arXiv subjects

Ko Okumura

Publications and source records attributed to Ko Okumura.

At least 19 recordsLinked to original sources

arXiv2026

Inclination-Induced Crossover in the Velocity Scaling of Lubrication-Mediated Droplet Motion

We experimentally investigate the creeping motion of water droplets sliding along an inclined surface immersed in a viscous oil. The droplet velocity, width, and height are measured over a broad range of droplet sizes and inclination angles. The velocity increases with droplet radius according to a power law, but the corresponding exponent depends strongly on the inclination angle. At small inclinations, the exponent is close to 3/2, whereas at larger inclinations it progressively approaches 9/4. The results therefore reveal a continuous inclination-induced crossover in the velocity-size scaling of lubrication-mediated droplet motion. A scaling analysis based on Landau-Levich-Derjaguin film formation and viscous dissipation in the dynamic meniscus reproduces these limiting behaviors, which correspond to the quasi-spherical and pancake scaling regimes, respectively. Remarkably, the evolution of the velocity scaling is substantially more pronounced than the corresponding evolution of the macroscopic droplet shape. While the velocity data progressively approach the pancake scaling law at large inclinations, the global droplet dimensions evolve in a more complex manner than expected from a simple pancake-shape picture. In particular, the approach to pancake-like velocity scaling occurs even when the measured droplet dimensions remain far from the corresponding pancake-limit geometry. These observations suggest a crossover in the dominant lubrication-dissipation mechanism beneath the droplet that is not directly reflected in the global droplet morphology. The results identify inclination angle as a key control parameter governing lubrication-mediated droplet motion and highlight the distinction between global shape evolution and local dissipation dynamics in liquid-liquid systems.

physics.flu-dyn↗

arXiv2026

Front Selection Is Not Determined by Renormalization-Group Stability

The Fisher--Kolmogorov--Petrovsky--Piskunov equation provides a paradigmatic example of front propagation and asymptotic-state selection. Using a unified renormalization-group (RG) framework, we show that its traveling-wave solutions form a continuous family of RG fixed points and that all fronts with $v \ge 2$ are RG-stable. Nevertheless, the asymptotically selected front is not determined by RG stability. The FKPP equation therefore provides an explicit example in which RG fixed-point stability and asymptotic-state selection are distinct concepts.

cond-mat.stat-mech↗

arXiv2026

Predictive Renormalization-Group Theory of Universality Classes in Nonlinear Systems

Universal scaling behavior appears across a wide range of nonlinear systems despite substantial differences in their governing equations and physical mechanisms. We develop a renormalization-group (RG) framework that identifies two complementary RG mechanisms underlying such universality. First, scale invariance generates RG fixed points corresponding to asymptotic self-similar solutions. Second, repeated RG transformations eliminate non-scale-invariant irrelevant structures, causing broad classes of equations to flow toward the same fixed points and thereby form universality classes. The framework applies to finite-time singularities, long-time intermediate asymptotics, stochastic Edwards--Wilkinson growth, nonlinear diffusion, density-dependent biological diffusion, and fluid-interface dynamics. In each case, it reproduces known scaling behavior and identifies the associated universality class through explicit irrelevance criteria. A central feature of the framework is its predictive character. Once a scale-invariant fixed point is identified, the theory predicts entire families of nonlinear equations sharing the same asymptotic self-similar solution. While the diffusion class is partially supported by existing mathematically rigorous results, most universality classes identified here have not previously been established and therefore constitute testable predictions. These results provide a unified RG perspective on universality in nonlinear systems and show that universality emerges from the same fundamental RG principles that underlie critical phenomena. In contrast to critical phenomena, where observable behavior is typically governed by unstable fixed points requiring fine tuning, self-similar dynamics are generally selected through dynamically stable RG fixed points.

cond-mat.stat-mech↗

arXiv2026

Memory Retention and the Classification of Renormalization-Group Fixed Points in Self-Similar Dynamics

Universality is usually associated with the loss of information about initial conditions under repeated coarse-graining or renormalization-group (RG) transformations. We show that the unified RG framework for nonlinear partial differential equations can accommodate a broader class of asymptotic fixed points in which relevant scales remain encoded in the asymptotic state. By retaining relevant length scales within the RG description, asymptotic self-similar solutions, identified with RG fixed points, become functions of all scales that survive the RG flow. A modified density-dependent diffusion model yields a memory-retaining RG fixed point with scaling form η^{α}F(ξ/η^{\b{eta}}), where η represents a surviving relevant scale, while the Barenblatt equation emerges as the special case η^{α}F(ξ) with \b{eta}=0. These examples suggest that asymptotic RG fixed points may be classified according to whether relevant scales survive repeated RG transformations. We refer to the fixed points retaining such information as memory-retaining fixed points. Within this perspective, anomalous scaling can be interpreted as a manifestation of information retention. The resulting classification distinguishes fixed points according to how initial-condition information survives RG flow and remains encoded in the asymptotic fixed-point function itself. The results suggest that memory retention constitutes an organizing principle of RG fixed points complementary to the conventional classification by universality classes. In contrast with conventional Hamiltonian-based RG, the surviving information appears as an explicit variable of the asymptotic RG fixed-point function itself.

cond-mat.stat-mech↗

arXiv2026

Traveling Waves as Renormalization-Group Fixed Points without Universality Classes

Traveling waves are fundamental asymptotic structures in nonlinear physical systems. While their connection to self-similarity is recognized, their renormalization-group (RG) status remains elusive. We extend a recently developed unified RG framework for nonlinear PDEs to traveling-wave solutions, using Burgers' and KdV equations as paradigmatic examples. By employing a logarithmic transformation, we map traveling waves onto asymptotically self-similar solutions, allowing for a systematic RG treatment. Our analysis reveals a striking departure from the standard RG paradigm: for traveling waves, scale invariance uniquely forces the field's scaling dimension to vanish (A=0). This vanishing dimension implies that the RG transformation rescales space and time while leaving the field magnitude unchanged. Consequently, all analytic perturbations become scale-invariant, eliminating the conventional classification into relevant and irrelevant structures. While classical shock-wave and soliton solutions emerge as stationary RG fixed points, the mechanism for universality class formation - the progressive elimination of irrelevant structures - is fundamentally absent. Traveling waves thus represent a unique class of RG fixed points without universality classes. This finding establishes a crucial distinction between these two concepts and provides a rigorous theoretical basis for why traveling waves exhibit strong memory of initial conditions and system parameters.

cond-mat.stat-mech↗

arXiv2025

Universality in the velocity jump in the crack propagation observed for food-wrapping films for daily use

The velocity jump found in the crack propagation for rubbers has been a powerful tool for developing tough rubber materials. Although it is suggested by a theory that the jump could be observed widely for viscoelastic materials, the report on a clear jump is very limited and, even in such a case, reproducibility is low, except for elastomers. Here, we use a mundane food-wrapping film as a sample and observe the crack propagation velocity with pulling the sample at a constant speed in the direction perpendicular to the crack. As a result, we find the jump occurs at a critical strain with high reproducibility. Remarkably, the plot of the crack-propagation velocity as a function of strain can be collapsed onto a master curve by an appropriate rescaling, where the master curve is found to be universal for change in the pulling speed and in the sample height. The result reveals a key parameter for the jump is the strain, suggesting the existence of a small length that governs the deformation along the crack. The present study sets limitations on future theories and opens an avenue for the velocity jump to become a tool for developing a wide variety of tough polymer-based materials.

cond-mat.soft↗

arXiv2025

Breakup to non-breakup transition of air entrained into viscous liquid by a disk: analogy of the self-similar dynamics with critical phenomena

Self-similarity in partial differential equations has been widely exploited to study many phenomena in physical sciences. We have studied the interfacial dynamics when air is entrained into viscous liquid by a disk in a confined geometry. In a previous study using an original experimental system, we found the sheet- and corn-forming regimes, in which a sheet and cone of air are respectively formed before air detaches from the disk. The sheet eventually breaks up but the corn, which appears when a bit more confined, does not. Here, we find a third regime, in which a corn eventually breaks up, by investigating different ranges of confining parameters: the transition from breakup to non-breakup can occur within the corn regime. Furthermore, with the data obtained in the third regime we deeply explore analogy with critical phenomena to find out that the counterpart of the critical exponents dependent on a length scale. Since the scale is a number not discrete but continuous, the present hydrodynamic analog suggests the existence of an uncountably infinite number of universality classes. The rich physics revealed in our study suggests a promising direction of the study of the self-similar dynamics: exploring analogy with critical phenomena, focusing on confined geometries in many natural and industrial phenomena.

cond-mat.stat-mech↗

arXiv2025

Partial persistence of memory in bubble breakup: incomplete universality acquired by broken symmetry

When a water drop falls from a faucet, the drop is created with the formation of an axisymmetric constriction region, which thins down to breakup. Such formation of a fluid drop has been extensively studied as a representative of the singular dynamics widely observed in nature. The singular dynamics is often self-similar, i.e., shapes at different times collapsing onto a master curve after rescaling, and the self-similar dynamics has been categorized as either universal or non-universal: the master curve is independent of or dependent on the length scales that set the initial boundary conditions, as if memory is erased or retained. Here, we focus on the post-breakup dynamics and confine the system to break the axisymmetry, introducing three length scales, which leads to a third category of incomplete universality, where memory is partially retained: the master curve could be dependent on the smallest scale but independent of the other two scales. Affecting of only the smallest length scale on the master curve underscores the importance of scale separation for the emergence of universality. The present study suggests a promising direction for the study on the singular dynamics by exploring the symmetry.

cond-mat.stat-mech↗

arXiv2025

Continuous generation of confined bubbles: viscous effect on the gravito-capillary pinch off

We investigate continuous generation of bubbles from a bath of air in viscous liquid in a confined geometry. In our original setup, bubbles are spontaneously generated by virtue of buoyancy and a gate placed in the cell: the gate acts like an inverted funnel trapping air beneath it before continuously generating bubbles at the tip. The dynamics is characterized by the bubble-formation period and the bubble size as a function of the amount of air under the gate. By analyzing the data obtained for various parameters, we clearly identified that the dynamics of the bubble formation is governed by dissipation in the viscous fluid beneath the trapped air balanced by a gravitational energy change due to buoyancy, after examining numerous possibilities of dissipation, which demonstrates the potential of scaling analysis even in complex cases. Furthermore, we uncover a novel type of pinch-off condition, which convincingly explains the bubble size: in the present case viscosity plays a vital role, different from the conventional mechanism of Tate, in which gravity competes with capillarity, revealing a general mechanism of pinching-off at low Reynolds number. Accordingly, the present study significantly and fundamentally advances our knowledge of generation and pinch-off of bubbles, with the results relevant for a wide variety of applications in many fields. In particular, the present study demonstrates a promising avenue in microfluidics for understanding physical principles by scaling up the system, without losing the characteristics of the flow at low Reynolds numbers.

physics.flu-dyn↗

arXiv2024

Universality in the mechanics of soft Kirigami

Recently, simple scaling laws concerning the mechanical response and mechanical transition of Kirigami have been revealed through agreement between theory and experiment for kirigami made of paper [M. Isobe and K. Okumura, Sci. Rep. 2016]. Here, we provide experimental data obtained from kirigami made of soft elastic sheets to demonstrate good agreement with previous theories, although a number of assumptions in the theory are violated and the elastic modulus is three orders of magnitude smaller in the present case. This remarkable universality in the mechanics of Kirigami, which could be useful for applications, is reported with physical insights based on previous theories.

cond-mat.soft↗

arXiv2023

Viscous friction acting on a solid disk falling in confined fluid: lessons for the scaling analysis

We fill a viscous liquid in a vertically stood cell of millimeter thickness, called the Hele-Shaw cell, and insert a disk in the liquid whose thickness is smaller than the cell thickness. The disk starts falling in the liquid due to gravity opposed by viscous friction. We focus on the case in which lubricating films formed in the gap between the cell surface and the disk surface are thinner than the disk thickness. As a result, we find an apparent scaling regime for the falling velocity of a disk, in which the thickness of the lubricating film characterizes the dynamics. We further show that the apparent scaling regime is explained simply as a result of competition of two scaling regimes, elucidating the physics of the viscous friction. The present study is thus relevant to fundamental issues and applications in various fields in which small-scale physics in the flow at low Reynolds numbers is essential, such as microfluidics, bioconvection, and active matter. The simple scenario for explaining an apparent scaling law demonstrated in the present study would be useful in diverse fields, considering that the generality and strength of scaling analysis in science and that simple arguments usually lead to a few different scaling laws for a given problem.

cond-mat.soft↗

arXiv2020

Rising obstacle in a one-layer granular bed induced by continuous vibrations: two dynamical regimes governed by vibration velocity

Rising motion of an obstacle in a vibrated granular medium is a classic problem of granular segregation, and called the Brazil nut (BN) effect. The controlling vibration parameters of the effect has been a long-standing problem. A simple possibility that the BN effect can be characterized solely by vibration velocity has recently been pointed out. The issue has become controversial before a long history of research, with only a few systems have provided for the simple possibility. Here, we investigate the rising motion of an obstacle in a vertically positioned one-layer granular bed under continuous vibrations. We find the rising motion is composed of two distinct regimes, and the first and second regimes are both governed, in terms of vibration parameters, solely by the vibration velocity. We further demonstrate simple scaling laws well describe the two regimes. Our results support the emergent possibility on the controlling parameters of the BN effect and suggests that this feature would be universal. We propose two possible mechanisms of convection and arch effect for the two distinct regimes and demonstrate these mechanism explain the scaling laws followed by our experimental data.

cond-mat.soft↗

arXiv2019

Liquid-liquid capillary replacement in a horizontal geometry: universal dynamics and replacement time

Capillary invasion of a liquid into an empty tube, which is called capillary rise when the tube axis is in the vertical direction, is one of the fundamental phenomena representing capillary effects. Usually, the tube is actually filled with another pre-existing fluid, air, whose viscosity and inertia can be practically neglected. In this study, we considered the effect of the pre-existing fluid, when its viscosity is non-negligible, in a horizontally geometry. This geometry is free from gravity and thus simpler than the geometry of capillary rise. We observed the dynamics when a capillary tube that is submerged horizontally in a liquid gets in contact with a second liquid. An appropriate combination of liquids allowed us to observe that the second liquid replaces the first without any prewetting process, thanks to a careful cleaning of capillary tubes. Furthermore, we experimentally observed three distinct viscous dynamics: (i) the conventional slowing-down dynamics, (ii) an unusual accelerating dynamics, and (iii) another unusual dynamics, which is linear in time. We developed a theory in viscous regimes, which accounts well for the observations through a unified expression describing the three distinct dynamics. We also demonstrated a thorough experimental confirmation on the initial velocity of the replacement. We further focused on the replacement time, the time required for the invading fluid to replaces completely the pre-existing fluid in the horizontal geometry, which is again well explained by the theory.

physics.flu-dyn↗

arXiv2019

Continuity and discontinuity of kirigami's high-extensibility transition: a statistical-physics viewpoint

Recently, kirigami's high extensibility has been understood as a transition in the force-elongation curve. In this paper, we consider a model, which modifies our previous model, to show a striking analogy between the present theory and Landau theory of continuous thermodynamic transitions, if we regard a rotation angle and elongation of kirigami as the order parameter and the inverse temperature, respectively. The present study opens a new avenue in physics, pointing out the importance of the distinction between discontinuity and continuity of the high-extensibility transition in an elementary kirigami structure, and showing that the mechanical response of kirigami can be understood using the tools of statistical physics, which have been proved to be useful in many fields of physics.

cond-mat.soft↗

arXiv2019

Crack propagation under static and dynamic boundary conditions

Velocity jumps observed for crack propagation under a static boundary condition have been used as a controlling factor in developing tough rubbers. However, the static test requires many samples to detect the velocity jump. On the contrary, crack propagation performed under a dynamic boundary condition is timesaving and cost-effective in that it requires only a single sample to monitor the jump. In addition, recent experiments show that velocity jump occurs only in the dynamic test for certain materials, for which the velocity jump is hidden in the static test because of the effect of stress relaxation. Although the dynamic test is promising because of these advantages, the interrelation between the dynamic test and the more established static test has not been explored in the literature. Here, by using two simulation models, we elucidate this interrelation and clarify a universal condition for obtaining the same results from the two tests, which will be useful for designing the dynamic test.

cond-mat.soft↗

arXiv2019

Toughening in a nacre-like soft-hard layered structure due to weak nonlinearity in the soft layer

Recently, it has been found experimentally that hydrated nacre exhibits a nonlinear mechanical response. While mechanical nonlinearity has been shown to be important in other biological structures, such as spider webs, the implications of mechanical nonlinearity in nacre have not been explored. Here, we show that the nonlinear mechanical response of nacre can be reproduced by an analytical model, which reflects a nacre-like layered structure, consisting of linear-elastic hard sheets glued together by weakly nonlinear-elastic soft sheets. We develop scaling analysis on this analytical model, and perform numerical simulations using a lattice model, which is a discrete counterpart of the analytical model. Unexpectedly, we find the weak nonlinearity in the soft component significantly contributes to enhancing toughness by redistributing the stress at a crack tip over a wider area. Beyond demonstrating a mechanism that explains the unusual properties of biological nacre, this study points to a general design principle for constructing tough composites using weak nonlinearity, and is useful as a guiding principle to develop artificial layered structures mimicking nacre.

physics.bio-ph↗

arXiv2019

Velocity jump in the crack propagation induced on a semi-crystalline polymer sheet by constant-speed stretching

It has long been known for elastomers that the velocity of crack propagation jumps as a function of strain. On the other hand, such a jump has not been reported in the literature for polymers which do not exhibit a rubbery plateau in the storage-modulus plot. Here, we report observation of jumps in crack propagation for semi-crystalline polymer sheets without the rubbery plateau, as a result of pulling the sheets at a constant speed. We discuss the advantages of this crack-propagation test under constant-speed stretching and provide physical interpretation of the velocity jump observed for non-elastomer sheets on the basis of a recently proposed theory for the velocity jump in crack propagation.

cond-mat.soft↗

arXiv2019

Visco- and plasto-elastic fracture of nano-porous polymer sheets

We study the dependence of the fracture surface energy on the pulling velocity for nano-porous polypropylene (PP) sheets to find two components: the static and dynamic ones. We show that these terms can be interpreted respectively as plastoelastic and viscoelastic components, as has been shown for soft polyethylene (PE) foams in a previous work. Considering significant differences in the pore size, volume fraction and Young's modulus of the present PP and previous PE sheets, the present results suggest a universal physical mechanism for fracture of porous polymer sheets. The simple physical interpretation emerging from the mechanism could be useful for developing tough polymers. Equivalence of Griffith's energy balance in fracture mechanics to a stress criterion is also discussed and demonstrated using the present experimental data.

cond-mat.soft↗