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We analyze the hydrodynamics of a rotating disk in a two-dimensional compressible fluid layer with odd viscosity. Unlike conventional fluids, odd viscosity introduces a radial flow component that can be directed either inward or outward, depending on its sign. This phenomenon is expected to significantly impact the hydrodynamic interactions between two rotating disks, potentially causing effective attraction or repulsion depending on the sign of the odd viscosity and the direction of rotation. Furthermore, we calculate the rotational resistance coefficient and find that odd viscosity increases this coefficient, regardless of its sign., Comment: 11 pages, 4 figures

Chiral active fluids can exhibit odd viscosity, a property that breaks the time-reversal and parity symmetries. Here, we examine the hydrodynamic flows of a rigid disk moving in a compressible 2D fluid layer with odd viscosity, supported by a thin lubrication layer of a conventional fluid. Using the 2D Green's function in Fourier space, we derive an exact analytical solution for the flow around a disk of arbitrary size, as well as its resistance matrix. The resulting resistance coefficients break the Onsager reciprocity, but satisfy the Onsager-Casimir reciprocity to any order in odd viscosity., Comment: 13 pages, 6 figures

A point force acting on a Brinkman fluid in confinement is always counterbalanced by the force on the porous medium, the force on the walls and the stress at open boundaries. We discuss the distribution of those forces in different geometries: a long pipe, a medium with a single no-slip planar boundary, a porous sphere with an open boundary and a porous sphere with a no-slip wall. We determine the forces using the Lorentz reciprocal theorem and additionally validate the results with explicit analytical flow solutions. We discuss the relevance of our findings for cellular processes such as cytoplasmic streaming and centrosome positioning., Comment: 17 pages, 5 figures

We present a two-phase field model and a hybrid particle-phase field model to simulate dilute colloidal sedimentation and flotation near a liquid-gas interface (or fluid-fluid interface in general). Both models are coupled to the incompressible Stokes equation, which is solved numerically using a combination of sine and regular Fourier transforms to account for the no-slip boundary conditions at the boundaries. The continuum two-phase field model allows us to analytically solve the equilibrium interfacial profile using a perturbative approach, demonstrating excellent agreement with numerical simulations. Notably, we show that strong coupling to particle dynamics can significantly alter the liquid-gas interface, thereby modifying the liquid-gas interfacial tension. In particular, we show that the renormalized surface tension is monotonically decreasing with increasing colloidal particle concentration and decreasing buoyant mass.

Dynamics at low Reynolds numbers experiences recent revival in the fields of biophysics and active matter. While in bulk isotropic fluids it is exhaustively studied, this is less so in anisotropic fluids and in confined situations. Here, we combine the latter two by studying the rotation of a disk-like inclusion in a uniaxially anisotropic, globally oriented, incompressible two-dimensional fluid film. In terms of a perturbative expansion in parameters that quantify anisotropies in viscosity and in additional linear friction with a supporting substrate or other type of confinement, we derive analytical expressions for the resulting hydrodynamic flow and pressure fields as well as for the resistance and mobility coefficients of the rotating disk. It turns out that, in contrast to translational motion, the solutions remain well-behaved also in the absence of the additional linear friction. Comparison with results from finite-element simulations show very good agreement with those from our analytical calculations. Besides applications to describe technological systems, for instance, in the area of microfluidics and thin cells of aligned nematic liquid crystals, our solutions are important for quantitative theoretical approaches to fluid membranes and thin films in general featuring a preferred direction., Comment: 17 pages, 5 figures

Functionalized thin elastic films and membranes frequently feature internal sites of net forces or stresses. These are, for instance, active sites of actuation, or rigid inclusions in a strained membrane that induce counterstress upon externally imposed deformations. We theoretically analyze the geometry of isotropic, flat, thin, linearly elastic films or membranes of finite thickness, laterally extended to infinity. At the mathematical core of such characterizations are the fundamental solutions for localized force and stress singularities associated with corresponding Green's functions. We derive such solutions in three dimensions and place them into the context of previous two-dimensional calculations. To this end, we consider both no-slip and stress-free conditions at the top and/or bottom surfaces. We provide an understanding for why the fully free-standing thin elastic membrane leads to diverging solutions in most geometries and compare these situations to the truly two-dimensional case. A no-slip support of at least one of the surfaces stabilizes the solution, which illustrates that the divergences in the fully free-standing case are connected to global deformations. Within the mentioned framework, our results are important for associated theoretical characterizations of thin elastic films, whether supported or free-standing, and of membranes subject to internal or external forces or stresses., Comment: 13 pages

To make progress towards the development of a theory on the motion of inclusions in thin structured films and membranes, we here consider as an initial step a circular disk in a two-dimensional, uniaxially anisotropic fluid layer. We assume overdamped dynamics, incompressibility of the fluid, and global alignment of the axis of anisotropy. Motion within this layer is affected by additional linear friction with the environment, for instance, a supporting substrate. We investigate the induced flows in the fluid when the disk is translated parallel or perpendicular to the direction of anisotropy. Moreover, expressions for corresponding mobilities and resistance coefficients of the disk are derived. Our results are obtained within the framework of a perturbative expansion in the parameters that quantify the anisotropy of the fluid. Good agreement is found for moderate anisotropy when compared to associated results from finite-element simulations. At pronounced anisotropy, the induced flow fields are still predicted qualitatively correctly by the perturbative theory, although quantitative deviations arise. We hope to stimulate with our investigations corresponding experimental analyses, for example, concerning fluid flows in anisotropic thin films on uniaxially rubbed supporting substrates., Comment: 14 pages, 5 figures

Microorganisms and synthetic microswimmers often encounter complex environments consisting of networks of obstacles embedded into viscous fluids. Such settings include biological media, such as mucus with filamentous networks, as well as environmental scenarios, including wet soil and aquifers. A fundamental question in studying their locomotion is how the impermeability of these porous media impact their propulsion performance compared with the case that in a purely viscous fluid. Previous studies showed that the additional resistance due to the embedded obstacles leads to an enhanced propulsion of different types of swimmers, including undulatory swimmers, helical swimmers, and squirmers. In this work we employ a canonical three-sphere swimmer model to probe the impact of propulsion in porous media. The Brinkman equation is utilized to model a sparse network of stationary obstacles embedded into an incompressible Newtonian liquid. We present both a far-field theory and numerical simulations to characterize the propulsion performance of the swimmer in such porous media. In contrast to enhanced propulsion observed in other swimmer models, our results reveal that both the propulsion speed and efficiency of the three-sphere swimmer are largely reduced by the impermeability of the porous medium. We attribute the substantial reduction in propulsion performance to the screened hydrodynamic interactions among the spheres due to the more rapid spatial decays of flows in Brinkman media. These results highlight how enhanced or hindered propulsion in porous media is largely dependent on individual propulsion mechanisms. The specific example and physical insights provided here may guide the design of synthetic microswimmers for effective locomotion in porous media in their potential biological and environmental applications., Comment: 23 pages, 4 figures

The first SRG/eROSITA All-Sky Survey (eRASS1) provides the largest intracluster medium-selected galaxy cluster and group catalog covering the western galactic hemisphere. Compared to samples selected purely on X-ray extent, the sample purity can be enhanced by identifying cluster candidates using optical and near-infrared data from the DESI Legacy Imaging Surveys. Using the red-sequence-based cluster finder eROMaPPer, we measured individual photometric properties (redshift $z_\lambda$, richness $\lambda$, optical center, and BCG position) for 12,000 eRASS1 clusters over a sky area of 13,116 deg$^2$, augmented by 247 cases identified by matching the candidates with known clusters from the literature. The median redshift of the identified eRASS1 sample is $z=0.31$, with 10% of the clusters at $z>0.72$. The photometric redshifts have an accuracy of $\delta z/(1+z)<0.005$ for $0.0595% for $z>0.05$. For these and further quality assessments of the eRASS1 identified catalog, we applied our identification method to a collection of galaxy cluster catalogs in the literature, as well as blindly on the full Legacy Surveys covering 24,069 deg$^2$. Using a combination of these cluster samples, we investigated the velocity dispersion-richness relation, finding $\log(\lambda)=2.401\times\log(\sigma)-5.074$ with an intrinsic scatter of $0.10\pm0.01$ dex. Our main result is the identified eRASS1 cluster catalog with a high purity and a well-defined X-ray selection process, enabling precise cosmological analyses presented in companion papers., Comment: 36 pages, 23 figures, 6 tables. Accepted for publication in A&A

Aims: During the Spectrum Roentgen Gamma (SRG)/ eROSITA all-sky surveys, X-ray sources close to the South Ecliptic Pole (SEP) are observed almost every 4 hours. We aim to identify the sources exhibiting the most significant long-term X-ray variability within 3 degrees of the SEP in the first three surveys, and investigate their properties. Methods: We determined the variability significance of all sources observed by eROSITA within 3 degrees of the SEP by using thresholds on the Bayesian excess variance (SCATT_LO) and the maximum amplitude deviation (AMPL_SIG). Sources exhibiting a variability significance above $3\sigma$ were subdivided into likely Galactic and extragalactic sources, by using spectral and photometric information of their optical counterparts. We quantified the X-ray normalised excess variances of all variable sources, and also calculated the periodograms of the brightest ones. Results: Out of more than $10^4$ X-ray sources detected by eROSITA within 3 degrees of the SEP, we identified 453 that exhibit significant X-ray variability. SCATT_LO is significantly more sensitive to detecting variable sources in this field, but AMPL_SIG helps provide a more complete variability sample. Of those variable sources, 168 were classified as likely extragalactic, and 235 as likely Galactic. The periodograms of most bright and variable extragalactic sources are approximately described by an aliased power law ($P\propto\nu^{-\alpha}$) with an index of $\alpha\approx 1$. We identified a potential tidal disruption event, and long-term transient sources. The stellar X-ray variability was predominantly caused by bright X-ray flares from coronally active stars., Comment: 22 pages, 29 figures

The eROSITA telescope array aboard the Spektrum Roentgen Gamma (SRG) satellite began surveying the sky in December 2019, with the aim of producing all-sky X-ray source lists and sky maps of an unprecedented depth. Here we present catalogues of both point-like and extended sources using the data acquired in the first six months of survey operations (eRASS1; completed June 2020) over the half sky whose proprietary data rights lie with the German eROSITA Consortium. We describe the observation process, the data analysis pipelines, and the characteristics of the X-ray sources. With nearly 930000 entries detected in the most sensitive 0.2-2.3 keV energy range, the eRASS1 main catalogue presented here increases the number of known X-ray sources in the published literature by more than 60%, and provides a comprehensive inventory of all classes of X-ray celestial objects, covering a wide range of physical processes. A smaller catalogue of 5466 sources detected in the less sensitive but harder 2.3-5 keV band is the result of the first true imaging survey of the entire sky above 2 keV. We show that the number counts of X-ray sources in eRASS1 are consistent with those derived over narrower fields by past X-ray surveys of a similar depth, and we explore the number counts variation as a function of the location in the sky. Adopting a uniform all-sky flux limit (at 50% completeness) of F_{0.5-2 keV} > 5 \times 10^{-14}$ erg\,s$^{-1}$\,cm$^{-2}$, we estimate that the eROSITA all-sky survey resolves into individual sources about 20% of the cosmic X-ray background in the 1-2 keV range. The catalogues presented here form part of the first data release (DR1) of the SRG/eROSITA all-sky survey. Beyond the X-ray catalogues, DR1 contains all detected and calibrated event files, source products (light curves and spectra), and all-sky maps. Illustrative examples of these are provided., Comment: 39 pages, 23 figures. Accepted for publication in A&A. Accompanying eROSITA-DE Data Release 1

A Marangoni surfer is an object embedded in a gas-liquid interface, propelled by gradients in surface tension. We derive an analytical theorem for the lower bound on the viscous dissipation by a Marangoni surfer in the limit of small Reynolds and capillary numbers. The minimum dissipation can be expressed with the reciprocal difference between drag coefficients of two passive bodies of the same shape as the Marangoni surfer, one in a force-free interface and the other in an interface with surface incompressibility. The distribution of surface tension that gives the optimal propulsion is given by the surface tension of the solution for the incompressible surface and the flow is a superposition of both solutions. For a surfer taking the form of a thin circular disk, the minimum dissipation is $16\mu a V^2$, giving a Lighthill efficiency of $1/3$. This places the Marangoni surfers among the hydrodynamically most efficient microswimmers., Comment: 17 pages, 5 figures

Swimming at the microscale has recently garnered substantial attention due to the fundamental biological significance of swimming microorganisms and the wide range of biomedical applications for artificial microswimmers. These microswimmers invariably find themselves surrounded by different confining boundaries, which can impact their locomotion in significant and diverse ways. In this work, we employ a widely used three-sphere swimmer model to investigate the effect of confinement on swimming at low Reynolds numbers. We conduct theoretical analysis via the point-particle approximation and numerical simulations based on the finite element method to examine the motion of the swimmer along the centerline in a capillary tube. The axisymmetric configuration reduces the motion to one-dimensional movement, which allows us to quantify how the degree of confinement affects the propulsion speed in a simple manner. Our results show that the confinement does not significantly affect the propulsion speed until the ratio of the radius of the tube to the radius of the sphere is in the range of $\mathcal{O}(1)-\mathcal{O}(10)$, where the swimmer undergoes substantial reduction in its propulsion speed as the radius of the tube decreases. We provide some physical insights into how reduced hydrodynamic interactions between moving spheres under confinement may hinder the propulsion of the three-sphere swimmer. We also remark that the reduced propulsion performance stands in stark contrast to the enhanced helical propulsion observed in a capillary tube, highlighting how the manifestation of confinement effects can vary qualitatively depending on the propulsion mechanisms employed by the swimmers., Comment: 10 pages, 7 figures, revised manuscript resubmitted to Phys Fluids

The use of galaxy clusters as cosmological probes relies on a detailed understanding of their properties. We aim to update the spectroscopic cluster identification of CODEX by running the spectroscopic group finder on the follow-up spectroscopy results and connecting the dynamical state of clusters to their scaling relations. We implemented a reproducible spectroscopic membership determination and cleaning procedures, based on the redMaPPer membership, running the spectroscopic group finder on the follow-up spectroscopy results and cleaning the membership for spectroscopic outliers. We applied the Anderson-Darling test for velocity substructure and analysed its influence on the scaling relations. We also tested the effect of the X-ray-to-optical centre offset on the scaling relations. We report on the scaling relations between richness, X-ray luminosity, and velocity dispersion for a complete sample of clusters with at least 15 members. Clusters with velocity substructure exhibit enhanced velocity dispersion for a given richness and are characterized by 2.5 times larger scatter. Clusters that have a strong offset in X-ray-to-optical centres have comparable scaling relations as clusters with substructure. We demonstrate that there is a consistency in the parameters of the scaling relations for the low- and high-richness galaxy clusters. Splitting the clusters by redshift, we note a decrease in scatter with redshift in all scaling relations. We localize the redshift range where a high scatter is observed to $z<0.15$, which is in agreement with the literature results on the scatter. We note that the increase in scatter for both high- and low-luminosity clusters is $z<0.15$, suggesting that both cooling and the resulting active galactic nucleus feedback are at the root of this scatter. Abridged., Comment: 23 pages, A&A in press, catalogs are released through CDS

Green's function plays an important role in many areas of physical sciences and is a prime tool for solving diverse hydrodynamic equations in the linear regime. In the present contribution, the axisymmetric low-Reynolds-number Brinkman flow induced by monopole and dipole singularities in proximity of a stationary plate of circular shape is theoretically investigated. The flow singularities are directed along the central axis of the plate. No-slip boundary conditions are assumed to hold at the surface of the plate. The Green's functions are determined to a large extent analytically, reducing the solution of the linear hydrodynamic equations to well-behaved one-dimensional integrals amenable to numerical computation. In our approach, the Brinkman flow problem is formulated as a mixed boundary value problem that is subsequently mapped in the form of dual integral equations on the domain boundaries. Thereupon, the solution of the equations of fluid motion is eventually reduced to the solution of two independent Fredholm integral equations of the first kind. The overall flow structure and emerging eddy patterns are found to strongly depend on the magnitude of the relevant geometrical and physical parameters of the system. Moreover, the effect of the confining plate on the dynamics of externally driven or force-free particles is assessed through the calculation of the relevant hydrodynamic reaction functions. The effect of the plate on the locomotory behavior of a self-propelling active dipole swimmer is shown to be maximum when the radius of the plate is comparable to the distance separating the swimmer from the plate. Our results may prove useful for characterizing transport processes in microfluidic devices and may pave the way toward understanding and controlling of small-scale flows in porous media., Comment: 17 pages, 7 figures, resubmitted to Phys Rev Res

We theoretically and computationally study the low-Reynolds-number hydrodynamics of a linear active microswimmer surfing on a compressible thin fluid layer characterized by an odd viscosity. Since the underlying three-dimensional fluid is assumed to be very thin compared to any lateral size of the fluid layer, the model is effectively two-dimensional. In the limit of small odd viscosity compared to the even viscosities of the fluid layer, we obtain analytical expressions for the self-induced flow field, which includes non-reciprocal components due to the odd viscosity. On this basis, we fully analyze the behavior of a single linear swimmer, finding that it follows a circular path, the radius of which is, to leading order, inversely proportional to the magnitude of the odd viscosity. In addition, we show that a pair of swimmers exhibits a wealth of two-body dynamics that depends on the initial relative orientation angles as well as on the propulsion mechanism adopted by each swimmer. In particular, the pusher-pusher and pusher-puller-type swimmer pairs exhibit a generic spiral motion, while the puller-puller pair is found to either co-rotate in the steady state along a circular trajectory or exhibit a more complex chaotic behavior resulting from the interplay between hydrodynamic and steric interactions. Our theoretical predictions may pave the way toward a better understanding of active transport in active chiral fluids with odd viscosity, and may find potential applications in the quantitative microrheological characterization of odd-viscous fluids., Comment: 21 pages, 8 figures

The energy dissipation and entropy production by self-propelled microswimmers differ profoundly from passive particles pulled by external forces. The difference extends both to the shape of the flow around the swimmer, as well as to the internal dissipation of the propulsion mechanism. Here we derive a general theorem that provides an exact lower bound on the total, external and internal, dissipation by a microswimmer. The problems that can be solved include an active surface-propelled droplet, swimmers with an extended propulsive layer and swimmers with an effective internal dissipation. We apply the theorem to determine the swimmer shapes that minimize the total dissipation while keeping the volume constant. Our results show that the entropy production by active microswimmers is subject to different fundamental limits than the entropy production by externally driven particles., Comment: 14+5 pages, 6+1 figures

The characterization of the dynamical state of clusters is key to study their evolution, their selection, and use them as a cosmological probe. The offsets between different definitions of the center have been used to estimate the cluster disturbance. Our goal is to study the distribution of the offset between the X-ray and optical centers in clusters of galaxies. We study the offset for eROSITA clusters. We aim to connect observations to hydrodynamical simulations and N-body models. We assess the astrophysical effects affecting the displacements. We measure the offset for clusters observed in eFEDS and eRASS1. We focus on a subsample of 87 massive eFEDS clusters at low redshift. We link the observations to the offset parameter Xoff measured on dark matter halos in N-body simulations, using the hydrodynamical simulations as a bridge. eFEDS clusters show a smaller offset compared to eRASS1, because the latter contains a larger fraction of massive and disturbed structures. We measure an average offset of 76.3+30.1-27.1 kpc on the subsample of 87 eFEDS clusters. This is in agreement with the predictions from TNG and Magneticum, and the distribution of Xoff from DMO simulations. The tails of the distributions are different. Using the offset to classify relaxed and disturbed clusters, we measure a relaxed fraction of 31% in the eFEDS subsample. Finally, we find a correlation between the offset in hydrodynamical simulations and Xoff measured on their parent DMO run and calibrate a relation between them. There is good agreement between eROSITA data and simulations. Baryons cause a decrement (increment) in the low (high) offset regime compared to the Xoff distribution. The offset-Xoff relation provides an accurate prediction of the true Xoff distribution in Magneticum and TNG. It allows introducing the offsets in cosmology, marginalizing on dynamical selection effects., Comment: Accepted for publication on A&A

Although the dynamics of colloids in the vicinity of a solid interface has been widely characterized in the past, experimental studies of Brownian diffusion close to an air-water interface are rare and limited to particle-interface gap distances larger than the particle size. At the still unexplored lower distances, the dynamics is expected to be extremely sensitive to boundary conditions at the air-water interface. There, ad hoc experiments would provide a quantitative validation of predictions. Using a specially designed dual wave interferometric setup, the 3D dynamics of 9 micrometers diameter particles at a few hundreds of nanometers from an air-water interface is here measured in thermal equilibrium. Intriguingly, while the measured dynamics parallel to the interface approaches expected predictions for slip boundary conditions, the Brownian motion normal to the interface is very close to the predictions for no-slip boundary conditions. These puzzling results are rationalized considering current models of incompressible interfacial flow and deepened developing an ad hoc model which considers the contribution of tiny concentrations of surface active particles at the interface. We argue that such condition governs the particle dynamics in a large spectrum of systems ranging from biofilm formation to flotation process., Comment: 33 pages, 5 figures. Submitted to Journal of Colloid and Interface Science

Anticipating price developments in financial markets is a topic of continued interest in forecasting. Funneled by advancements in deep learning and natural language processing (NLP) together with the availability of vast amounts of textual data in form of news articles, social media postings, etc., an increasing number of studies incorporate text-based predictors in forecasting models. We contribute to this literature by introducing weak learning, a recently proposed NLP approach to address the problem that text data is unlabeled. Without a dependent variable, it is not possible to finetune pretrained NLP models on a custom corpus. We confirm that finetuning using weak labels enhances the predictive value of text-based features and raises forecast accuracy in the context of predicting cryptocurrency returns. More fundamentally, the modeling paradigm we present, weak labeling domain-specific text and finetuning pretrained NLP models, is universally applicable in (financial) forecasting and unlocks new ways to leverage text data., Comment: 29 pages

Casimir forces in quantum electrodynamics emerge between microscopic metallic objects because of the confinement of the vacuum electromagnetic fluctuations occurring even at zero temperature. Their generalization at finite temperature and in material media are referred to as Casimir--Lifshitz forces. These forces are typically attractive, leading to the widespread problem of stiction between the metallic parts of micro- and nanodevices. Recently, repulsive Casimir forces have been experimentally realized but their reliance on specialized materials prevents their dynamic control and thus limits their further applicability. Here, we experimentally demonstrate that repulsive critical Casimir forces, which emerge in a critical binary liquid mixture upon approaching the critical temperature, can be used to actively control microscopic and nanoscopic objects with nanometer precision. We demonstrate this by using critical Casimir forces to prevent the stiction caused by the Casimir--Lifshitz forces. We study a microscopic gold flake above a flat gold-coated substrate immersed in a critical mixture. Far from the critical temperature, stiction occurs because of dominant Casimir--Lifshitz forces. Upon approaching the critical temperature, however, we observe the emergence of repulsive critical Casimir forces that are sufficiently strong to counteract stiction. This experimental demonstration can accelerate the development of micro- and nanodevices by preventing stiction as well as providing active control and precise tunability of the forces acting between their constituent parts., Comment: 27 pages, 5 figures

This paper documents the seventeenth data release (DR17) from the Sloan Digital Sky Surveys; the fifth and final release from the fourth phase (SDSS-IV). DR17 contains the complete release of the Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) survey, which reached its goal of surveying over 10,000 nearby galaxies. The complete release of the MaNGA Stellar Library (MaStar) accompanies this data, providing observations of almost 30,000 stars through the MaNGA instrument during bright time. DR17 also contains the complete release of the Apache Point Observatory Galactic Evolution Experiment 2 (APOGEE-2) survey which publicly releases infra-red spectra of over 650,000 stars. The main sample from the Extended Baryon Oscillation Spectroscopic Survey (eBOSS), as well as the sub-survey Time Domain Spectroscopic Survey (TDSS) data were fully released in DR16. New single-fiber optical spectroscopy released in DR17 is from the SPectroscipic IDentification of ERosita Survey (SPIDERS) sub-survey and the eBOSS-RM program. Along with the primary data sets, DR17 includes 25 new or updated Value Added Catalogs (VACs). This paper concludes the release of SDSS-IV survey data. SDSS continues into its fifth phase with observations already underway for the Milky Way Mapper (MWM), Local Volume Mapper (LVM) and Black Hole Mapper (BHM) surveys., Comment: 40 pages, 8 figures, 6 tables. In press at ApJSS (arxiv v2 corrects some minor typos and updates references)

The eROSITA Final Equatorial-Depth Survey (eFEDS), executed during the performance verification phase of the Spectrum-Roentgen-Gamma (SRG)/eROSITA telescope, was completed in Nov. 2019. One of the science goals of this survey is to demonstrate the ability of eROSITA to detect samples of clusters and groups at the final depth of the eROSITA all-sky survey. Because of the sizeable point-spread function of eROSITA, high-redshift clusters of galaxies or compact nearby groups hosting bright active galactic nuclei (AGN) can be misclassified as point sources by the source detection algorithms. A total of 346 galaxy clusters and groups in the redshift range of 0.1

We investigate the scaling relations between X-ray observables of the clusters detected in the eFEDS field using Spectrum-Roentgen-Gamma/eROSITA observations taking into account the selection effects and the distributions of observables with cosmic time. We extract X-ray observables (Lx, Lbol, T, Mgas, Yx) within R500 for the sample of 542 clusters in the eFEDS field. By applying detection and extent likelihoods, we construct a subsample of 265 clusters with a contamination level of <10% (including AGNs and spurious fluctuations) to be utilized in the scaling relation analysis. The selection function based on the state-of-the-art simulations of the eROSITA sky is fully accounted for in our work. We provide the X-ray observables in the core-included 3sigma confidence level however, our results are in good agreement with the simulations including non-gravitational physics and the recent results that take into account selection effects. Strong deviations we find from the self-similar scenario indicate that the non-gravitational effects play an important role in shaping the observed physical state of clusters. This work extends the scaling relations to low mass, low luminosity galaxy cluster and group regime using eFEDS observations, demonstrating eROSITA's ability to measure ICM emission out to R500 with survey-depth exposures and constrain the scaling relations in a wide mass-luminosity-redshift range., Comment: 35 pages, 7 figures, 5 tables, Submitted to A&A for the Special Issue: The Early Data Release of eROSITA and Mikhail Pavlinsky ART-XC on the SRG Mission

Breaking spatial symmetry is an essential requirement for phoretic active particles to swim at low Reynolds number. This fundamental prerequisite for swimming at the micro-scale is fulfilled either by chemical patterning of the surface of active particles or alternatively by exploiting geometrical asymmetries to induce chemical gradients and achieve self-propulsion. In the present manuscript, a far-field analytical model is employed to quantify the leading-order contribution to the induced phoretic velocity of a chemically homogeneous isotropic active colloid near a finite-sized disk of circular shape resting on an interface separating two immiscible viscous incompressible Newtonian fluids. To this aim, the solution of the phoretic problem is formulated as a mixed-boundary-value problem which is subsequently transformed into a system of dual integral equations on the inner and outer domains. Depending on the ratio of different involved viscosities and solute solubilities, the sign of phoretic mobility and chemical activity, as well as the ratio of particle-interface distance to the radius of the disk, the isotropic active particle is found to be either repelled from the interface, attracted to it, or reach a stable hovering state and remains immobile near the interface. Our results may prove useful in controlling and guiding the motion of self-propelled phoretic active particles near aqueous interfaces.

Geometric confinements play an important role in many physical and biological processes and significantly affect the rheology and behavior of colloidal suspensions at low Reynolds numbers. On the basis of the linear Stokes equations, we investigate theoretically and computationally the viscous azimuthal flow induced by the slow rotation of a small spherical particle located in the vicinity of a rigid no-slip disk or inside a gap between two coaxially positioned rigid no-slip disks of the same radius. We formulate the solution of the hydrodynamic problem as a mixed-boundary-value problem in the whole fluid domain, which we subsequently transform into a system of dual integral equations. Near a stationary disk, we show that the resulting integral equation can be reduced into an elementary Abel integral equation that admits a unique analytical solution. Between two coaxially positioned stationary disks, we demonstrate that the flow problem can be transformed into a system of two Fredholm integral equations of the first kind. The latter are solved by means of numerical approaches. Using our solution, we further investigate the effect of the disks on the slow rotational motion of a colloidal particle and provide expressions of the hydrodynamic mobility as a function of the system geometry. We compare our results with corresponding finite-element simulations and observe very good agreement., Comment: 14 pages, 9 figures, revised manuscript resubmitted to Phys. Fluids (invited article)

Understanding the cluster population of clusters of galaxies is of the utmost importance for using cluster samples in both astrophysical and cosmological studies. We present an in-depth analysis of the X-ray morphological parameters of the galaxy clusters and groups detected in the eROSITA Final Equatorial-Depth Survey (eFEDS). We study the eROSITA X-ray imaging data for a sample of 325 clusters and groups that are significantly detected in the eFEDS field. We characterize their dynamical properties by measuring a number of dynamical estimators: concentration, central density, cuspiness, ellipticity, power-ratios, photon asymmetry, and Gini coefficient. The galaxy clusters and groups detected in eFEDS, covering a luminosity range of more than three orders of magnitude and large redshift range out to 1.2 provide an ideal sample for studying the redshift and luminosity evolution of the morphological parameters and characterization of the underlying dynamical state of the sample. Based on these measurements we construct a new dynamical indicator, relaxation score, for all the clusters in the sample. We find no evidence for bimodality in the distribution of morphological parameters of our clusters, rather we observe a smooth transition from the cool-core to non-cool-core and from relaxed to disturbed states. A significant evolution in redshift and luminosity is also observed in the morphological parameters examined in this study after carefully taking into account the selection effects. We determine that our eFEDS-selected cluster sample, differently than ROSAT-based cluster samples, is not biased toward relaxed clusters, but contains a similar fraction of disturbed as SZ surveys., Comment: 21 pages, 10 figures, 2 tables, Submitted to A&A for the Special Issue: The Early Data Release of eROSITA and Mikhail Pavlinsky ART-XC on the SRG Mission

The eROSITA Final Equatorial-Depth Survey has been carried out during the PV phase of the SRG/eROSITA telescope and completed in November 2019. This survey is designed to provide the first eROSITA-selected sample of galaxy clusters and groups and to test the predictions for the all-sky survey in the context of cosmological studies with clusters. In the 140 deg$^2$ area covered by eFEDS, 542 candidate clusters and groups are detected as extended X-ray sources, down to a flux of $\sim10^{-14} $erg/s/cm$^2$ in the soft band (0.5-2 keV) within 1'. In this work, we provide the catalog of candidate galaxy clusters and groups in eFEDS. We perform imaging and spectral analysis on the eFEDS clusters with eROSITA X-ray data, and study the properties of the sample. The clusters are distributed in the redshift range [0.01, 1.3], with the median redshift at 0.35. We obtain the ICM temperature measurement with $>2\sigma$ c.l. for $\sim$1/5 (102/542) of the sample. The average temperature of these clusters is $\sim$2 keV. Radial profiles of flux, luminosity, electron density, and gas mass are measured from the precise modeling of the imaging data. The selection function, the purity and completeness of the catalog are examined and discussed in detail. The contamination fraction is $\sim1/5$ in this sample, dominated by misidentified point sources. The X-ray Luminosity Function of the clusters agrees well with the results obtained from other recent X-ray surveys. We also find 19 supercluster candidates in eFEDS, most of which are located at redshifts between 0.1 and 0.5. The eFEDS cluster and group catalog provides a benchmark proof-of-concept for the eROSITA All-Sky Survey extended source detection and characterization. We confirm the excellent performance of eROSITA for cluster science and expect no significant deviations from our pre-launch expectations for the final All-Sky Survey., Comment: Submitted to A&A for the Special Issue: The Early Data Release of eROSITA and Mikhail Pavlinsky ART-XC on the SRG Mission. 25 pages, 13 figures

In this work the evolution of two fields of matter in planar symmetric black holes D-dimensional with symmetry of Lifshitz whose dynamic exponent is $z$ were analyzed. The fields investigated were a scalar field non-minimal coupled to the Einstein tensor and the Ricci scalar and the electromagnetic field. Two black holes were chosen, one with 5-dimensions and z=1 and another with 6-dimensions and $z=0$. The equations of motion for both fields were developed in general and applied to each black hole mentioned. In some cases exact solutions of the equations were obtained in terms of hypergeometric functions and confluent Heun functions. The quasinormal modes (MQN) of evolution of the analyzed fields were calculated numerically using two different approaches: HH and AIM. In all the black holes studied the NSM's did not indicate instabilities neither regarding the couplings nor the space-times. In general, the quasinormal modes behave like the oscillation modes of a damped harmonic oscillator, presenting three regimes: underdamped $(\omega_R \neq0, \omega_I <0) $, critically damped $ (\omega_R=0,\omega_I^{crit} <0) $ and overdamped $ (\omega_R=0,\omega_I <0) $. In the analyzed cases an interesting behavior was found for $\omega_I $ when $ k \neq0 $ and $ r_+<10 $. In general, $\omega_I $ increase with $k$, but here we find a quadratic growth for $ k\sim r_+$ and then a decrease when $k>>r_+$. This behavior may be relevant in the context of gravity/gauge duality. Additionally, we also analyzed the evolution of the same fields in two black holes with symmetry of Lifshtiz in $ 2 + 1 $ dimensions., Comment: Master dissertation (in Portuguese), Advisor: Prof. Dr. Alan Pavan, 117 pages, 37 figures

The ability of microswimmers to deploy optimal propulsion strategies is of paramount importance for their locomotory performance and survival at low Reynolds numbers. Although for perfectly spherical swimmers minimum dissipation requires a neutral type swimming, any departure from the spherical shape may lead the swimmer to adopt a new propulsion strategy, namely those of puller- or pusher-type swimming. In this study, by using the minimum dissipation theorem for microswimmers, we determine the flow field of an optimal nearly spherical swimmer, and show that indeed depending on the shape profile, the optimal swimmer can be a puller, pusher, or neutral. Using an asymptotic approach, we find that amongst all the modes of the shape function, only the third mode determines to leading order the swimming type of the optimal swimmer., Comment: 9 pages, 3 figures