Correspondence Principle Research Articles

Viscoelastic Solution for Axial Forces of Point-Anchored Rock Bolts in a Circular Tunnel

In this study, a deeply buried circular tunnel supported with point-anchored rock bolts was investigated. Assuming that the effects of each rock bolt on the surrounding rock are simplified to two identical concentrated forces acting in opposite directions, a viscoelastic analytical solution for the axial forces of the rock bolts is presented herein based on the complex variable method and correspondence principle. First, in the solution process, the surrounding rock is considered as an elastic material. A linear equation system for the axial forces was established according to the deformation coordination condition between the surrounding rock and the rock bolts. Second, the surrounding rock was considered as a viscoelastic material. Based on the correspondence principle, Laplace transformation was performed for the equation system of the axial forces to obtain its expression in the Laplace domain, and the values of the axial forces in the Laplace domain could be determined by solving the obtained expression. Finally, the viscoelastic semi-analytical solution for the axial forces was established using the numerical method of the Laplace inverse transformation. The results obtained were also compared with the numerical methods of ANSYS. Accordingly, the effects of the lateral stress coefficient, rock mass Young’s modulus, rock bolt length, viscosity coefficient, and preload on the axial forces of the rock bolts were discussed.

On modification of eutectic cast iron graphite

It has been shown that elementary crystalline cells of graphite and basic products of iron modification do not correspond to the principle of structural and dimensional correspondence of Dankov –Konobeevsky. Modifying elements Al, Ca, Mg, Ba, Ce increase the phase tension melt‑graphite by binding surface‑active oxygen and sulfur. Modifying cast iron eutectic graphite is a nanostructured process in which modifying elements refine elemental graphite nanocrystals from adsorbed oxygen and sulfur atoms. This contributes to an increase in the concentration of graphite nuclei upon solidification of the cast iron melt. The modification reduces the concentration of dissolved hydrogen, which increases the effectiveness of the modifying effect. Reduced concentrations of demodifying surface‑active elements, melt degassing, increased heat removal contribute to increasing the degree of branching and compactness of graphite dendrites during iron crystallization. The strongest modifying element of eutectic cast iron graphite is magnesium.

On deoxidation and modification of carbon steel

It has been shown that the elementary crystal cells of the basic products of deoxidation and modification of carbon steel, δ ferrite and austenite do not correspond to the principle of structural and dimensional correspondence of Dankov – Konobeevsky. Modifying elements Ba, Ca, Mg, Ce, Al increase the surface energy of the iron‑carbonaceous melt by binding surface active oxygen. Deoxidizers combine dissolved (free) oxygen into oxides, and modifiers – adsorbed oxygen. Steel modification is a nanostructural process in which modifying elements refine elemental iron nanocrystals from adsorbed oxygen and hydrogen atoms. Modifying elements reduce the concentration of dissolved hydrogen, which contributes to the modifying effect. The strongest deoxidizer and modifier of carbon steel is magnesium.

On modification of silumins

It has been shown that the elementary crystal cells of the basic products of modification of silumins, aluminum and silicon do not correspond to the principle of structural and dimensional correspondence of Dankov – Konobeevsky. Modifying elements B, Sr, P significantly increase the surface energy of liquid silumins, and Zr and Ti practically do not affect it. Modification of silumins is a nanostructured process. Ti, Zr, B form intermetallides that refine aluminum nanocrystals from demodifying adsorbed hydrogen atoms. Phosphorus, atomically dissolving in silumin, refiners silicon nanocrystals from adsorbed oxygen. Na and Sr form an emulsion and colloid in liquid silumin, which protect eutectic microcrystals of α‑and βSi‑phases from demodifying molecular hydrogen. All these processes increase the concentration of crystallization centers of dendritic microcrystals α‑and βSi‑phase, make them more branched and compact.

Analysis of fractures in linear viscoelastic media using a generalized finite element method and the elastic–viscoelastic correspondence principle

A methodology for an efficient analysis of 3-D fracture mechanics problems in linear viscoelastic media is presented. It combines the Elastic–Viscoelastic Correspondence Principle (EVCP), a Generalized Finite Element Method (GFEM), and an inverse Laplace transform (ILT) method to compute Energy Release Rate (ERR) and Crack Mouth Opening Displacement (CMOD) for viscoelastic fracture problems in the time domain. The method is denoted EVCP-GFEM-ILT and consists of solving a reference elastic problem in the Laplace domain using a quadratic p-hierarchical GFEM, computing quantities of interest in this domain, and transforming them to the time domain with the aid of a numerical ILT method. One of the key features of the method is that a single elastic solution is required, regardless of the time interval of the target viscoelastic problem. A detailed verification of the methodology against analytical and reference numerical solutions is performed. Problems subjected to either non-homogeneous Neumann or Dirichlet boundary conditions of increasing complexity are considered. Two ILT methods are studied and the one based on Fourier series is shown to deliver accurate results for all tested boundary conditions, as well as non-trivial viscoelastic material models. The computational cost of the method applied to a 3-D problem is compared with the one for Abaqus which solves the problem directly in the time domain using a FEM mesh with quarter-point elements. A fully 3-D mixed-mode fracture problem with a non-trivial viscoelastic material model is solved to highlight the applicability of the proposed methodology. Finally, a problem of practical interest is analyzed in order to show how the methodology proposed in this work can be applied to efficiently handle large-scale simulations.

Quantum Physical Observables with Conjectural Modeling: Paradigm shifting Formalisms II: A Review

In continuation with the previous Review Force General Conjectural Modeling Transforms Formalism PHYSICS33 (Physics & Astronomy International Journal under publication), the current review article will try to develop quantum gravity gage transforms Algorithm Graphical Equation of micro-blackhole force to gauge fields-wavefunctions algorithm transforms equations. Theoretical derivations of experimental observable measurable parameters having scalar quantum gauge field as function in terms of Laplacian, Fourier, and the Legendre transform gaging the spin, rotation, revolution, and rotational angular velocity have been shown. These transforms appear only as a function of time, and that makes the formulation independent of assumptions of invariability of fundamental universally known constants. We consider examples of universal eonic parametric observables as well. The question of whether the time is a linear operator has been answered by employing Correspondence Principle’s linear operator four-vector time matrix spatial range algorithm equivalence and is estimated to be about ¼ mile. Theoretically derived algorithm physics designs enable prototype testing by utilizing experimental instrumentations measuring observables. A flowchart has been configured simplifying theoretical to experimental mathematical physical sciences to profile signal/noise intensity and the density matrix. Additionally, estimation of Hod PDP mechanistic probability, grand unifying physics operations, schematics of potential scalar gauge field alongside incorporating typical wavefunction general quantum computing signal/noise matrix graphing, simple lab-top prototype sound and light profiling intensity, and spectral density point-to-point matrix oscilloscopic observational measurement techniques have been schematically sketched out to enhance facilitation of future implementations of state-of-the-art physics techniques practically!!

Transient wave-leak interaction analysis for improved leak detection in viscoelastic pipelines

Transient wave reflection methods (TWRMs) have exhibited favorable capability in leak detection for elastic pipelines, but applications have demonstrated their relatively low accuracy for viscoelastic pipelines. This paper investigates the transient wave behaviour, the principal tenet for leak detection by TWRMs, in a leaky viscoelastic pipeline to understand the mechanism of wave modification by leaks and viscoelasticity. Based on the correspondence principle, this research derives analytical formulations of the leak-induced wave reflection and phase difference at any measurement point in a viscoelastic pipe. According to the measured reflection coefficient, an optimization algorithm is further developed to detect the leak. The methodologies are then assessed and discussed through sinusoidal and sigmoid perturbations in numerical and laboratory tests. The extensive analyses indicate that measurement distance and leak ratio affect the magnitude of the reflected wave, yet, the wave phase shift is relatively independent of the leak ratio for practical applications.

A computational computing system and its implementation for resource broker in IoT

In the computing world Internet of Things or even more normally IoT is an arising idea in the specialized world. We need more solace in our life. The web has turned into a centerpiece of our life. This IoT depends on this coordinated effort of solace and the Web. open new security challenges in light of multiple factors. First and foremost, security techniques should be adjusted because proposed calculation that in view of appropriated design require extra various agents and different correspondence principles that might increment security dangers and increment security the executive’s intricacy. Besides, proposed calculation is intrinsically missing productive security highlights since it performs username/secret word-based validation in a plain text, that safeguarded by cryptographic convention SSL/TSL which is not consider as lightweight convention for assets obliged gadgets. This paper will introduce scientific categorization and acknowledgment interaction of IoT confirmation conspire. Moreover, the paper will talk about difficulties of applying validation components for IoT frameworks that in view of circulated.

СУТНІСТЬ ТА КЛАСИФІКАЦІЯ ДОХОДІВ СІЛЬСЬКОГОСПОДАРСЬКОГО ПІДПРИЄМСТВА

The main goal of the activity of any enterprise is to obtain the maximum profit, which cannot be realized without obtaining the necessary level of income. The income of the enterprise, regardless of the field of activity, form of ownership and other factors, is of exceptional importance not only for a separate subject of entrepreneurial activity, but also for the economy as a whole. The article examines the main approach to determining the income of an enterprise in the legal framework and modern scientific sources, identifies its shortcomings, and proposes clarification of the definition. we believe that it is advisable to supplement the definition in the legal framework with a clarification – without taking into account the factor of unprofitability of the enterprise. As for the income of the agricultural enterprise, it is necessary to point out its main features. The first feature of the formation of the income of an agricultural enterprise is that it includes not only directly the income from the sale of agricultural products, but also the results of the assessment of the initial value of biological assets and the growth of their fair value. The second feature is that the amount of income of an agricultural enterprise is influenced by the seasonality factor, especially in the field of crop production. The third feature of the formation of income of agricultural enterprises is that it is often recognized before the sale of agricultural products directly after their production. As a fourth feature, it should be pointed out that agricultural products, in respect of which income is recognized, may be transferred to the category of expenses in subsequent reporting periods. Classification characteristics of income are summarized and the dynamics of incomes of agricultural enterprises in different sections are analyzed. A clear and logical structure of income classification makes it possible to organize an effective system of their accounting. The study of the peculiarities of the formation of incomes of agricultural enterprises provides grounds for the conclusion of the need for further research and improvement of the process of formation of incomes of enterprises with a seasonal nature of production. In particular, in the accounting of the income of agricultural enterprises, it is necessary to take into account the time factor caused by the peculiarities of seasonal production, when applying the principle of accrual and correspondence of income and expenses.

Nonlinear photonic disclination states

Higher-order topological insulators are unusual materials that can support topologically protected states, whose dimensionality is lower than the dimensionality of the structure at least by 2. Among the most intriguing examples of such states are zero-dimensional corner modes existing in two-dimensional higher-order insulators. In contrast to corner states, recently discovered disclination states also belong to the class of higher-order topological states but are bound to the boundary of the disclination defect of the higher-order topological insulator and can be predicted using the bulk-disclination correspondence principle. Here, we present the first example of the nonlinear photonic disclination state bifurcating from its linear counterpart in the disclination lattice with a pentagonal or heptagonal core. We show that nonlinearity allows us to tune the location of the disclination states in the bandgap and notably affects their shapes. The structure of the disclination lattice is crucial for the stability of these nonlinear topological states: for example, disclination states are stable in the heptagonal lattice and are unstable nearly in the entire gap of the pentagonal lattice. Nonlinear disclination states reported here are thresholdless and can be excited even at low powers. Nonlinear zero-energy states coexisting in these structures with disclination states are also studied. Our results suggest that disclination lattices can be used in the design of various nonlinear topological functional devices, while disclination states supported by them may play an important role in applications, where strong field confinement together with topological protection are important, such as the design of topological lasers and enhancement of generation of high harmonics.

Improving the predictor-criterion consistency of mindset measures: Application of the correspondence principle

Increasing the level of correspondence between measures of growth mindset and their related outcomes could afford more precise prediction of the relationships between growth mindset and social-emotional outcomes. To illustrate the value of measurement correspondence, two studies were conducted in Hong Kong. Study 1 showed that an agent-correspondent growth mindset measure (parents’ perception of the malleability of their children's personal qualities), compared to an agent-non-correspondent one (parents’ belief in the malleability of personal qualities of a generalized other), had stronger predictive relationship with children's likelihood of displaying difficult behaviors. Study 2 found that children's self-theories about the malleability of their intelligence (an intrapersonal construct) had stronger predictive relationship with academic engagement (an intrapersonal outcome) than did their perception of growth mindset norm (a normative construct). However, perceived growth mindset norm regarding personal qualities had stronger predictive relationship with peer relationship quality (an interpersonal outcome). Together these results demonstrated that when corresponding measures of growth mindset were used to predict an outcome, more reliable growth mindset effects would emerge.

The classifiability scale

Abstract In many languages, nouns need a numeral classifier to combine with number words or quantifiers. Even though languages may have an elaborate system of numeral classifiers, there usually are exceptional nouns that combine directly with number words. This paper deals with the following questions: Which nouns trigger a numeral classifier when counted? Which nouns are more likely to occur without an additional classifier in a numeral context? Data from 32 languages reveal a classifiability scale of nouns depending on their semantics. The more animate a noun, the more likely is the occurrence of a classifier. With inanimate nouns, classifiers often may or must be omitted. The investigation extends to units, with units of time being much more likely to be accompanied by a numeral classifier than other units. These findings are surprising in the light of the predominant view that numeral classifiers are individuating units in languages where nouns appear to be uncountable mass nouns. I discuss several approaches, of which animacy and the form-frequency correspondence principle are most promising.

Viscoelastic analysis of surface deformation above salt caverns for gas storage based on semi-infinite space

The construction of salt caverns for energy storage is of strategic significance, but the operation of underground gas storages in salt formations will cause surface deformation. The research and analysis of surface deformation is an important part of the stability evaluation of salt caverns for gas storage. From the perspective of classical mechanics theory, the analytical solution of surface deformation above salt caverns for gas storage is deduced. The surface displacement caused by the contraction of a salt cavern is regarded as the boundary displacement caused by the surface force acting on a spherical cavern in a semi-infinite space. The equivalent conversion of load form is carried out based on the mirror principle. The vertical subsidence and horizontal displacement of the surface of the elastic semi-infinite space is obtained. According to the elastic-viscoelastic correspondence principle, the viscoelastic solution of the surface displacement of the semi-infinite body, regarded as Maxwell body, can be obtained. A numerical model of a salt cavern for gas storage is established based on the engineering practice. The results of the analytical solution and the numerical simulation are compared and analyzed to verify the accuracy of the analytical solution. The analytical solution was applied to predict the surface displacement above a group of caverns, and the influence of the layout of salt caverns and cavern center spacing on the surface displacement is analyzed. The research results show that the regular triangular layout is slightly better than the square layout. The larger the cavern center spacing, the smaller the maximum surface subsidence. The proposed theoretical prediction model can provide a theoretical basis for controlling surface deformation for the construction of gas storage caverns.

Scattering of plane SH waves by a semi-circular discontinuity in an elastic half-plane

A curved discontinuity near the ground can cause the scattering of seismic waves and significantly affect the ground and underground motions, posing some challenges in seismic design. In this paper, a series solution for the scattering and diffraction of plane SH waves from a semi-circular discontinuity in an elastic half-plane is first presented using the wave function expansion method, aiming to reveal the effects of the discontinuity properties on wave scattering and seismic motion. Based on the correspondence principle of viscoelasticity, the influence of the damping ratio of the medium on the seismic motion is also discussed. Finally, by combining the series solution and the inverse Fourier transform, the ground and underground motions induced by a transient plane SH wave are analyzed by exhibiting the wave field snapshots at different times and the waveform curves of different measurement points on the ground. The results indicate that both the stiffness of the discontinuity and the damping ratio of the medium have a great influence on the propagation of seismic waves and play an important role in seismic calculations.

An explanation of causal-noncausal verb alternations in terms of frequency of use

Abstract To account for the cross-linguistic trends in the coding of causal-noncausal verb pairs, such as break (tr.)/break (intr.), Haspelmath et al. (2014) proposed, and provided corpus-based support for, an explanation in terms of usage frequency (Prediction 1, hereafter P1). However, this explanation cannot be applied to English causal-noncausal verb pairs. Since English mostly uses the same verb form for the causal and noncausal verb use, the explanation does not follow the form–frequency correspondence principle (hereafter FFCP) that Prediction 1 (hereafter P1) is based upon. In this article I argue, by using causative-affixed verbs, that for a linguistic pair there is a strong correlation in terms of frequency between form and earlier occurrence. Therefore, in place of the FFCP and P1, I propose the earlier occurrence – frequency correspondence principle (hereafter EOFCP) and the Revised Prediction 1 (hereafter RP1) based on it. This study tests the validity of the EOFCP and RP1 by applying them to 20 English verb pairs of sound emission. The investigation of frequency was made not only in present-day English but also at the time when the intransitive or transitive use came to be paired with its counterpart. The analysis shows that by applying the RP1 to the frequency data at the two time periods, we can obtain considerably high scores of matching rate, with a significant Spearman rank order correlation between the two groups.

Long-wavelength closures for collisional and neutral interaction terms in gyro-fluid models

A collisional gyro-fluid model is presented. The goal of the model is edge and scrape-off layer turbulence. The emphasize in the model derivation heavily lies on ”implementability” with today’s numerical methods. This translates to an avoidance of infinite sums, strongly coupled equations in time and intricate elliptic operator functions. The resulting model contains the four moments density, parallel momentum, perpendicular pressure and parallel energy and is closed by a polarisation equation and parallel Ampere law. The central ingredient is a collisional long-wavelength closure that relies on a drift-fluid gyro-fluid correspondence principle. In this way the extensive literature on fluid collisions can be incorporated into the model including sources, plasma-neutral interactions and scattering collisions. Even though this disregards the characteristic finite Larmor radius terms in the collisional terms the resulting model is at least as accurate as the corresponding drift-fluid model in these terms. Furthermore, the model does enjoy the benefits of an underlying variational principle in an energy-momentum theorem and an inherent symmetry in moment equations with regards to multiple ion species. Consistent particle drifts as well as finite Larmor radius corrections and high amplitude effects in the advection and polarization terms are further characteristics of the model. Extensions and improvements like short-wavelength expressions, a trans-collisional closure scheme for the low-collisionality regime or zeroth order potential must be added at a later stage.

Transient chaos analysis of string scattering

It has long been thought that a highly excited string can be regarded as a black hole: the correspondence principle between strings and a black hole, while recent studies found that black holes are characterized by chaos. This suggests that highly excited strings are the source of the black hole chaoticity. We study the chaoticity of a string amplitude where a tachyon is scattered by a highly excited string. Our strategy to extract the chaos in the amplitude is a generalization of the transient chaos analysis for classical scattering. We look for the fractal structure in the plots of incoming/outgoing scattering angles, where the outgoing angle is defined as the maximum pole of the amplitude. Within our strategy, we could not identify any fractal structure in the scattering data. We also discuss other possible setups and strategies to extract the chaos, hoping that our present work serves as a step toward the formulation of chaos in string scattering amplitudes.

Point Cloud Convolution Network Based on Spatial Location Correspondence

The study of convolutional neural networks for 3D point clouds is becoming increasingly popular, and the difficulty lies mainly in the disorder and irregularity of point clouds. At present, it is straightforward to propose a convolution operation and perform experimental validation. Although good results are achieved, the principles behind them are not explained—i.e., why this can solve the disorder and irregularity of point clouds—and it is difficult for the researchers to design a point cloud convolution network suitable for their needs. For this phenomenon, we propose a point convolution network framework based on spatial location correspondence. Following the correspondence principle can guide us in designing convolution networks adapted to our needs. We analyzed the intrinsic mathematical nature of the convolution operation, and we argue that the convolution operation remains the same when the spatial location correspondence between the convolution kernel points and the convolution range elements remains unchanged. Guided by this principle, we formulated a general point convolution framework based on spatial location correspondence, which explains how to handle a disordered point cloud. Moreover, we discuss different kinds of correspondence based on spatial location, including M-to-M, M-to-N, and M-to-1 relationships, etc., which explain how to handle the irregularity of point clouds. Finally, we give the example of a point convolution network whose convolution kernel points are generated based on the sample’s covariance matrix distribution according to our framework. Our convolution operation can be applied to various point cloud processing networks. We demonstrated the effectiveness of our framework for point cloud classification and semantic segmentation tasks, achieving competitive results with state-of-the-art networks.

Anisotropic Continuum-Molecular Models: A Unified Framework Based on Pair Potentials for Elasticity, Fracture and Diffusion-Type Problems

This paper presents a unified framework for continuum-molecular modeling of anisotropic elasticity, fracture and diffusion-based problems within a generalized two-dimensional peridynamic theory. A variational procedure is proposed to derive the governing equations of the model, that postulates oriented material points interacting through pair potentials from which pairwise generalized actions are computed as energy conjugates to properly defined pairwise measures of primary field variables. While mass is considered as continuous function of volume, we define constitutive laws for long-range interactions such that the overall anisotropic behavior of the material is the result of the assigned elastic, conductive and failure micro-interaction properties. The non-central force assumption in elasticity, together with the definition of specific orientation-dependent micromoduli functions respecting material symmetries, allow to obtain a fully anisotropic non-local continuum using a purely pairwise description of deformation and constitutive properties. A general and consistent micro-macro moduli correspondence principle is also established, based on the formal analogy with the classic elastic and conductivity tensors. The main concepts presented in this work can be used for further developments of anisotropic continuum-molecular formulations to include other mechanical behaviors and coupled phenomena involving different physics.

Mean-field descriptions for the viscoelastic response of thermorheologically complex reinforced solids

Mean-field descriptions for the thermo-viscoelastic response of reinforced solids undergoing small deformations but large temperature changes are presented. The descriptions follow from an approximate homogenization scheme that identifies macroscopic internal variables with low-order statistics of the microscopic internal variable fields as a result of a variational model reduction. Unlike descriptions based on the correspondence principle, these descriptions can account for thermorheologically complex constitutive laws with multiple internal times and/or temperature-dependent stiffnesses, and can provide information not only on the macroscopic response but also on the statistics of the microscopic mechanical fields; it is further demonstrated that the descriptions can even accommodate a special class of hereditary laws often employed for polymeric materials. Simple expressions for material systems with elastically rigid but thermally dilatant reinforcements are provided. By way of example, reduced descriptions are presented for a special class of material systems for which the thermomechanical response can be computed exactly by means of the correspondence principle. In the case of isotropic particle-reinforced solids under hydrostatic loadings, the reduced descriptions can reproduce the exact response identically; in the case of transversely isotropic fiber-reinforced solids subject to monotonic coolings, the reduced and exact descriptions provide indistinguishable macroscopic strains and stresses for the entire range of temperature drops and cooling rates considered.