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Inspirals of stellar mass compact objects into supermassive black holes are known as extreme mass ratio inspirals. In the simplest approximation, the motion of the compact object is modeled as a geodesic in the space-time of the massive black hole with the orbit decaying due to radiated energy and angular momentum, thus yielding a highly regular inspiral. However, once the spin of the secondary compact body is taken into account, integrability is broken and prolonged resonances along with chaotic motion appear. We numerically integrate the motion of a spinning test body in the field of a non-spinning black hole and analyse it using various methods. We show for the first time that resonances and chaos can be found even for astrophysical values of spin. On the other hand, we devise a method to analyse the growth of the resonances, and we conclude that the resonances we observe are only caused by terms quadratic in spin and will generally stay very small in the small-mass-ratio limit. Last but not least, we compute gravitational waveforms by solving numerically the Teukolsky equations in the time-domain and establish that they carry information on the motion's dynamics. In particular, we show that the time series of the gravitational wave strain can be used to discern regular from chaotic motion of the source., Comment: 18 pages, 14 figures

Black holes are unique among astrophysical sources: they are the simplest macroscopic objects in the Universe, and they are extraordinary in terms of their ability to convert energy into electromagnetic and gravitational radiation. Our capacity to probe their nature is limited by the sensitivity of our detectors. The LIGO/Virgo interferometers are the gravitational-wave equivalent of Galileo's telescope. The first few detections represent the beginning of a long journey of exploration. At the current pace of technological progress, it is reasonable to expect that the gravitational-wave detectors available in the 2035-2050s will be formidable tools to explore these fascinating objects in the cosmos, and space-based detectors with peak sensitivities in the mHz band represent one class of such tools. These detectors have a staggering discovery potential, and they will address fundamental open questions in physics and astronomy. Are astrophysical black holes adequately described by general relativity? Do we have empirical evidence for event horizons? Can black holes provide a glimpse into quantum gravity, or reveal a classical breakdown of Einstein's gravity? How and when did black holes form, and how do they grow? Are there new long-range interactions or fields in our universe, potentially related to dark matter and dark energy or a more fundamental description of gravitation? Precision tests of black hole spacetimes with mHz-band gravitational-wave detectors will probe general relativity and fundamental physics in previously inaccessible regimes, and allow us to address some of these fundamental issues in our current understanding of nature., Comment: 24 pages, 4 figures. White paper submitted to ESA's Voyage 2050 on behalf of the LISA Consortium 2050 Task Force

We present new calculations of the energy flux of a spinning test-body on circular orbits around a Schwarzschild black hole at linear order in the particle spin. We compute the multipolar fluxes up to $\ell=m=6$ using two independent numerical solvers of theTeukolsky equation, one in the time domain and the other in the frequency domain. After linearization in the spin of the particle, we obtain an excellent agreement ($\sim 10^{-5}$) between the two numerical results.The calculation of the multipolar fluxes is also performed analytically (up to $\ell=7$) using the post-Newtonian (PN) expansion of the Teukolsky equation solution; each mode is obtained at 5.5PN order beyond the corresponding leading-order contribution. From the analytical fluxes we obtain the PN-expanded analytical waveform amplitudes. These quantities are then resummed using new procedures either based on the factorization of the orbital contribution (and resumming it independently from the spin-dependent factor) or on the factorization of the tail contribution solely for odd-parity multipoles. We compare these prescriptions and the resummation procedure proposed in Pan et al. [Phys. Rev. D 83 (2011) 064003] to the numerical data. We find that the new procedures significantly improve over the existing one that, notably, is inconsistent with the numerical data for $\ell+m=\text{odd}$ multipoles already at low orbital frequencies. Our study suggests that the approach to waveform resummation used in current effective-one-body-based waveform models should be modified to improve its robustness and accuracy all over the binary parameter space., Comment: 33 pages, 7 figures. Submitted to Phys. Rev. D

Super-resolution optical fluctuation imaging (SOFI) provides a resolution beyond the diffraction limit by analysing stochastic fluorescence fluctuations with higher-order statistics. Using nth order spatio-temporal cross-cumulants the spatial resolution as well as the sampling can be increased up to n-fold in all three spatial dimensions. In this study, we extend the cumulant analysis into the spectral domain and propose a novel multicolor super-resolution scheme. The simultaneous acquisition of two spectral channels followed by spectral cross-cumulant analysis and unmixing increase the spectral sampling. The number of discriminable fluorophore species is thus not limited to the number of physical detection channels. Using two color channels, we demonstrate spectral unmixing of three fluorophore species in simulations and multiple experiments with different cellular structures, fluorophores and filter sets. Based on an eigenvalue/ vector analysis we propose a scheme for an optimized spectral filter choice. Overall, our methodology provides a novel route for easy-to-implement multicolor sub-diffraction imaging using standard microscopes while conserving the spatial super-resolution property. This makes simultaneous multiplexed super-resolution fluorescence imaging widely accessible to the life science community interested to probe colocalization between two or more molecular species., Comment: main: 21 pages & 4 figures, supplementary 20 pages & 16 figures

This work investigates whether an extended test body obeying the Mathisson-Papapetrou- Dixon equations under the Ohashi-Kyrian-Semerak spin supplementary condition can follow geodesic trajectories in curved spacetimes. In particular, we explore what are the requirements under which pole-dipole and pole-dipole-quadrupole approximated bodies moving in the Schwarzschild or Kerr spacetimes can follow equatorial geodesic trajectories. We do this exploration thoroughly in the pole-dipole case, while we focus just on particular trajectories in the pole-dipole-quadrupole case. Using the Ohashi-Kyrian-Semerak spin supplementary condition to fix the center of the mass of a pole-dipole body has the advantage that the hidden momentum is eliminated. This allows the four-velocity to be parallel to the four-momentum, which provides a convenient framework for our investigation. We discuss how this feature can be recovered at a pole-dipole-quadrupole approximation and what are the consequences., Comment: 28 pages, no figure. v2, title changed, new author added, revised version

In this work we perform a dynamical analysis of a broad class of non-minimally coupled real scalar fields in the Friedmann-Robertson-Walker (FRW) spacetime framework. The first part of our study concerns the dynamics of an unspecified positive potential in a spatially curved FRW spacetime, for which we define a new set of dimensionless variables and a new evolution parameter. In the framework of this general setup we have recognized several general features of the system, like symmetries, invariant subsets and critical points, and provide their cosmological interpretation. The second part of our work focuses on flat FRW cases for which the tracker parameter is constant, i.e. we examine specific classes of potentials. After analyzing these cases dynamically, we discuss their physical interpretation., Comment: 13 pages, 7 figures

Using an additional decade of CNLSY data, this study replicated and extended Deming's (2009) evaluation of Head Start's life-cycle skill formation impacts in three ways. Extending the measurement interval for Deming's adulthood outcomes, we found no statistically significant impacts on earnings and mixed evidence of impacts on other adult outcomes. Applying Deming's sibling comparison framework to more recent birth cohorts born to CNLSY mothers revealed mostly negative Head Start impacts. Combining all cohorts shows generally null impacts on school-age and early adulthood outcomes., Comment: Remy J.-C. Pages and Dylan J. Lukes are co-equal first authors. Before collaborating, both individuals separately and contemporaneously worked on individual papers which substantially overlapped. After careful consideration all parties agreed to collaborate and produce a single unified paper. Online appendix included

In this work the dynamics of a spinning particle moving in the Schwarzschild background is studied. In particular, the methods of Poincar\'{e} section and recurrence analysis are employed to discern chaos from order. It is shown that the chaotic or regular nature of the orbital motion is reflected on the gravitational waves., Comment: 8 pages, 2 figures, to appear in the RAGtime20 conference proceedings (Opava, October 15-19 2018)

We demonstrate that the thermodynamics of a perfect fluid describing baryonic matter can, in certain limits, lead to an equation of state similar to that of dark energy. We keep the cosmic fluid equation of state quite general by just demanding that the speed of sound is positive and less than the speed of light. In this framework, we discuss some propositions by looking at the asymptotic behavior of the cosmic fluid., Comment: 10 pages, 1 figure, to appear in the RAGtime20 conference proceedings (Opava, October 15-19 2018)

The paper deals with the homogenization of deformable porous media saturated by two-component electrolytes. The model relevant to the microscopic scale describes steady states of the medium while reflecting essential physical phenomena, namely electrochemical interactions in a dilute Newtonian solvent under assumptions of a small external electrostatic field and slow flow. The homogenization is applied to a linearized micromodel, whereby the thermodynamic equilibrium represents the reference state. Due to the dimensional analysis, scaling of the viscosity and electric permitivity is introduced, so that the limit model retains the characteristic length associated with the pore size and the electric double layer thickness. The homogenized model consists of two weakly coupled parts: the flow of the electrolyte can be solved in terms of a global pressure and streaming potentials of the two ions, independently of then the solid phase deformations which is computed afterwards for the fluid stress acting on pore walls. The two-scale model has been implemented in the SfePy finite element software. The numerical results show dependence of the homogenized coefficients on the microstructure porosity. By virtue of the corrector result of the homogenization, microscopic responses in a local representative cell can be reconstructed from the macroscopic solutions., Comment: This manuscript version is made available under the CC-BY-NC-ND 4.0 license

The paper deals with modelling of acoustic waves which propagate in inviscid fluids interacting with perforated elastic plates. The plate can be replaced by an interface on which transmission conditions are derived by homogenization of a problem describing vibroacoustic fluid-structure interactions in a transmission layer in which the plate is embedded. The Reissner-Mindlin theory of plates is adopted for periodic perforations designed by arbitrary cylindrical holes with axes orthogonal to the plate midplane. The homogenized model of the vibroacoustic transmission is obtained using the two-scale asymptotic analysis with respect to the layer thickness which is proportional to the plate thickness and to the perforation period. The nonlocal, implicit transmission conditions involve a jump in the acoustic potential and its normal one-side derivatives across the interface which represents the plate with a given thickness. The homogenized model was implemented using the finite element method and validated using direct numerical simulations of the non-homogenized problem. Numerical illustrations of the vibroacoustic transmission are presented., Comment: This manuscript version is made available under the CC-BY-NC-ND 4.0 license

In this paper we present the two-level homogenization of the flow in a deformable double-porous structure described at two characteristic scales. The higher level porosity associated with the mesoscopic structure is constituted by channels in a matrix made of a microporous material consisting of elastic skeleton and pores saturated by a viscous fluid. The macroscopic model is derived by the homogenization of the flow in the heterogeneous structure characterized by two small parameters involved in the two-level asymptotic analysis, whereby a scaling ansatz is adopted to respect the pore size differences. The first level upscaling of the fluid-structure interaction problem yields a Biot continuum describing the mesoscopic matrix coupled with the Stokes flow in the channels. The second step of the homogenization leads to a macroscopic model involving three equations for displacements, the mesoscopic flow velocity and the micropore pressure. Due to interactions between the two porosities, the macroscopic flow is governed by a Darcy-Brinkman model comprising two equations which are coupled with the overall equilibrium equation respecting the hierarchical structure of the two-phase medium. Expressions of the effective macroscopic parameters of the homogenized double-porosity continuum are derived, depending on the characteristic responses of the mesoscopic structure. Some symmetry and reciprocity relationships are shown and issues of boundary conditions are discussed. The model has been implemented in the finite element code SfePy which is well-suited for computational homogenization. A numerical example of solving a nonstationary problem using mixed finite element method is included., Comment: This manuscript version is made available under the CC-BY-NC-ND 4.0 license

SfePy (Simple finite elements in Python) is a software for solving various kinds of problems described by partial differential equations in one, two or three spatial dimensions by the finite element method. Its source code is mostly (85\%) Python and relies on fast vectorized operations provided by the NumPy package. For a particular problem two interfaces can be used: a declarative application programming interface (API), where problem description/definition files (Python modules) are used to define a calculation, and an imperative API, that can be used for interactive commands, or in scripts and libraries. After outlining the SfePy package development, the paper introduces its implementation, structure and general features. The components for defining a partial differential equation are described using an example of a simple heat conduction problem. Specifically, the declarative API of SfePy is presented in the example. To illustrate one of SfePy's main assets, the framework for implementing complex multiscale models based on the theory of homogenization, an example of a two-scale piezoelastic model is presented, showing both the mathematical description of the problem and the corresponding code., Comment: This manuscript version is made available under the CC-BY-NC-ND 4.0 license

The spin-curvature coupling as captured by the so-called Mathisson-Papapetrou-Dixon (MPD) equations is the leading order effect of the finite size of a rapidly rotating compact astrophysical object moving in a curved background. It is also a next-to-leading order effect in the phase of gravitational waves emitted by extreme-mass-ratio inspirals (EMRIs), which are expected to become observable by the LISA space mission. Additionally, exploring the Hamiltonian formalism for spinning bodies is important for the construction of the so-called Effective-One-Body waveform models that should eventually cover all mass ratios. The MPD equations require supplementary conditions determining the frame in which the moments of the body are computed. We review various choices of these supplementary spin conditions and their properties. Then, we give Hamiltonians either in proper-time or coordinate-time parametrization for the Tulczyjew-Dixon, Mathisson-Pirani, and Kyrian-Semer\'ak conditions. Finally, we also give canonical phase-space coordinates parametrizing the spin tensor. We demonstrate the usefulness of the canonical coordinates for symplectic integration by constructing Poincar\'e surfaces of section for spinning bodies moving in the equatorial plane in Schwarzschild space-time. We observe the motion to be essentially regular for EMRI-ranges of the spin, but for larger values the Poincar\'e surfaces of section exhibit the typical structure of a weakly chaotic system. A possible future application of the numerical integration method is the inclusion of spin effects in EMRIs at the precision requirements of LISA., Comment: 37 pages, 2 figures. Accepted at CQG

The paper is devoted to the shape optimization of microstructures generating porous locally periodic materials saturated by viscous fluids. At the macroscopic level, the porous material is described by the Biot model defined in terms of the effective medium coefficients, involving the drained skeleton elasticity, the Biot stress coupling, the Biot compressibility coefficients, and by the hydraulic permeability of the Darcy flow model. By virtue of the homogenization, these coefficients are computed using characteristic responses of the representative unit cell consisting of an elastic solid skeleton and a viscous pore fluid. For the purpose of optimization, the sensitivity analysis on the continuous level of the problem is derived. We provide sensitivities of objective functions constituted by the Biot model coefficients with respect to the underlying pore shape described by a B-spline box which embeds the whole representative cell. We consider material design problems in the framework of which the layout of a single representative cell is optimized. Then we propose a sequential linearization approach to the two-scale problem in which local microstructures are optimized with respect to macroscopic design criteria. Numerical experiments are reported which include stiffness maximization with constraints allowing for a sufficient permeability, and vice versa. Issues of the design anisotropy, the spline box parametrization are discussed. In order to avoid remeshing a geometric regularization technique based on injectivity constraints is applied., Comment: This manuscript version is made available under the CC-BY-NC-ND 4.0 license

The paper is devoted to the homogenization of porous piezoelectric materials saturated by electrically inert fluid. The solid part of a representative volume element consists of the piezoelectric skeleton with embedded conductors. The pore fluid in the periodic structure can constitute a single connected domain, or an array of inclusions. Also the conducting parts are represented by several mutually separated connected domains, or by inclusions. Two of four possible arrangements are considered for upscaling by the homogenization method. The macroscopic model of the first type involves coefficients responsible for interactions between the electric field and the pore pressure, or the pore volume. For the second type, the electrodes can be used for controlling the electric field at the pore level, so that the deformation and the pore volume can be influenced locally. Effective constitutive coefficients are computed using characteristic responses of the microstructure. The two-scale modelling procedure is implemented numerically using the finite element method. The macroscopic strain and electric fields are used to reconstruct the corresponding local responses at the pore level. For validation of the models, these are compared with results obtained by direct numerical simulations of the heterogeneous structure; a good agreement is demonstrated, showing relevance of the two-scale numerical modelling approach., Comment: This manuscript version is made available under the CC-BY-NC-ND 4.0 license

The Mathisson-Papapetrou-Dixon (MPD) equations, providing the "pole-dipole" description of spinning test particles in general relativity, have to be supplemented by a condition specifying the worldline that will represent the history of the studied body. It has long been thought that the Mathisson-Pirani (MP) spin condition -- unlike other major choices made in the literature -- does not yield an explicit momentum-velocity relation. We derive here the desired (and very simple) relation and show that it is in fact equivalent to the MP condition. We clarify the apparent paradox between the existence of such a definite relation and the known fact that the MP condition is degenerate (does not specify a unique worldline), thus shedding light on some conflicting statements made in the literature. We then show how, for a given body, this spin condition yields infinitely many possible representative worldlines, and derive a detailed method how to switch between them in a curved spacetime. The MP condition is a convenient choice in situations when it is easy to recognize its "non-helical" solution, as exemplified here by bodies in circular orbits and in radial fall in the Schwarzschild spacetime., Comment: 18 pages, 7 Figures. Slightly improved version, references added, Figure 4 rescaled. Supplemental material is provided in the ancillary files "CircularOrbits.nb" and "AdditionalPlots.pdf". Matches the final published version

The Johannsen-Psaltis spacetime is a perturbation of the Kerr spacetime designed to avoid pathologies like naked singularities and closed timelike curves. This spacetime depends not only on the mass and the spin of the compact object, but also on extra parameters, making the spacetime deviate from Kerr; in this work we consider only the lowest order physically meaningful extra parameter. We use numerical examples to show that geodesic motion in this spacetime can exhibit chaotic behavior. We study the corresponding phase space by using Poincar\'{e} sections and rotation numbers to show chaotic behavior, and we use Lyapunov exponents to directly estimate the sensitivity to initial conditions for chaotic orbits., Comment: 8 pages, 3 figures, submitted to the proceedings of RAGtime 19, Opava 23.-26.10.2017

The thermally-induced structural evolution of silicon- and oxygen-containing hydrogenated amorphous carbon (a-C:H:Si:O) was investigated by X-ray photoelectron and absorption spectroscopy, as well as molecular dynamics (MD) simulations. The spectroscopic results indicate that the introduction of Si and O in hydrogenated amorphous carbon (a-C:H) increases the activation energy for the conversion of sp3- to sp2-bonded C. MD simulations indicate that the higher thermal stability of a-C:H:Si:O compared to a-C:H derives from the lower fraction of strained C-C sp3 bonds in a-C:H:Si:O.

The implications of two different time constraints on the Mathisson-Papapetrou-Dixon (MPD) equations are discussed under three spin supplementary conditions (SSC). For this reason the MPD equations are revisited without specifying the affine parameter and several relations are reintroduced in their general form. The latter allows to investigate the consequences of combining the Mathisson-Pirani (MP) SSC, the Tulczyjew-Dixon (TD) SSC and the Ohashi-Kyrian-Semer\'{a}k (OKS) SSC with two affine parameter types: the proper time on one hand and the parameterizations introduced in [Gen. Rel. Grav. 8, 197 (1977)] on the other. For the MP SSC and the TD SSC it is shown that quantities that are constant of motion for the one affine parameter are not for the other, while for the OKS SSC it is shown that the two affine parameters are the same. To clarify the relation between the two affine parameters in the case of the TD SSC the MPD equations are evolved and discussed., Comment: 7 pages, 3 figures

Recurrence analysis is a well settled method allowing to discern chaos from order, and determinism from noise. We apply this tool to study time series representing geodesic and inspiraling motion of a test particle in a deformed Kerr spacetime, when deterministic chaos and different levels of stochastic noise are present. In particular, we suggest a recurrence-based criterion to reveal whether the time series comes from a deterministic source and find a noise-level threshold of its applicability., Comment: 16 pages, 6 figures

In a recent work, [Phys. Rev. D. 94, 104010 (2016)], hereafter Paper I, we have numerically studied different prescriptions for the dynamics of a spinning particle in circular motion around a Schwarzschild black hole. In the present work, we continue this line of investigation to the rotating Kerr black hole. We consider the Mathisson-Papapetrou formalism under three different spin-supplementary-conditions (SSC), the Tulczyjew SSC, the Pirani SSC and the Ohashi-Kyrian-Semerak SSC, and analyze the different circular dynamics in terms of the ISCO shifts and the frequency parameter ${x \equiv (M \Omega)^{2/3}}$, where $\Omega$ is the orbital frequency and $M$ is the Kerr black hole mass. Then, we solve numerically the inhomogeneous $(2+1)D$ Teukolsky equation to contrast the asymptotic gravitational wave fluxes for the three cases. Our central observation made in Paper I for the Schwarzschild limit is found to hold true for the Kerr background: the three SSCs reduce to the same circular dynamics and the same radiation fluxes for small frequency parameters but differences arise as $x$ grows close to the ISCO. For a positive Kerr parameter $a=0.9$ the energy fluxes mutually agree with each other within a $0.2\%$ uncertainty up to $x<0.14$, while for $a=-0.9$ this level of agreement is preserved up to $x<0.1$. For large frequencies ($x \gtrsim 0.1$), however, the spin coupling of the Kerr black hole and the spinning body results in significant differences of the circular orbit parameters and the fluxes, especially for the $a=-0.9$ case. Instead, in the study of ISCO the negative Kerr parameter $a=-0.9$ results in less discrepancies in comparison with the positive Kerr parameter $a=0.9$., Comment: 12 pages, 4 figures, 7 tables

Solving the atomic structure of metallic clusters is fundamental to understanding their optical, electronic, and chemical properties. We report the structure of Au$_{\text{146}}$(p-MBA)$_{\text{57}}$ at subatomic resolution (0.85 {\AA}) using electron diffraction (MicroED) and atomic resolution by X-ray diffraction. The 146 gold atoms may be decomposed into two constituent sets consisting of 119 core and 27 peripheral atoms. The core atoms are organized in a twinned FCC structure whereas the surface gold atoms follow a C$_{2}$ rotational symmetry about an axis bisecting the twinning plane. The protective layer of 57 p-MBAs fully encloses the cluster and comprises bridging, monomeric, and dimeric staple motifs. Au$_{\text{146}}$(p-MBA)$_{\text{57}}$ is the largest cluster observed exhibiting a bulk-like FCC structure as well as the smallest gold particle exhibiting a stacking fault., Comment: S. Vergara, D. A. Lukes, and M. W. Martynowycz contributed equally to this work. Correspondence to: guc9@pitt.edu, tgonen@ucla.edu, and robert.whetten@utsa.edu

Super-resolution fluorescence microscopy provides unprecedented insight into cellular and subcellular structures. However, going "beyond the diffraction barrier" comes at a price since most far-field super-resolution imaging techniques trade temporal for spatial super-resolution. We propose the combination of a novel label-free white light quantitative phase tomography with fluorescence imaging to provide high-speed imaging and spatial super-resolution. The non-iterative phase reconstruction relies on the acquisition of single images at each z-location and thus enables straightforward 3D phase imaging using a classical microscope. We realized multi-plane imaging using a customized prism for the simultaneous acquisition of 8 planes. This allowed us to not only image live cells in 3D at up to 200 Hz, but also to integrate fluorescence super-resolution optical fluctuation imaging within the same optical instrument. This 4D microscope platform unifies the sensitivity and high temporal resolution of phase tomography with the specificity and high spatial resolution of fluorescence imaging.

Surface molecules, distributed in diverse patterns and clusters on cell membranes, influence vital functions of living cells. It is therefore important to understand their molecular surface organisation under different physiological and pathological conditions. Here, we present a model-free, quantitative method to determine the distribution of cell surface molecules based on TIRF illumination and super-resolution optical fluctuation imaging (SOFI). This SOFI-based approach is robust towards single emitter multiple-blinking events, high labelling densities and high blinking rates. In SOFI, the molecular density is not based on counting events, but results as an intrinsic property due to the correlation of the intensity fluctuations. The effectiveness and robustness of the method was validated using simulated data, as well as experimental data investigating the impact of palmitoylation on CD4 protein nanoscale distribution in the plasma membrane of resting T cells., Comment: 9 pages, 3 figures plus Supplementary Information