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Humanoid robots are expected to navigate in changing environments and perform a variety of tasks. Frequently, these tasks require the robot to make decisions online regarding the speed and precision of following a reference path. For example, a robot may want to decide to temporarily deviate from its path to overtake a slowly moving obstacle that shares the same path and is ahead. In this case, path following performance is compromised in favor of fast path traversal. Available global trajectory tracking approaches typically assume a given -- specified in advance -- time parametrization of the path and seek to minimize the norm of the Cartesian error. As a result, when the robot should be where on the path is fixed and temporary deviations from the path are strongly discouraged. Given a global path, this paper presents a Model Predictive Contouring Control (MPCC) approach to selecting footsteps that maximize path traversal while simultaneously allowing the robot to decide between faithful versus fast path following. The method is evaluated in high-fidelity simulations of the bipedal robot Digit in terms of tracking performance of curved paths under disturbances and is also applied to the case where Digit overtakes a moving obstacle., Comment: Accepted for publication in 2023 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)

A non-linear dispersion can significantly impact the Kondo problem, resulting in anomalous effects on electronic transport. By analyzing a special bath with a $\theta=\frac{\pi}{3}$ symmetry rotation in the Brillouin zone or 3-fold symmetry in momentum, we derive an effective spin-spin interacting model. Combining the anisotropic Dzyaloshinskii-Moriya (DM) interaction with non-linear dispersion can lead to exceptional points $(E_p)$ in a Hermitian model. Our RG analysis reveals that the spin relaxation time has the signature of coalescence in momentum-resolved couplings and an ideal logarithmic divergence in resistivity over a range of nonlinearity ($\beta$). The effective model at the impurity subspace has a Lie group structure of Dirac matrices. We show nontrivial renormalization within a Poorman approximation with the inclusion of potential scattering, and the invariant obtained will not be altered by potential scattering. We expand the model to a two-impurity Kondo model and investigate the Kondo destruction and anomalous spin transport signature by calculating the spin-relaxation time ($\tau$).Analysis of RG equations zeros and poles show a "Sign Reversion" regime exists for a Hermitian problem with a critical value of nonlinear coupling $J_{k^3}$. Our results show the existence of an out-of-phase RKKY oscillation above and below the critical value of the chemical potential., Comment: 20 pages, 15 figures

Narrow transient emission lines (flash-ionization features) in early supernova (SN) spectra trace the presence of circumstellar material (CSM) around the massive progenitor stars of core-collapse SNe. The lines disappear within days after the SN explosion, suggesting that this material is spatially confined, and originates from enhanced mass loss shortly (months to a few years) prior to explosion. We performed a systematic survey of H-rich (Type II) SNe discovered within less than two days from explosion during the first phase of the Zwicky Transient Facility (ZTF) survey (2018-2020), finding thirty events for which a first spectrum was obtained within $< 2$ days from explosion. The measured fraction of events showing flash ionisation features ($>36\%$ at $95\%$ confidence level) confirms that elevated mass loss in massive stars prior to SN explosion is common. We find that SNe II showing flash ionisation features are not significantly brighter, nor bluer, nor more slowly rising than those without. This implies that CSM interaction does not contribute significantly to their early continuum emission, and that the CSM is likely optically thin. We measured the persistence duration of flash ionisation emission and find that most SNe show flash features for $\approx 5 $ days. Rarer events, with persistence timescales $>10$ days, are brighter and rise longer, suggesting these may be intermediate between regular SNe II and strongly-interacting SNe IIn.

The Parity-Time $\mathcal{PT}$-symmetric non-Hermitian Sine-Gordon(nhSG) model derived from the nonequilibrium spin-boson model. We have derived the Keldysh rotation for spin operators, from which the SG model can be derived. We perform renormalization group calculations in the Keldysh fields and compare the fixed points and the flow of the effective couplings of nonequilibrium and non-Hermitian models. Also, we explicitly find the self-energies and compare the two methods to understand the regimes where $\mathcal{PT}$ symmetry preserved regime, and nonequilibrium regimes persist.RG flow of couplings of nonequilibrium model and non-hermitian model both capture the standard Berezinskii-Kosterlitz-Thouless(BKT) physics in a strong coupling regime.

Local quantum criticality in itinerant fermion systems has been extensively investigated through the soft-gap Anderson impurity model, wherein a localized, correlated impurity, hybridizes with a broad conduction band with a singular, $|\omega|^r$, density of states. However, lattice models hosting quantum critical points (QCPs), do not appear to have such a spectrum emerging at the QCP. In this work, we report the emergence of such a singular form of the density of states in a three-orbital lattice model, within dynamical mean field theory, precisely at a quantum critical point, separating a gapless, Fermi liquid, metallic phase from a gapped, Mott insulating phase. A temperature-dependent exponent, $\alpha$, defined using the corresponding Matsubara self-energy, is found to vary from $+1$ deep in the FL regime, to $-1$ in the Mott insulator regime. Interestingly, we find that $\alpha$ becomes temperature independent, and hence isosbestic, precisely at the QCP. The isosbestic exponent is shown to lead to an emergent soft-gap spectrum, $|\omega|^r$ at the QCP, where $r = |\alpha_{\rm iso}|$. We discuss the implications of our findings for non-Fermi liquid behaviour in the quantum critical region of the phase diagram., Comment: 16 pages, 16 figures

Power electronic devices such as HVDC and FACTS can be used to improve the damping of poorly damped inter-area modes in large power systems. This involves the use of wide-area feedback signals, which are transmitted via communication networks. The performance of the closed-loop system is strongly influenced by the delay associated with wide-area signals. The random nature of this delay introduces a switched linear system model. The stability assessment of such a system requires linear matrix inequality based approaches. This makes the stability analysis more complicated as the system size increases. To address this challenge, this paper proposes a delay-processing strategy that simplifies the modelling and analysis in discrete-domain. In contrast to the existing stability assessment techniques, the proposed approach is advantageous because the stability, as well as damping performance, can be accurately predicted by a simplified analysis. The proposed methodology is verified with a case study on the 2-area 4-machine power system with a series compensated tie-line. The results are found to be in accordance with the predictions of the proposed simplified analysis.

The non-interacting and non-Hermitian, parity-time ($\mathcal{PT}$)-symmetric Anderson model exhibits an exceptional point (EP) at a non-Hermitian coupling $g=1$, which remains unrenormalized in the presence of interactions (Lourenco et al, arXiv:1806.03116), where the EP was shown to coincide with the quantum critical point (QCP) for Kondo destruction. In this work, we consider a quantum dot hybridizing with metallic leads having Rashba spin-orbit coupling ($\lambda$). We show that for a non-Hermitian hybridization, $\lambda$ can renormalize the exceptional point even in the non-interacting case, stabilizing $\mathcal{PT}$-symmetry beyond $g=1$. Through exact diagonalization of a zero-bandwidth, three-site model, we show that the quantum critical point and the exceptional point bifurcate, with the critical point for Kondo destruction at $g_c=1$, and the exceptional coupling being $g_{\scriptscriptstyle{EP}} > 1$ for all $U\neq 0$ and $\lambda\geq 0; \lambda\neq U/2$. On the line $\lambda=U/2$, the critical point and the EP again coincide at $g_c=g_{\scriptscriptstyle{EP}}=1$. The full model with finite bandwidth leads is investigated through the slave-boson approach, using which we show that, in the strong coupling regime, $\lambda$ and interactions co-operate in strongly reducing the critical point associated with Kondo destruction, below the $\lambda=0$ value., Comment: 15 pages, 11 figures, 1 table

An arbitrary form of complex potential perturbation in an oscillator consists of many exciting questions in open quantum systems. These often provide valuable insights in a realistic scenario when a quantum system interacts with external environments. Action renormalization will capture the phase of the wave functions; hence we construct wave function from Bethe ansatz and Frobenius methods. The unitary and non-unitary regimes are discussed to connect with functional calculations. We present a functional renormalization calculation for a non-hermitian oscillator. A dual space Left-Right formulation is worked out in functional bosonic variables to derive the flow equation for scale dependent action. We show equivalence between vertex operator and permutation operators. The results can be compared with Wentzel Kramers Brillouin(WKB) calculation. We formally construct the Bosonic coherent states in the dual space;breaking symmetry will lead to anyonic coherent states. The limit cycle in renormalization trajectories for complex flow parameters, especially in extended, complex time limits indicates the need for revisiting the Bendixson theorem.

The increasing penetration of converter-interfaced distributed energy resources has brought out the need to develop decentralized criteria that would ensure the small-signal stability of the inter-connected system. Passivity of the D-Q admittance or impedance is a promising candidate for such an approach. It is facilitated by the inherent passivity of the D-Q impedance of an electrical network. However, the passivity conditions are generally restrictive and cannot be complied with in the low frequency range by the D-Q admittance of devices that follow typical power control strategies. However, this does not imply that the system is unstable. Therefore, alternative formulations that use polar variables (magnitude/phase angle of voltages and real/reactive power injection instead of the D-Q components of voltages and currents) are investigated. Passivity properties of the electrical network using these different formulations are brought out in this paper through analytical results and illustrative examples.