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The Weak Equivalence Principle is the founding pillar of General Relativity, and as such, it should be verified as precisely as possible. The Microscope experiment tested it in low Earth orbit, finding that Pt and Ti test masses fall toward Earth with the same acceleration to about 1 part in 10 15 , an improvement of about two orders of magnitude over ground tests. Space missions, even if small, are expensive and hard to replicate; yet, the essence of physics is repeatability. This work is an assessment of the Microscope results based on the laws of physics and knowledge from previous experiments, focusing on the limiting thermal noise and the treatment of acceleration outliers. Thermal noise reveals anomalies that we explain by stray sub- μ V potentials caused by patch charges, giving rise to an unstable zero. The measurements were affected by numerous acceleration spikes occurring at the synodic frequencies relative to the Earth (the signal frequency) and the Sun, which we interpret as evidence of a thermal origin. In Microscope authors' analysis, the spikes were removed and the resulting gaps replaced with artificial data (up to 35 % , 40 % of the sessions data), which retain memory of the gaps and may simulate or cancel an effect (signal or systematic). An alternative approach based exclusively on real measured data would avoid any ambiguity. The lessons of Microscope are crucial to any future improved mission. [ABSTRACT FROM AUTHOR]

The status of the equivalence principle in modified symmetric teleparallel gravity is examined. In this theory, minimum length geodesics are distinct from autoparallel geodesics, that is, the "shortest" paths are not the "straightest" paths. We show that a standard argument that singles out metric geodesics in general relativity does not apply in modified symmetric teleparallel gravity. This is because the latter theory does not obey the equivalence principle in the sense of Weinberg. We argue, however, that the structure of the theory makes it inevitable that a freely falling test particle follows a shortest path, a geodesic of the metric. The geodesic equation that governs the motion of a freely falling test particle involves the Levi-Civita connection, not some other connection obtained by solving the connection field equations of the theory. This also has bearing on whether, under appropriate conditions, modified symmetric teleparallel gravity is fully equivalent to general relativity. [ABSTRACT FROM AUTHOR]

The high speeds seen in rapidly rotating pulsars after supernova explosions present a longstanding puzzle in astrophysics. Numerous theories have been suggested over the years to explain this sudden "kick" imparted to the neutron star, yet each comes with its own set of challenges and limitations. Key explanations for pulsar kicks include hydrodynamic instabilities in supernovae, anisotropic neutrino emission, asymmetries in the magnetic field, binary system disruption, and physics beyond the Standard Model. Unraveling the origins of pulsar kicks not only enhances our understanding of supernova mechanisms but also opens up possibilities for exploring new physics. In this brief review, we will introduce pulsar kicks, examine the leading hypotheses, and explore future directions for this intriguing phenomenon. [ABSTRACT FROM AUTHOR]

Chae's analyses on GAIA observations of wide binary stars have fortified the paradigm of extended gravity with particular attention to MOND-like theories. We recall that, starting from the origin of Einstein's general relativity, the request of Mach on the structure of the theory has been the core of the foundational debate. This issue is strictly connected with the nature of the mass–energy equivalence. This was exactly the key point that Einstein used to derive the same general relativity. On the other hand, the current requirements of particle physics and the open questions within extended gravity theories, which have recently been further strengthened by the analyses of GAIA observations, request a better understanding of the Equivalence Principle. By considering a direct coupling between the Ricci curvature scalar and the matter Lagrangian, a nongeodesic ratio between the inertial and gravitational masses can be fixed and MOND-like theories are retrieved at low energies. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the scenarios in which a holonomic versus a non-holonomic frame description of gravity theories are equivalent. It turns out that classically, the equivalence holds in a way that is independent of the particular dynamics and/or spacetime dimension. This includes general metric-affine dynamics. A global bundle-theoretical investigation is carried out, uncovering the equivalence principle as the culprit. The equivalence holds as long as the equivalence principle holds. This is not something to be expected when non-invertible configurations of the vielbein field are taken into account. In such cases, the gauge-theoretical description of gravity “unsolders” from spacetime, and one has to decide if gravity is spacetime geometry or an internal gauge theory. [ABSTRACT FROM AUTHOR]

The equivalence principle is considered in the framework of metric-affine gravity. We show that it naturally emerges as a Noether symmetry starting from a general non-metric theory. In particular, we discuss the Einstein equivalence principle and the strong equivalence principle showing their relations with the non-metricity tensor. Possible violations are also discussed pointing out the role of non-metricity in this debate. [ABSTRACT FROM AUTHOR]

This paper introduces an innovative sell-type home reversion product aimed at monetizing Singapore’s public flats, serving as a new alternative to the existing Singapore Lease Buyback Scheme (LBS). This new product not only retains the LBS’s guaranteed period of residence in the property along with life annuity incomes but also enhances the product features to meet specific homeowner needs, including the ability to age in place, flexibility in retaining part of the property, options for bequests, and guaranteed principal return. By incorporating these additional features, the new product seeks to stimulate greater demand for monetizing public flats among asset-rich but cash-poor homeowners. An actuarial pricing model is developed to establish a transparent and fair framework for justifying the cost of each product feature. Additionally, we present a cost–benefit analysis from both the provider and consumer perspectives to highlight the major contributions of the new product when compared to the LBS.

Copyright of Zeitschrift für Sozialreform is the property of De Gruyter and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Loan-type reverse mortgage plans and sell-type home reversion plans for retirement financing are two well-known equity release plans that entitle homeowners not only to release cash from their properties but also to allow them to age in place. Recently, a new hybrid equity release plan was proposed to incorporate the home reversion plan's features with an option of staying in the property for a fixed period without being subject to survival. This additional option provides flexibility to homeowners to better meet their retirement financial and personal needs by reducing the financial uncertainty of home reversion products. In this article, we propose an enhanced home reversion plan with some new features to meet retirees' other financial needs, such as life annuity incomes and guaranteed return of principal invested. An actuarial framework is provided to analyze the cost components of each benefit offered under the enhanced home reversion product. Numerical illustrations are presented to demonstrate and examine the actuarial values of the benefits and product risks with different parameter configurations under the recent Singapore mortality data set. [ABSTRACT FROM AUTHOR]

Paragraph 53(a) of the new insurance accounting standard IFRS 17 suggests there is a relationship between the liability for remaining coverage ("LFRC") calculated under the general measurement model ("GMM") and premium allocation approach ("PAA"), although it is not immediately obvious how the two are related or could result in a similar estimate for the LFRC. This paper explores the underlying relationship between the GMM and PAA through the equivalence principle and presents a set of sufficient mathematical conditions that result in an identical LFRC when calculated under the GMM and PAA. An illustrative example is included to demonstrate how the sufficient conditions can be applied in practice and the optimisation opportunities offered to actuaries and accountants when conducting PAA eligibility testing. [ABSTRACT FROM AUTHOR]

Entanglement can be generated through the gravitational interaction between two massive bodies that are initially in a product state. This shows that the gravitational field is quantum. When the third massive body is introduced and the gravitational interaction only between the third body with either one of the former two bodies is considered, we find that no entanglement is generated between the former two bodies up to the monopole approximation, even though the considered gravitational interaction is quantum. This resembles the behavior of two accelerating two-level atoms that is usually regarded as the Unruh–DeWitt detectors. By linking the acceleration to that generated by the gravitational field, we show that the equivalence principle is still valid even though the gravitational field is quantum.

Due to the total lack of reliable experimental data on the kinetics of solid-phase transformations at high temperatures, adequate estimates of the ignition and combustion characteristics of real energetic materials are currently unavailable. In combustion theory, balance relations in the form of ignition criteria and in the form of the principle of equivalence of the burning rate increase under the action of a radiant flux to the corresponding increase in the initial temperature are used in most cases without sufficient theoretical justification, what can lead to incorrect results. Numerical simulation of the ignition and combustion of model energetic materials can provide a basis for determining the conditions for the correct use of balance relations. In this work, using a model of unsteady combustion of melting energetic materials, ignition and combustion under the action of a radiant flux have been studied numerically and the fitting coefficients in the balance relations have been obtained. It has been shown that the values of these coefficients depend on the kinetic parameters of solid-phase transformations and the intensity of the external heating source. It is concluded that it is necessary to continue the theoretical research aimed at developing valid approaches to determine the parameters of global reactions in the condensed phase using data on the delay of ignition by heat flux and to determine the correct fitting coefficients when using the equivalence principle. [ABSTRACT FROM AUTHOR]

The article refines the axiomatic foundation of central place theory (CPT) and identifies the possibilities and limitations of a logical transition in research from real settlement systems to central place (CP) systems. The necessity of relying on the CPT axioms in the following form is determined: (1) the space of a CP system is not infinite, but finite: the basis of each system is formed by an isolated lattice; the theory deals with physical space, not mathematical or geographical; (2) the space is homogeneous and isotropic in all respects, except for the distribution of not only the urban, but also the rural population; (3) a hexagonal lattice corresponds to the equilibrium state of an isolated CP system as an attractor; deviations from a hexagonal shape result only from external impact on the system; (4) CP systems are polymorphic: they can exist in modifications with both the same and different values for all levels of the hierarchy and not necessarily an integer value K ∈ (1, 7]. The axiom about a consumer's "rational" behavior is accepted when establishing the CP hierarchy in terms of the volume of functions performed; when establishing their hierarchy in terms of population, it is redundant. In contrast to the foreign approach to CPT, which presupposes the transfer of properties of an ideal CP system to a real settlement system, in the approach of the Russian school, they are compared. The possibility of the latter is due to the equivalence principle in the relativistic version of the theory, according to which settlement systems form in the geographic space similarly to how CP systems form in the physical space. In both cases, if the gravitational effects are compensated, it is impossible to distinguish a settlement system from a CP system; i.e., a heterogeneous and anisotropic geographical space cannot be distinguished from a homogeneous and isotropic physical one. The immediate consequence of this is equivalence, on the one hand, of the population of settlements and CP, and, on the other, the distances between them in real settlement systems and CP systems. [ABSTRACT FROM AUTHOR]

In this paper, I discuss the impact of the positive cosmological constant on the interplay between the equivalence principle in general relativity, and the rules of quantum mechanics. At the nonrelativistic level, there is an ambiguity in the definition of a phase of a wave function measured by inertial and accelerating observes. This is the cosmological analogue of the Penrose effect, which can also be seen as a nonrelativistic limit of the Unruh effect. The symmetries of the associated Schrödinger equation are generated by the Newton–Hooke algebra, which arises from a nonrelativistic limit of a cosmological twistor space. [ABSTRACT FROM AUTHOR]

Loan-type reverse mortgage plans and sell-type home reversion plans for retirement financing are two well-known equity release plans that entitle homeowners not only to release cash from their properties but also to allow them to age in place. Recently, a new hybrid equity release plan was proposed to incorporate the home reversion plan’s features with an option of staying in the property for a fixed period without being subject to survival. This additional option provides flexibility to homeowners to better meet their retirement financial and personal needs by reducing the financial uncertainty of home reversion products. In this article, we propose an enhanced home reversion plan with some new features to meet retirees’ other financial needs, such as life annuity incomes and guaranteed return of principal invested. An actuarial framework is provided to analyze the cost components of each benefit offered under the enhanced home reversion product. Numerical illustrations are presented to demonstrate and examine the actuarial values of the benefits and product risks with different parameter configurations under the recent Singapore mortality data set.

Einstein's general relativity theory provides a successful understanding of the flow of time in the gravitational field. From Einstein's equivalence principle, the influence of the Sun and Moon masses on clocks is given in the form of tidal potentials. Two clocks fixed on the surface of the Earth, compared to each other, can measure the tidal effects of the Sun and Moon. The measurement of tidal effects can provide a test for general relativity. Based on the standard general relativity method, we rigorously derive the formulas for clock comparison in the Barycentric Celestial Reference System and Geocentric Celestial Reference System, and demonstrate the tidal effects on clock comparison experiments. The unprecedented performance of atomic clocks makes it possible to measure the tidal effects on clock comparisons. We propose to test tidal effects with the laboratory clock comparisons and some international missions, and give the corresponding estimations. By comparing the state-of-the-art clocks over distances of 1000 km, the laboratory may test tidal effects with a level of 1%. Future space missions, such as the China space station and FOCOS mission, can also be used to test tidal effects, and the best accuracy may reach 0.3%. [ABSTRACT FROM AUTHOR]

The Einstein equivalence principle is based on the equality of gravitational and inertial mass, which has led to the universality of a free-fall concept. The principle has been extremely well tested so far and has been tested with a great precision. However, all these tests and the corresponding arguments are based on a classical setup where the notion of position and velocity of the mass is associated with a classical value as opposed to the quantum entities.Here, we provide a simple quantum protocol based on creating large spatial superposition states in a laboratory to test the quantum regime of the equivalence principle where both matter and gravity are treated at par as a quantum entity. The two gravitational masses of the two spatial superpositions source the gravitational potential for each other. We argue that such a quantum protocol is unique with regard to testing especially the generalisation of the weak equivalence principle by constraining the equality of gravitational and inertial mass via witnessing quantum entanglement. [ABSTRACT FROM AUTHOR]

The essence of Newtonian mechanics is entanglement, which was inherited by quantum mechanics. Entanglement is a classical phenomenon based on the conservation of angular momentum and does not relate to quantization. Entanglement and propagation are the two wheels of physics. In this report, we show black hole mergers prove gravity entanglement. If we assume that gravity has a finite velocity, black holes are pulled slightly forward in the direction of travel, and gravity acts to accelerate the black holes; therefore, simulation conditions cannot be set, and we find that the assumption that gravity has a finite velocity is incorrect. This is because we cannot use the condition that the sum of kinetic and potential energies is constant. Gravity entanglement shows that entanglement continues permanently. Furthermore, Newtonian mechanics involves entanglement, ether, and equivalence principle. [ABSTRACT FROM AUTHOR]

The space mission MICROSCOPE dedicated to the test of the equivalence principle (EP) operated from April 25, 2016 until the deactivation of the satellite on October 16, 2018. In this analysis we compare the free-fall accelerations (a A and a B) of two test masses in terms of the Eötvös parameter η (A,B) = 2 a A âˆ' a B a A + a B . No EP violation has been detected for two test masses, made from platinum and titanium alloys, in a sequence of 19 segments lasting from 13 to 198 h down to the limit of the statistical error which is smaller than 10âˆ'14 for η (Ti, Pt). Accumulating data from all segments leads to η (Ti, Pt) = [âˆ'1.5 ± 2.3 (stat) ± 1.5 (syst)] Ă— 10âˆ'15 showing no EP violation at the level of 2.7 Ă— 10âˆ'15 if we combine stochastic and systematic errors quadratically. This represents an improvement of almost two orders of magnitude with respect to the previous best such test performed by the Eöt-Wash group. The reliability of this limit has been verified by comparing the free falls of two test masses of the same composition (platinum) leading to a null Eötvös parameter with a statistical uncertainty of 1.1 Ă— 10âˆ'15. [ABSTRACT FROM AUTHOR]

After performing highly sensitive acceleration measurements during two years of drag-free flight around the Earth, MICROSCOPE provided the best constraint on the weak equivalence principle (WEP) to date. Beside being a technological challenge, this experiment required a specialised data analysis pipeline to look for a potential small signal buried in the noise, possibly plagued by instrumental defects, missing data and glitches. This paper describes the frequency-domain iterative least-square technique that we developed for MICROSCOPE. In particular, using numerical simulations, we prove that our estimator is unbiased and provides correct error bars. This paper therefore justifies the robustness of the WEP measurements given by MICROSCOPE. [ABSTRACT FROM AUTHOR]

Testing the weak equivalence principle to a precision of 10âˆ'15 requires a quantity of data that give enough confidence on the final result: ideally, the longer the measurement the better the rejection of the statistical noise. The science sessions had a duration of 120 orbits maximum and were regularly repeated and spaced out to accommodate operational constraints but also in order to repeat the experiment in different conditions and to allow time to calibrate the instrument. Several science sessions were performed over the 2.5 years duration of the experiment. This paper aims to describe how the data have been produced on the basis of a mission scenario and a data flow process, driven by a tradeoff between the science objectives and the operational constraints. The mission was led by the Centre National d’Etudes Spatiales (CNES) which provided the satellite, the launch and the ground operations. The ground segment was distributed between CNES and Office National d’Etudes et de Recherches AĂ©rospatiales (ONERA). CNES provided the raw data through the Centre d’Expertise de Compensation de TraĂ®nĂ©e (CECT: drag-free expertise centre). The science was led by the Observatoire de la CĂ´te d’Azur (OCA) and ONERA was in charge of the data process. The latter also provided the instrument and the Science Mission Centre of MICROSCOPE (CMSM). [ABSTRACT FROM AUTHOR]

This paper focuses on the description of the design and performance of the MICROSCOPE satellite and its drag-free and attitude control system. The satellite is derived from CNES’ Myriade platform family, albeit with significant upgrades dictated by the unprecedented MICROSCOPE’s mission requirements. The 300 kg drag-free microsatellite has completed its 2 years flight with higher-than-expected performances. Its passive thermal concept allowed for temperature variations smaller than 1 ÎĽ K at the frequency of the equivalence principle test f EP. The propulsion system provided a six-axis continuous and very low noise thrust from zero to some hundreds of micronewtons. Finally, the performance of its DFACS (aimed at compensating the disturbing forces and torques applied to the satellite) is the finest ever achieved in low Earth orbit, with residual accelerations along the three axes lower than 10âˆ'12 m sâˆ'2 at f EP over 8 days. [ABSTRACT FROM AUTHOR]

This paper focuses on the dedicated accelerometers developed for the MICROSCOPE mission taking into account the specific range of acceleration to be measured on board the satellite. Considering one micro-g and even less as the full range of the instrument with an objective of one femto-g resolution, that leads to a customized concept and a high-performance electronics for the sensing and servo-actuations of the accelerometer test-masses. This range and performance directed the payload development plan. In addition to a very accurate geometrical sensor core, a high performance electronics architecture provides the measurement of the weak electrostatic forces and torques applied to the test-masses. A set of capacitive detectors delivers the position and the attitude of the test-mass with respect to a very steady gold-coated cage made in silica. The voltages applied on the electrodes surrounding each test-mass are finely controlled to generate the adequate electrical field and so the electrostatic pressures on the test-mass. This field maintains the test-mass motionless with respect to the instrument structure. Digital control laws are implemented in order to enable instrument operation flexibility and a weak position detector noise. These electronics provide both the scientific data for MICROSCOPE’s test of the weak equivalence principle and the input for the satellite drag-free and attitude control system. [ABSTRACT FROM AUTHOR]

The MICROSCOPE mission aimed to test the weak equivalence principle (WEP) to a precision of 10âˆ'15. The WEP states that two bodies fall at the same rate on a gravitational field independently of their mass or composition. In MICROSCOPE, two masses of different compositions (titanium and platinum alloys) are placed on a quasi-circular trajectory around the Earth. They are the test-masses of a double accelerometer. The measurement of their accelerations is used to extract a potential WEP violation that would occur at a frequency defined by the motion and attitude of the satellite around the Earth. This paper details the major drivers of the mission leading to the specification of the major subsystems (satellite, ground segment, instrument, orbit…). Building upon the measurement equation, we derive the objective of the test in statistical and systematic error allocation and provide the mission’s expected error budget. [ABSTRACT FROM AUTHOR]

This paper introduces the current special issue focussed on the MICROSCOPE mission. This mission is the first experimental test in space of the weak equivalence principle (WEP) using man-made test-massesâ€"as opposed to astronomical testsâ€"with the goal to reach a precision two orders of magnitude better than ground-based experiments. Selected in 1999 by CNES as part of its MYRIADE microsatellite programme, the satellite was launched in 2016 and the mission lasted 2.5 years. This paper summarises the articles of the special issue and highlights the key technological and data analysis aspects that allowed for an unprecedented precision on the test of the WEP. [ABSTRACT FROM AUTHOR]

We review the possible violation of the Equivalence Principle at finite temperature T in the framework of curvature-based Extended Theories of Gravity. Specifically, we first show how it is possible to derive Equivalence Principle violation from Quantum Field Theory at T ≠ 0. Subsequently, we exhibit how this result can be precisely recovered by following an alternative path that envisages the employment of generalized Einstein equations with a temperature-dependent energy-momentum tensor. Finally, we adopt the latter formalism in the context of some Extended Gravity models to quantify the amount of Equivalence Principle violation. Specifically, Brans–Dicke Theory, Standard Model Extension and Conformal Gravity are considered in detail. [ABSTRACT FROM AUTHOR]

We discuss some difficulties that arise in attempting to interpret the Page–Wootters and Internal Quantum Reference Frames formalisms, then use a 'final measurement' approach to demonstrate that there is a workable single-world realist interpretation for these formalisms. We note that it is necessary to adopt some interpretation before we can determine if the 'reference frames' invoked in these approaches are operationally meaningful, and we argue that without a clear operational interpretation, such reference frames might not be suitable to define an equivalence principle. We argue that the notion of superposition should take into account the way in which an instantaneous state is embedded in ongoing dynamical evolution, and this leads to a more nuanced way of thinking about the relativity of superposition in these approaches. We conclude that typically the operational content of these approaches appears only in the limit as the size of at least one reference system becomes large, and therefore these formalisms have an important role to play in showing how our macroscopic reference frames can emerge out of wholly relational facts. [ABSTRACT FROM AUTHOR]

Copyright of Transportation Science & Technolgy is the property of Transportation Science & Technology Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

A modeling of natural phenomena based on the principle of 100% efficiency of mathematics is presented. The fundamental distinction between abstract and material entities is discussed and the probabilistic nature of natural phenomena is explained. The paper provides explanations for many observed phenomena. A general definition of the virtual state of matter, the concept of entropic interaction, and the phenomenon of quantum entanglement is given. An additional interpretation of the Hubble law is considered. It is shown how local entropy changes in world space lead to the bifurcation of its state and subsequent “Big Bangs” with the formation of an infinite number of parallel universes that do not interact with each other. The correlation between the change in entropy and the rhythm of time, which is valid for isolated non-equilibrium thermodynamic systems, including our Universe, is presented. The fundamental principles of thermodynamics, quantum mechanics, quantum field theory and the theory of relativity, as well as the origin and evolution of our Universe are discussed. An alternative explanation for the curvature of space is given for the effects of deflection of a light beam towards the sun, the shift of the perihelion of Mercury, the periastron of binary stars, and the gravitational slowing of the rhythm of time. The interference pattern is considered as the result of small-angle scattering in a weak potential field without using the wave mechanism and is interpreted as the result of the entropic interaction of photons or particles passing through the corresponding slots. The presented paper applies equally to both living and non-living nature objects, and contains information about the laws of dialectics. [ABSTRACT FROM AUTHOR]

In the traditional integrity analysis of solid rocket motors, solid propellants failure and propellant-liner interface debonding were intentionally differentiated. This empirical distinction of failure regions based on the macroscopic phenomenon neglects their physical correlation, consequently increasing both experiment quantity and simulation complexity. Here, by experiments and simulations, propellant-liner interface debonding is shown to be induced by propellant breakage, i.e., the substrate failure. In experiments, interface debonding and propellants failure share the same cavitation and stringing processes in crack initiation, and the measured break strain of solid propellants and fracture energy of interface satisfy a similar temperature/strain-rate dependent shifting phenomenon. The finite element model can well predict both the strain field and the stress-strain response of interface debonding by using the parameters calibrated by tensile tests of solid propellants, verifying that interface debonding is induced by propellants breakage. Overall, failure envelopes of both propellants and interfaces satisfy a similar peak-position shifting phenomenon but different peak-value shifting phenomena. The time-temperature superposition of HTPB polymer binders induces the peak-position shift, and strain concentration and relaxation of propellants in the crack front induce the peak-value evolution. This study is promising to unify and simplify the solid propellants failure and interface debonding in the integrity analysis.

In this letter, an efficient hybrid method is proposed to analyze array structures when frequency and material parameters sweep. Using the frequency and material independent reactions method, the impedance matrix is split into the product of a geometry dependent matrix and a wavenumber dependent factor. The geometry dependent matrix needs to be solved and stored only once when parameters sweep. However, the memory requirement will be very huge for electrically large objects such as array structures. To deal with this problem, the equivalence principle algorithm is used to decompose the array into subdomains and transfer unknowns on the subdomains to the unknowns on the equivalence surfaces. Furthermore, the characteristic basis functions are constructed on the equivalence surfaces to reduce the number of unknowns and matrix storage significantly. Several numerical results are shown to demonstrate the accuracy and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

In this article, we review the topic of Huygens' metasurfaces with an emphasis on existing and emerging applications at microwave frequencies. Huygens' metasurfaces have demonstrated unprecedented capabilities of controlling electromagnetic wavefronts by means of electric and magnetic dipole moments arranged in a thin sheet. We present the fundamental principles of Huygens' metasurfaces based on the boundary conditions governing their operation. Then, we discuss the aspect of practical realization of Huygens' metasurfaces and the different types of constituent subwavelength scatterers (unit cells). Moreover, we summarize recent developments in several areas related to metasurfaces, such as perfect anomalous refraction, polarization control, antenna beamforming and reconfigurable metasurfaces. Lastly, we provide a brief outlook on emerging metasurface-based microwave technologies that are expected to further grow in the future.

The Mössbauer rotor effect recently gained a renewed interest due to the discovery and explanation of an additional effect of clock synchronization which has been missed for about 50 years, i.e. starting from a famous book of Pauli, till some recent experimental analyses. The theoretical explanation of such an additional effect is due to some recent papers in both the general relativistic and the special relativistic frameworks. In the first case (general relativistic framework) the key point of the approach is the Einstein’s equivalence principle (EEP), which, in the words of the same Einstein, enables “the point of view to interpret the rotating system K’ as at rest, and the centrifugal field as a gravitational field”. In this paper, we analyse both the history of the Mössbauer rotor effect and its interpretation from the point of view of Einstein’s general theory of relativity (GTR) by adding some new insight. In particular, it will be shown that, if on one hand the “traditional” effect of redshift has a strong analogy with the gravitational redshift, on the other hand the additional effect of clock synchronization has an intriguing analogy with the cosmological redshift. Finally, we show that a recent claim in the literature that the second effect of clock synchronization does not exist is not correct. [ABSTRACT FROM AUTHOR]

In this article, we want to analyze a relativistic paradox in a very simple way, which, in our opinion, could be useful for a pedagogical purpose. Indeed we want to solve it using only Einstein's relativity principle and the Einstein equivalence principle. We think it could be useful from a pedagogical point of view. [ABSTRACT FROM AUTHOR]

The MICROSCOPE space experiment aimed to test the Equivalence Principle with a much better accuracy than ever before. Its principle is to compare the free fall of concentric test masses embedded in a space accelerometer onboard a satellite orbiting the Earth. The effect of non-gravitational forces on the motion of the satellite is strongly reduced thanks to the so-called drag-free system. MICROSCOPE ran from April 2017 until October 2019. The analysis of the first series of measurements leads to an improvement of about an order of magnitude on the accuracy of the test of the Equivalence Principle. No violation has been detected for the pair of masses in platinum and titanium at the level of $10^{-14}$.MICROSCOPE, proposed by ONERA and OCA as science leaders and developed by CNES as project manager, is the first European space mission dedicated to fundamental physics on low Earth orbit. ZARM, PTB and ESA are the main European contributors.

Radial (or circular) cooling fin is an extension of a cylindrical surface widely used to increase the rate of heat transfer from the heated surface to a surrounding cooler fluid. The only type of radial fins for which an exact closed-form expression for the one-dimensional temperature distribution is available in the literature is radial fins of constant thickness. In this article, we discover a new family of radial fins for which the temperature distribution along the fin can be computed in closed form. The profile curve of the new radial fin satisfies a non-linear, non-autonomous ODE and, depending on the initial condition and the sign of the right-hand side of the ODE, can have three distinct geometric shapes. We found that partial-length novel radial fins described in this work have the following equivalence property: If the ratio, σ , of the heat transfer coefficient on the fin's tip to that on its lateral surface is not too large (specifically, satisfies inequality (39) in Sect. 7), then the temperature distribution within a fin with a non-adiabatic tip is identical to that for a longer fin with adiabatic tip. Our analysis of heat transfer by radial fins is only based on standard homogeneity, steady-state and one-dimensionality assumptions. In particular and most importantly, we dispensed with the "length-of-arc" assumption that underlies most of the previous work on heat transfer by radial, straight and pin fins. Although the analytic form of the temperature distribution for the family of radial fins discovered in this work is remarkably similar to that for the families of straight and pin fins found in Hanin and Brown (J Eng Math 119(1):93–114, 2019), the geometries of these fin families are strikingly dissimilar. [ABSTRACT FROM AUTHOR]

An equivalence-principle-based method (EPM) for calculating the magnetic field around the coil assemblies applied in electric vehicle inductive chargers is proposed. The ferrite core and the aluminum shielding plate are substituted with surface equivalent sources (ESs), the distribution of which is solved from surface boundary conditions. The magnetic field is the sum of the incident field (induced by the coil current) and the scattered field (induced by ES). The impacts of ferrite core and aluminum plate are quantitatively characterized using their respective source–field relations. The optimization of coil assemblies to improve the efficiency is selected as an application of EPM. The key factors that affect efficiency, e.g., mutual inductance and stray losses, are approximated using simple functions of ES. An exemplary circular coil assembly pair is manually optimized via EPM. Comparisons with finite element analysis (FEA) prove the accuracy and speediness of EPM. The other benefits of EPM are also discussed. Due to the immeasurability of ES, experimental test results of two coils are compared with FEA results to indirectly validate the accuracy of EPM. [ABSTRACT FROM AUTHOR]

In this paper, we take a closer and new look at the effects of tidal forces on the free fall of a quantum particle inside a spherically symmetric gravitational field. We derive the corresponding Schrödinger equation for the particle by starting from the fully relativistic Klein–Gordon equation in order (i) to briefly discuss the issue of the equivalence principle and (ii) to be able to compare the relativistic terms in the equation to the tidal-force terms. To the second order of the nonrelativistic approximation, the resulting Schrödinger equation is that of a simple harmonic oscillator in the horizontal direction and that of an inverted harmonic oscillator in the vertical direction. Two methods are used for solving the equation in the vertical direction. The first method is based on a fixed boundary condition, and yields a discrete-energy spectrum with a wavefunction that is asymptotic to that of a particle in a linear gravitational field. The second method is based on time-varying boundary conditions and yields a quantized-energy spectrum that is decaying in time. Moving on to a freely-falling reference frame, we derive the corresponding time-dependent energy spectrum. The effects of tidal forces yield an expectation value for the Hamiltonian and a relative change in time of a wavepacket's width that are mass-independent. The equivalence principle, which we understand here as the empirical equivalence between gravitation and inertia, is discussed based on these various results. For completeness, we briefly discuss the consequences expected to be obtained for a Bose–Einstein condensate or a superfluid in free fall using the nonlinear Gross–Pitaevskii equation. [ABSTRACT FROM AUTHOR]

A simple yet accurate model for the transmission of surface plasmon polaritons (SPPs) in a finite metal–insulator–metal (MIM) waveguide to the sides of the apertures is proposed and demonstrated to be more accurate than the available models. It is as simple as using a magnetic current density across the plane of the aperture whose value is defined by the SPPs with any number of modes in the waveguide through the equivalence principle. Then, the generated SPPs on both sides of the aperture are extracted from the convolution integral of the equivalent current density and Green’s function. As a result, the model provides the transmission coefficients of the SPPs in the MIM waveguide to the side walls of the aperture accurately and efficiently; not only for symmetric MIM waveguides with a single isolating layer but also non-symmetric ones with multi-layered insulating materials. The results are in very good agreement with those obtained by the finite-difference time-domain method and better than the other approximations available in literature for a wide range of aperture widths.

Due to stringent electromagnetic compatibility (EMC) regulations, all electronic devices need to go through rigorous radiated emission tests before launching to market. Thus, efficient, accurate, and cheap characterization approaches are quite of interest. Instead of utilizing the time-consuming and expensive direct far-field measurement, in this work, a novel methodology on the basis of numerical Green’s function (NGF) is proposed to acquire the parasitic EM emissions from PCBs placed in a shielding enclosure with ventilation slots. Referring to Schelkunoff’s equivalence principle, the whole modeling procedure can be decomposed into two steps in order to obtain the emissions in the entire space. For the first step, the tangential electric fields over the surface of ventilation slots are sampled first; then, the NGF over a spherical surface tightly enclosing the perfectly electric conductor (PEC) filled shielding box is numerically evaluated; finally, the tangential component of the magnetic field over the spherical surface enclosing the shielding box is calculated in terms of the NGF and the sampled near electric field. As for the second step, by filling the sphere with a perfectly magnetic conductor (PMC) first, the pertinent Green’s function is further expanded by the spherical modal functions; later, the radiated emission outside this sphere can be analytically evaluated in terms of the previously obtained tangential magnetic field and the modal function expanded Green’s function. Therefore, the novelty of the proposed method has two folds: 1) only the tangential electric field over the ventilation slots is required, thus saving a lot of time in near-field measurement and 2) the NGF is independent of the PCBs in the shielding enclosure and, thus, only needs to be calculated once even though the PCBs inside the shielding enclosure is changed. To validate and verify the effectiveness of this proposed modality, several representative examples are presented. [ABSTRACT FROM AUTHOR]

In his address to the 21st International Congress of Actuaries, the late Professor William S. Jewell pointed out that, for a whole life insurance policy with level premiums payable continuously and a death benefit of constant amount payable at the moment of death, even though the equivalence principle stipulates that the insurer's expected gain at issue is zero, the insurer's expected gain at the moment of death of the insured is positive. This seemingly surprising result turns out to be true for more general life insurance policies. We present a simple derivation of and some elaboration on this fact. [ABSTRACT FROM AUTHOR]

We have developed a two-dimensional neutron imager based on a semiconductor pixelated sensor, especially designed for experiments measuring of a spatial and a temporal behavior of quantum bound states of ultra-cold neutrons. Through these measurements, we expect to measure the ratio between the inertial and gravitational masses of neutrons and to test the equivalence principle in the quantum regime. As one of the principal neutron imagers, we fabricated a sensor with a sandwich configuration, named 10B-INTPIX4-sw, and tested its response to ultra-cold neutrons at the Los Alamos Neutron Science Center (LANSCE). We observed simultaneous events on both sandwiching sensors without significant loss of detection efficiency. The efficiency was evaluated to be about 16%, relative to the 10B/ZnS reference detector. The coincidence condition reduces its efficiency by a factor of about 3. [ABSTRACT FROM AUTHOR]