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We present the first comparison of waveforms evaluated using the effective-one-body (EOB) approach and gravitational self-force (GSF) theory for inspiralling black hole binaries with a non-spinning primary and a spinning secondary. This paper belongs to a series of papers comparing the EOB model TEOBResumS to GSF results, where the latter are used to benchmark the EOB analytical choices in the large-mass-ratio regime. In this work, we explore the performance of two gauge choices for the gyro-gravitomagnetic functions GS, GS* entering the spin-orbit sector within the EOB dynamics. In particular, we consider the usual gauge of TEOBResumS, where GS and GS* only depend on the inverse radius and the radial momentum, and a different gauge where these functions also depend on the azimuthal momentum. The latter choice allows us to exploit as prefactor in GS* the complete expression GKS* for a spinning particle on Kerr. As done previously, we employ both waveform alignments in the time domain and a gauge-invariant frequency-domain analysis to gain a more complete understanding of the impact of the new analytical choice. The frequency-domain analysis is particularly useful in confirming that the gyro-gravitomagnetic functions in the new chosen gauge bring the EOB spin contribution at 1st post-adiabatic order closer to the GSF one. We finally implement the improved functions within the public code for TEOBResumS-Dal\'i, which already incorporates eccentricity. In this way, we upgrade the EOB model for extreme-mass-ratio inspirals presented in our previous work., Comment: 15 pages, 6 figures

While previous work has found success in deploying visualizations as museum exhibits, it has not investigated whether museum context impacts visitor behaviour with these exhibits. We present an interactive Deep-time Literacy Visualization Exhibit (DeLVE) to help museum visitors understand deep time (lengths of extremely long geological processes) by improving proportional reasoning skills through comparison of different time periods. DeLVE uses a new visualization idiom, Connected Multi-Tier Ranges, to visualize curated datasets of past events across multiple scales of time, relating extreme scales with concrete scales that have more familiar magnitudes and units. Museum staff at three separate museums approved the deployment of DeLVE as a digital kiosk, and devoted time to curating a unique dataset in each of them. We collect data from two sources, an observational study and system trace logs. We discuss the importance of context: similar museum exhibits in different contexts were received very differently by visitors. We additionally discuss differences in our process from Sedlmair et al.'s design study methodology which is focused on design studies triggered by connection with collaborators rather than the discovery of a concept to communicate. Supplemental materials are available at: https://osf.io/z53dq/

Chaos is an intriguing phenomenon that can be found in an immense variate of systems. Its detection and discrimination from its counterpart order poses an interesting challenge. To address it, we present a deep classifier capable of classifying chaos from order in the discretised dynamics of Hamiltonian systems of two degrees of freedom, through the machinery of Poincar\'{e} maps. Our deep network is based predominantly on a convolutional architecture, and generalises with good accuracy on unseen datasets, thanks to the universal features of a perturbed pendulum learned by the deep network. We discuss in detail the significance and the preparation of our training set, and we showcase how our deep network can be applied to the dynamics of geodesic motion in an axi-symmetric and stationary spacetime of a compact object deviating from the Kerr black hole paradigm. Finally, we discuss current challenges and some promising future directions., Comment: 11 pages, 5 figures

We compute the stochastic gravitational wave (GW) background generated by black hole-black hole (BH-BH) hyperbolic encounters with eccentricities close to one and compare them with the respective sensitivity curves of planned GW detectors. We use the Keplerian potential to model the orbits of the encounters and the quadrupole formula to compute the emitted GWs. We take into account hyperbolic encounters that take place in clusters up to redshift $5$ and with BH masses spanning from $5 M_{\odot}$ to $55 M_{\odot}$. We assume the clusters to be virialized and study several cluster models with different mass and virial velocity, and finally obtain an accumulative result, displaying the background as an average. Using the maxima and minima of our accumulative result for each frequency, we provide analytical expressions for both optimistic and pessimistic scenarios. Our results suggest that the background from these encounters is likely to be detected by the third-generation detectors Cosmic explorer and Einstein telescope, while the tail section at lower frequencies intersects with DECIGO, making it a potential target source for both ground- and space-based future GW detectors., Comment: 8 pages, 3 figures, 1 table

We provide an extension of the analysis on whether an extended test body can follow a geodesic trajectory given by Mukherjee, S., Lukes-Gerakopoulos, G. and Nayak, R. K. (2022), Extended bodies moving on geodesic trajectories, General Relativity and Gravitation, 54(9), 113, arXiv: 1907.05659. In particular, we consider a test body in a pole-dipole-quadrupole approximation under the Ohashi-Kyrian-Semer\'{a}k spin supplementary condition moving in the Schwarzschild and Kerr background. Using orbital setups under which a pole-dipole body can follow geodesic motion, we explore under which conditions this can take place also in the pole-dipole-quadrupole approximation, when only the mass quadrupole is taken into account. For our analysis we employ the assumption that the dipole contribution and the quadrupole contribution vanish independently., Comment: 8 pages, Proceedings of RAGtime 23-25, Edited by Z. Stuchl\'{i}k, G. T\"{o}r\"{o}k , V. Karas and D. Lan\v{c}ov\'{a}, Silesian University in Opava

This work studies the dynamics of geodesic motion within a curved spacetime around a Schwarzschild black hole, perturbed by a gravitational field of a far axisymmetric distribution of mass enclosing the system. This spacetime can serve as a versatile model for a diverse range of astrophysical scenarios and, in particular, for extreme mass ratio inspirals as in our work. We show that the system is non-integrable by employing Poincar\'e surface of section and rotation numbers. By utilising the rotation numbers, the widths of resonances are calculated, which are then used in establishing the relation between the underlying perturbation parameter driving the system from integrability and the quadrupole parameter characterising the perturbed metric. This relation allows us to estimate the phase shift caused by the resonance during an inspiral., Comment: 11 pages, 3 figures, 1 table, Proceedings of RAGtime 23-25. Edited by Z. Stuchl\'ik, G. T\"or\"ok and V. Karas. Institute of Physics in Opava

LISA, the Laser Interferometer Space Antenna, will usher in a new era in gravitational-wave astronomy. As the first anticipated space-based gravitational-wave detector, it will expand our view to the millihertz gravitational-wave sky, where a spectacular variety of interesting new sources abound: from millions of ultra-compact binaries in our Galaxy, to mergers of massive black holes at cosmological distances; from the beginnings of inspirals that will venture into the ground-based detectors' view to the death spiral of compact objects into massive black holes, and many sources in between. Central to realising LISA's discovery potential are waveform models, the theoretical and phenomenological predictions of the pattern of gravitational waves that these sources emit. This white paper is presented on behalf of the Waveform Working Group for the LISA Consortium. It provides a review of the current state of waveform models for LISA sources, and describes the significant challenges that must yet be overcome., Comment: 239 pages, 11 figures, white paper from the LISA Consortium Waveform Working Group, invited for submission to Living Reviews in Relativity, updated with comments from community

This is the first in a collection of three papers introducing the science with an ultra-violet (UV) space telescope on an approximately 130~kg small satellite with a moderately fast re-pointing capability and a real-time alert communication system approved for a Czech national space mission. The mission, called Quick Ultra-Violet Kilonova surveyor - QUVIK, will provide key follow-up capabilities to increase the discovery potential of gravitational wave observatories and future wide-field multi-wavelength surveys. The primary objective of the mission is the measurement of the UV brightness evolution of kilonovae, resulting from mergers of neutron stars, to distinguish between different explosion scenarios. The mission, which is designed to be complementary to the Ultraviolet Transient Astronomy Satellite - ULTRASAT, will also provide unique follow-up capabilities for other transients both in the near- and far-UV bands. Between the observations of transients, the satellite will target other objects described in this collection of papers, which demonstrates that a small and relatively affordable dedicated UV-space telescope can be transformative for many fields of astrophysics., Comment: Accepted for publication in Space Science Reviews

This work discusses the motion of extended test bodies as described by the Mathisson-Papapetrou-Dixon (MPD) equations in the pole-dipole-quadrupole approximation. We focus on the case that the quadrupole is solely induced by the spin of the body which is assumed to move on a circular equatorial orbit in a Kerr background. To fix the center of mass of the MPD body we use two different spin supplementary conditions (SSCs): the Tulczyjew-Dixon SSC and the Mathisson-Pirani SSC. We provide the frequencies of the circular equatorial orbits for the pole-dipole-(spin induced) quadrupole approximation of the body for both SSCs. In the process we develop an explicit four-velocity four-momentum relation for a pole-dipole-quadrupole body under the Mathisson-Pirani SSC., Comment: 9 pages, 2 figures, 3 tables

The paper presents a new type of weakly nonlinear two-scale model of controllable periodic porous piezoelectric structures saturated by Newtonian fluids. The flow is propelled by peristaltic deformation of microchannels which is induced due to piezoelectric segments embedded in the microstructure and locally actuated by voltage waves. The homogenization is employed to derive a macroscopic model of the poroelastic medium with effective parameters modified by piezoelectric properties of the skeleton. To capture the peristaltic pumping, the nonlinearity associated with deforming configuration must be respected. In the macroscopic model, this nonlinearity is introduced through homogenized coefficients depending on the deforming micro-configurations. For this, linear expansions based on the sensitivity analysis of the homogenized coefficients with respect to deformation induced by the macroscopic quantities are employed. This enables to avoid the two-scale tight coupling of the macro- and microproblems otherwise needed in nonlinear problems. The derived reduced-order model is implemented and verified using direct numerical simulations of the periodic heterogeneous medium. Numerical results demonstrate the peristaltic driven fluid propulsion in response to the electric actuation and the efficiency of the proposed treatment of the nonlinearity. The paper shows new perspectives in homogenization-based computationally efficient modelling of weakly nonlinear problems where continuum microstructures are perturbed by coupled fields.

This work provides gravitational wave energy and angular momentum asymptotic fluxes from a spinning body moving on generic orbits in a Kerr spacetime up to linear in spin approximation. To achieve this, we have developed a new frequency domain Teukolsky equation solver that calculates asymptotic amplitudes from generic orbits of spinning bodies with their spin aligned with the total orbital angular momentum. However, the energy and angular momentum fluxes from these orbits in the linear in spin approximation are appropriate for adiabatic models of extreme mass ratio inspirals even for spins non-aligned to the orbital angular momentum. To check the newly obtained fluxes, they were compared with already known frequency domain results for equatorial orbits and with results from a time domain Teukolsky equation solver called Teukode for off-equatorial orbits. The spinning body framework of our work is based on the Mathisson-Papapetrou-Dixon equations under the Tulczyjew-Dixon spin supplementary condition., Comment: 19 pages, 8 figures

We present a new approach and an algorithm for optimizing the material configuration and behaviour of a fluid saturated porous medium in a two-scale setting. The state problem is governed by the Biot model describing the fluid-structure interaction in homogenized poroelastic structures. However, the approach is widely applicable to multiphysics problems involving several macroscopic fields where homogenization provides the relationship between the microconfigurations and the macroscopic mathematical model. The optimization variables describe the local microstructure design by virtue of the pore shape which determines the effective medium properties - the material coefficients - computed by the homogenization method. The main idea of the numerical optimization strategy consists in a) employing a precomputed database of the material coefficients associated to the geometric parameters and b) applying the sequential global programming (SGP) method for solving the problem of macroscopically optimized distribution of material coefficients. Although there are similarities with the free material optimization (FMO) approach, only effective material coefficients are considered admissible, for which a well-defined set of corresponding configurable microstructures exist. Due to the flexibility of the SGP approach, different types of microstructures with fully independent parametrizations can easily be handled. The efficiency of the concept is demonstrated by a series of numerical experiments. We show that the SGP method can handle simultaneously multiple types of microstructures with nontrivial parametrizations using a considerably low and stable number of state problems to be solved., Comment: 26 pages, 19 figures, 2 tables

We introduce an action-angle formalism for bounded geodesic motion in Kerr black hole spacetime using canonical perturbation theory. Namely, we employ a Lie series technique to produce a series of canonical transformations on a Hamiltonian function describing geodesic motion in Kerr background written in Boyer-Lindquist coordinates to a Hamiltonian system written in action-angle variables. This technique allows us to produce a closed-form invertible relation between the Boyer-Lindquist variables and the action-angle ones, while it generates in analytical closed form all the characteristic functions of the system as well. The expressed in the action-angle variable Hamiltonian system is employed to model an extreme mass ratio inspiral (EMRI), i.e. a binary system where a stellar compact object inspirals into a supermassive black hole due to gravitational radiation reaction. We consider the adiabatic evolution of an EMRI, for which the energy and angular momentum fluxes are computed by solving the Teukolsky equation in the frequency domain. To achieve this a new Teukolsky equation solver code was developed., Comment: 22 pages, 9 figures, 7 tables, includes CPKerrGeodesics (a Mathematica package) as supplemental material

Strong second harmonic generation (SHG) in silicon nitride has been extensively studied-among others, in terms of laser-induced SHG enhancement in Si3N4 waveguides. This enhancement has been ascribed to the all-optical poling induced by the coherent photogalvanic effect. Yet, an analogous process for Si3N4 thin films has not been reported. Our article reports on the observation of laser-induced 3-fold SHG enhancement in Si3N4 thin films. The observed enhancement has many features similar to all-optical poling, such as highly nonlinear power dependence, cumulative effect, or connection to the Si3N4-Si interface. However, identical experiments for low-oxygen silicon oxynitride thin films lead to complex behavior, including laser-induced SHG reduction. By a thorough experimental study, the observed results were ascribed to heat-induced SHG variation caused by multiphoton absorption. Such behavior indicates that the origin of optically-induced SHG enhancement in SiOxNy-Si structures can be a complex interplay of various phenomena., Comment: 13 pages, 3 figures

We consider acoustic waves propagating in an inviscid fluid interacting with a rigid periodically perforated plate in the presence of permanent flows. The paper presents a model of an acoustic interface obtained by the asymptotic homogenization of a thin transmission layer in which the plate is embedded. To account for the flow, a decomposition of the fluid pressure and velocity in the steady and fluctuating parts is employed. This enables for a linearization and an efficient use of the homogenization method which leads to a model order reduction effect. The dependence of an extended Helmholtz equation on the permanent flow introduces a locally periodic velocity field in the perforated plate vicinity, so that the coefficients of the homogenized interface depend on the flow. The derived model extended by natural coupling conditions provides an implicit Dirichlet-to-Neumann operator. Numerical simulations of wave propagation in a waveguide illustrate the flow speed influence on the acoustic transmission. Also some geometrical aspects are explored.

The Laser Interferometer Space Antenna (LISA) mission, scheduled for launch in the mid-2030s, is a gravitational wave observatory in space designed to detect sources emitting in the millihertz band. LISA is an ESA flagship mission, currently entering the Phase B development phase. It is expected to help us improve our understanding about our Universe by measuring gravitational wave sources of different types, with some of the sources being at very high redshifts $z\sim 20$. On the 23rd of February 2022 we organized the 1$^\mathrm{st}$ {\it LISA in Greece Workshop}. This workshop aimed to inform the Greek scientific and tech industry community about the possibilities of participating in LISA science and LISA mission, with the support of the Hellenic Space Center (HSC). In this white paper, we summarize the outcome of the workshop, the most important aspect of it being the inclusion of $15$ Greek researchers to the LISA Consortium, raising our total number to $22$. At the same time, we present a road-map with the future steps and actions of the Greek Gravitational Wave community with respect to the future LISA mission., Comment: 11 pages, 2 figures

Coded aperture snapshot spectral imaging (CASSI) makes it possible to recover 3D hyperspectral data from a single 2D image. However, the reconstruction problem is severely underdetermined and efforts to improve the compression ratio typically make the imaging system more complex and cause a significant loss of incoming light intensity. In this paper, we propose a novel approach to CASSI which enables capturing both spectrally sheared and integrated image of a scene with a single camera. We performed hyperspectral imaging of three different testing scenes in the spectral range of 500-900 nm. We demonstrate the prominent effect of using the non-diffracted image on the reconstruction of data from our camera. The use of the spectrally integrated image improves the reconstruction quality and we observed an approx. fivefold reduction in reconstruction time.

We propose a novel concept of differential coded aperture snapshot spectral imaging (D-CASSI) technique exploiting the benefits of using {-1,+1} random mask, which is demonstrated by a broadband single-snapshot hyperspectral camera using compressed sensing. To double the information, we encode the image by two complementary random masks, which proved to be superior to two independent patterns. We utilize dispersed and non-dispersed encoded images captured in parallel onto a single detector. We explored several different approaches to processing the measured data, which demonstrates significant improvement in retrieving complex hyperspectral scenes. The experiments were completed by simulations in order to quantify the reconstruction fidelity. The concept of differential CASSI could be easily implemented also by multi-snapshot CASSI without any need for optical system modification.

The worldline of a spinning test body moving in curved spacetime can be provided by the Mathisson-Papapetrou-Dixon (MPD) equations when its centroid, i.e. its center of mass, is fixed by a Spin Supplementary Condition (SSC). In the present study, we continue the exploration of shifts between different centroids started in a recently published work [ Phys. Rev. D 104, 024042 (2021)], henceforth Paper I, for the Schwarzschild spacetime, by examining the frequencies of circular equatorial orbits under a change of the SSC in the Kerr spacetime. In particular, we examine the convergence in the terms of the prograde and retrograde orbital frequencies, when these frequencies are expanded in power series of the spin measure and the centroid of the body is shifted from the Mathisson-Pirani or the Ohashi-Kyrian-Semerak frame to the Tulczyjew-Dixon one. Since in Paper I, we have seen that the innermost stable circular orbits (ISCOs) hold a special place in this comparison process, we focus on them rigorously in this work. We introduce a novel method of finding ISCOs for any SSC and employ it for the Tulczyjew-Dixon and the Mathisson-Pirani formalisms. We resort to numerical investigation of the convergence between the SSCs for the ISCO case, due to technical difficulties not allowing Paper's I analytical treatment. Our conclusion, as in Paper I, is that there appears to be a convergence in the power series of the frequencies between the SSCs, which is improved when the proper shifts are taken into account, but there exists a limit in this convergence due to the fact that in the spinning body approximation we consider only the first two lower multipoles of the extended body and ignore all the higher ones., Comment: 15 pages, 4 figures, 5 tables, 2 Mathematica notebooks

We investigate resonance crossings of a charged body moving around a Kerr black hole immersed in an external homogeneous magnetic field. This system can serve as an electromagnetic analogue of a weakly non-integrable extreme mass ratio inspiral (EMRI). In particular, the presence of the magnetic field renders the conservative part of the system non-integrable in the Liouville sense, while the electromagnetic self-force causes the charged body to inspiral. By studying the system without the self-force, we show the existence of an approximate Carter-like constant and discuss how resonances grow as a function of the perturbation parameter. Then, we apply the electromagnetic self-force to investigate crossings of these resonances during an inspiral. Averaging the energy and angular momentum losses during crossings allows us to employ an adiabatic approximation for them. We demonstrate that such adiabatic approximation provides results qualitatively equivalent to the instantaneous self-force evolution, which indicates that the adiabatic approximation may describe the resonance crossing with sufficiently accuracy in EMRIs., Comment: 17 pages, 9 figures

Inspirals of stellar-mass compact objects into massive black holes, known as extreme mass ratio inspirals (EMRIs), are one of the key targets for upcoming space-based gravitational-wave detectors. In this paper we take the first steps needed to systematically incorporate the effect of external gravitating matter on EMRIs. We model the inspiral as taking place in the field of a Schwarzschild black hole perturbed by the gravitational field of a far axisymmetric distribution of mass enclosing the system. We take into account the redshift, frame-dragging, and quadrupolar tide caused by the enclosing matter, thus incorporating all effects to inverse third order of the characteristic distance of the enclosing mass. Then, we use canonical perturbation theory to obtain the action-angle coordinates and Hamiltonian for mildly eccentric precessing test-particle orbits in this background. Finally, we use this to efficiently compute mildly eccentric inspirals in this field and document their properties. This work shows the advantages of canonical perturbation theory for the modeling EMRIs, especially in the cases when the background deviates from the standard black hole fields.

The detection of gravitational waves from Extreme mass Ratio Inspirals (EMRIs) by the future space-based gravitational-wave detectors demands the generation of accurate enough waveform templates. Since the spin of the smaller secondary body cannot be neglected for the detection and parameter estimation of EMRIs, we study its influence on the phase of the gravitational waves from EMRIs with spinning secondary. We focus on generic eccentric equatorial orbits around a Kerr black hole. To model the spinning secondary object, we use the Mathisson-Papapetrou-Dixon equations in the pole-dipole approximation. Furthermore, we linearize in spin the orbital variables and the gravitational-wave fluxes from the respective orbits. We obtain these fluxes by using the Teukolsky formalism in the frequency domain. We derive the evolution equations for the spin induced corrections to the adiabatic evolution of an inspiral. Finally, through their numerical integration we find the gravitational-wave phase shift between an inspiral of a spinning and a non-spinnig body., Comment: 22 pages, 13 figures

The Mathisson-Papapetrou-Dixon (MPD) equations describe the motion of an extended test body in general relativity. This system of equations, though, is underdetermined and has to be accompanied by constraining supplementary conditions, even in its simplest version, which is the pole-dipole approximation corresponding to a spinning test body. In particular, imposing a spin supplementary condition (SSC) fixes the center of the mass of the spinning body, i.e. the centroid of the body. In the present study, we examine whether characteristic features of the centroid of a spinning test body, moving in a circular equatorial orbit around a massive black hole, are preserved under the transition to another centroid of the same physical body, governed by a different SSC. For this purpose, we establish an analytical algorithm for deriving the orbital frequency of a spinning body, moving in the background of an arbitrary, stationary, axisymmetric spacetime with reflection symmetry, for the Tulzcyjew-Dixon, the Mathisson-Pirani and the Ohashi-Kyrian-Semer\'{a}k SSCs. Then, we focus on the Schwarzschild black hole background and a power series expansion method is developed, in order to investigate the discrepancies in the orbital frequencies expanded in power series of the spin among the different SSCs. Lastly, by employing the fact that the position of the centroid and the measure of the spin alters under the centroid's transition, we impose proper corrections to the power expansion of the orbital frequencies, which allows to improve the convergence between the SSCs. Our concluding argument is that when we shift from one circular equatorial orbit to another in the Schwarzschild background, under the change of a SSC, the convergence between the SSCs holds only up to certain powers in the spin expansion, and it cannot be achieved for the whole power series., Comment: 16 pages, 5 tables

Based on our previous work, we propose a homogenized model of acoustic waves propagating through periodically perforated elastic plates with metamaterial properties due to embedded arrays of soft elastic inclusions serving for resonators. Such structures enable to suppress the acoustic transmission for selected frequency bands. Homogenization of the vibro-acoustic fluid-structure interaction problem in a 3D complex geometry of the transmission layer leads to effective transmission conditions prescribed on the acoustic meta-surface associated with the mid-plane of the Reissner-Mindlin plate. Asymptotic analysis with respect to the layer thickness, proportional to the plate thickness and to the perforation period, yields an implicit Dirichlet-to-Neumann operator defined on the homogenized metasurface. An efficient method is proposed for computing frequency-dependent effective parameters involved in the homogenized model of the layer. These can change their signs, thus modifying the acoustic impedance and the effective mass of the metasurface. The global problem of the acoustic wave propagation in a waveguide fitted with the plate is solved using the finite element method. The homogenized interface allows for a significant reduction of the computational model. Numerical illustrations are presented.

The largest part of any gravitational-wave inspiral of a compact binary can be understood as a slow, adiabatic drift between the trajectories of a certain referential conservative system. In many contexts, the phase space of this conservative system is smooth and there are no "topological transitions" in the phase space, meaning that there are no sudden qualitative changes in the character of the orbital motion during the inspiral. However, in this chapter we discuss the cases where this assumption fails and non-linear and/or non-smooth transitions come into play. In integrable conservative systems under perturbation, topological transitions suddenly appear at resonances, and we sketch how to implement the passage through such regions in an inspiral model. Even though many of the developments of this chapter apply to general inspirals, we focus on a particular scenario known as the Extreme mass ratio inspiral (EMRI). An EMRI consists of a compact stellar-mass object inspiralling into a supermassive black hole. At leading order, the referential conservative system is simply geodesic motion in the field of the supermassive black hole and the rate of the drift is given by radiation reaction. In Einstein gravity the supermassive black hole field is the Kerr space-time in which the geodesic motion is integrable. However, the equations of motion can be perturbed in various ways so that prolonged resonances and chaos appear in phase space as well as the inspiral, which we demonstrate in simple physically motivated examples., Comment: 44 pages, 9 figures, 1 table. Invited chapter for "Handbook of Gravitational Wave Astronomy" (Eds. C. Bambi, S. Katsanevas, and K. Kokkotas; Springer, Singapore, 2021)

We use the frequency and time domain Teukolsky formalism to calculate gravitational-wave fluxes from a spinning body on a bound eccentric equatorial orbit around a Kerr black hole. The spinning body is represented as a point particle following the pole-dipole approximation of the Mathisson-Papapetrou-Dixon equations. Reformulating these equations we are not only able to find the trajectory of a spinning particle in terms of its constants of motion, but also to provide a method to calculate the azimuthal and the radial frequency of this trajectory. Using these orbital quantities, we introduce the machinery to calculate through the frequency domain Teukolsky formalism the energy and the angular momentum fluxes at infinity, and at the horizon, along with the gravitational strain at infinity. We crosscheck the results obtained from the frequency domain approach with the results obtained from a time domain Teukolsky equation solver called Teukode., Comment: 24 pages, 10 figures

In this article, we summarize two agnostic approaches in the framework of spatially curved Friedmann-Robertson-Walker (FRW) cosmologies discussed in detail in (Kerachian et al., 2020, 2019). The first case concerns the dynamics of a fluid with an unspecified barotropic equation of state (EoS), for which the only assumption made is the non-negativity of the fluid's energy density. The second case concerns the dynamics of a non-minimally coupled real scalar field with unspecified positive potential. For each of these models, we define a new set of dimensionless variables and a new evolution parameter. In the framework of these agnostic setups, we are able to identify several general features, like symmetries, invariant subsets and critical points, and provide their cosmological interpretation., Comment: 11 pages, 2 figures, 1 table

An extreme mass ratio inspiral takes place when a compact stellar object is inspiraling into a supermassive black hole due to gravitational radiation reaction. Gravitational waves (GWs) from this system can be calculated using the Teukolsky equation (TE). In our case, we compute the asymptotic GW fluxes of a spinning body orbiting a Kerr black hole by solving numerically the TE both in time and frequency domain. Our ultimate goal is to produce GW templates for space-based detectors such as LISA.

The two-scale computational homogenization method is proposed for modelling of locally periodic fluid-saturated media subjected a to large deformation induced by quasistatic loading. The periodic heterogeneities are relevant to the mesoscopic scale at which a double porous medium constituted by hyperelastic skeleton and an incompressible viscous fluid is featured by large contrasts in the permeability. Within the Eulerian framework related to the current deformed configuration, the two-scale homogenization approach is applied to a linearized model discretized in time, being associated with an incremental formulation. For this, the equilibrium equation and the mass conservation expressed in the spatial configuration are differentiated using the material derivative with respect to a convection velocity field. The homogenization procedure of the linearized equations provides effective (homogenized) material properties are computed to constitute the incremental macroscopic problem. The coupled algorithm for the multiscale problem is implemented using the finite element method. Illustrative 2D numerical simulations of a poroelastic medium are presented including a simple validation test.

Relying on previous results that link entanglement entropy and parton distribution functions in deep inelastic scattering and focusing on the small Bjorken scaling region we present here indications that gluon shadowing might indeed be explained as due to a depletion of the entanglement entropy between observed and unobserved degrees of freedom per nucleon within a nucleus with respect to the free nucleon case. We apply to gluon shadowing the general Page approach to the calculation of the entanglement entropy in bipartite systems, giving physical motivations of the results., Comment: 7 pages, 5 figures

Diffraction unlimited super-resolution imaging critically depends on the switching of fluorophores between at least two states, often induced using intense laser light and special buffers. The high illumination power or UV light required for appropriate blinking kinetics is currently hindering live-cell experiments. Recently, so-called self-blinking dyes that switch spontaneously between an open, fluorescent "on"-state and a closed colorless "off"-state were introduced. Here we exploit the synergy between super-resolution optical fluctuation imaging (SOFI) and spontaneously switching fluorophores for 2D functional and for volumetric imaging. SOFI tolerates high labeling densities, on-time ratios, and low signal-to-noise by analyzing higher-order statistics of a few hundred to thousand frames of stochastically blinking fluorophores. We demonstrate 2D imaging of fixed cells with a uniform resolution up to 50-60 nm in 6th order SOFI and characterize changing experimental conditions. We extend multiplane cross-correlation analysis to 4th order using biplane and 8-plane volumetric imaging achieving up to 29 (virtual) planes. The low laser excitation intensities needed for self-blinking SOFI are ideal for live-cell imaging. We show proof-of-principal time-resolved imaging by observing slow membrane movements in cells. Self-blinking SOFI provides a route for easy-to-use 2D and 3D high-resolution functional imaging that is robust against artefacts and suitable for live-cell imaging., Comment: main: 3 figures, SI: 9 figures

In this article we perform dynamical analysis of a broad class of barotropic fluids in the spatially curved Friedmann-Robertson-Walker (FRW) spacetime background without considering the cosmological constant. The first part of our study concerns the dynamics of a fluid with an unspecified barotropic equation of state (EoS) having as the only assumption the non-negativity of the fluid's energy density. After defining a new set of dimensionless variables and a new evolution parameter, we introduce the function $\Gamma$ that encodes the EoS. In this general setup several features of the system are identified: critical points, invariant subsets and the characteristics of the function $\Gamma$, along with their cosmological interpretations. The second part of our work provides two examples with specific $\Gamma$ functions. In the first example we provide a $\Gamma$ function and then we exhibit how it can be trimmed down to a specific class of EoS through physical arguments, while in the second example we discuss the quadratic EoS studied in Phys.Rev. D {\bf 74}, 023523 (2006) by comparing our approach with their analysis., Comment: 19 pages, 20 figures