arXiv subjects
Publications and source records attributed to Yuta Takahashi.
For a $p$-adic field of any residual characteristic, we determine irreducible decompositions of the Weil representation restricted to the maximal open compact subgroups and the Iwahori subgroup by using the Schrödinger model. In particular, these decompositions show that the restrictions are multiplicity free.
We classify rank $2$ weak Fano bundles on a four-dimensional smooth quadric hypersurface $Q^4$. Up to twisting with a line bundle, such a bundle is either a split bundle, a spinor bundle, or one of the stable bundles with Chern classes $c_1=-1$ and $c_2=(1,1)$ constructed in [APW94].
We investigate photothermal effects in monolayer transition metal dichalcogenides (TMDCs) integrated with an ultrahigh-Q silica microcavity. Launching a continuous-wave laser into a cavity resonance enables controlled intracavity heating, allowing direct observation of excitonic photoluminescence (PL) modulation. A distinct redshift of the PL peak energy is observed as the pump wavelength is tuned across resonance. This behavior is quantitatively reproduced by a temperature-dependent bandgap model that combines the Varshni relation with the thermo-optic response of the microcavity, from which the local temperature rise can be estimated. We further find that PL collected through a fiber waveguide exhibits spectral and temporal characteristics markedly different from free-space emission, indicating selective coupling of the microcavity to specific excitonic channels. These results provide a quantitative framework for understanding photothermal effects in TMDC-microcavity hybrid systems and offer a versatile approach for all-optical control and probing of thermal states in integrated nanophotonic devices.
We give a lower bound on the Ulrich complexity of hypersurfaces in terms of their dimension.
We study smooth polarized projective varieties $(X,H)$ whose exterior powers of the tangent bundle are Ulrich. We prove that if $\bigwedge^rT_X$ is $H$-Ulrich for some $0<r<\dim X$, then $X$ is Fano and the intersection number $(-K_X)\cdot H^{n-1}$ is determined explicitly. We then classify the Picard number one case: the only example is the Veronese surface $(\mathbb P^2,\mathcal O_{\mathbb P^2}(2))$.
A vector bundle whose projectivization becomes a weak Fano variety is called a weak Fano bundle. We present classification results for rank 2 weak Fano bundles on higher-dimensional quadrics $Q^n$ of dimension $\ge 5$.
Distributed space antennas using electromagnetic formation flight (EMFF) are a promising architecture for large-aperture, long-life space communication systems. Their feasible aperture, however, is governed by coupled constraints on antenna performance, satellite mass, power generation, coil geometry, and formation-keeping power. This paper proposes a system-level design framework for EMFF-based distributed space antennas. It links phased-array requirements with satellite-level sizing constraints and provides a static grid-based reference for designing feasible apertures under a fixed system mass. Unlike our previous bucket-brigade disturbance-compensation model, the formation-maintenance requirement is incorporated through a control index derived from distributed-control simulations. This index is integrated into an antenna-aperture maximization problem with sizing, power, coil, and sidelobe-envelope constraints. Parametric case studies examine margin magnetic moment, prescribed transmit power, and large inter-satellite spacing. Results show that increasing system mass improves footprint reduction or effective isotropic radiated power only while satellite-level design headroom remains. In direct-to-device cases with 0.15 m spacing, generated-power and coil-geometry constraints dominate the feasible aperture. In the 0.60 m large-spacing case, the required coil burden can exceed satellite-level mass, size, and power capacities, making the design infeasible despite favorable communication performance. The proposed framework enables the design and evaluation of feasible static grid-based EMFF distributed antennas under coupled antenna, satellite, and control constraints.
This correspondence presents a convex-optimization-based evaluation framework of satellite-swarm-based apertures maintained by magnetic-field interactions. Spaceborne distributed apertures are composed of multiple satellites and are attractive for scientific and commercial missions because their scalability enables high-gain, narrow-beam, and large-aperture capabilities beyond the launch-size limitations. A key challenge is that the long-term maintenance of such virtual structures requires consistent formation control amid unstable orbital dynamics, and magnetic interactions generated by satellite-mounted magnetorquers offer a desirable propellant-free position-control strategy. However, the nonlinearities of the electromagnetic force and torque model lead to a nonconvex power-consumption constraint, making system-level configuration analysis difficult. To address this issue, we develop a convex optimization-based framework to analyze the power consumption of large magnetically actuated satellite swarms. The resulting analysis shows that increasing the number of satellites can improve formation-keeping power efficiency. This indicates that magnetically actuated swarm architectures provide a power-efficient alternative to the conventional few-satellite electromagnetic formation-flight concept for constructing large-scale space systems.
This paper presents a learning-based current calculation model to achieve power-optimal magnetic-field interaction for multi-agent formation and attitude control. In aerospace engineering, electromagnetic coils are referred to as magnetorquer (MTQ) coils and used as satellite attitude actuators in Earth's orbit and for long-term formation and attitude control. This study derives a unique, continuous, and power-optimal current solution via sequential convex programming and approximates it using a multilayer perceptron model. The effectiveness of our strategy was demonstrated through numerical simulations and experimental trials on the formation and attitude control.
High-speed modulation and deterministic control of optical nonlinear processes in nanomaterials are essential for realizing future nanoscale optoelectronic devices. Applying strain is a ubiquitous and versatile approach to deform atomically thin materials, allowing direct modification of their electronic and optical properties. Yet, strain engineering of nonlinear processes has so far relied predominantly on static approaches, which inherently limit modulation speed, reproducibility, and device scalability. Here, we demonstrate ultrafast acoustic modulation of second-harmonic (SH) generation in monolayer transition metal dichalcogenides using surface acoustic waves (SAWs). By employing a fully phase-synchronized SH measurement combined with stroboscopic surface displacement detection, we directly visualize dynamic SH modulation at a frequency of 226 MHz. Moreover, theoretical modeling and determination of photoelastic coefficients enable quantitative extraction of the SAW-induced dynamic strain. Our results establish a direct link between acoustic fields and optical nonlinearities, providing a robust platform for dynamic strain engineering in two-dimensional nanophotonic devices.
This paper presents a learning-based framework for approximating an exact magnetic-field interaction model, supported by both numerical and experimental validation. High-fidelity magnetic-field interaction modeling is essential for achieving exceptional accuracy and responsiveness across a wide range of fields, including transportation, energy systems, medicine, biomedical robotics, and aerospace robotics. In aerospace engineering, magnetic actuation has been investigated as a fuel-free solution for multi-satellite attitude and formation control. Although the exact magnetic field can be computed from the Biot-Savart law, the associated computational cost is prohibitive, and prior studies have therefore relied on dipole approximations to improve efficiency. However, these approximations lose accuracy during proximity operations, leading to unstable behavior and even collisions. To address this limitation, we develop a learning-based approximation framework that faithfully reproduces the exact field while dramatically reducing computational cost. This framework directly derives a coefficient matrix that maps inter-satellite current vectors to the resulting forces and torques, enabling efficient computation of control current commands. The proposed method additionally provides a certified error bound, derived from the number of training samples, ensuring reliable prediction accuracy. The learned model can also accommodate interactions between coils of different sizes through appropriate geometric transformations, without retraining. To verify the effectiveness of the proposed framework under challenging conditions, a spacecraft docking scenario is examined through both numerical simulations and experimental validation.
In the initial deployment of large-scale distributed space systems using small satellites, achieving a reliable transition to passively stable orbits while maintaining inter-satellite distances within effective control and communication ranges is crucial, particularly given the presence of deployment errors and uncontrolled coasting phases. This study presents a framework for designing formation initialization that provides probabilistic safety guarantees. The scope covers the initial deployment phase, from sequential release by a single carrier to commissioning, control activation, and transition to passive stabilization. Strict separation limits during initialization necessitate low release velocities to minimize relative drift before control activation. However, in the low-velocity regime, the allowable tolerances for release velocity and angular rate errors tighten significantly to satisfy distance constraints, making hardware requirements a critical bottleneck. To address this, we model the initialization sequence as a stochastic process and derive closed-form constraints on deployment errors and control activation intervals. These conditions ensure that inter-satellite distances remain within the allowable separation limit with a prescribed probability. Monte Carlo simulations, configured using the error bounds and intervals derived from the proposed constraints, demonstrate that inter-satellite distances are successfully maintained within the allowable range. The proposed framework enables the safe initialization of large-scale distributed space systems by translating strict separation constraints into quantifiable hardware requirements.
Electromagnetic Formation Flight is a technology that uses electromagnetic forces and torques to control multiple satellites without conventional fuel-based propulsion. In this paper, the controllability of the system is discussed based on the conservation of the entire system's angular momentum, which constitutes a nonholonomic constraint. This paper designs a new controller for multiple satellites without an additional attitude actuator.
Electromagnetic formation flight (EMFF) uses the electromagnetic force to control the relative positions of multiple satellites without using conventional fuel-based propulsion. To compensate for the electromagnetic torque generated alongside the electromagnetic force, in most previous studies, all satellites were assumed to have reaction wheels (RWs) besides electromagnetic coils. However, the RW-loaded angular momentum becomes non-uniformly distributed among the satellites, because the electromagnetic torque usually differs between satellites. Without a proper control scheme, this deviation increases over time, and the RWs become saturated quickly, preventing the attitudes of the satellites from being controlled. In this study, a new controller is proposed that enables the electromagnetic force and torque to be controlled simultaneously. The EMFF kinematics derived from the conservation of angular momentum are used for the controller design. This controller can control $n$ satellites without saturating the RWs, and only one set of RWs is required among all satellites. The combination of the proposed controller with a simple unloading control exclusive to the chief satellite results in the elimination of the accumulation of angular momentum in the entire system. The effectiveness of the proposed controller is demonstrated through numerical simulations of the formation maintenance and formation reconfiguration of a five-satellite system.
This paper presents an autonomous guidance and control strategy for a satellite swarm that enables scalable distributed space structures for innovative science and business opportunities. The averaged $J_2$ orbital parameters that describe the drift and periodic orbital motion were derived along with their target values to achieve a distributed space structure in a decentralized manner. This enabled the design of a distance-based orbital stabilizer to ensure autonomous deployment into a monolithic formation of a coplanar equidistant configuration on a user-defined orbital plane. Continuous formation control was assumed to be achieved through fuel-free actuation, such as satellite magnetic field interaction and differential aerodynamic forces, thereby maintaining long-term formation stability without thruster usage. A major challenge for such actuation systems is the potential loss of control capability due to increasing inter-satellite distances resulting from unstable orbital dynamics, particularly for autonomous satellite swarms. To mitigate this risk, our decentralized deployment controller minimized drift distance during unexpected communication outages. As a case study, we consider the deployment of palm-sized satellites into a coplanar equidistant formation in a $J_2$-perturbed orbit. Moreover, centralized grouping strategies are presented.
Rathjen proved that Aczel's constructive set theory $\mathbf{CZF}$ extended with inaccessible sets of all transfinite orders can be interpreted in Martin-Löf type theory $\mathbf{MLTT}$ extended with Setzer's Mahlo universe and another universe above it. In this paper we show that this interpretation can be carried out bottom-up without the universe above the Mahlo universe, provided we add an accessibility predicate instead. If we work in Martin-Löf type theory with extensional identity types the accessibility predicate can be defined in terms of $\mathrm{W}$-types. The main part of our interpretation has been formalised in the proof assistant Agda.
This study experimentally validates the principle of large-scale satellite swarm control through learning-aided magnetic field interactions generated by satellite-mounted magnetorquers. This actuation presents a promising solution for the long-term formation maintenance of multiple satellites and has primarily been demonstrated in ground-based testbeds for two-satellite position control. However, as the number of satellites increases beyond three, fundamental challenges coupled with the high nonlinearity arise: 1) nonholonomic constraints, 2) underactuation, 3) scalability, and 4) computational cost. Previous studies have shown that time-integrated current control theoretically solves these problems, where the average actuator outputs align with the desired command, and a learning-based technique further enhances their performance. Through multiple experiments, we validate critical aspects of learning-aided time-integrated current control: (1) enhanced controllability of the averaged system dynamics, with a theoretically guaranteed error bound, and (2) decentralized current management. We design two-axis coils and a ground-based experimental setup utilizing an air-bearing platform, enabling a mathematical replication of orbital dynamics. Based on the effectiveness of the learned interaction model, we introduce NODA-MMH (Neural power-Optimal Dipole Allocation for certified learned Model-based Magnetically swarm control Harness) for model-based power-optimal swarm control. This study complements our tutorial paper on magnetically actuated swarms for the long-term formation maintenance problem.
We introduce a new topology for weakly supervised anomaly detection searches, di-object plus~X. In this topology, one looks for a resonance decaying to two standard model particles produced in association with other anomalous event activity (X). This additional activity is used for classification. We demonstrate how anomaly detection techniques which have been developed for di-jet searches focusing on jet substructure anomalies can be applied to event-level anomaly detection in this topology. To robustly capture event-level features of multi-particle kinematics, we employ new physically motivated variables derived from the geometric structure of a collision's phase space manifold. As a proof of concept, we explore the application of this approach to several benchmark signals in the di-$τ$ and di-$μ$ plus~X final states. We demonstrate that our anomaly detection approach can reach discovery-level significances for signals that would be missed in a conventional bump-hunt approach.