Scarring in classical chaotic dynamics with noise.

We report the numerical observation of scarring, which is enhancement of probability density around unstable periodic orbits of a chaotic system, in the eigenfunctions of the classical Perron-Frobenius operator of noisy Anosov ("perturbed cat") maps, as well as in the noisy Bunimovich stadium. A parallel is drawn between classical and quantum scars, based on the unitarity or nonunitarity of the respective propagators. For uniformly hyperbolic systems such as the cat map, we provide a mechanistic explanation for the classical phase-space localization detected, based on the distribution of finite-time Lyapunov exponents, and the interplay of noise with deterministic dynamics. Classical scarring can be measured by studying autocorrelation functions and their power spectra.

A jamming plane of sphere packings.

The concept of jamming has attracted great research interest due to its broad relevance in soft-matter, such as liquids, glasses, colloids, foams, and granular materials, and its deep connection to sphere packing and optimization problems. Here, we show that the domain of amorphous jammed states of frictionless spheres can be significantly extended, from the well-known jamming-point at a fixed density, to a jamming-plane that spans the density and shear strain axes. We explore the jamming-plane, via athermal and thermal simulations of compression and shear jamming, with initial equilibrium configurations prepared by an efficient swap algorithm. The jamming-plane can be divided into reversible-jamming and irreversible-jamming regimes, based on the reversibility of the route from the initial configuration to jamming. Our results suggest that the irreversible-jamming behavior reflects an escape from the metastable glass basin to which the initial configuration belongs to or the absence of such basins. All jammed states, either compression- or shear-jammed, are isostatic and exhibit jamming criticality of the same universality class. However, the anisotropy of contact networks nontrivially depends on the jamming density and strain. Among all state points on the jamming-plane, the jamming-point is a unique one with the minimum jamming density and the maximum randomness. For crystalline packings, the jamming-plane shrinks into a single shear jamming-line that is independent of initial configurations. Our study paves the way for solving the long-standing random close-packing problem and provides a more complete framework to understand jamming.

Multiple glass transitions and higher-order replica symmetry breaking of binary mixtures.

We extend the replica liquid theory in order to describe the multiple glass transitions of binary mixtures with large size disparities, by taking into account the two-step replica symmetry breaking (2RSB). We determine the glass phase diagram of the mixture of large and small particles in the large-dimension limit where the mean-field theory becomes exact. When the size ratio of particles is beyond a critical value, the theory predicts three distinct glass phases; (i) the one-step replica symmetery breaking (1RSB) double glass where both components vitrify simultaneously, (ii) the 1RSB single glass where only large particles are frozen while small particles remain mobile, and (iii) a glass phase called the 2RSB double glass where both components vitrify simultaneously but with an energy landscape topography distinct from the 1RSB double glass.

Spin-Orbital Glass Transition in a Model of a Frustrated Pyrochlore Magnet without Quenched Disorder.

We show theoretically that spin and orbital degrees of freedom in the pyrochlore oxide Y_{2}Mo_{2}O_{7}, which is free of quenched disorder, can exhibit a simultaneous glass transition, working as dynamical disorder for each other. The interplay of spins and orbitals is mediated by the Jahn-Teller lattice distortion that selects the choice of orbitals, which then generates variant spin exchange interactions ranging from ferromagnetic to antiferromagnetic ones. Our Monte Carlo simulations detect the power-law divergence of the relaxation times and the negative divergence of both the magnetic and dielectric nonlinear susceptibilities, resolving the long-standing puzzle on the origin of the disorder-free spin glass.

A stability-reversibility map unifies elasticity, plasticity, yielding, and jamming in hard sphere glasses.

Amorphous solids, such as glasses, have complex responses to deformations, with substantial consequences in material design and applications. In this respect, two intertwined aspects are important: stability and reversibility. It is crucial to understand, on the one hand, how a glass may become unstable due to increased plasticity under shear deformations, and, on the other hand, to what extent the response is reversible, meaning how much a system is able to recover the original configuration once the perturbation is released. Here, we focus on assemblies of hard spheres as the simplest model of amorphous solids such as colloidal glasses and granular matter. We prepare glass states quenched from equilibrium supercooled liquid states, which are obtained by using the swap Monte Carlo algorithm and correspond to a wide range of structural relaxation time scales. We exhaustively map out their stability and reversibility under volume and shear strains using extensive numerical simulations. The region on the volume-shear strain phase diagram where the original glass state remains solid is bounded by the shear yielding and the shear jamming lines that meet at a yielding-jamming crossover point. This solid phase can be further divided into two subphases: the stable glass phase, where the system deforms purely elastically and is totally reversible, and the marginal glass phase, where it experiences stochastic plastic deformations at mesoscopic scales and is partially irreversible. The details of the stability-reversibility map depend strongly on the quality of annealing of the glass. This study provides a unified framework for understanding elasticity, plasticity, yielding, and jamming in amorphous solids.

Orientational ordering of closely packed Janus particles.

We study the orientational ordering of 2-dimensional closely packed Janus particles by extensive Monte Carlo simulations. For smaller patch sizes, the system remains in the plastic crystal phase where the rotational degrees of freedom are disordered down to the lowest temperatures. There the liquid consists of dimers and trimers of the attractive patches. For large enough patch sizes, the system exhibits a thermodynamic transition into a phase with the stripe patterns of the patches breaking the three-fold rotational symmetry. Our results strongly suggest that the latter is a 2nd order phase transition whose universality is the same as that of the 3-state Potts model in 2-dimensions. Furthermore we analyzed the relaxation dynamics of the system performing quenching simulations on the stripe phase. We found growth of the domains of the stripes. The relaxation of key dynamical quantities follows universal scaling features in terms of the domain size.

Exploring the complex free-energy landscape of the simplest glass by rheology.

For amorphous solids, it has been intensely debated whether the traditional view on solids, in terms of the ground state and harmonic low energy excitations on top of it, such as phonons, is still valid. Recent theoretical developments of amorphous solids revealed the possibility of unexpectedly complex free-energy landscapes where the simple harmonic picture breaks down. Here we demonstrate that standard rheological techniques can be used as powerful tools to examine nontrivial consequences of such complex free-energy landscapes. By extensive numerical simulations on a hard sphere glass under quasistatic shear at finite temperatures, we show that above the so-called Gardner transition density, the elasticity breaks down, the stress relaxation exhibits slow, and ageing dynamics and the apparent shear modulus becomes protocol-dependent. Being designed to be reproducible in laboratories, our approach may trigger explorations of the complex free-energy landscapes of a large variety of amorphous materials.

Following the evolution of hard sphere glasses in infinite dimensions under external perturbations: compression and shear strain.

We consider the adiabatic evolution of glassy states under external perturbations. The formalism we use is very general. Here we use it for infinite-dimensional hard spheres where an exact analysis is possible. We consider perturbations of the boundary, i.e., compression or (volume preserving) shear strain, and we compute the response of glassy states to such perturbations: pressure and shear stress. We find that both quantities overshoot before the glass state becomes unstable at a spinodal point where it melts into a liquid (or yields). We also estimate the yield stress of the glass. Finally, we study the stability of the glass basins towards breaking into sub-basins, corresponding to a Gardner transition. We find that close to the dynamical transition, glasses undergo a Gardner transition after an infinitesimal perturbation.

Shear modulus of glasses: results from the full replica-symmetry-breaking solution.

We compute the shear modulus of amorphous hard and soft spheres, using the exact solution in infinite spatial dimensions that has been developed recently. We characterize the behavior of this observable in the whole phase diagram, and in particular around the glass and jamming transitions. Our results are consistent with other theoretical approaches, which are unified within this general picture, and they are also consistent with numerical and experimental results. Furthermore, we discuss some properties of the out-of-equilibrium dynamics after a deep quench close to the jamming transition, and we show that a combined measure of the shear modulus and of the mean square displacement allows one to probe experimentally the complex structure of phase space predicted by the full replica-symmetry-breaking solution.

[An autopsy case report of adenosquamous cell carcinoma of the duodenal papilla with multiple liver and lung metastases].

A 63-year-old man was admitted to Saitama-Kyodo Hospital for the management of obstructive jaundice. Gastrointestinal endoscopy revealed a tumor of the duodenal papilla, and tumor biopsy suggested adenosquamous cell carcinoma. Computed tomography revealed multiple tumors in both the liver and lung, and these were diagnosed as metastases using bronchoscopy-guided lung biopsy and ultrasound-guided liver biopsy, respectively. The patient was treated with gemcitabine therapy after successful management of the jaundice by percutaneous transhepatic cholangiodrainage. However, he died three months after hospitalization. Autopsy confirmed a tumor of the duodenal papilla that had invaded both the pancreas and bile duct; moreover, multiple liver and lung metastases were observed. The pathological diagnoses were adenosquamous cell carcinoma. Histopathological findings revealed a mixture of adenocarcinoma and squamous cell carcinoma and promotion of multiplication of the adenocarcinoma. Adenosquamous cell carcinoma of the duodenal papilla is rare and preoperative diagnosis is challenging. Our case is unique because biopsy suggested the diagnosis before treatment.

Transition by breaking of analyticity in the ground state of Josephson junction arrays as a static signature of the vortex jamming transition.

We investigate the ground state of the irrationally frustrated Josephson junction array with a controlling anisotropy parameter λ that is the ratio of the longitudinal Josephson coupling to the transverse one. We find that the ground state has one-dimensional periodicity whose reciprocal lattice vector depends on λ and is incommensurate with the substrate lattice. Approaching the isotropic point λ=1, the so-called hull function of the ground state exhibits analyticity breaking similar to the Aubry transition in the Frenkel-Kontorova model. We find a scaling law for the harmonic spectrum of the hull functions, which suggests the existence of a characteristic length scale diverging at the isotropic point. This critical behavior is directly connected to the jamming transition previously observed in the current-voltage characteristics by a numerical simulation. On top of the ground state there is a gapless continuous band of metastable states, which exhibit the same critical behavior as the ground state.

Replica theory of the rigidity of structural glasses.

We present a first principle scheme to compute the rigidity, i.e., the shear-modulus of structural glasses at finite temperatures using the cloned liquid theory, which combines the replica theory and the liquid theory. With the aid of the replica method which enables disentanglement of thermal fluctuations in liquids into intra-state and inter-state fluctuations, we extract the rigidity of metastable amorphous solid states in the supercooled liquid and glass phases. The result can be understood intuitively without replicas. As a test case, we apply the scheme to the supercooled and glassy state of a binary mixture of soft-spheres. The result compares well with the shear-modulus obtained by a previous molecular dynamic simulation. The rigidity of metastable states is significantly reduced with respect to the instantaneous rigidity, namely, the Born term, due to non-affine responses caused by displacements of particles inside cages at all temperatures down to T = 0. It becomes nearly independent of temperature below the Kauzmann temperature T(K). At higher temperatures in the supercooled liquid state, the non-affine correction to the rigidity becomes stronger suggesting melting of the metastable solid state. Inter-state part of the static response implies jerky, intermittent stress-strain curves with static analogue of yielding at mesoscopic scales.

Emergence of rigidity at the structural glass transition: a first-principles computation.

We compute the shear modulus of structural glasses from a first-principles approach based on the cloned liquid theory. We find that the intrastate shear modulus, which corresponds to the plateau modulus measured in linear viscoelastic measurements, strongly depends on temperature and vanishes continuously when the temperature is increased beyond the glass temperature.

Asperity characteristics of the Olami-Feder-Christensen model of earthquakes.

Properties of the Olami-Feder-Christensen (OFC) model of earthquakes are studied by numerical simulations. The previous study indicated that the model exhibited "asperity"-like phenomena, i.e., the same region ruptures many times near periodically [T. Kotani, Phys. Rev. E 77, 010102(R) (2008)]. Such periodic or characteristic features apparently coexist with power-law-like critical features, e.g., the Gutenberg-Richter law observed in the size distribution. In order to clarify the origin and the nature of the asperity-like phenomena, we investigate here the properties of the OFC model with emphasis on its stress distribution. It is found that the asperity formation is accompanied by self-organization of the highly concentrated stress state. Such stress organization naturally provides the mechanism underlying our observation that a series of asperity events repeat with a common epicenter site and with a common period solely determined by the transmission parameter of the model. Asperity events tend to cluster both in time and in space.

Vortex solid phase with frozen undulations in superconducting Josephson-junction arrays in external magnetic fields.

A vortex solid with self-generated randomness is found theoretically in a frustrated Josephson-junction array under external magnetic field with anisotropic couplings. Vortices induced by the external magnetic field develop stripes parallel to the direction of weaker coupling. It is shown analytically that there is a continuous, gapless band of metastable states in which stripes are deformed randomly by transverse undulation. The vortex solid with the frozen undulation in a metastable state freely slides along the direction of stronger coupling, thereby destroying the ordering of phases even at zero temperature, but is jammed along the direction of weaker coupling.

Periodicity and criticality in the Olami-Feder-Christensen model of earthquakes.

Characteristic versus critical features of earthquakes are studied on the basis of the Olami-Feder-Christensen model. It is found that the local recurrence-time distribution exhibits a sharp delta -function-like peak corresponding to rhythmic recurrence of events with a fixed "period" uniquely determined by the transmission parameter of the model, together with a power-law-like tail corresponding to scale-free recurrence of events. The model exhibits phenomena closely resembling the asperity known in seismology.

Genetic and acoustic population structuring in the Okinawa least horseshoe bat: are intercolony acoustic differences maintained by vertical maternal transmission?

The origin and meaning of echolocation call frequency variation within rhinolophid bats is not well understood despite an increasing number of allopatric and sympatric examples being documented. A bimodal distribution of mean regional call frequency within the Okinawa-jima Island population of Rhinolophus cornutus pumilus (Rhinolophidae) provided a unique opportunity to investigate geographic call frequency variation early in its development. Individual resting echolocation frequencies, partial mitochondrial DNA D-loop sequences and genotypes from six microsatellite loci were obtained from 288 individuals in 11 colonies across the entire length of the island, and nearby Kume-jima Island. Acoustic differences (5-8 kHz) observed between the north and south regions have been maintained despite evidence of sufficient nuclear gene flow across the middle of the island. Significant subdivision of maternally inherited D-loop haplotypes suggested a limitation of movement of females between regions, but not within the regions, and was evidence of female philopatry. These results support a 'maternal transmission' hypothesis whereby the difference in the constant frequency (CF) component between the regions is maintained by mother-offspring transmission of CF, the restricted dispersal of females between regions and small effective population size. We suggest that the mean 5-8 kHz call frequency difference between the regions might develop through random cultural drift.

Geographical variation in echolocation call and body size of the Okinawan least horseshoe bat, Rhinolophus pumilus (Mammalia: Rhinolophidae), on Okinawa-jima Island, Ryukyu Archipelago, Japan.

The Okinawan least horseshoe bat, Rhinolophus pumilus, is a cave-dwelling species endemic to the central and southern Ryukyus, Japan. We analyzed variation in the constant frequency (CF) of the echolocation call and in forearm length (FAL) of this species on Okinawa-jima Island on the basis of data for 479 individuals from 11 caves scattered over the island. CF values in samples from six caves, all located in the southwestern half of Okinawa-jima, were significantly higher than those in samples from five caves in the northeastern half of the island. Also, FAL was significantly greater in the latter group than in the former group, although the ranges of variation in this character substantially overlapped between the two groups. These results suggest substantial differentiation between R. pumilus populations on Okinawa-jima. The implications of our findings for the conservation of this endangered bat species are briefly discussed.

Fragility of the free-energy landscape of a directed polymer in random media.

We examine the sensitiveness of the free-energy landscape of a directed polymer in random media with respect to various kinds of infinitesimally weak perturbation including the intriguing case of temperature chaos. To this end, we combine the replica Bethe Ansatz approach outlined by Sales and Yoshino (e-print cond-mat/0112384), the mapping to a modified Sinai model, and numerically exact calculations by the transfer-matrix method. Our results imply that for all the perturbations under study there is a slow crossover from a weakly perturbed regime, where rare events take place, to a strongly perturbed regime at larger length scales beyond the so-called overlap length, where typical events take place leading to chaos, i.e., a complete reshuffling of the free-energy landscape. Within the replica space, the evidence for chaos is found in the factorization of the replicated partition function induced by infinitesimal perturbations. This is the reflex of explicit replica-symmetry breaking.