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Hajime Tanaka

Publications and source records attributed to Hajime Tanaka.

At least 19 recordsLinked to original sources
arXiv2026

On the spherical design properties of a $P$- and $Q$-polynomial association scheme

We show that the strength as a spherical design of the spherical embedding of a $P$- and $Q$-polynomial association scheme with at least three classes with respect to a $Q$-polynomial idempotent is at most five, provided that the multiplicity is at least three. We also identify the examples that attain this upper bound on the strength. Our result improves on Suda's earlier upper bound of eight [J. Combin. Des. 19 (2011)], and is considered dual to the results of Lewis [Discrete Math. 223 (2000)] and Miklavič [Electron. J. Combin. 32 (2025)] concerning the girth of a $Q$-polynomial distance-regular graph with diameter and valency both at least three. To establish our upper bound, we introduce and discuss a polynomial method that works by constructing an appropriate polynomial that vanishes at every point of the spherical embedding.

math.CO↗
arXiv2026

A semidefinite programming approach to cross $2$-intersecting families

Let $k\geq 2$ and $n\geq 3(k-1)$. Let $\mathcal{F}$ and $\mathcal{G}$ be families of $k$-element subsets of an $n$-element set. Suppose that $|F\cap G|\geq 2$ for all $F\in\mathcal{F}$ and $G\in\mathcal{G}$. We show that $|\mathcal{F}||\mathcal{G}|\leq\binom{n-2}{k-2}^2$, and determine the extremal configurations. This settles the last unsolved case of a recent result by Zhang and Wu (J. Combin. Theory Ser. B, 2025). We also obtain the corresponding result in the product measure setting. Our proof is done by solving semidefinite programming problems.

math.CO↗
arXiv2026

Active motility and wetting cooperatively regulate liquid-liquid phase separation

Liquid--liquid phase separation in aqueous two-phase systems is fundamental across physical and biological sciences. While well understood for passive mixtures, how it is regulated by active agents such as motile bacteria remains largely unexplored. By combining experiments on Pseudomonas aeruginosa in a dextran--polyethylene glycol mixture with hydrodynamic simulations, we show that the coupling between bacterial activity and interfacial wetting converts self-propulsion into mechanically effective interfacial stresses, giving rise to a robust sequence of morphologies, including self-spinning droplets, elongated droplet chains, and branched capillary-like clusters. More importantly, it gives activity a dual kinetic role: activity suppresses coarsening in the droplet regime through rotation-induced hydrodynamic repulsion, but accelerates coarsening when dextran is the minority phase, where wetting-mediated attraction drives aggregation. To probe the biological relevance of this mechanism, we further show that a biofilm-associated protein can act as an interfacial ``wetting glue,'' promoting bacterial clustering even in dilute suspensions. Our findings establish activity--wetting coupling, rather than activity or wetting alone, as a mechanism by which active motility regulates pattern morphology and coarsening dynamics, and reveal a physical route to enhancing bacterial aggregation from dilute suspensions.

cond-mat.soft↗
arXiv2026

Wetting-coupled phase separation as an energetic mechanism for active bacterial adhesion

The rapid adhesion of motile bacteria from dilute suspensions poses a fundamental non-equilibrium problem: hydrodynamic interactions bias bacterial motion near surfaces without generating stable confinement, while electrostatic interactions are predominantly repulsive. Here, combining experiments on Pseudomonas aeruginosa and Staphylococcus aureus in a polyethylene glycol/dextran aqueous two-phase system with large-scale hydrodynamic simulations, we identify wetting-coupled liquid--liquid phase separation (LLPS) as an energetic trapping mechanism for bacterial adhesion. When bacteria partition into a phase that preferentially wets the substrate, interfacial free-energy minimization creates a deep energetic trap that stabilizes adhesion and induces lateral clustering via capillary interactions. Crucially, bacterial motility plays a dual role: at low phase volume fractions, activity enhances transport into the wetting layer and promotes accumulation, whereas at higher phase volumes it suppresses adhesion through the formation of self-spinning droplets that generate hydrodynamic lift opposing interfacial trapping. Our results establish wetting-coupled LLPS as a generic physical route governing interfacial organization in active suspensions. This provides a unified energetic framework for bacterial adhesion in complex fluids, with broad implications for deciphering bacterial-cell interactions and controlling biofilm formation.

cond-mat.soft↗
arXiv2025

Friction-controlled reentrant aging and fluidization in granular materials

Granular materials densify under repeated mechanical perturbations, a nonequilibrium dynamics that underlies many natural and industrial processes. Because granular relaxation is governed by frictional contacts and energy dissipation, this aging behavior fundamentally differs from that of thermal glasses despite their apparent similarities. Here, we uncover how friction controls the compaction dynamics of granular packings subjected to cyclic shear. Using discrete element simulations, we construct a dynamic state diagram as a function of strain amplitude and friction, revealing a rich interplay between jamming marginality, stabilization, and fluidization. We identify a friction-dependent crossover strain that separates aging and fluidized regimes, showing reentrant, non-monotonic behavior: Increasing friction first suppresses fluidization, then promotes it through smooth, creep-like rearrangements. This transition is marked by a shift from intermittent, avalanche-like rearrangements to continuous, diffusive motion. Our findings demonstrate that friction exerts a dual role in granular aging -- both stabilizing and fluidizing -- thereby uncovering the fundamental nonequilibrium mechanisms that govern compaction, rheology, and aging in athermal disordered systems. More broadly, our results reveal a general principle for how friction governs metastability and flow in athermal matter -- from granular and frictional colloids to soils and seismic faults -- linking microscopic contact mechanics to macroscopic dynamics.

cond-mat.soft↗
arXiv2025

Burning numbers via eigenpolytopes -- Hamming graphs, Johnson graphs, and halved cubes

We give lower and upper bounds on the burning number of Hamming graphs, Johnson graphs, and halved cube graphs. For the lower bounds, we use the fact that $1$-skeletons of the eigenpolytopes of these graphs are isomorphic to the original graphs. Then, we present a dynamic search algorithm performed on the eigenpolytope to find an unburned vertex. This idea was originally used by Alon (Discrete Appl.\ Math.,\ 1992), who determined the burning number of the hypercube graphs.

math.CO↗
arXiv2025

Acceleration Theorem for Low-Dimensional Electron Systems with Off-Diagonal Effective Mass Components

The motion of electrons under homogeneously applied electric fields in low-dimensional systems with non-zero off-diagonal effective mass (ODEM) is studied. The equation describing the time evolution of a probability coefficient of finding an electron in a subband is derived using the Krieger-Iafrate theory in the effective mass approximation. It is shown that an electron can change subbands during free flight due to the ODEM-induced inter-subband transitions. By introducing an effective dispersion defined as a weighted average of the subband dispersions, it is also shown that the initial acceleration of an electron effectively follows the bulk dispersion relation. The results obtained suggest that the transport properties of the quantized systems when many subbands are occupied in the weak confinement limit approach the values one would find without considering the quantization.

physics.app-ph↗
arXiv2025

Disentangling hierarchical relaxations in glass formers via dynamic eigenmodes

Hierarchical dynamics in glass-forming systems span multiple timescales, from fast vibrations to slow structural rearrangements, appearing in both supercooled fluids and glassy states. Understanding how these diverse processes interact across timescales remains a central challenge. Here, by combining direct particle-level observations with a dynamic eigenmode approach that decomposes intermediate-timescale responses into distinct modes, we reveal the microscopic organisation of relaxation dynamics in two-dimensional colloidal systems. We identify five classes of modes characterizing hierarchical dynamics: (i) quasi-elastic modes, (ii) slow-reversible string modes contributing to dynamic heterogeneity, (iii) slow-irreversible string modes leading to flow, (iv) fast-$β$ modes with fast-reversible strings, and (v) random noise modes. The emergence of quasi-elastic modes marks the onset of glassy dynamics, while reversible string modes dominate dynamic heterogeneity throughout both supercooled and glassy regimes. Our findings offer a unified microscopic framework for understanding how distinct relaxation processes interconnect across timescales, illuminating the mechanisms driving glass formation.

cond-mat.soft↗
arXiv2025

Unraveling the impact of competing interactions on non-equilibrium colloidal gelation

Competing interactions stabilize exotic mesoscopic structures, yet the microscopic mechanisms by which they influence non-equilibrium processes leading to disordered states remain largely unexplored, despite their critical role in self-assembly across a range of nanomaterials and biological systems. Here, we numerically investigate the structural evolution in charged colloidal model systems, where short-range attractions and long-range repulsions compete. We reveal that these two interaction scales drive sequential ordering within clusters, from tetrahedra motifs to linear aggregates with chiral order. This process disrupts early-stage percolated networks, resulting in reentrant behavior -- a dynamic transition from disordered cluster to network to chiral rigid cluster. On the other hand, the cluster-elastic network boundary in the final state is governed by isostatic percolation, which slows structural rearrangements, preserves branching points, and sustains a long-lived network. The resulting structure consist of rigid Bernal spiral-like branches connected through flexible branching points lacking order. These insights advance our microscopic understanding of out-of-equilibrium ordering driven by competing interactions, particularly phenomena like temporally delayed frustration reflecting different length scales of competing interactions. The mechanisms identified here may play a crucial role in mesoscale self-organization across soft materials, from nanoparticle assemblies to biological gels and cytoskeletal networks. Understanding how competing interactions regulate structure and dynamics could guide the design of adaptive materials with tunable mechanical properties and offer new perspectives on biological processes such as cytoplasmic organization and cellular scaffolding.

cond-mat.soft↗
arXiv2024

Network-forming phase separation of oppositely charged polyelectrolytes forming coacervates in a solvent

The formation of coacervates through phase separation of oppositely charged polyelectrolytes (PEs) is critical for understanding biological condensates and developing responsive materials. Traditionally, coacervates are viewed as spherical droplets with growth dynamics resembling liquid-liquid phase separation. However, our fluid particle dynamics simulations incorporating hydrodynamic and electrostatic interactions challenge this perspective. Here, we find that oppositely charged PEs form a percolated network even in semi-dilute solutions, coarsening with a unique growth law, $\ell \propto t^{1/2}$. This self-similarity, absent for neutral polymers in poor solvents, arises because PEs in good solvents exhibit weaker, longer-range attractions due to spatial charge inhomogeneity under global charge neutrality. This results in a lower density of the PEs-rich phase and reduced interfacial tension. Increased charge asymmetry further slows network coarsening. Additionally, coacervate droplets initially display irregular shapes due to weak interfacial tension, transitioning slowly to spherical forms. Our research provides new insights into coacervate morphology and coarsening dynamics.

cond-mat.soft↗
arXiv2024

Ideal noncrystals: A possible new class of ordered matter without apparent broken symmetry

Order and disorder constitute two fundamental and opposite themes in condensed matter physics and materials science. Crystals are considered the epitome of order, characterised by long-range translational order. The discovery of quasicrystals, which exhibit rotational symmetries forbidden in crystals and lack periodicity, led to a paradigm shift in solid-state physics. Moving one step forward, it is intriguing to ask whether ordered matter can exist without apparent symmetry breaking. The same question arises considering how ordered amorphous (noncrystalline) solids can be structured. Here, we present the discovery of ideal noncrystals in two dimensions, which are disordered in the conventional sense, lacking Bragg peaks, but exhibit high orderliness based on the steric order, i.e., they are ideally packed. A path-integral-like scheme reveals the underlying long-range structural correlation. We find that these ideal noncrystals are characterised by phononic vibrational modes following the Debye law, fully affine elastic responses, and suppressed density fluctuations at longer wavelengths, reminiscent of hyperuniformity -- all characteristics typically associated with crystals. Therefore, ideal noncrystals represent a peculiar form of matter with a mixed nature -- noncrystalline yet possessing crystal-like properties. Notably, these states are found to be thermodynamically favourable, indicating them as a possible new class of ordered matter without apparent symmetry breaking. Our findings significantly broaden the conceptualization of ordered states of matter and may contribute to a deeper understanding of entropy-driven ordering, particularly in generic amorphous materials.

cond-mat.soft↗
arXiv2024

Online Photon Guiding with 3D Gaussians for Caustics Rendering

In production rendering systems, caustics are typically rendered via photon mapping and gathering, a process often hindered by insufficient photon density. In this paper, we propose a novel photon guiding method to improve the photon density and overall quality for caustic rendering. The key insight of our approach is the application of a global 3D Gaussian mixture model, used in conjunction with an adaptive light sampler. This combination effectively guides photon emission in expansive 3D scenes with multiple light sources. By employing a global 3D Gaussian mixture, our method precisely models the distribution of the points of interest. To sample emission directions from the distribution at any observation point, we introduce a novel directional transform of the 3D Gaussian, which ensures accurate photon emission guiding. Furthermore, our method integrates a global light cluster tree, which models the contribution distribution of light sources to the image, facilitating effective light source selection. We conduct experiments demonstrating that our approach robustly outperforms existing photon guiding techniques across a variety of scenarios, significantly advancing the quality of caustic rendering.

cs.GR↗
arXiv2024

The real equiangular tight frames obtained from rank $3$ graphs

We present all nontrivial real equiangular tight frames $\{φ_m\}_{m=1}^M$ in $\mathbb{R}^N$ obtained as spherical embeddings of primitive rank $3$ graphs on $M$ vertices, and those such that one of their associated $M$ strongly regular graphs on $M-1$ vertices is a primitive rank $3$ graph.

math.CO↗
arXiv2024

Online Neural Path Guiding with Normalized Anisotropic Spherical Gaussians

The variance reduction speed of physically-based rendering is heavily affected by the adopted importance sampling technique. In this paper we propose a novel online framework to learn the spatial-varying density model with a single small neural network using stochastic ray samples. To achieve this task, we propose a novel closed-form density model called the normalized anisotropic spherical gaussian mixture, that can express complex irradiance fields with a small number of parameters. Our framework learns the distribution in a progressive manner and does not need any warm-up phases. Due to the compact and expressive representation of our density model, our framework can be implemented entirely on the GPU, allowing it produce high quality images with limited computational resources.

cs.CV↗
arXiv2024

Multimarked Spatial Search by Continuous-Time Quantum Walk

The quantum-walk-based spatial search problem aims to find a marked vertex using a quantum walk on a graph with marked vertices. We describe a framework for determining the computational complexity of spatial search by continuous-time quantum walk on arbitrary graphs by providing a recipe for finding the optimal running time and the success probability of the algorithm. The quantum walk is driven by a Hamiltonian derived from the adjacency matrix of the graph modified by the presence of the marked vertices. The success of our framework depends on the knowledge of the eigenvalues and eigenvectors of the adjacency matrix. The spectrum of the Hamiltonian is subsequently obtained from the roots of the determinant of a real symmetric matrix $M$, the dimensions of which depend on the number of marked vertices. The eigenvectors are determined from a basis of the kernel of $M$. We show each step of the framework by solving the spatial searching problem on the Johnson graphs with a fixed diameter and with two marked vertices. Our calculations show that the optimal running time is $O(\sqrt{N})$ with an asymptotic probability of $1+o(1)$, where $N$ is the number of vertices.

quant-ph↗
arXiv2023

Crystal nucleation in a vapor deposited Lennard-Jones mixture

Understanding the pathways to crystallization during the deposition of a vapor phase on a cold solid substrate is of great interest in industry, e.g., for the realization of electronic devices made of crystallites-free glassy materials, as well as in the atmospheric science in relation to ice nucleation and growth in clouds. Here we numerically investigate the nucleation process during the deposition of a glassformer by using a Lennard-Jones mixture, and compare the properties of this nucleation process with both its quenched counterpart and the bulk system. We find that all three systems homogeneously nucleate crystals in a narrow range of temperatures. However, the deposited layer shows a peculiar formation of ordered domains, promoted by the faster relaxation dynamics toward the free surface even in an as-deposited state. In contrast, the formation of such domains in the other systems occurs only when the structures are fully relaxed by quenching. Furthermore, the nucleus initially grows in an isotropic symmetrical manner, but eventually shows sub-3D growth due to its preference to grow along the basal plane, irrespective of the layer production procedure.

cond-mat.soft↗
arXiv2023

From ultra-fast growth to avalanche growth in devitrifying glasses

During devitrification, pre-existing crystallites grow by adding particles to their surface via a process that is either thermally activated (diffusive mode) or happens without kinetic barriers (fast crystal growth mode). It is yet unclear what factors determine the crystal growth mode and how to predict it. With simulations of repulsive hard-sphere-like (Weeks-Chandler-Andersen) glasses, we show for the first time that the same system at the same volume fraction and temperature can devitrify via both modes depending on the preparation protocol of the glass. We prepare two types of glass, a conventional glass (CG) via fast quenching and a uniform glass (UG) via density homogenization. Firstly, we bring either glass into contact with a crystal (X) and find the inherent structure (CGX/UGX). During energy minimization, the crystal front grows deep into the CG interface, while the growth is minimal for UG. When thermal noise is added, this behavior is reflected in different crystallization dynamics. CGX exhibits a density drop at the crystal growth front which correlates with enhanced dynamics at the interface and a fast growth mode. This mechanism may explain the faster crystal growth observed below the glass transition experimentally. In contrast, UGX grows via intermittent avalanche-like dynamics localized at the interface, a combination of localized mechanical defects and the exceptional mechanical stability imposed by the UG glass phase.

cond-mat.soft↗