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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...

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 ...

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

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.

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.

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.

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.

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.

The oscillation of neutrino flavors, due to its interferometry nature, is extremely sensitive to the phase differences developing during the propagation of neutrinos. In this paper we investigate the effect of the Violation of Equivalence Principle (VEP) on the flavor oscillation probabilities of atmospheric and cosmic neutrinos observed at neutrino telescopes such as IceCube. Assuming a general parameterization of VEP, dubbed extended parameter space, we show that the synergy between the collected data of high energy atmospheric and cosmic neutrinos severely constrains the VEP parameters. Also, the projected sensitivity of IceCube-Gen2 to VEP parameters is discussed., Comment: 19 pages, 8 figures; v2: minor clarifications added, matches the version published in JCAP

A recent proposal by Shuler regarding a postulate-based derivation of a family of metrics describing the gravitational field outside a static spherically symmetric mass distribution is reviewed. All of Shuler’s gravities agree with the Schwarzschild solution in the weak-field limit, but they differ in the strong-field domain, i.e., close enough to a sufficiently compact source of the field. It is found that the evoked postulates of i) momentum conservation and ii) consistency of field strength measurement are satisfied in all metric theories of gravity compatible with the Einstein equivalence principle, no matter what the form of the metric. Therefore, they cannot be used, within any correct deduction, to derive a particular metric. Shuler’s derivations are based on an inconsistent set of correspondences between local and distant measurements. Furthermore, it is shown here that out of the family of possible metrics given by Shuler only one member, the Schwarzschild metric, satisfies a standard relativistic generalization of Newton’s law of gravitation, suggesting the others to be unphysical.

The Zhaoshan long-baseline Atom Interferometer Gravitation Antenna (ZAIGA) is a new type of underground laser-linked interferometer facility, and is currently under construction. It is in the 200-meter-on-average underground of a mountain named Zhaoshan which is about 80 km southeast to Wuhan. ZAIGA will be equipped with long-baseline atom interferometers, high-precision atom clocks, and large-scale gyros. ZAIGA facility will take an equilateral triangle configuration with two 1-km-apart atom interferometers in each arm, a 300-meter vertical tunnel with atom fountain and atom clocks mounted, and a tracking-and-ranging 1-km-arm-length prototype with lattice optical clocks linked by locked lasers. The ZAIGA facility will be used for experimental research on gravitation and related problems including gravitational wave detection, high-precision test of the equivalence principle of micro-particles, clock based gravitational red-shift measurement, rotation measurement and gravito-magnetic effect., 20 pages, 15 figures

Reduction of flow compressibility with the corresponding ideally invariant helicities, universally for various fluid models of neutral and ionized gases, can be argued statistically and associated with the geometrical scenario in the Taylor-Proudman theorem and its analogues. A `chiral base flow/field', rooted in the generic intrinsic local structure, as well as an `equivalence principle' is explained and used to bridge the single-structure mechanics and the helical statistics. The electric field fluctuations may similarly be depressed by the (self-)helicities of the two-fluid plasma model, with the geometry lying in the relation between the electric and density fields in a Maxwell equation., Comment: 1 figure

A space with deformed Poisson brackets for coordinates and momenta leading to the minimal length is considered. Features of description of motion of a body in the space are examined. We propose conditions on the parameters of deformation on which Poisson brackets for coordinates and momenta of the center-of-mass reproduce relations of deformed algebra, kinetic energy of a body is independent of its composition, and the weak equivalence principle is preserved in the deformed space. Influence of minimal length on the motion of the Sun-Earth-Moon system is studied. We find that deformation of the Poisson brackets leads to corrections to the accelerations of the Earth and the Moon toward the Sun, as a result the Eotvos-parameter does not vanish even if we consider equality of gravitational and inertial masses. The upper bound for the minimal length is estimated using results of the Lunar laser ranging experiment., Comment: to appear in International Journal of Modern Physics D

We investigate the particle-antiparticle symmetry of the gravitationally coupled Dirac equation, both on the basis of the gravitational central-field problem and in general curved space-time backgrounds. First, we investigate the central-field problem with the help of a Foldy-Wouthuysen transformation. This disentangles the particle from the antiparticle solutions, and leads to a "matching relation" of the inertial and the gravitational mass, which is valid for both particles as well as antiparticles. Second, we supplement this derivation by a general investigation of the behavior of the gravitationally coupled Dirac equation under the discrete symmetry of charge conjugation, which is tantamount to a particle -> antiparticle transformation. Limitations of the Einstein equivalence principle due to quantum fluctuations are discussed. In quantum mechanics, the question of where and when in the Universe an experiment is being performed, can only be answered up to the limitations implied by Heisenberg's Uncertainty Principle, questioning an assumption made in the original formulation of the Einstein equivalence principle. Furthermore, at some level of accuracy, it becomes impossible to separate non-gravitational from gravitational experiments, leading to further limitations., 19 pages; LaTeX article style

The application of the mass-energy-information equivalence principle developed after the experimentally demonstrated Landauer's principle on thermodynamics, entropy, and information is an unexplored but promising path in search of objectivity and compatibility between strict physical and mathematical entities and relative human behavior in biodiversity conservation issues. Conservation culturomics is proposed as the epistemic methodology and programme to trace the evolution in cultural human-nature relationships. Historically, controversies do persist between pro- vs. non- environmental opinions and policies. The proposed combination of physics and culturomics is feasible, although complex, multileveled, and depending on a series of academic, technical, and political prerequisites. In the era of staggering information technologies, Internet use proliferation and cultural relativism, reliable information on conservation knowledge vs. often unfounded story-tellings is a sine qua non for the development of badly needed modern global conservation strategies, targets, and goals., Mass; energy; information; public interest; Conservation Culturomics

In this paper, we aim to determine an optimal insurance premium rate for health-care in deterministic and stochastic SEIR models. The studied models consider two standard SEIR centres characterised by migration fluxes and vaccination of population. The premium is calculated using the basic equivalence principle. Even in this simple set-up, there are non-intuitive results that illustrate how the premium depends on migration rates, the severity of a disease and the initial distribution of healthy and infected individuals through the centres. We investigate how the vaccination program affects the insurance costs by comparing the savings in benefits with the expenses for vaccination. We compare the results of deterministic and stochastic models.

A mathematical model employing the concept of the energy-equivalent inhomogeneity combined with the method of conditional moments has been applied to analyze short-fiber composites. The fibers are parallel, randomly distributed, and their interphase is assumed to be adequately described by the Gurtin-Murdoch material surface model. The properties of the energy-equivalent fiber, incorporating properties of the original fiber and its interphase, are determined on the basis of Hill's energy equivalence principle assuming its cylindrical shape. To describe random distribution of fibers a statistical method, the method of conditional moments, has been employed. Closed-form formulas for the components of the effective stiffness tensor of short-fiber reinforced composites have been developed which, in the limit, compare well with the results available in the literature for infinite parallel fibers with Gurtin-Murdoch interphase model. Influence of fiber length on contribution of the surface effects to the effective properties of the material containing cylindrical cavities has been analyzed for all five independent components of its stiffness tensor, and for two sets of surface properties in the Gurtin-Murdoch model.

The Weak Equivalence Principle (WEP) is at the basis of General Relativity – the best theory for gravitation today. It has been and still is tested with different methods and accuracies. In this paper an overview of tests of the Weak Equivalence Principle done in the past, developed in the present and planned for the future is given. The best result up to now is derived from the data of torsion balance experiments by Schlamminger et al. (2008). An intuitive test of the WEP consists of the comparison of the accelerations of two free falling test masses of different composition. This has been carried through by Kuroda & Mio (1989, 1990) with the up to date most precise result for this setup. There is still more potential in this method, especially with a longer free fall time and sensors with a higher resolution. Providing a free fall time of 4.74 s (9.3 s using the catapult) the drop tower of the Center of Applied Space Technology and Microgravity (ZARM) at the University of Bremen is a perfect facility for further improvements. In 2001 a free fall experiment with high sensitive SQUID (Superconductive QUantum Interference Device) sensors tested the WEP with an accuracy of 10 - 7 (Nietzsche, 2001). For optimal conditions one could reach an accuracy of 10 - 13 with this setup (Vodel et al., 2001). A description of this experiment and its results is given in the next part of this paper. For the free fall of macroscopic test masses it is important to start with precisely defined starting conditions concerning the positions and velocities of the test masses. An Electrostatic Positioning System (EPS) has been developed to this purpose. It is described in the last part of this paper.

We propose a multiscale solver of equivalence principle algorithm with a body of revolution (BoR) equivalence surface (ES). First, the whole object is decomposed into subdomains; the ESs are defined as proper BoRs (e.g., spheres in this work) to enclose each subdomain. The Rao–Wilton–Glisson (RWG) and BoR basis functions are defined on each sphere, respectively. Second, the octree is constructed in each nonzero subdomain; the multilevel fast multipole algorithm (MLFMA) is employed to solve the equivalent currents on the ES individually, and then the equivalent currents are projected from RWG onto the BoR basis functions. The couplings between neighboring subdomains are evaluated directly using MLFMA, and the separated subdomains are substituted by the ES-to-ES couplings, and are evaluated efficiently by the BoR method of moments (BoR–MoM). To solve the equation system, a hybrid inner and outer iterative solver is employed, where the inner iteration is used to solve each local subdomains and the outer iteration is used to update the global solutions by collecting all the local solutions. Numerical results and discussions demonstrate the validity of the proposed work.

Comparing the parameterized post-Newtonian parameter $\gamma$ values for different types of particles, or the same type of particles with different energies is an important method to test the Einstein Equivalence Principle (EEP). Assuming that the observed time delays are dominated by the gravitational potential of the Laniakea supercluster of galaxies, better results of EEP constraints can be obtained. In this paper, we apply photons from three kinds of cosmic transients, including TeV blazars, gamma-ray bursts as well as fast radio bursts to constrain EEP. With a gravitational field far more stronger than a single galaxy, we obtain 4--5 orders of magnitude more stringent than the pervious results., Comment: Accepted by Journal of High Energy Astrophysics. 12 pages

Spherical actuator is a device that can achieve multiple degree-of-freedom (DOF) rotary motions in a single joint. It has a bright application prospect on moment gyros and satellite systems. Cylindrical shaped PM pole is widely used because of easy fabrication and pattern of magnetization. However, its topology and structure cause difficulties in accuracy magnetic modeling. Thus, the structure optimization and performance design become complicated. This paper proposes a novel magnetic field method for spherical actuator with cylindrical shaped PM poles based on geometrical equivalence principle. For convenient expression of magnetic field, three types of approximated dihedral cone shaped magnet poles are put forward based on different equivalent principles. On the basis of optimal equivalent principle, accurate harmonic model is set up with the magnetic field formulated. In addition, the analytical result is confirmed by numerical simulation from different dimensions. A research prototype with 8-PM-poles outer rotor and 24-coils stator is assembled and an experimental setup is established. The experimental results show experimental curves, analytical curves and FEM curves match with each other well which proves the accuracy of the proposed model. Thus, the indirect method of modeling magnetic field for spherical actuator with cylindrical shaped PM poles can be an effective tool. The magnetic field results can be the foundation for further study.

This essay examines Friedman’s recent approach to the analysis of physical theories. Friedman argues against Quine that the identification of certain principles as 'constitutive' is essential to a satisfactory methodological analysis of physics. I explicate Friedman’s characterization of a constitutive principle, and I evaluate his account of the constitutive principles that Newtonian and Einsteinian gravitation presuppose for their formulation. I argue that something close to Friedman’s thesis is defensible.

Lorentz symmetry violation (LV) was recently proposed to be testable with a new method, in which the effect of the violation is described as a certain local interaction Shaniv et al (2018 Phys. Rev. Lett. 120 103202). We revisit this LV effect in the paper and show that it is not only local, but it also represents a classical violation according to the recent quantum formulation of the Einstein equivalence principle (EEP). Based on a harmonically trapped spin-1/2 atomic system, we apply the results of table-top experiments testing LV effect to estimate the corresponding violation parameter in the quantum formulation of EEP. We find that the violation parameter is indeed very small, as expected by the earlier theoretical estimation.