arXiv subjects

Yuta Kimura

Publications and source records attributed to Yuta Kimura.

At least 19 recordsLinked to original sources

arXiv2026

A Physics-Regularized Neural Network and Kirchhoff Markov Random Field Framework for Inferring Internal Electrochemical States from Operando Spectromicroscopy

Quantitative understanding of coupled reaction and transport processes in lithium-ion battery (LIB) composite electrodes remains challenging because key internal states cannot be measured directly. In this study, we develop a physics-integrated, data-driven analysis pipeline to estimate internal electrochemical states from operando microscopic X-ray absorption fine structure ($μ$-XAFS) hyperspectral data of LIB cathodes with LiPF$_6$ electrolyte. State-of-charge (SOC) maps are first constructed from Co K-edge spectra. To resolve ambiguities in the two-phase reaction region, a physics-regularized three-layer neural network is introduced, enforcing spatial continuity of SOC and current conservation. The inferred SOC dynamics are then incorporated into a Kirchhoff-based Markov random field framework that integrates Kirchhoff's current and voltage laws, Ohm's law, and a symmetric Butler-Volmer relation to estimate interfacial current, ionic current, electrolyte potential, and effective ionic conductivity. Application to composite electrodes with different initial electrolyte concentrations (0.3, 1, and 2M LiPF$_6$) reveals distinct reaction propagation behaviors governed by electrolyte concentration-dependent conductivity. The inferred electrolyte concentration distributions show qualitative agreement with independent operando X-ray transmission imaging performed on LIB composite cathodes employing a LiAsF$_6$ electrolyte. This framework enables quantitative visualization of otherwise inaccessible internal transport phenomena.

physics.chem-ph↗

arXiv2026

Cohen-Macaulay representations of Artin-Schelter Gorenstein algebras of dimension one

Tilting theory is one of the central tools in modern representation theory, in particular in the study of Cohen-Macaulay representations. We study Cohen-Macaulay representations of $\mathbb N$-graded Artin-Schelter Gorenstein algebras $A$ of dimension one, without assuming the connectedness condition. This framework covers a broad class of noncommutative Gorenstein rings, including classical $\mathbb N$-graded Gorenstein orders. We prove that the stable category $\underline{\mathsf{CM}}_0^{\mathbb Z}A$ admits a silting object if and only if $A_0$ has finite global dimension. In this case we give such a silting object explicitly. Assuming that $A$ is ring-indecomposable, we further show that $\underline{\mathsf{CM}}_0^{\mathbb Z}A$ admits a tilting object if and only if either $A$ is Artin-Schelter regular or the average Gorenstein parameter of $A$ is non-positive. These results generalize those of Buchweitz, Iyama, and Yamaura. We give two proofs of the second result: one via Orlov-type semiorthogonal decompositions, and the other via a direct calculation. As an application, we show that for a Gorenstein tiled order $A$, the category $\underline{\mathsf{CM}}^{\mathbb Z}A$ is equivalent to the derived category of the incidence algebra of an explicitly constructed poset. We also apply our results and Koszul duality to study smooth noncommutative projective quadric hypersurfaces $\mathsf{qgr}\,B$ of arbitrary dimension. We prove that $\mathsf{D}^{\mathrm b}(\mathsf{qgr}\,B)$ admits an explicitly constructed tilting object, which contains the tilting object of $\underline{\mathsf{CM}}^{\mathbb Z}B$ due to Smith and Van den Bergh as a direct summand via Orlov's semiorthogonal decomposition.

math.RT↗

arXiv2025

Plasmon-enhanced ultrafast time-resolved spectroscopy of NV-containing diamond

We investigated ultrafast nonlinear optical effects in nitrogen-vacancy (NV)-containing diamond which is in contact with a gold-coated blazed diffraction grating using a pump-probe reflectivity technique. The reflectivity change caused by optical Kerr effect and two-photon absorption was enhanced several times because of the electric field enhancement induced by the propagating surface plasmon (PSP). Furthermore, by performing measurements with varying the incident angle of the pump beam and numerical simulations of the electric field using the Finite Difference Time Domain method, signal enhancement due to the PSP was confirmed both experimentally and theoretically. This study paves the way for applications based on enhanced nonlinear optical effects in diamond.

physics.optics↗

arXiv2025

Tilting theoretic approach to quasi-hereditary structures

A quasi-hereditary algebra is an algebra equipped with a certain partial order $\unlhd$ on its simple modules. Such a partial order -- called a quasi-hereditary structure -- gives rise to a characteristic tilting module $T_{\unlhd}$ by a classical result due to Ringel. A fundamental question is to determine which tilting modules can be realised as characteristic tilting modules. We answer this question by using the notion of IS-tilting module, which is a pair $(T,\unlhd)$ of a tilting module $T$ and a partial order $\unlhd$ on its direct summands such that iterative idempotent truncation along $\unlhd$ always reveals a simple direct summand. Specifically, we show that a tilting module $T$ is characteristic if, and only if, there is some $\unlhd$ so that $(T,\unlhd)$ is IS-tilting; in which case, we have $T=T_{\unlhd}$. This result enables us to study quasi-hereditary structures using tilting theory. As an application of the above result, we show that, for an algebra $A$, all tilting modules are characteristic if, and only if, $A$ is a quadratic linear Nakayama algebra. Furthermore, for such an $A$, we provide a decomposition of the set of its tilting modules that can be used to derive a recursive formula for enumerating its quasi-hereditary structures. Finally, we describe the quasi-hereditary structures of $A$ via `nodal gluing' and binary tree sequences.

math.RT↗

arXiv2025

Torsion classes of extended Dynkin quivers over commutative rings

For a Noetherian $R$-algebra $Λ$, there is a canonical inclusion $\mathsf{tors}Λ\to\prod_{\mathfrak{p}\in \mathrm{Spec} R}\mathsf{tors}(κ(\mathfrak{p})Λ)$, and each element in the image satisfies a certain compatibility condition. We call $Λ$ compatible if the image coincides with the set of all compatible elements. For example, for a Dynkin quiver $Q$ and a commutative Noetherian ring $R$ containing a field, the path algebra $RQ$ is compatible. In this paper, we prove that $RQ$ is compatible when $Q$ is an extended Dynkin quiver and $R$ is either a Dedekind domain or a Noetherian semilocal normal ring of dimension two.

math.RT↗

arXiv2025

Schur roots and tilting modules of acyclic quivers over commutative rings

Let $Q$ be a finite acyclic quiver and $A_Q$ the cluster algebra of $Q$. It is well-known that for each field $k$, the additive equivalence classes of support tilting $kQ$-modules correspond bijectively with the clusters of $A_Q$. The aim of this paper is to generalize this result to any ring indecomposable commutative Noetherian ring $R$, that is, the additive equivalence classes of 2-term silting complexes of $RQ$ correspond bijectively with the clusters of $A_Q$. As an application, for a Dynkin quiver $Q$, we prove that the torsion classes of $\mathrm{mod} RQ$ corresponds bijectively with the order preserving maps from $\mathrm{Spec} R$ to the set of clusters.

math.RT↗

arXiv2024

$τ$-tilting theory and silting theory of skew group algebra extensions

Let $Λ$ be a finite dimensional algebra with an action by a finite group $G$ and $A:= Λ*G$ the skew group algebra. One of our main results asserts that the canonical restriction-induction adjoint pair of the skew group algebra extension $Λ\subset A$ induces a poset isomorphism between the poset of $G$-stable support $τ$-tilting modules over $Λ$ and that of $(\!\!\!\mod G)$-stable support $τ$-tilting modules over $A$. We also establish a similar poset isomorphism of posets of appropriate classes of silting complexes over $Λ$ and $A$. These two results generalize and unify preceding results by Huang-Zhang, Breaz-Marcus-Modoi and the second and the third authors. Moreover, we give a practical condition under which $τ$-tilting finiteness and silting discreteness of $Λ$ are inherited to those of $A$. As applications we study $τ$-tilting theory and silting theory of the (generalized) preprojective algebras and the folded mesh algebras. Among other things, we determine the posets of support $τ$-tilting modules and of silting complexes over preprojective algebra $Π(\Bbb{L}_{n})$ of type $\Bbb{L}_{n}$.

math.RT↗

arXiv2023

Classifying subcategories of modules over Noetherian algebras

The aim of this paper is to unify classification theories of torsion classes of finite dimensional algebras and commutative Noetherian rings. For a commutative Noetherian ring $R$ and a module-finite $R$-algebra $Λ$, we study the set $\mathsf{tors} Λ$ (respectively, $\mathsf{torf}Λ$) of torsion (respectively, torsionfree) classes of the category of finitely generated $Λ$-modules. We construct a bijection from $\mathsf{torf}Λ$ to $\prod_{\mathfrak{p}} \mathsf{torf}(κ(\mathfrak{p}) \otimes_R Λ)$, and an embedding $Φ_{\rm t}$ from $\mathsf{tors} Λ$ to $\mathbb{T}_R(Λ):=\prod_{\mathfrak{p}} \mathsf{tors}(κ(\mathfrak{p}) \otimes_R Λ)$, where $\mathfrak{p}$ runs all prime ideals of $R$. When $Λ=R$, these give classifications of torsionfree classes, torsion classes and Serre subcategories of $\mathsf{mod} R$ due to Takahashi, Stanley-Wang and Gabriel. To give a description of $\mathrm{Im} Φ_{\rm t}$, we introduce the notion of compatible elements in $\mathbb{T}_R(Λ)$, and prove that all elements in $\mathrm{Im} Φ_{\rm t}$ are compatible. We give a sufficient condition on $(R, Λ)$ such that all compatible elements belong to $\mathrm{Im} Φ_{\rm t}$ (we call $(R, Λ)$ compatible in this case). For example, if $R$ is semi-local and $\dim R \leq 1$, then $(R, Λ)$ is compatible. We also give a sufficient condition in terms of silting $Λ$-modules. As an application, for a Dynkin quiver $Q$, $(R, RQ)$ is compatible and we have a poset isomorphism $\mathsf{tors} RQ \simeq \mathrm{Hom}_{\rm poset}(\mathrm{Spec} R, \mathfrak{C}_Q)$ for the Cambrian lattice $\mathfrak{C}_Q$ of $Q$.

math.RT↗

arXiv2023

Tilting theory for finite dimensional $1$-Iwanaga-Gorenstein algebras

In representation theory of graded Iwanaga-Gorenstein algebras, tilting theory of the stable category $\underline{\mathsf{CM}}^{\mathbb{Z}} A$ of graded Cohen-Macaulay modules plays a prominent role. In this paper we study the following two central problems of tilting theory of $\underline{\mathsf{CM}}^{\mathbb{Z}} A$ in the case where $A$ is finite dimensional: (1) Does $\underline{\mathsf{CM}}^{\mathbb{Z}} A$ have a tilting object? (2) Does the endomorphism algebras of tilting objects in $\underline{\mathsf{CM}}^{\mathbb{Z}} A$ have finite global dimension? To the problem (2) we give the complete answer. We show that the endomorphism algebra of any tilting object in $\underline{\mathsf{CM}}^{\mathbb{Z}}A$ has finite global dimension. To the problem (1) we give a partial answer. For this purpose, first we introduce an invariant $g(A)$ for a finite dimensional graded algebra $A$. Then, we prove that in the case where $A$ is 1-Iwanaga-Gorenstein, an inequality for $g(A)$ gives a sufficient condition that a specific Cohen-Macaulay module $V$ becomes a tilting object in the stable category. As an application, we study the existence of tilting objects in $\underline{\mathsf{CM}}^{\mathbb{Z}}Π(Q)_w$ where $Π(Q)_w$ is the truncated preprojective algebra of a quiver $Q$ associated to $w\in W_Q$. We prove that if the underling graph of $Q$ is tree, then $\underline{\mathsf{CM}}^{\mathbb{Z}}Π(Q)_w$ has a tilting object.

math.RT↗

arXiv2022

On deformed preprojective algebras

Deformed preprojective algebras are generalizations of the usual preprojective algebras introduced by Crawley-Boevey and Holland, which have applications to Kleinian singularities, the Deligne-Simpson problem, integrable systems and noncommutative geometry. In this paper we offer three contributions to the study of such algebras: (1) the 2-Calabi-Yau property; (2) the unification of the reflection functors of Crawley-Boevey and Holland with reflection functors for the usual preprojective algebras; and (3) the classification of tilting ideals in 2-Calabi-Yau algebras, and especially in deformed preprojective algebras for extended Dynkin quivers.

math.RT↗

arXiv2022

Tilting and silting theory of noetherian algebras

We develop silting theory of a noetherian algebra $Λ$ over a commutative noetherian ring $R$. We study mutation theory of $2$-term silting complexes of $Λ$, and as a consequence, we see that mutation exists. As in the case of finite dimensional algebras, functorially finite torsion classes of $Λ$ bijectively correspond to silting $Λ$-modules, if $R$ is complete local. We show a reduction theorem of $2$-term silting complexes of $Λ$, and by using this theorem, we study torsion classes of the module category of $Λ$. When $R$ has Krull dimension one, we describe the set of torsion classes of $Λ$ explicitly by using the set of torsion classes of finite dimensional algebras.

math.RT↗

arXiv2021

Combinatorics of quasi-hereditary structures

A quasi-hereditary algebra is an Artin algebra together with a partial order on its set of isomorphism classes of simple modules which satisfies certain conditions. In this article we investigate all the possible choices that yield to quasi-hereditary structures on a given algebra, in particular we introduce and study what we call the poset of quasi-hereditary structures. Our techniques involve certain quiver decompositions and idempotent reductions. For a path algebra of Dynkin type $\mathbb{A}$, we provide a full classification of its quasi-hereditary structures. For types $\mathbb{D}$ and $\mathbb{E}$, we give a counting method for the number of quasi-hereditary structures. In the case of a hereditary incidence algebra, we present a necessary and sufficient condition for its poset of quasi-hereditary structures to be a lattice.

math.RT↗

arXiv2021

Non-Negative Matrix Factorization for 2D-XAS Images of Lithium Ion Batteries

Lithium-ion secondary batteries have been used in a wide variety of purposes, such as for powering mobile devices and electric vehicles, but their performance should be improved. One of the factors that limits their performance is the non-uniformity of the chemical reaction in the process of charging and discharging. Many attempts have been made to elucidate the mechanism behind this reaction non-uniformity. In this paper, to detect non-uniformity in various physical properties from Co K-edge two-dimensional X-ray absorption spectroscopy (2D-XAS) images of lithium ion batteries, we propose a method that consists of one-sided orthogonal non-negative matrix factorization in combination with removal of the reference signal. The difference between X-ray absorption spectra acquired at different positions in the battery is very small. However, even in such a situation, our method can decompose the 2D-XAS data into different spatial domains and their corresponding absorption spectra. From the spectral decomposition of the obtained absorption spectra, we confirmed a transition-energy shift of the main peak as evidence for a change in the state of charge and also found spectral changes due to orbital hybridization in the decomposed spectral components.

physics.app-ph↗

arXiv2021

Evaluation of dynamic fracture toughness of a bonded bi-material interface subject to high-strain-rate shearing using digital image correlation

High-strain-rate shear tests were conducted on a three-layered bonded test piece comprising a central aluminum layer with PMMA resin layers bonded on both sides. Upon calculating the displacement field and the strain field using digital image correlation (DIC), the crack tip was located, and the fracture toughness was evaluated at the Aluminum/PMMA bonding interface. As a result of the DIC, it was possible to determine the process by which 1) the elastic stress wave propagated to the aluminum section, 2) the wave was transmitted to the PMMA section, and 3) the crack developed at the interface. The tip of the crack was identified using displacement distributions obtained using DIC. The fracture toughness of the interface was evaluated using the stress intensity factor. The true interfacial stress was calculated by correcting the strain value at the interface obtained using DIC. The distribution of the stress suggested that mode II fracture appears in the present test method when the crack is sufficiently shorter than the length of the bonding interface, and mode I and mode II fractures appear when the crack is longer in comparison. Although the value of the stress intensity factor was disturbed by the error of the DIC analysis, it was confirmed that the obtained values were similar regardless of the difference in the crack length, upon averaging the stress intensity factor values from the crack tips to the long-range with a ratio of 1 to the subset in DIC. As the obtained stress intensity factor value was similar to the values calculated in the related literature, it can be concluded that the method proposed in this study yields a reasonable stress intensity factor.

cond-mat.mtrl-sci↗

arXiv2019

Two-term tilting complexes for preprojective algebras of non-Dynkin type

In this paper, we study two-term tilting complexes for preprojective algebras of non-Dynkin type. We show that there exist two families of two-term tilting complexes, which are respectively parameterized by the elements of the corresponding Coxeter group. Moreover, we provide the complete classification in the case of affine type by showing that any two-term silting complex belongs one of them. For this purpose, we also discuss the Krull-Schmidt property for the homotopy category of finitely generated projective modules over a complete ring.

math.RT↗

arXiv2017

Tilting theory of preprojective algebras and $c$-sortable elements

For a finite acyclic quiver $Q$ and the corresponding preprojective algebra $Π$, we study the factor algebra $Π_w$ associated with a element $w$ in the Coxeter group introduced by Buan-Iyama-Reiten-Scott. The algebra $Π_w$ has a natural $\mathbb{Z}$-grading, and we prove that $\underline{\mathsf{Sub}}^{\mathbb{Z}}Π_w$ has a tilting object $M$. Moreover, we show that the endomorphism algebra of $M$ is isomorphic to the stable Auslander algebra of a certain torsion free class of $\mathsf{mod}\,kQ$.

math.RT↗

arXiv2017

Singularity categories of derived categories of hereditary algebras are derived categories

We show that for the path algebra $A$ of an acyclic quiver, the singularity category of the derived category $\mathsf{D}^{\rm b}(\mathsf{mod}\,A)$ is triangle equivalent to the derived category of the functor category of $\underline{\mathsf{mod}}\,A$, that is, $\mathsf{D}_{\rm sg}(\mathsf{D}^{\rm b}(\mathsf{mod}\,A))\simeq \mathsf{D}^{\rm b}(\mathsf{mod}(\underline{\mathsf{mod}}\,A))$. This extends a result of Iyama-Oppermann for the path algebra $A$ of a Dynkin quiver. An important step is to establish a functor category analog of Happel's triangle equivalence for repetitive algebras.

math.RT↗

arXiv2016

Tilting and cluster tilting for preprojective algebras and Coxeter groups

We study the stable category of the factor algebra of the preprojective algebra associated with an element $w$ of the Coxeter group of a quiver. We show that there exists a silting object $M(\bf{w})$ of this category associated with each reduced expression $\bf{w}$ of $w$ and give a sufficient condition on $\bf{w}$ such that $M(\bf{w})$ is a tilting object. In particular, the stable category is triangle equivalent to the derived category of the endomorphism algebra of $M(\bf{w})$. Moreover, we compare it with a triangle equivalence given by Amiot-Reiten-Todorov for a cluster category.

math.RT↗