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Here, we report on a new class active particles capable of dynamically programmable motion powered by electricity. We have implemented physical principles that separate the propulsion and steering mechanisms of active motion using optically activated, patterned, photoresponsive semiconductor coatings on intricate microstructures. Our engineered microswimmer robots employ an induced-charge electro-phoresis (ICEP) mechanism to achieve linear motion and optically modulated electrokinetic propulsion (OMEP) for steering. Optical modulation is achieved by manipulating the polarizability of patterned ZnO semiconductor coating through exposure to light with wavelengths above its bandgap, exploiting the semiconductor's photoconductive properties. Unlike previous methods that rely on changing the direction of optical illumination or spatially controlling narrow optical beams, our approach achieves optical steering under uniform ambient illumination conditions, thereby greatly reducing the complexity of the optical system. The decoupling of propulsion and steering allows for the programming of micromotor trajectories in both open and closed-loop control modes. We anticipate that our findings will pave the way for efficient optically gated control of the trajectory of photoresponsive active particles. Furthermore, they will enable the selective manipulation of specific subgroups of engineered active microparticles with various semiconducting coatings having different band gaps.

The stellar halo of the Milky Way is built up, at least in part, from debris from past mergers. Stars from such merger events define substructures in phase-space, for example in the form of streams, which are groups of stars moving on similar trajectories. The nearby Helmi streams discovered more than two decades ago are a well-known example. Using 6D phase-space information from the Gaia space mission, Dodd et al. (2022) have recently reported that the Helmi streams are split into two clumps in angular momentum space. Such substructure can be explained and sustained in time if the dark matter halo of the Milky Way takes a prolate shape in the region probed by the orbits of the stars in the streams. Here, we explore the behaviour of the two clumps identified in the Helmi streams in a Modified Newtonian Dynamics (MOND) framework to test this alternative model of gravity. We perform orbit integrations of Helmi streams member stars in a simplified MOND model of the Milky Way and using the more sophisticated Phantom of RAMSES simulation framework. We find with both approaches that the two Helmi streams clumps do not retain their identity and dissolve after merely 100 Myr. This extremely short timescale would render the detection of two separate clumps as very unlikely in MONDian gravity. The observational constraints provided by the streams, which MOND fails to reproduce in its current formulation, could potentially also be used to test other alternative gravity models., Comment: 10 pages, 7 figures

Several works have recently applied Jeans modelling to Gaia-based datasets to infer the circular velocity curve for the Milky Way. Such works have consistently found evidence for a continuous decline in the rotation curve beyond $\sim$15kpc possibly indicative of a light dark matter halo. We used Gaia DR3 RVS data, supplemented with Bayesian distances to determine the radial variation of the second moments of the velocity distribution for stars close to the Galactic plane. We have used these profiles to determine the rotation curve using the Jeans equations under the assumption of axisymmetry and explored how they vary with azimuth and above and below the Galactic disk plane. We have applied the same methodology to an N-body simulation of a Milky Way-like galaxy impacted by a satellite akin the Sagittarius dwarf and to the Auriga suite of cosmological simulations. We reveal evidence of disequilibrium and deviations from axisymmetry closer in. We find that the second moment of $V_R$ flattens out at $R \gtrsim 12.5$kpc, and that the second moment of $V_{\phi}$ is different above and below the plane for $R \gtrsim 11$kpc. The simulations indicate that these features are typical of galaxies that have been perturbed by external satellites. They also suggest that the difference between the true circular velocity curve and that inferred from Jeans equations can be as high as 15$\%$, but is likely of order 10$\%$ for the Milky Way. This is of larger amplitude than the systematics inherent to Jeans equations. However, if the density of the tracer population were truncated at large radii, the erroneous conclusion of a steeply declining rotation curve can be reached. We find that steady-state axisymmetric Jeans modelling becomes less robust at large radii, indicating that particular caution is needed when interpreting the rotation curve inferred in those regions., Comment: 20 pages, 22 figures

We present a numerical study of the evolution of power-law tails (PLTs) in the (column-)density distributions ($N$-PDF, $\rho$-PDF) in contracting star-forming clumps in primordial gas, without and with some initial rotational and/or turbulent support. In all considered runs multiple PLTs emerge shortly after the formation of the first protostar. The first PLT (PLT 1) in the $\rho$-PDF is a stable feature with slope $q_1\simeq -1.3$ which corresponds -- under the condition of preserved spherical symmetry -- to the outer envelope of the protostellar object with density profile $\rho\propto l^{-2}$ in the classical Larson-Penston collapse model, where $l$ is the radius. The second PLT (PLT 2) in the $\rho$-PDF is stable in the pure-infall runs but fluctuates significantly in the runs with initial support against gravity as dozens of protostars form and their mutual tidal forces change the density structure. Its mean slope, $\langle q_2\rangle\simeq -2$, corresponds to a density profile of $\rho\propto l^{-3/2}$ which describes a core in free fall in the classical Larson-Penston collapse model or an attractor solution at scales with dominating protostellar gravity. PLT 1 and PLT 2 in the $N$-PDFs are generally consistent with the observational data of Galactic low-mass star-forming regions from {\it Herschel} data. In the runs with initial support against gravity a third PLT (PLT~3) in the $\rho$-PDFs appears simultaneously with or after the emergence of PLT 2. It is very shallow, with mean slope of $\langle q_3\rangle\simeq -1$, and is associated with the formation of thin protostellar accretion disks., Comment: 14 pages, 12 figures; accepted for publication in MNRAS (main journal)

The halo of the Milky Way galaxy hosts multiple dynamically coherent substructures known as stellar streams that are remnants of tidally disrupted systems such as globular clusters (GCs) and dwarf galaxies (DGs). A particular case is that of the Jhelum stream, which is known for its complex morphology. Using the available data from Gaia DR3, we extracted a region on the sky that contains Jhelum. We then applied the novel Locally Aligned Ant Technique (LAAT) on the position and proper motion space of stars belonging to the selected region to highlight the stars that are closely aligned with a local manifold in the data and the stars belonging to regions of high local density. We find that the overdensity representing the stream in proper motion space is composed of two components, and show the correspondence of these two signals to the previously reported narrow and broad spatial components of Jhelum. We made use of the radial velocity measurements provided by the $S^5$ survey to confirm, for the first time, a separation between the two components in radial velocity. We show that the narrow and broad components have velocity dispersions of $4.84^{+1.23}_{-0.79}$~km/s and $19.49^{+2.19}_{-1.84}$~km/s, and metallicity dispersions of $0.15^{+0.18}_{-0.10}$ and $0.34^{+0.13}_{-0.09}$, respectively. These measurements, and the difference in component widths, could be explained with a scenario where Jhelum is the remnant of a GC embedded within a DG that were accreted onto the Milky Way during their infall. Although the properties of Jhelum can be explained with this merger scenario, other progenitors of the narrow component remain possible such as a nuclear star cluster or a DG. To rule these possibilities out, we would need more observational data of member stars of the stream. Our analysis highlights the importance of the internal structure of streams with regards to their formation history.

We present a simple visual description of the topology of the space of three-dimensional rotations, requiring just intuition, imagination and no advanced math., Comment: arXiv admin note: text overlap with arXiv:1607.05876

We present a new optimization-based method for aggregating preferences in settings where each voter expresses preferences over pairs of alternatives. Our approach to identifying a consensus partial order is motivated by the observation that collections of votes that form a cycle can be treated as collective ties. Our approach then removes unions of cycles of votes, or circulations, from the vote graph and determines aggregate preferences from the remainder. Specifically, we study the removal of maximal circulations attained by any union of cycles the removal of which leaves an acyclic graph. We introduce the strong maximum circulation, the removal of which guarantees a unique outcome in terms of the induced partial order, called the strong partial order. The strong maximum circulation also satisfies strong complementary slackness conditions, and is shown to be solved efficiently as a network flow problem. We further establish the relationship between the dual of the maximum circulation problem and Kemeny's method, a popular optimization-based approach for preference aggregation. We also show that identifying a minimum maximal circulation -- i.e., a maximal circulation containing the smallest number of votes -- is an NP-hard problem. Further an instance of the minimum maximal circulation may have multiple optimal solutions whose removal results in conflicting partial orders., Comment: INFORMS Journal on Optimization, Forthcoming

Herein we demonstrate the ability to optically tune the mobility of electrically powered Janus particles (JP) that are half coated with various Zinc Oxide (ZnO) semiconducting layers, i.e. polycrystalline, amorphous and amorphous with a SiO2 passivation layer. The ZnO semiconductor photo-response enables increase in its electrical conductivity with light having wavelengths of sufficient photon energy with respect to the semiconductor bandgap. This effect, termed optically modulated electrokinetic propulsion (OMEP), can be harnessed to increase the contrast in polarizability between the dielectric and semiconducting hemispheres, which in turn, results in an increased electrokinetic mobility. The addition of optical activation to the electrical field enables an additional degree of control of JP mobility. We also demonstrate optical control of collective behavior and particle-particle interactions for dense semi-conducting Janus particle populations.

Stellar streams are a promising tool to study the Milky Way's dark matter subhalo population, as interactions with subhalos could produce substructure in streams. However, other possible causes for substructure first need to be well understood. Here we studied the kinematics and the unusual morphology of the stellar stream Jhelum. Using a combination of ground-based photometry and Gaia EDR3 astrometry, we characterized the morphology of Jhelum. We combined this new data with radial velocities from the literature to perform orbit integrations of the stream in static Galactic potentials. We also carried out N-body simulations in the presence of the Sagittarius dwarf galaxy. The new data reveal a previously unreported tertiary component in the stream, as well as several gaps and a kink-like feature in its narrow component. We find that for a range of realistic Galactic potentials, no single orbit is able to reproduce Jhelum's radial velocity data entirely. A generic property of the orbital solutions is that they share a similar orbital plane to Sagittarius and this leads to repeated encounters with the stream. Using N-body simulations that include a massive Sagittarius, we explored its effect on Jhelum, and we show that these encounters can qualitatively reproduce the narrow and broad components in Jhelum, as well as create a tertiary component in some cases. We also find evidence that such encounters can result in an apparent increase in the velocity dispersion of the stream by a factor up to four due to overlapping narrow and broad components. Our findings suggest that the Jhelum stream is even more complex than once thought; however, its morphology and kinematics can tentatively be explained via the interactions with Sagittarius. In this scenario, the formation of Jhelum's narrow and broad components occurs naturally, yet some of the smaller gap-like features remain to be explained., Comment: 17 pages, 17 figures

Adjustment of the behavior of the potential energy of nuclear deformation, defined as the sum of the energies of lowest-lying occupied single-particle levels in a deformed finite potential with a pairing correction, is considered by taking into account the dependence of the diffuseness of the surface of the potential on deformation. To verify this approach we construct a non-axial ellipsoidally-deformed potential with a slight (of the order of 1\%) variation of the surface diffuseness at moderate deformations. Parameters of the variation are determined from a calculation for a group of 36 deformed, transitional, and spherical nuclei in the range $50 \le A \le 241$ using existing experimental data on static quadrupole moments. In order to test the performed parameter choice, we applied the model to description of the ground-state deformation of the isotopic chains $^{95-132}$Cd and $^{74-106}$Sr. The obtained description of the ground state deformation of the considered nuclei is in agreement with experimental data and results of macro-microscopic models and calculations using the Hartree-Fock-Bogoliubov method.

We exhibit a new presentation of the (equilateral) Von Dyck groups $D(2,3,n), \ n\ge 3$, in terms of two generators of order $n$ satisfying three relations, one of which is Artin's braid relation. By dropping the relation which fixes the order of the generators we obtain the universal covering groups of the corresponding Von Dyck groups. In the cases $n=3,\, 4,\,5$, these are respectively the double covers of the finite rotational tetrahedral, octahedral and icosahedral groups. When $n\ge 6$ we obtain infinite covers of the corresponding infinite Von Dyck groups. The interesting cases arise for $n\ge 7$ when these groups act as discrete groups of isometries of the hyperbolic plane. Imposing a suitable third relation we obtain a host of (efficient) presentations of finite simple Chevalley groups of type $A_1$ as well as the sporadic Janko group $J_2$., Comment: 16 pages, 3 figures

We present an $O(nm)$ algorithm for all-pairs shortest paths computations in a directed graph with $n$ nodes, $m$ arcs, and nonnegative integer arc costs. This matches the complexity bound attained by Thorup \cite{Thorup1999} for the all-pairs problems in undirected graphs. The main insight is that shortest paths problems with approximately balanced directed cost functions can be solved similarly to the undirected case. The algorithm finds an approximately balanced reduced cost function in an $O(m\sqrt{n}\log n)$ preprocessing step. Using these reduced costs, every shortest path query can be solved in $O(m)$ time using an adaptation of Thorup's component hierarchy method. The balancing result can also be applied to the $\ell_\infty$-matrix balancing problem.