3-D Velocity Regulation for Nonholonomic Source Seeking Without Position Measurement

We consider a three-dimensional problem of steering a nonholonomic vehicle to seek an unknown source of a spatially distributed signal field without any position measurement. In the literature, there exists an extremum seeking-based strategy under a constant forward velocity and tunable pitch and yaw velocities. Obviously, the vehicle with a constant forward velocity may exhibit certain overshoots in the seeking process and can not slow down even it approaches the source. To resolve this undesired behavior, this paper proposes a regulation strategy for the forward velocity along with the pitch and yaw velocities. Under such a strategy, the vehicle slows down near the source and stays within a small area as if it comes to a full stop, and controllers for angular velocities become succinct. We prove the local exponential convergence via the averaging technique. Finally, the theoretical results are illustrated with simulations.Comment: submitted to IEEE TCST;12 pages, 10 figure

catena-Poly[[diaqua­magnesium(II)]-bis­(μ-5-ammonio­isophthalato-κ2 O 1:O 3)]

In the title compound, [Mg(C8H6NO4)2(H2O)2]n, the MgII ion lies on a twofold roatation axis and is coordinated in a slightly distorted octa­hedral environment. Pairs of bridging ammonium­isophthalate ligands connect symmetry-related MgII ions, forming chains along [010]. In the crystal, inter­molecular O—H⋯O and N—H⋯O hydrogen bonds link these chains into a three-dimensional network. The centroids of pairs of symmetry-related benzene rings within a chain are separated by 3.5707 (12) Å

Constraining the Merger History of Primordial-Black-Hole Binaries from GWTC-3

Primordial black holes (PBHs) can be not only cold dark matter candidates but also progenitors of binary black holes observed by LIGO-Virgo-KAGRA (LVK) Collaboration. The PBH mass can be shifted to the heavy distribution if multi-merger processes occur. In this work, we constrain the merger history of PBH binaries using the gravitational wave events from the third Gravitational-Wave Transient Catalog (GWTC-3). Considering four commonly used PBH mass functions, namely the log-normal, power-law, broken power-law, and critical collapse forms, we find that the multi-merger processes make a subdominant contribution to the total merger rate. Therefore, the effect of merger history can be safely ignored when estimating the merger rate of PBH binaries. We also find that GWTC-3 is best fitted by the log-normal form among the four PBH mass functions and confirm that the stellar-mass PBHs cannot dominate cold dark matter.Comment: 11 pages, 8 figures, 2 tables; accepted for publication in PR

Post-Newtonian Approximation of Teleparallel Gravity Coupled with a Scalar Field

We use the parameterized post-Newtonian (PPN) formalism to explore the weak field approximation of teleparallel gravity non-minimally coupling to a scalar field $\phi$, with arbitrary coupling function $\omega(\phi)$ and potential $V(\phi)$. We find that all the PPN parameters are identical to general relativity (GR), which makes this class of theories compatible with the Solar System experiments. This feature also makes the theories quite different from the scalar-tensor theories, which might be subject to stringent constraints on the parameter space, or need some screening mechanisms to pass the Solar System experimental constraints.Comment: 15 pages, revtex4; v2: discussions added, Nucl. Phys. B in press; v3: published versio

Simultaneously probing the sound speed and equation of state of the early Universe with pulsar timing arrays

Recently, several major pulsar timing array (PTA) collaborations have assembled strong evidence for the existence of a gravitational-wave background at frequencies around the nanohertz regime. Assuming that the PTA signal is attributed to scalar-induced gravitational waves, we jointly employ the PTA data from the NANOGrav 15-year data set, PPTA DR3, and EPTA DR2 to probe the conditions of the early Universe. Specifically, we explore the equation of state parameter ($w$), the sound speed ($c_s$), and the reheating temperature ($T_\mathrm{rh}$), finding $w=0.60^{+0.32}_{-0.39}$, $c_s\gtrsim 0.09$, and $T_\mathrm{rh}\lesssim 0.2\,\mathrm{GeV}$ for a lognormal power spectrum of the curvature perturbation. Furthermore, we compute Bayes factors to compare different models against the radiation domination model ($c_s^2 = w = 1/3$), effectively excluding the pressure-less fluid domination model. Our study underscores the significance of scalar-induced gravitational waves as a powerful tool to explore the nature of the early Universe.Comment: 22 pages, 3 figures, 2 table

Poly[(μ5-5-amino­isophthalato)aqua­barium]

In the title compound, [Ba(C8H5NO4)(H2O)]n, the BaII ion is eight-coordinated by six O atoms and one N atom from five 5-amino­isophthalate ligands and one water mol­ecule in a distorted dodeca­hedral geometry. The BaII ions are connected via the ligands into a layer parallel to (011). The layers are linked by N—H⋯O hydrogen bonds. The coordinated water mol­ecule is involved in intra­layer O—H⋯O hydrogen bonds