arXiv subjects

Hajime Tanaka

Publications and source records attributed to Hajime Tanaka.

At least 73 records · Page 4Linked to original sources

arXiv2015

A novel coarsening mechanism of droplets in immiscible fluid mixtures

In our daily lives, after shaking a salad dressing, we see the coarsening of oil droplets suspended in vinegar. Such a demixing process is observed everywhere in nature and also of technological importance. For a case of high droplet density, domain coarsening proceeds with interdroplet collisions and the resulting coalescence. This phenomenon has been explained primarily by the so-called Brownian coagulation mechanism: stochastic thermal forces exerted by molecules induce random motion of individual droplets, causing accidental collisions and subsequent interface-tension driven coalescence. Contrary to this, we demonstrate that the droplet motion is not random, but hydrodynamically driven by the composition Marangoni force due to an interfacial tension gradient produced in each droplet as a consequence of composition correlation among droplets. This alters our physical understanding of droplet coarsening in immiscible liquid mixtures on a fundamental level.

cond-mat.soft↗

arXiv2015

Roles of energy dissipation in a liquid-solid transition of out-of-equilibrium systems

Self-organization of active matter as well as driven granular matter in non-equilibrium dynamical states has attracted considerable attention not only from the fundamental and application viewpoints but also as a model to understand the occurrence of such phenomena in nature. These systems share common features originating from their intrinsically out-of-equilibrium nature. It remains elusive how energy dissipation affects the state selection in such non-equilibrium states. As a simple model system, we consider a non-equilibrium stationary state maintained by continuous energy input, relevant to industrial processing of granular materials by vibration and/or flow. More specifically, we experimentally study roles of dissipation in self-organization of a driven granular particle monolayer. We find that the introduction of strong inelasticity entirely changes the nature of the liquid-solid transition from two-step (nearly) continuous transitions (liquid-hexatic-solid) to a strongly discontinuous first-order-like one (liquid-solid), where the two phases with different effective temperatures can coexist, unlike thermal systems, under a balance between energy input and dissipation. Our finding indicates a pivotal role of energy dissipation and suggests a novel principle in the self-organization of systems far from equilibrium. A similar principle may apply to active matter, which is another important class of out-of-equilibrium systems. On noting that interaction forces in active matter, and particularly in living systems, are often non-conservative and dissipative, our finding may also shed new light on the state selection in these systems.

cond-mat.soft↗

arXiv2015

Impact of size polydispersity on the nature of Lennard-Jones liquids

Polydisperse fluids are encountered everywhere in biological and industrial processes. These fluids naturally show a rich phenomenology exhibiting fractionation and shifts in critical point and freezing temperatures. Here, we study the impact of size polydispersity on the basic nature of Lennard-Jones (LJ) liquids, which represent most molecular liquids without hydrogen bonds, via two- and three-dimensional molecular dynamics computer simulations. A single-component liquid constituting spherical particles and interacting via the LJ potential is known to exhibit strong correlations between virial and potential energy equilibrium fluctuations at constant volume. This correlation significantly simplifies the physical description of the liquid, and these liquids are now known as Roskilde-simple (RS) liquids. We show that this simple nature of the single-component LJ liquid is preserved even for very high polydispersities (above 40% polydispersity for the studied uniform distribution). We also investigate isomorphs of moderately polydisperse LJ liquids. Isomorphs are curves in the phase diagram of RS liquids along which structure, dynamics, and some thermodynamic quantities are invariant in dimensionless units. We find that isomorphs are a good approximation even for polydisperse LJ liquids. The theory of isomorphs thus extends readily to multi-component systems and can be used to improve even further the understanding of these intriguing systems.

cond-mat.soft↗

arXiv2015

Assessing the role of static lengthscales behind glassy dynamics in polydisperse hard disks

The possible role of growing static order in the dynamical slowing down towards the glass transition has recently attracted considerable attention. On the basis of random first-order transition (RFOT) theory, a new method to measure the static correlation length of amorphous order, called "point-to-set (PTS)" length, has been proposed, and used to show that the dynamic length grows much faster than the static length. Here we study the nature of the PTS length, using a polydisperse hard disk system, which is a model that is known to exhibit a growing hexatic order upon densification. We show that the PTS correlation length is decoupled from the steeper increase of the correlation length of hexatic order, while closely mirroring the decay length of two-body density correlations. Our results thus provide a clear example that other forms of order can play an important role in the slowing down of the dynamics, casting a serious doubt on the order agnostic nature of the PTS length and its relevance to slow dynamics, provided that a polydisperse hard disk system is a typical glass former.

cond-mat.soft↗

arXiv2015

Purely hydrodynamic ordering of rotating disks at a finite Reynolds number

Self-organization of moving objects in hydrodynamic environments has recently attracted considerable attention in connection to natural phenomena and living systems. However, the underlying physical mechanism is much less clear due to the intrinsically nonequilibrium nature, compared with self-organization of thermal systems. Hydrodynamic interactions are believed to play a crucial role in such phenomena. To elucidate the fundamental physical nature of many-body hydrodynamic interactions at a finite Reynolds number, here we study a system of co-rotating hard disks in a two-dimensional viscous fluid at zero temperature. Despite the absence of thermal noise, this system exhibits rich phase behaviours, including a fluid state with diffusive dynamics, a cluster state, a hexatic state, a glassy state, a plastic crystal state and phase demixing.We reveal that these behaviours are induced by the off-axis and many-body nature of nonlinear hydrodynamic interactions and the finite time required for propagating the interactions by momentum diffusion.

cond-mat.soft↗

arXiv2015

Local non-equilibrium thermodynamics

Local Shannon entropy lies at the heart of modern thermodynamics, with much discussion of trajectory-dependent entropy production. When taken at both boundaries of a process in phase space, it reproduces the second law of thermodynamics over a finite time interval for small scale systems. However, given that entropy is an ensemble property, it has never been clear how one can assign such a quantity locally. Given such a fundamental omission in our knowledge, we construct a new ensemble composed of trajectories reaching an individual microstate, and show that locally defined entropy, information, and free energy are properties of the ensemble, or trajectory-independent true thermodynamic potentials. We find that the Boltzmann-Gibbs distribution and Landauer's principle can be generalized naturally as properties of the ensemble, and that trajectory-free state functions of the ensemble govern the exact mechanism of non-equilibrium relaxation.

cond-mat.stat-mech↗

arXiv2014

The nature of the glass and gel transitions in sticky spheres

Glasses and gels are the two dynamically arrested, disordered states of matter. Despite their importance, their similarities and differences remain elusive, especially at high density. We identify dynamical and structural signatures which distinguish the gel and glass transitions in a colloidal model system of hard and "sticky" spheres. Gelation is induced by crossing the gas-liquid phase-separation line and the resulting rapid densification of the colloid-rich phase leads to a sharp change in dynamics and local structure. Thus, we find that gelation is first-order-like and can occur at much higher densities than previously thought: far from being low-density networks, gels have a clear "thermodynamic" definition which nevertheless leads to a non-equilibrium state with a distinct local structure characteristic of a rapidly quenched glass. In contrast, approaching the glass transition, the dynamics slow continuously accompanied by the emergence of local five-fold symmetric structure. Our findings provide a general thermodynamic, kinetic, and structural basis upon which to distinguish gelation from vitrification.

cond-mat.soft↗

arXiv2014

Mackey's theory of $τ$-conjugate representations for finite groups. APPENDIX: On Some Gelfand Pairs and Commutative Association Schemes

The aim of the present paper is to expose two contributions of Mackey, together with a more recent result of Kawanaka and Matsuyama, generalized by Bump and Ginzburg, on the representation theory of a finite group equipped with an involutory anti-automorphism (e.g. the anti-automorphism $g\mapsto g^{-1}$). Mackey's first contribution is a detailed version of the so-called Gelfand criterion for weakly symmetric Gelfand pairs. Mackey's second contribution is a characterization of simply reducible groups (a notion introduced by Wigner). The other result is a twisted version of the Frobenius-Schur theorem, where "twisted" refers to the above-mentioned involutory anti-automorphism. APPENDIX: We consider a special condition related to Gelfand pairs. Namely, we call a finite group $G$ and its automorphism $σ$ satisfy Condition ($\bigstar$) if the following condition is satisfied: if for $x,y\in G$, $x\cdot x^{-σ}$ and $y\cdot y^{-σ}$ are conjugate in $G$, then they are conjugate in $K=C_G(σ)$. We study the meanings of this condition, as well as showing many examples of $G$ and $σ$ which do (or do not) satisfy Condition ($\bigstar$).

math.RT↗

arXiv2014

The Boson Peak and Disorder in Hard Sphere Colloidal Systems

The Boson peak is believed to be the key to the fundamental understanding of the anomalous thermodynamic properties of glasses, notably the anomalous peak in the heat capacity at low temperatures; it is believed to be due to an excess of low frequency vibrational modes and a manifestation of the structural disorder in these systems. We study the thermodynamics and vibrational dynamics of colloidal glasses and (defected) crystals. The experimental determination of the vibrational density of states allows us to directly observe the Boson peak as a strong enhancement of low frequency modes. Using a novel method [Zargar et al., Phys. Rev. Lett. 110, 258301 (2013)] to determine the free energy, we also determine the entropy and the specific heat experimentally. It follows that the emergence of the Boson peak and high values of the specific heat are directly related and are specific to the glass: for a very defected crystal with a disorder that is only slightly smaller than for the glass, both the low-frequency density of states and the specific heat are significantly smaller than in the glass.

cond-mat.soft↗

arXiv2014

Novel zone formation due to interplay between sedimentation and phase ordering

Usually, we expect large particles to sediment faster than small of the same material. Contrary to this intuition, we report a dynamical competition between sedimentation and phase ordering which leads to smaller particles settling faster than larger ones. We access this phenomenon using suspensions of polymers and two colloidal species which we image with confocal microscopy. Polymers mediate attractions between colloids, leading to phase separation and crystallisation. We find that the dynamical interplay between sedimentation, phase separation and crystal nucleation underlie this phenomenon. Furthermore, under certain conditions we find a kinetic pathway leading to an apparent coexistence between a one component crystal and binary fluid of equal buoyancy. These findings may be relevant to the basic understanding of sedimentation-induced zone formation in nature and industrial applications.

cond-mat.soft↗

arXiv2013

Understanding water's anomalies with locally favored structures

Water is a complex structured liquid of hydrogen-bonded molecules that displays a surprising array of unusual properties, also known as water anomalies, the most famous being the density maximum at about $4^\circ$C. The origin of these anomalies is still a matter of debate, and so far a quantitative description of water's phase behavior starting from the molecular arrangements is still missing. Here we provide a simple physical description from microscopic data obtained through computer simulations. We introduce a novel structural order parameter, which quantifies the degree of translational order of the second shell, and show that this parameter alone, which measures the amount of locally favored structures, accurately characterizes the state of water. A two-state modeling of these microscopic structures is used to describe the behavior of liquid water over a wide region of the phase diagram, correctly identifying the density and compressibility anomalies, and being compatible with the existence of a second critical point in the deeply supercooled region. Furthermore, we reveal that locally favored structures in water not only have translational order in the second shell, but also contain five-membered rings of hydrogen-bonded molecules. This suggests their mixed character: the former helps crystallization, whereas the latter causes frustration against crystallization.

cond-mat.soft↗

arXiv2013

Phase Separation in Soft Matter: Concept of Dynamic Asymmetry

Phase separation is a fundamental phenomenon that produces spatially heterogeneous patterns in soft matter. In this Lecture Note we show that phase separation in these materials generally belongs to what we call "viscoelastic phase separation", where the morphology is determined by the mechanical balance of not only the thermodynamic force (interface tension) but also the viscoelastic force. The origin of the viscoelastic force is dynamic asymmetry between the components of a mixture, which can be caused by either a size disparity or a difference in the glass transition temperature between the components. We stress that such dynamic asymmetry generally exists in soft matter. The key is that dynamical asymmetry leads to a non-trivial coupling between the concentration, velocity, and stress fields. Viscoelastic phase separation can be explained by viscoelastic relaxation in pattern evolution and the resulting switching of the relevant order parameter, which are induced by the competition between the deformation rate of phase separation and the slowest mechanical relaxation rate of a system. We also discuss an intimate link of viscoelastic phase separation, where deformation fields are spontaneously generated by phase separation itself, to mechanical instability (or fracture) of glassy material, which is induced by externally imposed strain fields. We propose that all these phenomena can be understood as mechanically-driven inhomogeneization in a unified manner.

cond-mat.soft↗

arXiv2013

The interplay of sedimentation and crystallization in hard-sphere suspensions

We study crystal nucleation under the influence of sedimentation in a model of colloidal hard spheres via Brownian Dynamics simulations. We introduce two external fields acting on the colloidal fluid: a uniform gravitational field (body force), and a surface field imposed by pinning a layer of equilibrium particles (rough wall). We show that crystal nucleation is suppressed in proximity of the wall due to the slowing down of the dynamics, and that the spatial range of this effect is governed by the static length scale of bond orientational order. For distances from the wall larger than this length scale, the nucleation rate is greatly enhanced by the process of sedimentation, since it leads to a higher volume fraction, or a higher degree of supercooling, near the bottom. The nucleation stage is similar to the homogeneous case, with nuclei being on average spherical and having crystalline planes randomly oriented in space. The growth stage is instead greatly affected by the symmetry breaking introduced by the gravitation field, with a slowing down of the attachment rate due to density gradients, which in turn cause nuclei to grow faster laterally. Our findings suggest that the increase of crystal nucleation in higher density regions might be the cause of the large discrepancy in the crystal nucleation rate of hard spheres between experiments and simulations, on noting that the gravitational effects in previous experiments are not negligible.

cond-mat.soft↗

arXiv2013

Bond orientational ordering in liquids: Towards a unified description of water-like anomalies, liquid-liquid transition, glass transition, and crystallization

There are at least three fundamental states of matter, depending upon temperature and pressure: gas, liquid, and solid (crystal). These states are separated by first-order phase transitions between them. In both gas and liquid phases the complete translational and rotational symmetry exist, whereas in a solid phase both symmetries are broken. In intermediate phases between liquid and solid, which include liquid crystal and plastic crystal phases, only one of the two symmetries is preserved. Among the fundamental states of matter, the liquid state is most poorly understood. We argue that it is crucial for a better understanding of liquid to recognize that a liquid generally has a tendency to have local structural order and its presence is intrinsic and universal to any liquid. Such structural ordering is a consequence of many body correlations, more specifically, bond angle correlations, which we believe are crucial for the description of the liquid state. We show that this physical picture may naturally explain difficult unsolved problems associated with the liquid state, such as anomalies of water-type liquids (water, Si, Ge, ...), liquid-liquid transition, liquid-glass transition, crystallization and quasicrystal formation, in a unified manner. In other words, we need a new order parameter representing low local free-energy configuration, which is bond orientational order parameter in many cases, in addition to density order parameter for the physical description of these phenomena. Here we review our two-order-parameter model of liquid and consider how transient local structural ordering is linked to all of the above-mentioned phenomena. The relationship between these phenomena are also discussed.

cond-mat.soft↗

arXiv2013

Nonequilibrium critical Casimir interactions in binary fluids

Colloids immersed in a critical binary liquid mixture are subject to critical Casimir forces (CCFs) because they confine its concentration fluctuations and influence the latter via effective surface fields. To date, CCFs have only been studied in thermodynamic equilibrium. However, due to the critical slowing down, the order parameter around a particle can easily be perturbed by any motion of the colloid or by solvent flow. This leads to significant but largely unexplored changes in the CCF. Here we study the drag force on a single colloidal particle moving in a near-critical fluid mixture and the relative motion of two colloids due to the CCF acting on them. In order to account for the kinetic couplings among the order parameter field, the solvent velocity field, and the particle motion, we use a fluid particle dynamics method. These studies extend the understanding of CCFs from thermal equilibrium to non-equilibrium processes, which are relevant to current experiments, and show the emergence of significant effects near the critical point.

cond-mat.soft↗

arXiv2013

Lifetimes and Lengthscales of Structural Motifs in a Model Glassformer

We use a newly-developed method to identify local structural motifs in a popular model glassformer, the Kob-Andersen binary Lennard-Jones mixture. By measuring the lifetimes of a zoo of clusters, we find that 11-membered bicapped square antiprisms, denoted as 11A, have longer lifetimes on average than other structures considered. Other long-lived clusters are similar in structure to the 11A cluster. These clusters group into ramified networks that are correlated with slow particles and act to retard the motion of neighbouring particles. The structural lengthscale associated with these networks does not grow as fast as the dynamical lengthscale $ξ_4$ as the system is cooled, in the range of temperatures our molecular dynamics simulations access. Thus we find a strong, but indirect, correlation between static structural ordering and slow dynamics.

cond-mat.soft↗

arXiv2013

The Erdős-Ko-Rado basis for a Leonard system

We introduce and discuss an Erdős-Ko-Rado basis for the underlying vector space of a Leonard system $Φ= (A; A^*; \{E_i\}_{i=0}^d ; \{E_i^* \}_{i=0}^d)$ that satisfies a mild condition on the eigenvalues of $A$ and $A^*$. We describe the transition matrices to/from other known bases, as well as the matrices representing $A$ and $A^*$ with respect to the new basis. We also discuss how these results can be viewed as a generalization of the linear programming method used previously in the proofs of the "Erdős-Ko-Rado theorems" for several classical families of $Q$-polynomial distance-regular graphs, including the original 1961 theorem of Erdős, Ko, and Rado.

math.RA↗

arXiv2013

A cross-intersection theorem for vector spaces based on semidefinite programming

Let $\mathscr{F}$ and $\mathscr{G}$ be families of $k$- and $\ell$-dimensional subspaces, respectively, of a given $n$-dimensional vector space over a finite field $\mathbb{F}_q$. Suppose that $x \cap y \ne 0$ for all $x \in \mathscr{F}$ and $y \in \mathscr{G}$. By explicitly constructing optimal feasible solutions to a semidefinite programming problem which is akin to Lovász's theta function, we show that $|\mathscr{F}| |\mathscr{G}| \leq {n-1 \brack k-1} {n-1 \brack \ell-1}$, provided that $n \geq 2k$ and $n \geq 2\ell$. The characterization of the extremal families is also established.

math.CO↗