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Joonhee Kim

Publications and source records attributed to Joonhee Kim.

7 recordsLinked to original sources
arXiv2026

Motion-Specific Battery Health Assessment for Quadrotors Using High-Fidelity Battery Models

Quadrotor endurance is ultimately limited by battery behavior, yet most energy aware planning treats the battery as a simple energy reservoir and overlooks how flight motions induce dynamic current loads that accelerate battery degradation. This work presents an end to end framework for motion aware battery health assessment in quadrotors. We first design a wide range current sensing module to capture motion specific current profiles during real flights, preserving transient features. In parallel, a high fidelity battery model is calibrated using reference performance tests and a metaheuristic based on a degradation coupled electrochemical model.By simulating measured flight loads in the calibrated model, we systematically resolve how different flight motions translate into degradation modes loss of lithium inventory and loss of active material as well as internal side reactions. The results demonstrate that even when two flight profiles consume the same average energy, their transient load structures can drive different degradation pathways, emphasizing the need for motion-aware battery management that balances efficiency with battery degradation.

cs.RO↗
arXiv2022

Some Remarks on Kim-dividing in NATP Theories

In this note, we prove that Kim-dividing over models is always witnessed by a coheir Morley sequence in NATP theories. Following the strategy of Chernikov and Kaplan [8], we obtain some corollaries which hold in NATP theories. Namely, (i) if a formula Kim-forks over a model, then it quasi-divides over the same model, (ii) for any tuple of parameters $b$ and a model $M$, there exists a global coheir $p$ containing $\text{tp}(b/M)$ such that $B \ind^K_M b'$ for all $b'\models p|_{MB}$. We also show that for coheirs in NATP theories, condition (ii) above is a necessary condition for being a witness of Kim-dividing, assuming that a witness of Kim-dividing exists (see Definition 4.1 in this note). That is, if we assume that a witness of Kim-dividing always exists over any given model, then a coheir $p\supseteq \text{tp}(a/M)$ must satisfy (ii) whenever it is a witness of Kim-dividing of $a$ over a model $M$. We also give a sufficient condition for the existence of a witness of Kim-dividing in terms of pre-independence relations. At the end of the paper, we leave a short remark on Mutchnik's recent work [16]. We point out that the class of $\omega$-NDCTP$_2$ theories, a subclass of the class of NATP theories, contains all NTP$_2$ theories and NSOP$_1$ theories. We also note that Kim-forking and Kim-dividing are equivalent over models in $\omega$-NDCTP$_2$ theories, where Kim-dividing is defined with respect to invariant Morley sequences, instead of coheir Morley sequences as in [16].

math.LO↗
arXiv2022

Preservation of NATP

We prove several preservation theorems for NATP and furnish several examples of NATP. First, we prove preservation of NATP for the parametrization and sum of the theories of Fra\"{i}ss\'{e} limits of Fra\"{i}ss\'{e} classes satisfying strong amalgamation property. Second, we prove preservation of NATP for two kinds of dense/co-dense expansions, that is, the theories of lovely pairs and of H-structures for geometric theories and dense/co-dense expansion on vector spaces. Third, we prove preservation of NATP for the generic predicate expansion and the pair of an algebraically closed field and its distinguished subfield; for the latter, not only NATP, but also preservations of NTP$_1$ and NTP$_2$ are considered. Fourth, we present some proper examples of NATP using the results proved in this paper. Most of all, we show that the model companion of the theory of algebraically closed fields with circular orders (ACFO) is NATP.

math.LO↗
arXiv2021

On the Antichain Tree Property

In this note, we investigate a new model theoretical tree property, called the antichain tree property (ATP). We develop combinatorial techniques for ATP. First, we show that ATP is always witnessed by a formula in a single free variable, and for formulas, not having ATP is closed under disjunction. Second, we show the equivalence of ATP and $k$-ATP, and provide a criterion for theories to have not ATP (being NATP). Using these combinatorial observations, we find algebraic examples of ATP and NATP, including pure group, pure fields, and valued fields. More precisely, we prove Mekler's construction for groups, Chatzidakis' style criterion for PAC fields, and the AKE-style principle for valued fields preserving NATP. And we give a construction of an antichain tree in the Skolem arithmetic and atomless Boolean algebras.

math.LO↗
arXiv2020

SOP$_1$, SOP$_2$, and antichain tree property

In this paper, we study some tree properties and their related indiscernibilities. First, we prove that SOP$_2$ can be witnessed by a formula with a tree of tuples holding 'arbitrary homogeneous inconsistency' (e.g., weak k-TP$_1$ conditions or other possible inconsistency configurations). And we introduce a notion of tree-indiscernibility, which preserves witnesses of SOP$_1$, and by using this, we investigate the problem of (in)equality of SOP$_1$ and SOP$_2$. Assuming the existence of a formula having SOP$_1$ such that no finite conjunction of it has SOP$_2$, we observe that the formula must witness some tree-property-like phenomenon, which we will call the antichain tree property (ATP, see Definition 4.1). We show that ATP implies SOP$_1$ and TP$_2$, but the converse of each implication does not hold. So the class of NATP theories (theories without ATP) contains the class of NSOP$_1$ theories and the class of NTP$_2$ theories. At the end of the paper, we construct a structure whose theory has a formula having ATP, but any conjunction of the formula does not have SOP$_2$. So this example shows that SOP$_1$ and SOP$_2$ are not the same at the level of formulas, i.e., there is a formula having SOP$_1$, while any finite conjunction of it does not witness SOP$_2$ (but a variation of the formula still has SOP$_2$).

math.LO↗