Brownian Model Research Articles

Spatial variation in shallow slow earthquake activity in Hyuga-nada, southwest Japan

SUMMARY Hyuga-nada, off the Pacific coast of Kyushu along the Nankai Trough in southwest Japan, is one of the most active slow earthquake regions around Japan. We estimated the energies of shallow tremors and moments of shallow very low frequency earthquakes (VLFEs) in Hyuga-nada using data from a permanent onshore broadband network and temporary ocean–bottom seismometer observations. The energies and moments of these slow earthquakes have a similar along-strike variation and are generally higher south of the subducted Kyushu–Palau Ridge than near the top of the ridge. This spatial variation is also related to the characteristics of slow earthquake migration. The along-strike migration speed was faster at initiation in the south, where the moments of slow earthquakes are higher. After migration entered the subducted Kyushu–Palau Ridge, its speed was decelerated with a parabolic pattern and their moments became smaller. Assuming a constant patch size of slow earthquakes, we estimated that the stress drop of VLFEs in the south of the subducted ridge was approximately three times higher than that near the top of the subducted ridge. According to our observations and a physical model, this stress drop difference between adjacent regions may cause parabolic migration. We also estimated the scaled energy of slow earthquakes from the ratio of the seismic energy rates of tremors to the seismic moment rates of accompanying VLFEs. The spatial variation in scaled energy is not identified inside the Hyuga-nada. Since the range of scaled energy is similar between the south and near the top of the subducted ridge, the apparent stress may be similar if the rigidity is the same. The dominant range of scaled energy of slow earthquakes in Hyuga-nada is 10−11.5–10−8.5. In addition to having similar or one order smaller values compared to other slow earthquake regions, the range of scaled energy in Hyuga-nada is broader. This broader range suggests wide range of characteristic time and various spectral features of slow earthquakes in Hyuga-nada. Based on a Brownian slow earthquake model, the wide range of characteristic time in this area suggests width variations of slow earthquake source area.

De Finetti’s control problem with a concave bound on the control rate

AbstractWe consider De Finetti’s control problem for absolutely continuous strategies with control rates bounded by a concave function and prove that a generalized mean-reverting strategy is optimal in a Brownian model. In order to solve this problem, we need to deal with a nonlinear Ornstein–Uhlenbeck process. Despite the level of generality of the bound imposed on the rate, an explicit expression for the value function is obtained up to the evaluation of two functions. This optimal control problem has, as special cases, those solved in Jeanblanc-Picqué and Shiryaev (1995) and Renaud and Simard (2021) when the control rate is bounded by a constant and a linear function, respectively.

Reaction coordinate flows for model reduction of molecular kinetics.

In this work, we introduce a flow based machine learning approach called reaction coordinate (RC) flow for the discovery of low-dimensional kinetic models of molecular systems. The RC flow utilizes a normalizing flow to design the coordinate transformation and a Brownian dynamics model to approximate the kinetics of RC, where all model parameters can be estimated in a data-driven manner. In contrast to existing model reduction methods for molecular kinetics, RC flow offers a trainable and tractable model of reduced kinetics in continuous time and space due to the invertibility of the normalizing flow. Furthermore, the Brownian dynamics-based reduced kinetic model investigated in this work yields a readily discernible representation of metastable states within the phase space of the molecular system. Numerical experiments demonstrate how effectively the proposed method discovers interpretable and accurate low-dimensional representations of given full-state kinetics from simulations.

Frame potential of Brownian SYK model of Majorana and Dirac fermions

We consider the Brownian SYK, i.e. a system of N Majorana (Dirac) fermions with a white-noise q-body interaction term. We focus on the dynamics of the Frame potentials, a measure of the scrambling and chaos, given by the moments of the overlap between two independent realisations of the model. By means of a Keldysh path-integral formalism, we compute its early and late-time value. We show that, for q > 2, the late time path integral saddle point correctly reproduces the saturation to the value of the Haar frame potential. On the contrary, for q = 2, the model is quadratic and consistently we observe saturation to the Haar value in the restricted space of Gaussian states (Gaussian Haar). The latter is characterised by larger system size corrections that we correctly capture by counting the Goldstone modes of the Keldysh saddle point. Finally, in the case of Dirac fermions, we highlight and resolve the role of the global U(1) symmetry.

Nonequilibrium phase transitions in a Brownian p-state clock model.

We introduce a Brownian p-state clock model in two dimensions and investigate the nature of phase transitions numerically. As a nonequilibrium extension of the equilibrium lattice model, the Brownian p-state clock model allows spins to diffuse randomly in the two-dimensional space of area L^{2} under periodic boundary conditions. We find three distinct phases for p>4: a disordered paramagnetic phase, a quasi-long-range-ordered critical phase, and an ordered ferromagnetic phase. In the intermediate critical phase, the magnetization order parameter follows a power-law scaling m∼L^{-β[over ̃]}, where the finite-size scaling exponent β[over ̃] varies continuously. These critical behaviors are reminiscent of the double Berezinskii-Kosterlitz-Thouless (BKT) transition picture of the equilibrium system. At the transition to the disordered phase, the exponent takes the universal value β[over ̃]=1/8, which coincides with that of the equilibrium system. This result indicates that the BKT transition driven by the unbinding of topological excitations is robust against the particle diffusion. On the contrary, the exponent at the symmetry-breaking transition to the ordered phase deviates from the universal value β[over ̃]=2/p^{2} of the equilibrium system. The deviation is attributed to a nonequilibrium effect from the particle diffusion.

Internal friction as a factor in the anomalous chain length dependence of DNA transcriptional dynamics.

Recent experiments by Brückner et al. [Science 380, 1357 (2023)] have observed an anomalous chain length dependence of the time of near approach of widely separated pairs of genomic elements on transcriptionally active chromosomal DNA. In this paper, I suggest that the anomaly may have its roots in internal friction between neighboring segments on the DNA backbone. The basis for this proposal is a model of chain dynamics formulated in terms of a continuum scaled Brownian walk (sBw) of polymerization index N. The sBw is an extension of the simple Brownian walk model widely used in path integral calculations of polymer properties, differing from it in containing an additional parameter H (the Hurst index) that can be tuned to produce varying degrees of correlation between adjacent monomers. A calculation using the sBw of the mean time τc for chain closure predicts-under the Wilemski-Fixman approximation for diffusion-controlled reactions-that at early times, τc varies as the 2/3 power of N, in close agreement with the findings of the Brückner et al. study. Other scaling relations of that study, including those related to the probability of loop formation and the mean square displacements of terminal monomers, are also satisfactorily accounted for by the model.

Active oscillator: Recurrence relation approach

The present work analyzes stationary distributions of active Brownian particles in a harmonic trap. Generally, obtaining stationary distributions for this system is non-trivial, and to date, no exact expressions are available. In this work, we develop and explore a method based on a transformation of the Fokker–Planck equation into a recurrence relation for generating moments of a distribution. The method, therefore, offers an analytically tractable approach, an alternative to numerical simulations, in a situation where more direct analytical approaches fail. Although the current work focuses on the active Brownian particle model, the method is general and valid for any type of active dynamics and any system dimension.

Phase separation kinetics and cluster dynamics in two-dimensional active dumbbell systems.

Molecular dynamics simulations were employed to investigate the phase separation process of a two-dimensional active Brownian dumbbell model. We evaluated the time dependence of the typical size of the dense component using the scaling properties of the structure factor, along with the averaged number of clusters and their radii of gyration. The growth observed is faster than in active disk models, and this effect is further enhanced under stronger activity. Next, we focused on studying the hexatic order of the clusters. The length associated with the orientational order increases algebraically with time and faster than for spherical active Brownian particles. Under weak active forces, most clusters exhibit a uniform internal orientational order. However, under strong forces, large clusters consist of domains with different orientational orders. We demonstrated that the latter configurations are not stable, and given sufficient time to evolve, they eventually achieve homogeneous configurations as well. No gas bubbles are formed within the clusters, even when there are patches of different hexatic order. Finally, attention was directed towards the geometry and motion of the clusters themselves. By employing a tracking algorithm, we showed that clusters smaller than the typical size at the observation time exhibit regular shapes, while larger ones display fractal characteristics. In between collisions or break-ups, the clusters behave as solid bodies. Their centers of mass undergo circular motion, with radii increasing with the cluster size. The angular velocity of the center of mass equals that of the constituents with respect to their center of mass. These observations were rationalised with a simple mechanical model.

Stronger interspecific sexual differences may be favored when females search for mates in the presence of congeners

Why are some species sexually dimorphic while other closely related species are not? While all females in genus Strauzia share a multiply-banded wing pattern typical of many other true fruit flies, males of four species have noticeably elongated wings with banding patterns “coalesced” into a continuous dark streak across much of the wing. We take an integrative phylogenetic approach to explore the evolution of this dimorphism and develop general hypotheses underlying the evolution of wing dimorphism in flies. We find that the origin of coalesced and other darkened male wing patterns correlate with the inferred origin of host plant sharing in Strauzia. While wing shape among non-host-sharing species tended to be conserved across the phylogeny, shapes of male wings for Strauzia species sharing the same host plant were more different from one another than expected under Brownian models of evolution and overall rates of wing shape change differed between non-host-sharing species and host-sharing species. A survey of North American Tephritidae finds just three other genera with specialist species that share host plants. Host-sharing species in these genera also have wing patterns unusual for each genus. Only genus Eutreta is like Strauzia in having the unusual wing patterns only in males, and of genera that have multiple species sharing hosts, only in Eutreta and Strauzia do males hold territories while females search for mates. We hypothesize that in species that share host plants, those where females actively search for males in the presence of congeners may be more likely to evolve sexually dimorphic wing patterns.

Parisian ruin with power-asymmetric variance near the optimal point with application to many-inputs proportional reinsurance

. This article investigates the Parisian ruin probability for a class of Gaussian processes with power-asymmetric behavior of the variance near the unique optimal point. We derive the exact asymptotics as the initial capital tends to infinity and extend the previous result[8] to the case when the length of the Parisian interval is on the Pickands scale. As a primary application, we extend the recent result[13] on the many inputs proportional reinsurance fractional Brownian motion risk model to the Parisian ruin.

Half-wormholes and ensemble averages

Recently, the concept of half-wormholes is introduced to give a resolution to the factorization puzzle in holography and help understand better the relation between ensemble average theories and gravity in the bulk. Half-wormholes are proposed to be the contributions to the gravitational path integral that correspond to fluctuations of each individual theory around the average of the whole ensemble of theories. In this paper, we further explore the extent to which the half-wormhole interpretation is applicable. In particular, to further demonstrate that the half-wormhole interpretation is not merely a feature of a specific theory but is a general feature of ensemble average theories, we examine various models, including different enriched 0-dimensional SYK-like models, the 1-dimensional Brownian SYK model and its generalization. To further demonstrate that the half-wormhole interpretation applies to more general probability distributions apart from the zero-mean Gaussian distribution, we consider random couplings with other non-trivial moments. Specifically, introducing a non-trivial mean value to the random coupling renders the spectral correlators to exhibit both disconnected saddles and connected saddles. The inclusion of higher-order moments leads to new “multi-linked half-wormhole” saddles. We also clarify the distinctions between the unlinked half-wormhole and the linked half-wormhole in our modified Brownian SYK model.

Conservation of Bewick’s swans (Cygnus columbianus bewickii): Insights from the identification of critical stopover sites and migration corridors

Migratory birds face diverse threats during migration. Critical stopover sites (CSSs) are essential refueling and resting sites for migratory birds that ensure their complete migration and survival. Therefore, identifying bird migration patterns, routes, and critical habitats is vital for conservation. From 2018–2022, we deployed satellite tracking devices on 30 Bewick’s swans (Cygnus columbianus bewickii) wintering in China to determine their migration routes. Using a dynamic Brownian bridge movement model, we identified migration corridors, core movement areas, and CSSs for Bewick’s swans. Combining protected area databases and human settlement types, we further assessed the swans’ conservation status and human impacts on CSSs. The results showed that Bewick’s swans migrated north from their wintering grounds using one of three routes (west, middle, and east), passing through Mongolia to reach the Russian Arctic (breeding grounds) in spring. They followed similar routes during autumn to return to wintering grounds. We found a new middle route within the East Asian–Australasian Flyway (EAAF) and several northward expanded wintering sites. Our study revealed similarities and differences in the spring and autumn migrations, with longer stopover durations in spring due to migration strategies and ice conditions. Moreover, our findings identified the Inner Mongolia region, the Songnen Plain, the Bohai Rim of China, and the main streams of the Lena River and the Ob River of Russia as CSSs for Bewick’s swans. However, the conservation status of the CSSs was relatively low; and the situation was more severe in spring than in autumn, only 4.3% of the total area was protected, likely due to the distribution of farmland and urban areas. Specifically, 14.3% of the CSSs in China were in urban areas during spring, while in Mongolia and Russia this figure was less than 1%. Therefore, it is necessary to balance waterbird conservation with sustainable agriculture and urban development. This research contributes to our understanding of the migratory ecology of Bewick’s swans wintering in China. The identified migration corridors and CSSs are crucial for the future conservation of swans along the EAAF.

Spatial Ecology of an Arboreal Iguana (Oplurus cyclurus) in a Treeless Landscape.

Understanding the spatial ecology of species has important implications for conservation, as it helps identify suitable habitats and minimum requirements for biodiversity monitoring and management. The spiny-tailed lizard Oplurus cyclurus is a widespread endemic iguanid occurring in dry areas of southern and western Madagascar. While the species is known to be mostly arboreal, populations of the Isalo sandstone massif suggest local adaptation to a less forested savannah and a more exposed habitat. We radio-tracked 19 spiny-tailed lizards to investigate the species' rock-dwelling behaviour and spatial ecology at Isalo National Park. Tracked individuals showed high site and burrow fidelity, and a basking behaviour mostly tied to the accessibility of their burrow, the time of day, and their life stage. Activity peaked during the sunniest hours, while juveniles were more active than adults with unfavourable weather conditions. Despite high burrow fidelity, lizards used shelters non-exclusively, regularly changing (approx. once a week) with neighbouring burrows (average distance between burrows = 13.6 m). However, there was no obvious relation between lizards' body and/or tail size and the width and depth of selected burrows. Dynamic Brownian Bridge Movement Models estimated frequented areas over 247.8 m2 (95% isopleth), where territorial overlap is common. Our results challenge the notion that burrow-site fidelity is the sole driving factor behind space utilization in the studied population. We argue that the apparently unusual saxicolous habits imposed by habitat features (the absence of trees) may lead to local behavioural adjustments influencing antipredatory and foraging strategies, as well as intraspecific interactions.

Paleoseismic Earthquake Recurrence Interval Derivation for the 2022 Revision of the New Zealand National Seismic Hazard Model

Abstract Recurrence intervals of ground-surface rupturing earthquakes are one of numerous datasets used to constrain the rates of fault ruptures in the 2022 revision of the New Zealand National Seismic Hazard Model (NZ NSHM 2022). Paleoearthquake timing and single-event displacement (SED) data in the New Zealand Paleoseismic Site Database version 1.0 alongside geologic and geodetic slip rates from the New Zealand Community Fault Model version 1.0 and NZ NSHM 2022 Geodetic Deformation Model were used to estimate recurrence intervals on faults across New Zealand for inclusion in the NZ NSHM 2022. Past earthquake timings were fit with lognormal, exponential, and Brownian Passage Time recurrence models to derive probability density functions (PDFs) of mean recurrence interval (MRI) in a Bayesian framework. At some sites, SED and slip-rate (SR) data were used to estimate PDFs of MRI; and at sites where timings, slip rate, and displacement data are available, the timings-based and slip-based PDFs were combined to develop tighter constraints on MRI. Using these approaches, we produce a database of maximum-likelihood MRIs and their uncertainties for 80 sites across New Zealand. The resulting recurrence interval dataset is publicly available and is the largest such dataset in New Zealand to date. It provides a valuable resource for future seismic hazard modeling and highlights areas that would benefit from future study.

Partial spontaneous intersubunit rotations in pretranslocation ribosomes

The two main steps of translation, peptidyl transfer, and translocation are accompanied by counterclockwise and clockwise rotations of the large and small ribosomal subunits with respect to each other. Upon peptidyl transfer, the small ribosomal subunit rotates counterclockwise relative to the large subunit, placing the ribosome into the rotated conformation. Simultaneously, tRNAs move into the hybrid conformation, and the L1 stalk moves inward toward the P-site tRNA. The conformational dynamics of pretranslocation ribosomes were extensively studied by ensemble and single-molecule methods. Different experimental modalities tracking ribosomal subunits, tRNAs, and the L1 stalk showed that pretranslocation ribosomes undergo spontaneous conformational transitions. Thus, peptidyl transfer unlocks the ribosome and decreases an energy barrier for the reverse ribosome rotation during translocation. However, the tracking of translation with ribosomes labeled at rRNA helices h44 and H101 showed a lack of spontaneous rotations in pretranslocation complexes. Therefore, reverse intersubunit rotations occur during EF-G catalyzed translocation. To reconcile these views, we used high-speed single-molecule microscopy to follow translation in real time. We showed spontaneous rotations in puromycin-released h44-H101 dye-labeled ribosomes. During elongation, the h44-H101 ribosomes undergo partial spontaneous rotations. Spontaneous rotations in h44-H101-labeled ribosomes are restricted prior to aminoacyl-tRNA binding. The pretranslocation h44-H101 ribosomes spontaneously exchanged between three different rotational states. This demonstrates that peptidyl transfer unlocks spontaneous rotations and pretranslocation ribosomes can adopt several thermally accessible conformations, thus supporting the Brownian model of translocation.

Operator size distribution in large N quantum mechanics of Majorana fermions

Under the Heisenberg evolution in chaotic quantum systems, initially simple operators evolve into complicated ones and ultimately cover the whole operator space. We study the growth of the operator “size” in this process, which is related to the out-of-time-order correlator (OTOC). We derive the full time evolution of the size distribution in large N quantum mechanics of Majorana fermions. As examples, we apply the formalism to the Brownian SYK model (infinite temperature) and the large q SYK model (finite temperature).

Habitat utilization distribution of sika deer (Cervus nippon)

Habitat-specific and movement-related behavioral studies are essential for the development of sustainable biodiversity management practices. Although the number of studies on sika deer is increasing, habitat utilization distribution (UD)-related studies remain limited. In this study, we investigated the habitat UD behavior of sika deer (Cervus nippon) using a literature survey and an experimental study on Suncheon Bonghwasan Mountain, South Korea. We reviewed home range-related literature on sika deer published between 1982 and 2019 in order to assess their estimation methods, study region, and research background. We observed that the number of studies on sika deer has increased. The minimum convex polygon (MCP) has been utilized the most to estimate habitat UD, followed by the kernel density (KD), the Brownian bridge model, and a combination of these methods. The average home ranges (95 % utilization distribution) of sika deer from the literature survey were 236.99 ha and 1183.96 ha using the minimum convex polygon and kernel density approaches, respectively. The five female deer in our experimental study on Suncheon Bonghwasan Mountain had a mean home range of 66.831 ± 15.241 ha using the MCP approach and 78.324 ± 20.82 ha using the KD approach. The UD behavior of sika deer explored in this research is expected to benefit future scholars and policymakers when formulating deer management and wildlife conservation strategies.

Control of Active Brownian Particles: An Exact Solution.

Control of stochastic systems is a challenging open problem in statistical physics, with a wealth of potential applications from biology to granulates. Unlike most cases investigated so far, we aim here at controlling a genuinely out-of-equilibrium system, the two dimensional active Brownian particles model in a harmonic potential, a paradigm for the study of self-propelled bacteria. We search for protocols for the driving parameters (stiffness of the potential and activity of the particles) bringing the system from an initial passivelike steady state to a final activelike one, within a chosen time interval. The exact analytical results found for this prototypical model of self-propelled particles brings control techniques to a wider class of out-of-equilibrium systems.

Quantum error correction from complexity in Brownian SYK

We study the robustness of quantum error correction in a one-parameter ensemble of codes generated by the Brownian SYK model, where the parameter quantifies the encoding complexity. The robustness of error correction by a quantum code is upper bounded by the “mutual purity” of a certain entangled state between the code subspace and environment in the isometric extension of the error channel, where the mutual purity of a density matrix ρAB is the difference {mathcal{F}}_{rho}left(A:Bright)equiv textrm{Tr} {rho}_{AB}^2-textrm{Tr} {rho}_A^2 textrm{Tr} {rho}_B^2 . We show that when the encoding complexity is small, the mutual purity is O(1) for the erasure of a small number of qubits (i.e., the encoding is fragile). However, this quantity decays exponentially, becoming O(1/N) for O(log N) encoding complexity. Further, at polynomial encoding complexity, the mutual purity saturates to a plateau of O(e−N). We also find a hierarchy of complexity scales associated to a tower of subleading contributions to the mutual purity that quantitatively, but not qualitatively, adjust our error correction bound as encoding complexity increases. In the AdS/CFT context, our results suggest that any portion of the entanglement wedge of a general boundary subregion A with sufficiently high encoding complexity is robustly protected against low-rank errors acting on A with no prior access to the encoding map. From the bulk point of view, we expect such bulk degrees of freedom to be causally inaccessible from the region A despite being encoded in it.

Recurrence and Long-Term Evaluation of Kanto Earthquakes

ABSTRACT The 1923 Taisho Kanto earthquake—an interplate event along the Sagami trough where the Philippine Sea plate subducts beneath the Kanto region—produced ground shaking, crustal deformation, landslides, and tsunamis, and caused the worst earthquake disaster in Japan. Based on seismological and geodetic data, many fault models have been proposed, extending ∼100 km from the epicenter, with a moment magnitude (Mw) of 7.8–8.2, and large slips of ∼8 m located near the epicenter and beneath the Miura Peninsula. The penultimate 1703 Genroku Kanto earthquake produced similar macroseismic effects around Sagami Bay and the Miura Peninsula, but larger coastal uplift and tsunami in the Boso Peninsula. The proposed fault models extend off the Boso Peninsula with Mw of 8.1–8.5. In 2004, the Earthquake Research Committee (ERC) classified the Kanto earthquakes as “Taisho type” and “Genroku type” with recurrence intervals of 200–400 yr and 2300 yr, respectively. In 2014, the ERC revised the long-term evaluation to a recurrence interval of 180–590 yr and a 30 yr probability of 0%–5% based on the Brownian passage time model. With the Cabinet Office, the ERC considered the source area of the maximum possible earthquake of Mw 8.6–8.7. The recent historiographical and paleoseismological studies have identified other candidates for the past Kanto earthquakes in 1495, 1433, 1293, and 878. Various combinations of these candidates give a mean recurrence interval of 210–315 yr, an aperiodicity parameter of 0.04–0.76, and a 30 yr probability of 0.0%–19%. The Cabinet Office has calculated the seismic intensity and tsunami heights of various types of Kanto earthquakes. National and local governments estimate the damage from these hazards. For the Tokyo metropolitan area, the estimated damage and occurrence probability are more significant for M ∼7 earthquakes with various types and depths, and most mitigation efforts are directed at such events.