arXiv subjects

Hajime Tanaka

Publications and source records attributed to Hajime Tanaka.

At least 37 records · Page 2Linked to original sources

arXiv2023

Distinct elastic properties and their origins in glasses and gels

Glasses and gels, widely encountered amorphous solids with diverse industrial and everyday applications, share intriguing similarities such as rigidity without crystalline order and dynamic slowing down during aging. However, the underlying differences between these two fascinating materials have remained elusive. Here we uncover distinct elastic properties concerning observation and aging times in glasses and gels, while delving into the underlying mechanisms. In glasses, we observe a gradual decrease in the shear modulus, while the bulk modulus remains constant throughout the observation time. In contrast, gels exhibit a decrease in both the shear and bulk moduli over the observation time. Additionally, during aging, glasses exhibit a steady trend of stiffening, while gels demonstrate initial stiffening followed by softening. By unravelling the intricate relationship between structure, dynamics, and elasticity, we attribute these differences to mechanisms that minimize free energy: structural ordering in glasses and interface reduction in gels. Our work not only uncovers the distinct behaviors of glasses and gels but also sheds light on the origin and evolution of elasticity in non-equilibrium disordered solids, offering significant implications for the application and design of amorphous materials.

cond-mat.soft↗

arXiv2023

Characterizing graphs with fully positive semidefinite $Q$-matrices

For $q\in\mathbb{R}$, the $Q$-matrix $Q=Q_q$ of a connected simple graph $G=(V,E)$ is $Q_q=(q^{\partial(x,y)})_{x,y\in V}$, where $\partial$ denotes the path-length distance. Describing the set $π(G)$ consisting of those $q\in \mathbb{R}$ for which $Q_q$ is positive semidefinite is fundamental in asymptotic spectral analysis of graphs from the viewpoint of quantum probability theory. Assume that $G$ has at least two vertices. Then $π(G)$ is easily seen to be a nonempty closed subset of the interval $[-1,1]$. In this note, we show that $π(G)=[-1,1]$ if and only if $G$ is isometrically embeddable into a hypercube (infinite-dimensional if $G$ is infinite) if and only if $G$ is bipartite and does not possess certain five-vertex configurations, an example of which is an induced $K_{2,3}$.

math.CO↗

arXiv2022

Roles of liquid structural ordering in glass transition, crystallization, and water's anomalies

The liquid state is one of the fundamental and essential states of matter, but its physical understanding is far behind the other states, such as the gas and solid states, due to the difficulties associated with the high density causing many-body correlations and the lack of long-range order. Significant open problems in liquid science include glass transition, crystallization, and water's anomalies. Austen Angell has contributed tremendously to these problems and proposed many new concepts of fundamental importance. In this article, we review how these concepts have influenced our work on liquid physics, focusing on the roles of liquid structural ordering in glass transition, crystallization, and water's anomalies.

cond-mat.soft↗

arXiv2021

A duality of scaffolds for translation association schemes

Scaffolds are certain tensors arising in the study of association schemes, and have been (implicitly) understood diagrammatically as digraphs with distinguished "root" nodes and with matrix edge weights, often taken from Bose-Mesner algebras. In this paper, we first present a slight modification of Martin's conjecture (2021) concerning a duality of scaffolds whose digraphs are embedded in a closed disk in the plane with root nodes all lying on the boundary circle, and then show that this modified conjecture holds true if we restrict ourselves to the class of translation association schemes, i.e., those association schemes that admit abelian regular automorphism groups.

math.CO↗

arXiv2021

Spatial Search on Johnson Graphs by Discrete-Time Quantum Walk

The spatial search problem aims to find a marked vertex of a finite graph using a dynamic with two constraints: (1) The walker has no compass and (2) the walker can check whether a vertex is marked only after reaching it. This problem is a generalization of unsorted database search and has many applications to algorithms. Classical algorithms that solve the spatial search problem are based on random walks and the computational complexity is determined by the hitting time. On the other hand, quantum algorithms are based on quantum walks and the computational complexity is determined not only by the number of steps to reach a marked vertex, but also by the success probability, since we need to perform a measurement at the end of the algorithm to determine the walker's position. In this work, we address the spatial search problem on Johnson graphs using the coined quantum walk model. Since Johnson graphs are vertex- and distance-transitive, we have found an invariant subspace of the Hilbert space, which aids in the calculation of the computational complexity. We have shown that, for every fixed diameter, the asymptotic success probability is $1/2$ after taking $π\sqrt N/(2\sqrt 2)$ steps, where $N$ is the number of vertices of the Johnson graph.

quant-ph↗

arXiv2021

Scaling Limits for the Gibbs States on Distance-Regular Graphs with Classical Parameters

We determine the possible scaling limits in the quantum central limit theorem with respect to the Gibbs state, for a growing distance-regular graph that has so-called classical parameters with base unequal to one. We also describe explicitly the corresponding weak limits of the normalized spectral distribution of the adjacency matrix. We demonstrate our results with the known infinite families of distance-regular graphs having classical parameters and with unbounded diameter.

math.CO↗

arXiv2021

Towards glasses with permanent stability

Unlike crystals, glasses age or devitrify over time, reflecting their non-equilibrium nature. This lack of stability is a serious issue in many industrial applications. Here, we show by numerical simulations that the devitrification of quasi-hard-sphere glasses is prevented by suppressing volume fraction inhomogeneities. A monodisperse glass known to devitrify with `avalanche'-like intermittent dynamics is subjected to small iterative adjustments to particle sizes to make the local volume fractions spatially uniform. We find that this entirely prevents structural relaxation and devitrification over aging time scales, even in the presence of crystallites. There is a dramatic homogenization in the number of load-bearing nearest neighbors each particle has, indicating that ultra-stable glasses may be formed via `mechanical homogenization'. Our finding provides a physical principle for glass stabilization and opens a novel route to the formation of mechanically stabilized glasses.

cond-mat.soft↗

arXiv2021

Spatial Search on Johnson Graphs by Continuous-Time Quantum Walk

Spatial search on graphs is one of the most important algorithmic applications of quantum walks. To show that a quantum-walk-based search is more efficient than a random-walk-based search is a difficult problem, which has been addressed in several ways. Usually, graph symmetries aid in the calculation of the algorithm's computational complexity, and Johnson graphs are an interesting class regarding symmetries because they are regular, Hamilton-connected, vertex- and distance-transitive. In this work, we show that spatial search on Johnson graphs by continuous-time quantum walk achieves the Grover lower bound $π\sqrt{N}/2$ with success probability $1$ asymptotically for every fixed diameter, where $N$ is the number of vertices. The proof is mathematically rigorous and can be used for other graph classes.

math.CO↗

arXiv2021

Microscopic understanding of ion solvation in water

Solvation of ions is ubiquitous on our planet. Solvated ions have a profound effect on the behavior of ionic solutions, which is crucial in nature and technology. Experimentally, ions have been classified into "structure makers" or "structure breakers", depending on whether they slow down or accelerate the solution dynamics. Theoretically, the dynamics of ions has been explained by a dielectric friction model combining hydrodynamics and charge-dipole interaction in the continuum description. However, both approaches lack a microscopic structural basis, leaving the microscopic understanding of salt effects unclear. Here we elucidate unique microscopic features of solvation of spherical ions by computer simulations. We find that increasing the ion electric field causes a sharp transitional decrease in the hydration-shell thickness, signaling the ion mobility change from the Stokes to dielectric friction regime. The dielectric friction regime can be further divided into two due to the competition between the water-water hydrogen bonding and ion-water electrostatic interactions: Whether the former or latter prevails determines whether the water dynamics are accelerated or decelerated. In the ion-water interaction predominant regime, a specific combination of ion size and charge stabilizes the hydration shell via orientational-symmetry breaking, reminiscent of the Thomson problem for the electron configuration of atoms. Notably, the hydration-shell stability is much higher for a composite coordination number than a prime one, a prime-number effect on solvent dynamics. These findings are fundamental to the structure breaker/maker concept and provide new insights into the solvent structure and dynamics beyond the continuum model, paving the way towards a microscopic theory of ionic solutions.

cond-mat.soft↗

arXiv2021

Crystallization and Vitrification Kinetics by Design: The Role of Chemical Bonding

Controlling a state of material between its crystalline and glassy phase has fostered many real-world applications. Nevertheless, design rules for crystallization and vitrification kinetics still lack predictive power. Here, we identify stoichiometry trends for these processes in phase change materials, i.e. along the GeTe-GeSe, GeTe-SnTe, and GeTe-Sb2Te3 pseudo-binary lines employing a pump-probe laser setup and calorimetry. We discover a clear stoichiometry dependence of crystallization speed along a line connecting regions characterized by two fundamental bonding types, metallic and covalent bonding. Increasing covalency slows down crystallization by six orders of magnitude and promotes vitrification. The stoichiometry dependence is correlated with material properties, such as the optical properties of the crystalline phase and a bond indicator, the number of electrons shared between adjacent atoms. A quantum-chemical map explains these trends and provides a blueprint to design crystallization kinetics.

cond-mat.mtrl-sci↗

arXiv2020

The Terwilliger algebra of the twisted Grassmann graph: the thin case

The Terwilliger algebra $T(x)$ of a finite connected simple graph $Γ$ with respect to a vertex $x$ is the complex semisimple matrix algebra generated by the adjacency matrix $A$ of $Γ$ and the diagonal matrices $E_i^*(x)=\operatorname{diag}(v_i)$ $(i=0,1,2,\dots)$, where $v_i$ denotes the characteristic vector of the set of vertices at distance $i$ from $x$. The twisted Grassmann graph $\tilde{J}_q(2D+1,D)$ discovered by Van Dam and Koolen in 2005 has two orbits of the automorphism group on its vertex set, and it is known that one of the orbits has the property that $T(x)$ is thin whenever $x$ is chosen from it, i.e., every irreducible $T(x)$-module $W$ satisfies $\dim E_i^*(x)W\leqslant 1$ for all $i$. In this paper, we determine all the irreducible $T(x)$-modules of $\tilde{J}_q(2D+1,D)$ for this "thin" case.

math.CO↗

arXiv2020

Single-particle level access to hydrodynamic and frictional coupling between spheres in dense colloidal suspensions

The rotational Brownian motion of colloidal spheres in dense suspensions reflects local hydrodynamics and friction, both key to non-linear rheological phenomena such as shear-thickening and jamming, and transport in crowded environments, including intracellular migration and blood flow. To fully elucidate the role of rotational dynamics experimentally, it is crucial to measure the translational and rotational motion of all spheres simultaneously. Here, we develop compositionally uniform colloidal spheres with an off-centre, fully embedded core with a different fluorophore to the particle body, allowing access to rotational motion for all particles at the single-particle level. We reveal interparticle hydrodynamic rotational coupling in charged colloidal crystals. We also find that higher local crystallinity in denser crystals enhances rotational diffusivity, and that nearly arrested particles exhibit a stick-slip rotational motion due to frictional coupling. Our method sheds new light on the largely-unexplored local rotational dynamics of spherical particles in dense colloidal materials.

cond-mat.soft↗

arXiv2020

Tight relative $t$-designs on two shells in hypercubes, and Hahn and Hermite polynomials

Relative $t$-designs in the $n$-dimensional hypercube $\mathcal{Q}_n$ are equivalent to weighted regular $t$-wise balanced designs, which generalize combinatorial $t$-$(n,k,λ)$ designs by allowing multiple block sizes as well as weights. Partly motivated by the recent study on tight Euclidean $t$-designs on two concentric spheres, in this paper we discuss tight relative $t$-designs in $\mathcal{Q}_n$ supported on two shells. We show under a mild condition that such a relative $t$-design induces the structure of a coherent configuration with two fibers. Moreover, from this structure we deduce that a polynomial from the family of the Hahn hypergeometric orthogonal polynomials must have only integral simple zeros. The Terwilliger algebra is the main tool to establish these results. By explicitly evaluating the behavior of the zeros of the Hahn polynomials when they degenerate to the Hermite polynomials under an appropriate limit process, we prove a theorem which gives a partial evidence that the non-trivial tight relative $t$-designs in $\mathcal{Q}_n$ supported on two shells are rare for large $t$.

math.CO↗

arXiv2019

Externally driven local colloidal ordering induced by a point-like heat source

We study here how phase transitions are induced in colloidal suspensions by a point-like heat source, an optically trapped metal oxide particle absorbing light. We find that thermophoresis increases the number density of colloids around the oxide particle, leading to the appearance of solid clusters. Our analysis based on thermophoresis reveals that the solid-fluid interface position is purely determined by the relationship of the particle concentration profile in the fluid state with the volume fraction of the phase transition, and no other effect of thermodynamics is seen in the cluster sizes. In this system, we observe the formation of face-centered cubic crystals, amorphous states, and structures with icosahedral order. This shows a rich possibility of non-trivial orderings under spatially controlled heterogeneous growth in external "semi-soft" potentials that are softer than walls but with substantial variations at the scale of a few particle diameters. Because of the tuneable rate of addition of particles to the clusters, we propose this method could be used to study the complex interplay of densification with local spatial confinement effects, kinetics, and ordering.

cond-mat.soft↗

arXiv2019

Complementary aspects of non-equilibrium thermodynamics

Bio-molecules are active agents in that they consume energy to perform tasks. The standard theoretical description, however, considers only a system-external work agent. Fluctuation theorems, for example, do not allow work-exchange between fluctuating molecules. This tradition leaves `action through work', an essential characteristic of an active agent, out of proper thermodynamic consideration. Here, we investigate thermodynamics that considers internal-work. We find a complementary set of relations that capture the production of free energy in molecular interactions while obeying the second law of thermodynamics. This thermodynamic description is in stark contrast to the traditional one. A choice of an axiom whether one treats a portion of Hamiltonian as `internal-work' or `internal-energy' decides which of the two complementary descriptions manifests among the dual. We illustrate, by examining an allosteric transition and a single-molecule fluorescence-resonance-energy-transfer measurement of proteins, that the complementary set is useful in identifying work content by experimental and numerical observation.

cond-mat.stat-mech↗

arXiv2019

The Independence Number of the Orthogonality Graph in Dimension $2^k$

We determine the independence number of the orthogonality graph on $2^k$-dimensional hypercubes. This answers a question by Galliard from 2001 which is motivated by a problem in quantum information theory. Our method is a modification of a rank argument due to Frankl who showed the analogous result for $4p^k$-dimensional hypercubes, where $p$ is an odd prime.

math.CO↗

arXiv2019

Distinct signature of two local structural motifs of liquid water in the scattering function

Liquids generally become more ordered upon cooling. However, it has been a long-standing debate on whether such structural ordering in liquid water takes place continuously or discontinuosly: continuum vs. mixture models. Here, by computer simulations of three popular water models and analysis of recent scattering experiment data, we show that, in the structure factor of water, there are two overlapped peaks hidden in the apparent "first diffraction peak", one of which corresponds to the neighboring O-O distance as in ordinary liquids and the other to the longest periodicity of density waves in a tetrahedral structure. This unambiguously proves the coexistence of two local structural motifs. Our findings not only provide key clues to settle long-standing controversy on the water structure but also allow experimental access to the degree and range of structural ordering in liquid water.

cond-mat.soft↗

arXiv2019

Crystalline clusters in mW water: stability, growth, and grain boundaries

With numerical simulations of the mW model of water, we investigate the energetic stability of crystalline clusters for both Ice I (cubic and hexagonal ice) and for the metastable Ice 0 phase as a function of the cluster size. Under a large variety of forming conditions, we find that the most stable cluster changes as a function of size: at small sizes the Ice 0 phase produces the most stable clusters, while at large sizes there is a crossover to Ice I clusters. We further investigate the growth of crystalline clusters with the seeding technique and study the growth patterns of different crystalline clusters. While energetically stable at small sizes, the growth of metastable phases (cubic and Ice 0) is hindered by the formation of coherent grain boundaries. A five-fold symmetric twin boundary for cubic ice, and a newly discovered coherent grain boundary in Ice 0, that promotes cross nucleation of cubic ice. Our work reveals that different local structures can compete with the stable phase in mW water, and that the low energy cost of particular grain boundaries might play an important role in polymorph selection.

cond-mat.soft↗