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We review our recent theoretical results about inequivalence between passive and active gravitational masses and energy in semiclassical variant of general relativity, where gravitational field is not quantized but matter is quantized. To this end, we consider the simplest quantum body with internal degrees of freedom - a hydrogen atom. We concentrate our attention on the following physical effects, related to electron mass. The first one is inequivalence between passive gravitational mass and energy at microscopic level. Indeed, quantum measurement of gravitational mass can give result, which is different from the expected, $m \neq m_e + \frac{E_1}{c^2}$, where electron is initially in its ground state; $m_e$ is the bare electron mass. The second effect is that the expectation values of both passive and active gravitational masses of stationary quantum states are equivalent to the expectation value of energy. The most spectacular effects are inequivalence of passive and active gravitational masses and energy at macroscopic level for ensemble of coherent superpositions of stationary quantum states. We show that, for such superpositions, the expectation values of passive and active gravitational masses are not related to the expectation value of energy by the famous Einstein's equation, $m \neq \frac{E}{c^2}$. In this review, we also improve several drawbacks of the original pioneering works., Based on talk presented at the Fifteenth Marcel Grossmann Meeting on General Relativity, Rome, July 2018. arXiv admin note: substantial text overlap with arXiv:1711.00116, arXiv:1903.03173

In this work, we develop an envelope of design solutions for combined intensified reaction/separation systems. The attainable region-based continuous flow stirred tank reactor equivalence principle...

Some issues related to the development of methods for forecasting creep processes are considered. For this purpose, the temporal equivalence principle, the temperature-time analogy, the stress-time analogy, other analogies, and the modern relations between stresses and strains of the heriditary type in the form that allows describing irreversible plastic deformations are used. The expressions for multiple reduction coefficients are obtained using the time equivalence principle. A brief description is given to implementation of the method of analogies. An example of application of the concept of reduced time directly to the creep diagram is provided.

The concept of the generalized hypersonic equivalence principle for viscous flows is proposed in this paper. The traditional hypersonic equivalence principle applies only to the inviscid flows and ...

Automatic fiber placement (AFP) is a type of labor-saving automatic technology for forming composite materials that are widely used in aviation and other fields. In this process, concave surface delamination is a common defect, as existing research on the conditions for this defect to occur is insufficient. To predict the occurrence of this defect, the concept of allowable interlaminar normal stress is proposed to define its occurrence conditions, and based on this concept, probe tests are carried out using the principle of time–temperature equivalence. Through the laying speed/allowable normal stress curve measured in the probe experiment, the physical meaning of allowable normal stress is discussed. At the same time, the measured curve is quantitatively analyzed, combined with viscoelastic theory and the molecular diffusion reptation model, and the dominating effect in the formation of a metal/prepreg layer and prepreg/prepreg layer is determined. Finally, the experimental data are used to guide the parameter selection in an automatic placement engineering case and prove its correctness.

International audience; The issue of how a semantics should deal with self-attacking arguments was always a subject of debate amongst argumentation scholars. A consensus exists for extension-based semantics because those arguments are always rejected (as soon as the semantics in question respect conflict-freeness). In case of gradual semantics, the question is more complex, since other criteria are taken into account. A way to check the impact of these arguments is to use the principles (i.e. desirable properties to be satisfied by a semantics) from the literature. Principles like Self-Contradiction and Strong Self-Contradiction prescribe how to deal with self-attacking arguments. We show that they are incompatible with the well-known Equivalence principle (which is satisfied by almost all the existing gradual semantics), as well as with some other principles (e.g. Counting). This incompatibility was not studied until now and the class of semantics satisfying Self-Contradiction is under-explored. In the present paper, we explore that class of semantics. We show links and incompatibilities between several principles. We define a semantics that satisfies (Strong) Self-Contradiction and a maximal number of compatible principles. We introduce an iterative algorithm to calculate our semantics and prove that it always converges. We also provide a characterisation of our semantics. Finally, we experimentally show that our semantics is computationally efficient.

Asphalt pavement contains dynamically changing moisture, and the movement of this moisture will change the relative humidity of the pavement, thereby affecting the dielectric properties of ...

In this paper, a domain decomposition algorithm based on equivalence principle for multiple bodies of multiple bodies of revolutions (EPA-BoR) is used to analyze the scattering characteristics of chaff clouds. It can be tested that the coupling effect of any two chaffs can be ignored when their distance is equal or greater than two wavelengths. Therefore, both memory and calculation time can be significantly reduced. Numerical results can prove the effectiveness of the proposed method.

Electromagnetic metamaterials (EMM) are a new kind of artificial synthetic material, and they have attracted extensive attention from academia and industry because of their special electromagnetic properties that natural substances do not possess. This paper reviews recent advances of equivalent modeling theory and method in the analysis and design of electromagnetic metamaterials. First, equivalent parameters extraction methods of electromagnetic metamaterials based on effective medium theory is briefly summarized. Second, material parameter synthesis using equivalence principle is introduced. Finally, the design method of electromagnetic metamaterials based on wave spectrum expansion theory is proposed.

It is proved that two Chevalley groups with indecomposable root systems of rank 1$?> over commutative rings (which contain in addition for the types , , , , and , and for the type ) are isomorphic or elementarily equivalent if and only if the corresponding root systems coincide, the weight lattices of the representation of the Lie algebra coincide, and the rings are isomorphic or elementarily equivalent, respectively. The isomorphisms of adjoint (elementary) Chevalley groups over the rings of the above types are also described. Bibliography: 25 titles.

Scattering of electromagnetic plane waves from normal chiral materials, chiral metamaterials, chiral nihility materials are presented. Based on the volume equivalence principle, the integral equati...

Targets and benchmarks are useful in chemical process design as they provide an objective, quantitative assessment of a proposed process flowsheet. In addition, with target bounds on reaction selectivity one can also explore the sustainability limits for a chemistry of interest. Unfortunately, targets for reaction selectivity are difficult to obtain using conventional design methods. In 2001, Feinberg and Ellison developed the Continuous Flow Stirred Tank Reactor (CFSTR) Equivalence Principle, providing a methodology to obtain ultimate bounds on steady-state productivity for a chemistry of interest entirely independent of process design. In previous articles, we showed how the CFSTR Equivalence Principle can be used to obtain bounds on reaction selectivity independent of process design for steady-state processes. In this article we prove that the CFSTR Equivalence Principle is also applicable to batch and semi-batch processes, thus providing a unifying framework to obtain an ultimate target for reaction selectivity applicable to all candidate processes for a chemistry of interest. This limit also applies to systems with periodic and chaotic operations. We demonstrate the method with an example for the production of lactic acid through the alkaline conversion of fructose.

In this paper, the plane-pair partial element equivalent circuit method coupled with the field equivalence principle is developed and applied to calculate the radiated fields of multilayer power planes. The proposed method can be used to solve near-field and far-field radiation problems for multilayer parallel-plane structures with decoupling capacitors. The proposed method is validated by full-wave simulation and experiment. In addition, the proposed method achieves ten times higher computational efficiency than the full-wave simulation.

For smooth compact connected manifolds with strictly convex boundary, no conjugate points and a hyperbolic trapped set, we prove an equivalence principle concerning the injectivity of the X-ray transform $I_m$ on symmetric solenoidal tensors and the surjectivity of an operator ${\pi_m}_*$ on the set of solenoidal tensors. This allows us to establish the injectivity of the X-ray transform on solenoidal tensors of any order in the case of a surface satisfying these assumptions., Comment: 24 pages, 2 figures. Theorem 1.2 improved thanks to a referee's suggestion: the condition "I^e_m is s-injective" is relaxed to "I_m is s-injective"

This paper studies the leader-following attitude coordination problems of multiple spacecraft in the presence of inertia parameter uncertainties. To achieve attitude coordination in the situation that even the leader’s attitude is only applicable to a part of the following spacecraft, a non-linear attitude observer is proposed to obtain an accurate estimation of the leader’s attitude and angular velocity for all the followers. In addition, a distributed control scheme based on non-certainty equivalence principle is presented for multiple spacecraft’ attitude synchronization. With a dynamic scaling, attitude consensus can be achieved asymptotically without any information of the bounds of the uncertain inertia parameters. Furthermore, once the estimations of inertia parameters reach their ideal values, the estimation process will stop and the ideal value of inertia parameter will be held. This is a special advantage of parameter estimation method based on non-certainty equivalence. Numerical simulations are presented to demonstrate that the proposed non-certainty equivalence-based method requires smaller control toque and converges faster compared with the certainty equivalence-based method. Keywords: Adaptive control, Attitude coordination, Leader-following consensus, Non-certainty equivalence, Spacecraft formation flying

The Continuous Flow Stirred Tank Reactor (CFSTR) Equivalence Principle, developed by Feinberg and Ellison, proves that any and every reaction/mixing/separation process is equivalent to a process comprising at most R+1 CFSTRs and a perfect mixer–separator, where R is the number of linearly independent chemical reactions. Frumkin and Doherty showed that the CFSTR Equivalence Principle can be used together with global optimization to find the maximum selectivity of a chemistry independent of process design. These selectivity targets are useful in the context of process intensification because they represent ultimate selectivity improvements that can be achieved by combining multiple unit operations into a single device. In this work, the model is reformulated as a mixed-integer nonlinear program to solve this nonlinear and nonconvex optimization problem. We implement a more robust, deterministic global optimization using a spatial branch-and-bound algorithm (BARON) to investigate the selectivity limits for p...

Einstein equivalence principle (EEP), as one of the foundations of general relativity, is a fundamental test of gravity theories. In this paper, we propose a new method to test the EEP of electromagnetic interactions through observations of black hole photon rings, which naturally extends the scale of Newtonian and post-Newtoian gravity where the EEP violation through a variable fine structure constant has been well constrained to that of stronger gravity. We start from a general form of Lagrangian that violates EEP, where a specific EEP violation model could be regarded as one of the cases of this Lagrangian. Within the geometrical optical approximation, we find that the dispersion relation of photons is modified: for photons moving in circular orbit, the dispersion relation simplifies, and behaves such that photons with different linear polarizations perceive different gravitational potentials. This makes the size of black hole photon ring depend on polarization. Further assuming that the EEP violation is small, we derive an approximate analytic expression for spherical black holes showing that the change in size of the photon ring is proportional to the violation parameters. We also discuss several cases of this analytic expression for specific models. Finally, we explore the effects of black hole rotation and derive a modified proportionality relation between the change in size of photon ring and the violation parameters. The numerical and analytic results show that the influence of black hole rotation on the constraints of EEP violation is relatively weak for small magnitude of EEP violation and small rotation speed of black holes., 16 pages, 6 figures

There are several theoretical models proposing dark matter candidates as well as different experimental searches for dark matter, collider, and non-collider ones. One of the most intriguing dark matter candidates is missing information in the cosmos. This is based on the mass-energy-information equivalence principle presented by M Vopson [1]. This review presents the historical development of this principle from its roots in the 1960s when Landauer principle was firstly presented to the latest data on the estimated value of the mass of one bit of information as well as data on missing energy as potential dark matter. Another theoretical discussion presented here is the reformulation of the second law of thermodynamics as a possible step to great unification. In addition to this theoretical postulation with a mathematical presentation focusing on statistics, we present some of the proposed experiments in this field. Two major proposals are in the direction of using an ultra-accurate balance with measurement uncertainty low enough to be comparable with proposed theoretical limits, and originally developed sensitive interferometer similar to the one in LIGO experiment.

In this publication, the near-field to far-field transformation using the self-built near-field scanner NFS3000 is examined with regard to its geometry. This device allows to measure electric and magnetic fields in small distances to the DUT (Device under Test) with high geometric precision and high sensitivity. Leading to a fast examination of EMC (Electromagnetic Compatibility) problems, because the electromagnetic properties are better understandable and therefore easier to solve than e.g. measurements in a far-field chamber. In addition, it is possible to extrapolate the near-fields into the far-field and to determine the radiation pattern of antennas and emitting objects. For this purpose, this paper deals with the basis of this transformation, the so-called surface equivalence theorem. This principle is then adapted to the measurement of near-field scanners and implemented accordingly. Due to the non-ideal design of the near-field scanner, the effects on a far-field transformation are finally presented and discussed.

In this paper, we apply the generalized transition matrix (GTM) method to analyze the scattering characteristics of dielectric coated cavities. Discontinuous Galerkin (DG) method is applied to ensure the weak continuity of normal current at the transitional junctions. An artificial reference surface is placed to separate the target cavity into interior region and exterior region. According to equivalence principle, the electromagnetic information of the inner dielectric materials can be extracted onto the reference surface. In this case, the computational burden can be effectively simplified. Numerical examples present the accuracy and feasibility of the proposed method.

The ordinary Structure Identity Principle states that any property of set-level structures (e.g., posets, groups, rings, fields) definable in Univalent Foundations is invariant under isomorphism: more specifically, identifications of structures coincide with isomorphisms. We prove a version of this principle for a wide range of higher-categorical structures, adapting FOLDS-signatures to specify a general class of structures, and using two-level type theory to treat all categorical dimensions uniformly. As in the previously known case of 1-categories (which is an instance of our theory), the structures themselves must satisfy a local univalence principle, stating that identifications coincide with "isomorphisms" between elements of the structure. Our main technical achievement is a definition of such isomorphisms, which we call "indiscernibilities", using only the dependency structure rather than any notion of composition., Comment: Long version of publication in LICS 2020 (DOI: 10.1145/3373718.3394755); v2: added sections "Axioms and Theories" and "Version History", other minor changes; v3: added examples

This work presents a two-player extraction game where the random terminal times follow (different) heavy-tailed distributions which are not necessarily compactly supported. Besides, we delve into the implications of working with logarithmic utility/terminal payoff functions. To this end, we use standard actuarial results and notation, and state a connection between the so-called actuarial equivalence principle, and the feedback controllers found by means of the Dynamic Programming technique. Our conclusions include a conjecture on the form of the optimal premia for insuring the extraction tasks, and a comparison for the intensities of the extraction for each player under different phases of the lifetimes of their respective machineries.

We review our recent theoretical results about inequivalence between passive gravitational mass and energy for a composite quantum body at a macroscopic level. In particular, we consider macroscopic ensembles of the simplest composite quantum bodies - hydrogen atoms. Our results are as follows. For the most ensembles, the Einstein's Equivalence Principle is valid. On the other hand, we discuss that for some special quantum ensembles - ensembles of the coherent superpositions of the stationary quantum states in the hydrogen atoms (which we call Gravitational demons) - the Equivalence Principle between passive gravitational mass and energy is broken. We show that, for such superpositions, the expectation values of passive gravitational masses are not related to the expectation values of energies by the famous Einstein's equation, i.e, $m_g \neq \frac{E}{c^2}$. Possible experiments at the Earth's laboratories are briefly discussed, in contrast to the numerous attempts and projects to discover the possible breakdown of the Einstein's Equivalence Principle during the space missions., Brief review

We argue that in a framework for emergent quantum mechanics, the weak equivalence principle is a consequence of concentration of measure in large dimensional spaces of $1$-Lipshitz functions. Furthermore, as a consequence of the emergent framework and the properties that we assume for the fundamental dynamics, it is argued that gravity must be a classical, emergent interaction., 25 pages; no figures. Accepted for publication in International Journal of Geometric Methods in Modern Physics. arXiv admin note: substantial text overlap with arXiv:1402.5070

We will use Fisher information to properly analyze the quantum weak equivalence principle. We argue that gravitational waves will be partially reflected by superconductors. This will occur as the violation of the weak equivalence principle in Cooper pairs is larger than the surrounding ionic lattice. Such reflections of virtual gravitational waves by superconductors can produce a gravitational Casimir effect, which may be detected using currently available technology., Essay received an honorable mention in the Gravity Research Foundation Essay Competition 2020. 9 pages, 3 figures. Matches published version in IJMPD

The construction and classification of symmetry-protected topological (SPT) phases in interacting bosonic and fermionic systems have been intensively studied in the past few years. Very recently, a complete classification and construction of space-group SPT phases were also proposed for interacting bosonic systems. In this Rapid Communication, we attempt to generalize this classification and construction scheme systematically into interacting fermion systems. In particular, we construct and classify point-group SPT phases for two-dimensional (2D) interacting fermion systems via lower-dimensional block-state decorations. We discover several intriguing fermionic SPT states that can only be realized in interacting fermion systems (i.e., not in free-fermion or bosonic SPT systems). Moreover, we also verify the recently conjectured crystalline equivalence principle for 2D interacting fermion systems. Finally, the potential experimental realization of these different classes of point-group SPT phases in 2D correlated superconductors is addressed.

An event occurring within a stationary environment, in the direction toward which an observer self-rotates, is perceived to precede a simultaneous event, in the direction away from which she moves. When self-rotation results from angular acceleration in the dark, perception of space is also distorted, such that the subjective straight-ahead shifts in the opposite direction to motion and temporal event promotion. A reference frameshift theory, based on the special theory of relativity, is proposed to explain these findings. Here, a hyperbolic tangent transformation of objective angular velocity constrains subjective self-rotation velocity within finite bounds, consistent with it being a limited perceptual resource. Identifying this subjective variable with vestibular nystagmus slow-phase angular velocity, the asymptotic perceived self-rotation velocity is estimated at ~200 °⁄s. When included in the Lorentz transformations of the new formalism, this value predicts experimental simultaneity distortion. Hypothetically, the hyperbolic tangent objective-to-subjective transfer function would maximize the differential entropy of the percept, and thereby also the stimulus/percept mutual information, if angular velocities of body rotation encountered in naturalistic environmental interaction have a logistic probability density distribution of scale 100 °⁄s, a proposed experimental test of the scheme.

This paper derives, based on reliability equivalence principle, the analytic expression of the equivalent singlevalued usage and stress level when the underlying life distribution is Weibull with a known shape parameter (slope). Numerical example is provided to illustrate the advantage of the method for reliability life test design over the traditional practice, especially for a high-reliability product.

It is well known, from Newtonian physics, that apparent forces appear when the motion of masses is described by using a non-inertial frame of reference. The generalized potential of such forces is rigorously analyzed focusing on their mathematical aspects., Comment: 8 pages, accepted for publication in Eur. J. Phys

We consider the model of the self-gravity driven spontaneous wavefunction reduction proposed by L. Diosi, R. Penrose et al. and based on a self-consistent system of the Schrodinger and Poisson equations. An analogous system of coupled Dirac and Maxwell-like equations is proposed as a relativization. Regular solutions to the latter form a discrete spectrum in which all the "active" gravitational masses are always positive, and approximately equal to inertial masses and to the mass $m$ of the quanta of Dirac field up to the corrections of order $\alpha^2$. Here $\alpha=(m/M_{pl})^2$ is the gravitational analogue of the fine structure constant negligibly small for nucleons. In the limit $\alpha \to 0$ the model reduces back to the nonrelativistic Schrodinger-Newton one. The equivalence principle is fulfilled with an extremely high precision. The above solutions correspond to various states of the same (free) particle rather than to different particles. These states possess a negligibly small difference in characteristics but essentially differ in the widths of the wavefunctions. For the ground state the latter is $\alpha$ times larger the Compton length, so that a nucleon cannot be sufficiently localized to model the reduction process, Comment: 5 pages. Talk presented at the 10-th Friedmann Seminar (Saint-Petersburg, Russia, 2019)

A set of coupled integral equations is presented based on Love’s and Schelkunoff’s field equivalence principles. According to Love’s equivalence principle and the boundary conditions, a general form of the Poggio–Miller–Chang–Harrington–Wu formulation is applied for modeling the waveguide cavities containing composite structures. The structures are discretized using the higher order polynomial basis functions, whose orders are adaptively adjusted for accurately modeling current distributions in this kind of strong near-field coupling and resonance problems. Moreover, the integral equations for the apertures involving the waveguide ports, each of which is terminated by a semi-infinite waveguide, are established according to Schelkunoff’s equivalence principle and the boundary conditions. Because the free-space Green’s function as well as the spatial discretization-based basis functions cannot be applied to semi-infinite waveguides, we employ waveguide eigenfunctions as the basis functions for the outer surface of an aperture. These coupled integral equations are then solved numerically using the method of moments accelerated by the parallel computing techniques. Comparisons with two well-developed software products demonstrate the accuracy and efficiency of the proposed method.

In this paper, we consider a stochastic linear quadratic mean field game for the continuum-parameterized multi-agent systems with multiplicative noise. Based on the Nash certain equivalence principle, we obtain a series of decentralized control laws. Then, Dynkin’s formula and comparison principle are employed to prove the boundedness of the state of the closed loop system in the mean square sense. Finally, we show that the set of decentralized controls has an ϵ-Nash equilibrium property.

Asphalt mixture is a kind of a viscoelastic material with viscoelastic characteristic of time-temperature equivalence. This paper, from the engineering practical consideration, and the perspective of time-temperature equivalence principle, based on the Rutting Test of Asphalt Mixture,has obtained equivalence relations of the effect of wheel speed and temperature on asphalt mixture rut index by different wheel speed and different temperatures rutting test, so as to provide the data support for the research of anti-rutting mechanism of asphalt pavement.

The Einstein equivalence principle of 1907 applies to the interior of a constantly accelerating long Rocketship in free outer space...

Some physicists and philosophers argue that unitarily inequivalent representations (UIRs) in quantum field theory (QFT) are mathematical surplus structure. Support for that view, sometimes ...

The principles underlying the theory of relativity, special and general, are presented. An easy to follow and pedagogical language is used and, based on physical examples, the motivation and some consequences of such principles are discussed. In addition, some roles of these principles when looking for a quantum gravity theory are mentioned

This study presents theoretical formulation and results for cavity-backed annular conical antennas. The formulation is based on equivalence principle and method of moments (MoM), in both point-matching and Galerkin forms. Results are presented for radiation diagram, and input impedance, and compared to those obtained using commercial software. The effects of dielectric thickness and of cavity dimensions on input impedance are presented. In addition, the feeding using two coaxial cables for radiation maximum at cone axis is also presented.

In the class of models of some theory in a countable first order language, we consider relationships between isomorphism, elementary embeddability, and elementary equivalence.

The Tone’s and embedded self shielding methods are based on a heterogeneous-homogeneous equivalence principle. They both provide a formula for an equivalent dilution parameter that can be used to interpolate pretabulated effective cross sections for the infinite homogeneous medium. These two methods have been traditionally applied to fast reactor analysis with fine or ultrafine group energy mesh. We are investigating the accuracy of these two methods for the generation of self-shielded cross sections for typical pressurized water reactor assemblies.

A novel equivalence principle algorithm (EPA) domain decomposition method previously for the surface integral equation is explored for volume integral equation in this work. The whole object is decomposed into several subdomains, the equivalence spheres are automatically produced to enclose each subdomain. The Rao–Wilton–Glisson (RWG) and body of revolution (BoR) basis functions are defined on the equivalence sphere surface. The equivalence currents defined on the RWG basis functions are evaluated with multilevel fast multipole algorithm, and then the currents defined on the RWGs can be projected onto the BoR basis functions. Compared with surface integral equation EPA-BoR algorithm, the ratio of the number of average original unknowns in each subdomain with respect to the equivalence unknowns is relatively larger, which leads to significant reduction of computations. Numerical simulations validate the accuracy and efficiency of the proposed method.

The paper revisits the use of a surface equivalence theorem in deriving the surface integral equation (SIE) based formulation for a homogeneous bio- electromagnetics problem. The vector analog of Green’s 2nd identity is used to obtain the expression for the electric field representing the mathematical foundation of the equivalence theorem. The particular emphasis is put on the treatment of boundary integral when the observation and source points, respectively, coincide. The boundary conditions at infinity are taken into account via the Sommerfeld radiation conditions. The derived coupled SIE set can be used in problems involving biological body exposed to electro- magnetic field radiation.

A unified elastoplastic model was proposed to describe the relation among load, displacement, and uniaxial constitutive parameters of ductile materials according to the von Mises energy equivalence principle at a special location or energy center in the deformed region of a structural component (SC). Two pairs of parameters were considered in the model: one was related to the volume of deformed region and the other to the Mises equivalent strain at the energy center. In addition, they are easily determined by finite element analysis (FEA). For eight kinds of SCs under proportional loading, the load–displacement behaviors of various materials predicted by the unified model were highly consistent with the results of FEA.

Shear effect is a crucial factor in determining crack propagation of mode II and mixed-mode fractures for brittle and quasi-brittle materials. Based on Timoshenko beam theory, shear effect is introduced into micropolar peridynamic model. The peridynamic parameters for two-dimensional and three-dimensional cases are derived with energy equivalence principle. Particle geometry is originally considered in the derived formulations to obtain independent rotational stiffness. An implicit algorithm in finite element framework is adopted to calculate elastic deformation and to simulate quasi-static crack propagation. Several numerical examples are conducted to verify the accuracy and efficiency of the developed model. The results show that the proposed model possesses high accuracy and numerical stability in simulating crack propagation of mode I, mode II and mixed-mode fractures.