Correspondence Principle Research Articles

Cladding-free Fermi arc surface states and topological directional couplers in ideal photonic Weyl metamaterials

Photons can freely propagate in a vacuum, making it not a simple insulator but rather a conductor for photons. Consequently, in topological photonics, domain wall structures with opposing effective mass terms are used as cladding to confine electromagnetic waves. This approach is necessary to demonstrate topological edge/surface waves and Fermi arc surface states (FASS). Here, we show that the cladding-free FASS with high field localization at the boundary can be achieved using ideal Weyl gyromagnetic metamaterials (GMs). In these GMs, the ideal Weyl semimetal phase exists due to the dispersionless longitudinal modes. At the boundary of the GMs-vacuum system, the cladding-free FASS connects the projections of Weyl nodes with opposite chirality, thanks to the bulk-boundary correspondence principle. We further confirm that chiral boundary modes can propagate without experiencing scattering or backward reflection, i.e., they can advance seamlessly approximately various types of defects. Remarkably, various types of topological directional couplers are achieved by utilizing cladding-free FASS in an ideal gyromagnetic medium. Our theoretical analysis reveals that the underlying operational principle for accomplishing these nonreflecting directional couplers is due to the single coupling channel between the cladding-free FASS and the multi-type scatterers of the continuous media. Furthermore, the controllable propagation and topological directional coupling of cladding-free FASS can be further explored by adjusting the ideal gyromagnetic medium and boundary configurations of the continuous media system. This research offers increased flexibility for the development of cladding-free and directionally coupled topological devices.

Real Virtuality and Actual Transitions: Historical Reflections on Virtual Entities before Quantum Field Theory

Abstract This paper studies the notion of virtuality in the Bohr-Kramers-Slater theory of 1924. We situate the virtual entities of BKS within the tradition of the correspondence principle and the radiation theory of the Bohr model. We show how, in this context, virtual oscillators emerged as classical substitute radiators and were used to describe the otherwise elusive quantum transitions. They played an effective role in the quantum theory of radiation while remaining categorically distinct and ontologically separated from the quantum world of the Bohr model. The notion of virtuality thus differs markedly from its counterpart in quantum mechanics or QFT.

Философско-методологические основания становления субъектно-ориентированной эргономики цифровых трансформаций

An analysis of the experience of ergonomics made it possible to substantiate its clear advan­tage over other fields of knowledge for the role of a system organizer (integrator) in the field of social and humanitarian support for digital transformations, including artificial intelli­gence systems. The interdisciplinary trend of increasing the role of subjectness is analyzed as a basis for the formation of subject-oriented ergonomics of digital transformations. Philo­sophical and methodological grounds for creating a subject-oriented ergonomics of digital transformations in social systems are proposed. The focus of this article is on aspects of the control and development of social systems. The basis of these foundations is the sys­tem of paradigms of classical, non-classical, post-non-classical scientific rationality and the system of paradigms of cybernetics (of the first, second and third order) correlated with them. The evolution of ergonomics is correlated with the evolution of types of scientific ra­tionality, which made it possible to single out the corresponding paradigms of ergonomics and fulfill the Bohr correspondence principle for them, which allows for continuity of previ­ous ergonomic experience. The formation of the subject-oriented ergonomics of digital transformations is a step towards the formation of the VII socio-humanitarian technological order is considered. The priority of Russian science in the development of subject-oriented ergonomics of digital transformations is substantiated, which is largely associated with the specifics of Russian philosophical and methodological research.

Analysis of reflective cracking in asphalt overlaid jointed concrete airfield pavements using a 3D generalized finite element approach

ABSTRACT Asphalt Concrete (AC) overlays are a common strategy for maintaining PCC airfield pavements. However, the movement of joints in the underlying pavement may lead to reflective cracks propagating to the overlay. The problem is highly three-dimensional resulting in mixed mode of cracks due to the aircraft gear loading configurations and underlying concrete pavement joint spacing and design. The development of a 3D model of airfield pavements to predict reflective cracking using Finite Element Method (FEM) and Generalized Finite Element Method (GFEM), is presented in this study. GFEM enrichment strategy and global-local approach are used to achieve efficient framework for developing the models from both computational and user time perspective. Viscoelastic fracture analysis was performed using elastic-viscoelastic correspondence principle. Sensitivity of the domain size, order of approximation and boundary conditions are investigated in the numerical simulations. It is shown that the crack initiation and propagation is a combination of Mode-I (tensile) and Mode-II (shearing) crack opening. The presented models contributes to the mechanistic empirical reflective cracking design algorithm for the FAA pavement design program.

P-wave propagation in attenuative elliptical VTI media

Elliptical anisotropy is convenient to use as the reference medium in perturbation methods designed to study P-wave propagation for transverse isotropy (TI). We make the elliptically anisotropic TI model attenuative and discuss the corresponding P-wave dispersion relation and the wave equation. Our analysis leads to two conditions in terms of the Thomsen-type parameters, which guarantee that the P-wave slowness surface and the dispersion relation satisfy elliptical equations. We also obtain the viscoacoustic wave equation for such elliptically anisotropic media and solve it for point-source radiation using the correspondence principle. For the constant- Q TI model, we use the weighting function method to derive the viscoacoustic wave equation in differential form. Numerical examples validate the proposed elliptical conditions and illustrate the behavior of the P wavefield in attenuative elliptical TI models.

Topological Signature of Stratospheric Poincaré-Gravity Waves

Abstract The rotation of Earth breaks time-reversal and reflection symmetries in an opposite sense north and south of the equator, leading to a topological origin for certain atmospheric and oceanic equatorial waves. Away from the equator, the rotating shallow-water and stably stratified primitive equations exhibit Poincaré inertia–gravity waves that have nontrivial topology as evidenced by their strict superinertial time scale and a phase singularity in frequency–wavevector space. This nontrivial topology then predicts, via the principle of bulk-interface correspondence, the existence of two equatorial waves along the equatorial interface, the Kelvin and Yanai waves. To directly test the nontrivial topology of Poincaré-gravity waves in observations, we examine ERA5 data and study cross correlations between the wind velocity and geopotential height of the midlatitude stratosphere at the 50 hPa height. We find the predicted vortex and antivortex in the relative phase of the geopotential height and velocity at the high frequencies of the waves. By contrast, lower-frequency planetary waves are found to have trivial topology also as expected from theory. These results demonstrate a new way to understand stratospheric waves and provide a new qualitative tool to investigate waves in other components of the climate system.

A 21st Century MONADOLOGY or Principles of Philosophy

This work presents a recasting and tribute to Gottfried Wilhelm Leibniz’s 1714 text, known as the Monadology_,_ on its 300th anniversary (first released in 2014 with some revisions in 2024), analysing it from a 21st century philosophical and scientific perspective. Leibniz’s monads are reinterpreted as indivisible dynamic modes of action as described by modern physics. His key insights regarding the relational and perspectival nature of reality, and the distinction between the telic causation of indivisible entities vs the efficient causation of aggregates, are highlighted as prescient of quantum physics and the correspondence principle. The practical biological application of his ideas requires updating, but even there, he shows some remarkably forward-looking thoughts. The traditional concept of an immortal human soul is replaced by an audience of ephemeral cellular “listeners” that apperceive the living story of a person. Leibniz’s principles are seen to contain powerful and still relevant insights into the nature of physical reality, human knowledge and ethics, meriting further exploration in light of contemporary science. In summary, while specific aspects of Leibniz’s synthesis require updating, his core logical principles and global vision retain surprising relevance and potential for reframing our understanding.

Effective thermodynamic potentials and internal variables: Linear viscoelastic composites

New theoretical relations in linear viscoelasticity are derived by combining two different points of view. On the one hand, the general thermodynamic framework makes it possible to define the energy stored and the energy dissipated in linearly viscoelastic composites. On the other hand, the correspondence principle permits to express the macroscopic strain–stress relation as ordinary differential equations for a set of effective internal variables. A finite and small number of internal variables is rigorously sufficient in several cases of interest, including in particular particulate composites. Interpreting the macroscopic response as a rheological generalized Maxwell model allows us to compute the macroscopic free and dissipated energy of the composite. This interpretation is proved to be exact in several cases of interest. Coupled with Hashin–Shtrikman estimates, these thermodynamic functions provide additional information on the statistics of the field within each individual phase of the composite.

On calculating glacial isostatic adjustment

Modeling the earth's fluid and elastic response to the melting of the glaciers of the last ice age is the most direct way to infer the earth's radial viscosity profile. Here, we compare two methods for calculating the viscoelastic response to surface loading. In one, the elastic equation of motion is converted to a viscoelastic equation using the Correspondence Principle. In the other, elastic deformation is added to the viscous flow as isostatic adjustment proceeds. The two modeling methods predict adjustment histories that are different enough to potentially impact the interpretation of the observed glacial isostatic adjustment (GIA). The differences arise from buoyancy and whether fluid displacements are subjected to hydrostatic pre-stress. The methods agree if they use the same equations and boundary conditions. The origin of the differences is determined by varying the boundary conditions and pre-stress application.

Development of the Concept of “Gene” in the Academic Subject “Biology” for Grade 10 in the Light of Niels Bohr’s Correspondence Principle

Development of the Concept of “Gene” in the Academic Subject “Biology” for Grade 10 in the Light of Niels Bohr’s Correspondence Principle

Localization of Chiral Edge States by the Non-Hermitian Skin Effect

Localization of Chiral Edge States by the Non-Hermitian Skin Effect

The strain gradient viscoelasticity full field solutions for Mode-I and Mode-II crack problems

The impacts of size and viscosity become distinctly evident when considering micro- and nano-scale phenomena for advanced materials with micro- and nanostructures. In this study, the mechanical behavior of the advanced material is characterized by using the strain gradient viscoelasticity theory, and a novel solution is presented for the mode-I and mode-II cracks, which is formulated based on the strain gradient viscoelasticity theory, employing the Wiener-Hopf method. Besides, the gradient-dependent viscoelastic crack solutions are directly derived by applying the correspondence principle that aligns strain gradient viscoelasticity with strain gradient elasticity within the Maxwell's standard linear solid model. Relative to the influence of elastic strain gradient effects, the involvement of viscous gradient effects instigates a reinforcement to the stress field around the crack tip, thereby offering a more reasonable representation of advanced materials crack behavior. When the viscosity effect is omitted or as time tends to infinity, the solutions based on strain gradient viscoelasticity theory converges to those on the classical strain gradient elasticity theory.

Non-KAM classical chaos topology for electrons in superlattice minibands determines the inter-well quantum transition rates

We investigate the quantum-classical correspondence for a particle tunnelling through a periodic superlattice structure with an applied bias voltage and an additional tilted harmonic oscillator potential. We show that the quantum mechanical tunnelling rate between neighbouring quantum wells of the superlattice is determined by the topology of the phase trajectories of the analogous classical system. This result also enables us to estimate, with high accuracy, the tunnelling rate between two spatially displaced simple harmonic oscillator states using a classical model, and thus gain new insight into this generic quantum phenomenon. This finding opens new directions for exploring and understanding the quantum-classical correspondence principle and quantum jumps between displaced harmonic oscillators, which are important in many branches of natural science.

Understanding the relation between classical and quantum mechanics: prospects for undergraduate teaching

Classical and quantum mechanics are two very different theories, each describing the world within its own range of validity. It is often stated that classical mechanics emerges from quantum mechanics in a certain limit. This is known as the correspondence principle. According to Planck’s version of the correspondence principle, classical mechanics is recovered when the limit in which a dimensionless parameter containing Planck’s constant h goes to zero is taken, while Bohr’s version entails taking the limit of large quantum numbers. However, despite what is usually stated in textbooks, the relation between the two theories is much more complex to state and understand. Here we deal with this issue by analysing some key examples, in some of which also the analogously subtle relation between wave and geometric optics is considered. Implications for quantum mechanics teaching at undergraduate level are carefully discussed.

Generalized ghost dark energy in [formula omitted] gravity

In this manuscript, we use the correspondence principle to construct the generalized ghost dark energy f(Q) model, where Q is the non-metricity. For this purpose, we use the Friedman–Robertson–Walker universe model with power-law scale factor. The energy density in this model linearly depends on the Hubble parameter, with a sub-leading term of H2, resulting in an energy density ρD=ξH+ζH2, where ξ and ζ are arbitrary constants. We reconstruct interacting fluid scenario of this dark energy with dark matter. The reformulated f(Q) gravity model shows how different epochs of the cosmic history can be reproduced by this modified gravity model. The physical characteristics of the model are discussed through the equation of state parameter with the planes of ωD−ωD′ and r−s. We also explore the stability criteria for the interacting model using the squared speed of sound. The equation of state parameter indicates phantom phase of the universe and the squared speed of sound represents stability of the interacting model. The (ωD−ωD′)-plane indicates freezing region, while the (r−s)-plane corresponds to the Chaplygin gas. We conclude that our findings coincide with the latest observational data.

Direct Determination of Photonic Stopband Topological Character: A Framework Based on Dispersion Measurements

Ascertainment of photonic stopband absolute topological character requires information regarding the Bloch eigenfunction spatial distribution. Consequently, the experimental investigations predominantly restrict themselves to the bulk‐boundary correspondence principle and the ensuing emergence of topological surface state. Although capable of establishing the equivalence/inequivalence of bandgaps, the determination of their absolute topological identity remains out of its purview. The alternate method of reflection phase‐based identification also provides only contentious improvements owing to the measurement complexities pertaining to the interferometric setups. To circumvent these limitations, the Kramers–Kronig amplitude‐phase causality considerations are resorted to and an experimentally conducive method is proposed for bandgap topological character determination directly from the parametric reflectance measurements. Particularly, it is demonstrated that in case of 1D photonic crystals, polarization‐resolved dispersion measurements suffice in qualitatively determining bandgaps’ absolute topological identities. By invoking the translational invariance of the investigated samples, a parameter “differential effective mass” is also defined, that encapsulates bandgaps’ topological identities and engenders an experimentally discernible bandgap classifier.

Computational multiphase micro‐periporomechanics for dynamic shear banding and fracturing of unsaturated porous media

AbstractDynamic shearing banding and fracturing in unsaturated porous media are significant problems in engineering and science. This article proposes a multiphase micro‐periporomechanics (PPM) paradigm for modeling dynamic shear banding and fracturing in unsaturated porous media. Periporomechanics (PPM) is a nonlocal reformulation of classical poromechanics to model continuous and discontinuous deformation/fracture and fluid flow in porous media through a single framework. In PPM, a multiphase porous material is postulated as a collection of a finite number of mixed material points. The length scale in PPM that dictates the nonlocal interaction between material points is a mathematical object that lacks a direct physical meaning. As a novelty, in the coupled PPM, a microstructure‐based material length scale is incorporated by considering micro‐rotations of the solid skeleton following the Cosserat continuum theory for solids. As a new contribution, we reformulate the second‐order work for detecting material instability and the energy‐based crack criterion and J‐integral for modeling fracturing in the PPM paradigm. The stabilized Cosserat PPM correspondence principle that mitigates the multiphase zero‐energy mode instability is augmented to include unsaturated fluid flow. We have numerically implemented the novel PPM paradigm through a dual‐way fractional‐step algorithm in time and a hybrid Lagrangian–Eulerian meshfree method in space. Numerical examples are presented to demonstrate the robustness and efficacy of the proposed PPM paradigm for modeling shear banding and fracturing in unsaturated porous media.

Abrogation and homeostatic restoration of IgE responses by a universal IgE allergy CTL vaccine-The three signal self/non-self/self (S/NS/S) theory.

Natural IgE cytotoxic peptides (nECPs), which are derived from the constant domain of the heavy chain of human IgE producing B cells via endoplasmic reticulum (ER) stress, are decorated onto MHC class 1a molecules (MHCIa) as unique biomarkers for CTL (cytotoxic T lymphocyte)-mediated immune surveillance. Human IgE exhibits only one isotype and lacks polymorphisms; IgE is pivotal in mediating diverse, allergen-specific allergies. Therefore, by disrupting self-IgE tolerance via costimulation, the CTLs induced by nECPs can serve as universal allergy vaccines (UAVs) in humans to dampen IgE production mediated by diverse allergen-specific IgE-secreting B cells and plasma cells expressing surface nECP-MHCIa as targets. The study herein has enabled the identification of nECPs, A32 and SP-1/SP-2 nonameric natural peptidesproduced through the correspondence principle. Vaccination using nECP induced nECP-specific CTL that profoundly suppressed human IgE production in vitro as well as chimeric human IgE production in human IgE/HLA-A2.01/HLA-B7.02 triple transgenic rodents. Furthermore, nECP-tetramer-specific CTLs were found to be converted into CD4 Tregs that restored IgE competence via the homeostatic principle, mediatepred by SREBP-1c suppressed DCs. Thus, nECPs showed causal efficacy and safety as UAVs for treating categorically type I hypersensitivity IgE-mediated allergies. The applied vaccination concept presented provides the foundation to unify, integrate through a singular class of tetramer-specific TCR clonotypes for regulaing human IgE production. The three signal theory pertains to mechanisms of three cells underlying central tolerance (S), breaking self tolerance (NS) and regaining peripheral tolerance (S) via homeostasisconcerning nECP as an efficacious and safe UAV to treat type I IgE-mediated hypersensitivity. The three signal theory impirically extended, may be heuritic for immuno-regulation of adaptive immune repertoire in general.

The free fall in three Physics theories

This paper explores the interplay between Classical Mechanics, Relativistic Mechanics, and Quantum Mechanics through an analysis of the free fall phenomenon. We investigate the probability density functions and corresponding plots in each theory, alongside calculating the expected values of position and momentum. By observing the behavior of these results as they approach the classical limit, we confirm the hypothesis that these theories can be connected through their probability density functions. Furthermore, we discuss the validity of the correspondence principle in Quantum Mechanics, while also examining, in a non-rigorous manner, the validity of the weak equivalence principle within each of the aforementioned theories.

Methods for modeling the dissipative characteristics of layered composites

The main methods for modeling dissipative characteristics of layered composites are considered: the principle of elastic-viscoelastic correspondence and energy method. Mathematical models of damped oscillations are given for layered anisotropic plates. A numerical procedure for solving the problem of damped oscillations of a three-layer monoclinic plate containing a two-stage method for solving a complex eigenvalue problem. It is noted that the energy method for modeling energy dissipation at vibrations of layered composite structures is a special case of the method, based on the principle of elasticviscoelastic correspondence. Shown, that in addition to the classical formulation of the energy method, in which the terms energy balance equations are approximately found by their own forms and vibration frequencies of a conservative mechanical system, there is one more an approximate method for calculating the dissipative characteristics of orthotropic composite structures. The advantages of this method are the possibility of using existing commercial software systems (Ansys et al.), which numerically implement the finite element method, and shortcomings - the need to be limited to the use of classical theories of thinwalled structures (Bernoulli-Euler, Kirchhoff-Love) for descriptions of deformation of composite structures. It has been found that the use the classical formulation of the energy method allows with a high accurately predict the values of mechanical loss coefficients up to ηmax = 0.02. Further increase in damping levels construction is accompanied by a decrease in the accuracy of the forecast.