obtained by using the correspondence principle in viscoelastic theory. It is assumed that the volume of the surface subsidence basin is directly proportional to the shrinkage volume of the cavern. The surface subsidence distribution curve is described by a Gaussian function. The spatiotemporal prediction of surface subsidence above gas storage in salt caverns based on viscoelastic theory is thus developed. The proposed theoretical model is used to analyze the surface subsidence above a gas storage cavern in rock salt in Jintan. The calculated subsidence is compared with the monitoring data. The accuracy of the theoretical model is verified by numerical simulation. The theoretical model can be used to predict the surface subsidence considering the solution stage in which the internal pressure changes with time. Results of this paper can provide guidance and suggestions for engineering practice of gas storage in salt caverns.

Thermal buckling and free vibration of viscoelastic functionally graded sandwich shells with tunable auxetic honeycomb core

In this paper, thermal buckling and free vibration of viscoelastic functionally graded sandwich shell with tunable auxetic honeycomb core is investigated. The sandwich shell has functionally graded material (FGM) skins at top and bottom and tunable auxetic honeycomb core at the middle. The viscoelastic behavior of the skins and core are modeled according to complex modulus approach in combination with the elastic–viscoelastic correspondence principle. Poisson's ratio of the auxetic honeycomb core is tunable. It has positive or negative value, which depends on an angle parameter of the unit cell of the auxetic honeycomb core. The equations of motion for the viscoelastic FGM sandwich shell with tunable auxetic honeycomb core are derived using Hamilton's principle. Analytical solution for simply supported shell is obtained using Navier's solution procedure. The effects of the geometry parameters, temperature rise, parameters of the tunable auxetic honeycomb core are studied.

Finite volume based asymptotic homogenization of viscoelastic unidirectional composites

The previously developed finite volume based asymptotic homogenization theory designed for unidirectional composites with finite-sized microstructures is further extended to non-ageing linear viscoelastic region via correspondence principle. The theory is a unified framework able to accommodate general loadings, both out-of-plane and in-plane. It first transforms the problems in time domain to Laplace domain via elastic–viscoelastic correspondence principle, solves the problems in transformed region, and transforms the solutions back to time domain through numerical inversion technique. In Laplace domain, the microscale problems are solved up to the third term of expansion, and the homogenized stiffness tensors of all orders are passed to the macroscale, leading to the solutions of macroscale displacements. The method’s capability is assessed through comparison with direct numerical solution, showing increasing accuracy with increasing truncation order and decreasing scale ratio, and further enhancement by reconstructing boundary layer. The robustness of theory is verified through parametric studies. The possibility of reducing the highest order of spatial derivative of homogenized displacement is also investigated. The finite volume based methodology marks the theory’s uniqueness among the existing higher order asymptotic homogenization methods, providing an efficient alternative to solve the viscoelastic composite structural problems.

ECCPA: Calculation of classical and quantum cross sections for elastic collisions of charged particles with atoms

ECCPA: Calculation of classical and quantum cross sections for elastic collisions of charged particles with atoms

THE PRINCIPLE OF COMPOSITIONAL AND FIGURATIVE COMPLIANCE IN THE ARCHITECTURE OF NON-FORMAL EDUCATION INSTITUTIONS

The article presents the author's view on the formation of composition and image in the architecture of non-formal education institutions (NFEI). Brief information about the basic principles of figurative design of the buildings of such institutions from the point of view of a systematic approach to the formation of their architecture is presented. Understanding the formation of the architecture of NFEI covers a fairly wide range of issues and compositional-figurative solutions are an important point, since the artificially created space for learning is now interpreted as a psycho-emotional and functional educational component. The architecture is very diverse and its formation depends on many factors: external and internal. Among the main principles of the figurative solution of the building, the author defines the following: the principle of compositional and figurative correspondence to the purpose of the institution and its planning solutions; the principle of conformity and opposition of the image of the building to the environment; the principle of scale (elements, materials, facade-shaped and interior solutions); the principle of attractiveness of a complex solution of an object (ensemble); the principle of conceptual integrity of architectural and imaginative solutions. The principle of compositional and figurative correspondence to the purpose of the institution and its planning solution is designated in this study as the first one, which requires making decisions related to the spatial and architectural and planning components. It is known that there are two main ways (approaches) of such solutions - from function to form and from form to function. The “function + environment = form” design path has been proven to be modern and productive. Its introduction is possible only with an analytical combination of the characteristics of the environment, its traditions, history and landscape properties with the functional purpose and content of the building. The example that was given (Zeimuls, Center of Creative Services of Eastern Latvia, SAALS Architectur) demonstrates the use of replication as one of the means to implement such a path. When designing in the existing urban development, adapting historical buildings and structures subject to renovation (refunctionalization), the “form-function” approach may turn out to be optimal, where the environment itself dictates certain decisions regarding the architectural formation of a non-formal education institution, and, at the same time, the creation of a unique educational recreational space (Experimentarium Science Center, CEBRA).
 The architecture of such institutions, although it is connected in a certain way with the educational processes and scenarios familiar to us, has a very wide range of creating unique buildings, given the above approaches to shaping.

A viscoelastic constitutive model for shape memory polymer composites: Micromechanical modeling, numerical implementation and application in 4D printing

In this work, a novel micromechanics-based thermo-viscoelastic constitutive model for shape memory polymer composites (SMPCs) is proposed and applied to four-dimensional (4D) printed SMPCs. The multi-branch constitutive model is used to simulate the time- and temperature-dependent mechanical behavior of the shape memory polymer matrix. According to the elastic–viscoelastic correspondence principle, the equivalent viscoelastic stiffness tensor of the composite is obtained in the micromechanics framework of energy-based effective strain theory and the Mori-Tanaka homogenization scheme, in which a two-parameter interfacial damage model is adopted to consider the displacement discontinuity and traction continuity conditions at the interface between the inclusion and the matrix. The numerical integration scheme for the three-dimensional (3D) viscoelastic constitutive model of SMPCs is presented, and the finite element application is implemented by the user material subroutine UMAT of ABAQUS. After identifying the model parameters with experimental data, the tensile stress-strain curves and stress relaxation phenomena of 4D printed unidirectional SMPCs are successfully described by theoretical simulations. Besides, theoretical simulations also adequately predict the shape memory behavior of 4D printed composites and complex members.

Stroh formalism for various types of materials and deformations

Abstract The Stroh formalism is a complex variable formulation developed originally for solving the problems of two-dimensional linear anisotropic elasticity. By separation of the third variable for the linear variation of displacements along the thickness direction, it was proved to be applicable for the problems with coupled stretching-bending deformation. By the Radon transform which maps a three-dimensional solid to a two-dimensional plane, it can be applied to the three-dimensional deformation. By the elastic-viscoelastic correspondence principle, it is also valid for the viscoelastic materials in the Laplace domain. By expansion of the matrix dimension, it can be generalized to the coupled-field materials such as piezoelectric, piezomagnetic and magneto-electro-elastic materials. By introducing a small perturbation on the material constants, it can also be applied to the degenerate materials such as isotropic materials. Thus, in this paper, the Stroh formalism for several different types of materials (anisotropic elastic, piezoelectric, piezomagnetic, magneto-electro-elastic, viscoelastic) and deformations (two-dimensional, coupled stretching-bending, three-dimensional) are organized together and presented in the same mathematical form.

Эффективные механические характеристики симметричного слоистого композита при различных условиях нагружения

Object and purpose of research. This paper discusses balanced and quasi-isotropic (in the reinforcement plane) symmetric layered composite structures made up by the layers of cloth-reinforced GRP. The purpose of this work was to demonstrate the necessity to justify the applicability of experimental results for effective mechanical parameters determined in the conditions of uniaxial tension/compression to the calculation of thin-walled layered composite structures that work in bending/twisting conditions. Materials and methods. The straining of layered composite structures is simulated as per the updated theory of first-order plates, the model of complex moduli and the principle of elastic-viscoelastic correspondence in linear viscoelasticity theory. Limit state predictions are based on Tsai-Wu tensor-polynomial strength criterion. Main results. This paper suggests the expressions that predict effective elastic constants, dissipation properties and strength limits for symmetric layered structures under investigation. The study shows that balanced symmetric structure made up by four layers of composite may be regarded, with the accuracy sufficient for engineering calculations, as an ortho-tropic material for all loading conditions. At the same time, symmetric quasi-isotropic (in the reinforcement plane) structure made up by thirty two composite layers must be regarded as orthotropic in case of tension/compression and monoclinic in case of bending/twisting. Conclusion. The study has shown the necessity to justify the application of experimental effective mechanical properties for uniaxial tension/compression to calculation of thin-walled layered composite structures exposed to bending/twisting.

An analytical model for 3D consolidation and creep process of layered fractional viscoelastic soils considering temperature effect

The behavior of long-term deformation of saturated soil under external loads has been one of the research focuses in geological engineering and geotechnical engineering. The temperature change, especially in the fields of geological radioactive waste disposal and geothermal system, usually significantly influence the consolidation and creep process of soils. This paper presents an analytical three-dimensional (3D) model for investigating the consolidation and creep behavior of layered soils considering temperature effect. Based on the analytical layer element elastic solution, fractional calculus theory and elastic-viscoelastic correspondence principle, an analytical 3D model is built by introducing the coefficients of thermal expansion and viscosity varying with temperature into the fractional Merchant model (FMM). Verifications against published analytical and numerical results are provided, followed by extensive parametric studies to investigate the effects of type of viscoelastic model, temperature change, fractional order and viscosity of FMM, layered characteristic of soils on consolidation and creep process. It’s evident that the present model predicts long-term behavior of layered viscoelastic soils well and can be used to evaluate the effect of temperature change on consolidation and creep process in geological engineering and geotechnical engineering.

Time-domain asymptotic homogenization for linear-viscoelastic composites: mathematical formulae and finite element implementation

Asymptotic homogenization (AH) is a rigorous method used for modeling multiscale mechanical behavior in periodic composites. Unlike conventional AH methods, which predict the effective viscoelasticity using the elastic–viscoelastic correspondence principle, an AH method was proposed to directly calculate the effective material properties in the time domain, thereby enabling the complex transform to be omitted between the time and Laplace domains. This time-domain AH method is reformulated based on the integral form rather than the differential form of the Kelvin–Voigt viscoelastic model. Thus, multiple time-domain-based characteristic elasticity and viscosity displacement tensors are replaced by one integral form characteristic displacement tensor in the polymer matrix composite. Using mathematical formulae, a numerical implementation method was then developed by establishing location- and time-related stress loads. An in-house Python subroutine was also programmed to compute the effective viscoelastic properties from the finite element implementation results. Unidirectional and woven fabric composite homogenization results were comparable to those obtained using the conventional representative volume element method, indicating high effectiveness and accuracy. The results suggest that the proposed time-domain AH method is a powerful tool for modeling the two-scale mechanical behavior of viscoelastic composites and is compatible with the existing commercial software.

The Viscoelastic Solution to Geertsma’s Subsidence Problem

Abstract This paper presents the viscoelastic analytical solution for stress and displacement due to prescribed time-varying changes in the pore fluid pressure of a disk-shaped inclusion embedded within a semi-infinite, viscoelastic medium. The correspondence principle of viscoelasticity, along with Hankel–Fourier and Laplace transforms, is used to derive the solution. The instantaneous viscoelastic solution, corresponding to the response immediately after the inclusion pore pressure change, recovers the elastic solution to the same problem (Geertsma 1973). Results are presented for fractional Maxwell and Burgers models of viscoelasticity after being applied to a set of experimental data from creep tests on shale. Solution results are demonstrated and discussed for the cases of constant inclusion depletion, as well as delayed injection of fluid into a previously depleted inclusion.

Mill Processability, Rheology and Structure Differences of Polyacrylate Elastomers

Abstract Two commercial polyacrylate elastomers, one having epoxide (EP) crosslinking sites and the other ethylidene norbornene (ENB) were selected. It was demonstrated that the former was more difficult to mill-process than the latter. The viscoelastic properties measured at very small strain in shear oscillation indicated that the ENB polymer was more branched than the EP polymer. The gel determination by filteration confirmed this. The tensile stress-strain measurements were conducted at four different deformation rates. These data were treated according to the strain-time correspondence principle to see if this principle applies to the data of these samples. The data of EP polymer did not form a master curve, thus, the above principle is not applicable; at the larger deformation the strain-hardening tendencies were observed. This indicates that the EP polymer has a rather extensive long branching, a type of which usually results from a chain transfer reaction. The data of the ENB polymer, on the other hand, form a master-curve; that is, the strain-time correspondence principle is applicable, in spite of the presence of the large amount of gel. This means that the gel in the ENB polymer is microgel. The micro-gel in this case is polymer-latex particle, crosslinked during emulsion polymerization with a difunctional comonomer. Thus, in this work polymer rheology was effectively used to find a major difference in the polymer chain structure. In this way it was shown that the results of polymerization may be related to mill processability.

Bonding between the decavanadate polyanion and the interstitial complex in pascoite-family minerals

ABSTRACTThe decavanadate isopolyanion, [V10O28]6–, is a constituent of pascoite-family vanadate minerals and synthetic materials, and both protonated, [HxV10O28](6–x)–, and mixed-valence, [V4+xV5+10–x)O28](6+x)–, varieties have been described. Here we analyze the interaction between the interstitial complex and the decavanadate structural unit using the principle of correspondence of Lewis acidity-basicity. The Lewis base strengths of the decavanadate polyanions vary from 0.054 to 0.154 vu and [V10O28] structures can form from the simple cations Cs+, Rb+, K+, Tl+, and Na+; simple cations with higher Lewis acidities are too acid to form structures. Cations may bond to transformer (H2O) groups to form polyatomic cations that have lower Lewis acidities than the corresponding simple cation. The occurrence of the polyatomic cation {(V5+O2)Al10(OH)20(H2O)18}11+ in caseyite shows the potential for decavanadate phases to incorporate large heteropolycations into their structures. In turn, this suggests that the [V10O28] polyanions may be used to induce co-crystallization of large aqueous polyatomic cations, thus facilitating their structural characterization. There is an inverse relation between the amount of (H2O) in the interstitial complex and the number of bonds between interstitial simple cations and the O2– ions of the vanadate units, and there is a strong correlation between the unit-cell volume per decavanadate unit and the number of (H2O) groups.