Dynamical Regimes Research Articles

Granular collapse in fluids: Dynamics and flow regime identification

The collapse of granular material in fluids is a prevalent phenomenon in both natural and industrial processes, displaying a notable sensitivity to initial configuration of the system. This study is specifically oriented towards falling process of collapsing material under various fluid conditions, employing the computational fluid dynamics-discrete element method (CFD-DEM) to primarily investigate the dynamics and scaling laws of deposit morphology of collapsed material. Through a comprehensive analysis of particle sedimentation in fluids, we introduce a refined inertial characteristic time for granular collapse within the inertial regime. Subsequently, we propose modifications to conventional fluid-particle density ratio and Reynolds number, aiming to enhance the accuracy of depicting collapse dynamics and identifying flow regimes across diverse column heights and fluid conditions. Finally, we construct a phase diagram of flow regimes using modified dimensionless numbers, emphasizing the role of column height in transition between viscous and inertial regimes. These parameters demonstrate enhanced relevance in governing the collapse of immersed granular columns, thereby contributing to a more nuanced understanding of fluid-particle interations in dense granular flows under different regimes.

Condition for metal fragmentation during Earth-forming collisions

The long-term evolution of the deep Earth depends on its initial temperature and composition. These were set by the large planetary collisions that formed the Earth. After each collision, the metallic core of the impactor fell into a molten silicate magma ocean. Previous investigations showed that, as it sank, the impactor core fragmented into drops. The overall fragmentation of the core controlled the efficiency of chemical transfers between the impactor metal and the magma ocean, and, as a consequence, the composition of the Earth's core and mantle. However, because previous studies lack an impact stage, it is unclear whether the projectile core fragmented during the impact at Earth's surface, or deeper in the magma ocean.To answer this question, we conduct laboratory experiments modeling the collision of single-phase and two-phase impactors. In a first series of experiments, we investigate the impact of a single-phase centimetric liquid volume, representing the impactor core, onto a lighter immiscible liquid, representing the magma ocean. Our experiments approach the dynamical regime of planetary collisions for which inertia is large compared to surface tension. Varying the velocity and size of the impactor, we determine the conditions under which the impactor fragments into drops. We find that fragmentation occurs when the Froude number, which measures the relative importance of inertia to gravity, is larger than 40, regardless of surface tension. This fragmentation results from the growth of a turbulent Rayleigh-Taylor instability at the interface between the impacting liquid and the target pool. In contrast, when Fr<10, the impactor remains coherent. In a second series of experiments, we use two-phase impactors to show that these results hold for impactors that are differentiated into a core and a mantle.Applied to planet formation, our results suggest that the core of impactors less than 330 km in radius impacting at the escape velocity onto an Earth-sized planet fully fragments into droplets during the impact process, whereas the core of a giant Mars-sized impactor remains coherent. We derive a model for the depth at which the impactor core fragments in the magma ocean as a function of the impactor size and velocity. This model predicts that impactors with a radius less than 800 km fully fragment before reaching the bottom of the magma ocean. For velocities higher than twice the escape speed, some degree of fragmentation is unavoidable for any impactor size.

Optimal superdense coding capacity in the non-Markovian regime

Superdense coding (SDC) is a significant technique widely used in quantum information processing. Indeed, it consists of sending two bits of classical information using a single qubit, leading to faster and more efficient quantum communication. In this paper, we propose a model to evaluate the effect of backflow information in a SDC protocol through a non-Markovian dynamics. The model considers a qubit interacting with a structured Markovian environment. In order to generate a non-Markovian dynamic, an auxiliary qubit contacts a Markovian reservoir in such a way that the non-Markovian regime can be induced. By varying the coupling strength between the central qubit and the auxiliary qubit, the two dynamical regimes can be switched interchangeably. An enhancement in non-Markovian effects corresponds to an increase in this coupling strength. Furthermore, we conduct an examination of various parameters, namely temperature weight, and decoherence parameters in order to explore the behaviors of SDC, quantum fisher information (QFI), and local quantum uncertainty using an exact calculation. The obtained results show a significant relationship between non-classical correlations and QFI since they behave similarly, allowing them to detect what is beyond entanglement. In addition, the presence of non-classical correlations enables us to detect the optimal SDC capacity in a non-Markovian regime.

Mean-field analysis of the glassy dynamics of an elastoplastic model of super-cooled liquids

We present a mean-field theory of a coarse-grained model of a super-cooled liquid in which relaxation occurs via local plastic rearrangements. Local relaxation can be induced by thermal fluctuations or by the long-range elastic consequences of other rearrangements. We extract the temperature dependence of both the relaxation time and the length scale of dynamical correlations. We find two dynamical regimes. First, a regime in which the characteristic time and length scales diverge as a power law at a critical temperature T c . This regime is found by an approximation that neglects activated relaxation channels, which can be interpreted as akin to the one found by the mode-coupling transition of glasses. In reality, only a crossover takes place at T c . The residual plastic activity leads to a second regime characterised by an Arrhenius law below T c . In this case, we show that the length scale governing dynamical correlations diverges as a power law as , and is logarithmically related to the relaxation time.

Moving contact line dynamics for capillary-driven microfluidics in wetting transition regime

The dynamics of moving contact lines (MCLs) dominate the behavior of capillary-driven microfluidics, which underlie many applications including microfluidic chips. The capillary displacement dynamics in the quasi-static regime has been extensively studied. However, the behavior of MCLs in the dynamic wetting transition regime remains largely unexplored, and previously established MCL dynamic models may be inadequate. In this study, a novel capillary displacement experiment is introduced, which is achieved by reversely introducing microfluidics with surface tension differences, where the one with low surface tension undergoes the wetting transition. In addition, a generalized Navier boundary condition (GNBC)-based model of capillary displacement dynamics is developed within the framework of diffusive interface theory to investigate the MCL dynamics in the wetting transition regime. The oscillation-relaxation process is experienced for phase interface and microscopic dynamic contact angle θd in the wetting transition regime. Spontaneous filling distance follows dfill*∼t1/2, and reaching quasi-static stage follows dfill*∼t1. The previously neglected mechanism of inertial-viscous competition dominates the early dynamics of such dynamic wetting transition processes. θd∝ucl is observed to be valid solely under conditions where viscosity dominates, but it breaks down in the presence of dominant inertial effects. An escalation in slip substantially diminishes the influence of inertia, with frictional dissipation mediated by slip emerging as the predominant factor in the capillary-driven early dynamics. The origin of uncompensated Young's stress in the GNBC and its correlation with capillary forces is unified, unveiling the underlying physical mechanism governing the dynamics at the MCL. Finally, by decoupling the analysis of viscosity and slip, a new θd-viscous-slip formulation is proposed, in agreement with the model predictions.

Ensemble learning and ground-truth validation of synaptic connectivity inferred from spike trains.

Probing the architecture of neuronal circuits and the principles that underlie their functional organization remains an important challenge of modern neurosciences. This holds true, in particular, for the inference of neuronal connectivity from large-scale extracellular recordings. Despite the popularity of this approach and a number of elaborate methods to reconstruct networks, the degree to which synaptic connections can be reconstructed from spike-train recordings alone remains controversial. Here, we provide a framework to probe and compare connectivity inference algorithms, using a combination of synthetic ground-truth and in vitro data sets, where the connectivity labels were obtained from simultaneous high-density microelectrode array (HD-MEA) and patch-clamp recordings. We find that reconstruction performance critically depends on the regularity of the recorded spontaneous activity, i.e., their dynamical regime, the type of connectivity, and the amount of available spike-train data. We therefore introduce an ensemble artificial neural network (eANN) to improve connectivity inference. We train the eANN on the validated outputs of six established inference algorithms and show how it improves network reconstruction accuracy and robustness. Overall, the eANN demonstrated strong performance across different dynamical regimes, worked well on smaller datasets, and improved the detection of synaptic connectivity, especially inhibitory connections. Results indicated that the eANN also improved the topological characterization of neuronal networks. The presented methodology contributes to advancing the performance of inference algorithms and facilitates our understanding of how neuronal activity relates to synaptic connectivity.

Reduced dimensional Monte Carlo method: Preliminary integrations.

A technique for reducing the number of integrals in a Monte Carlo calculation is introduced. For integrations relying on classical or mean-field trajectories with local weighting functions, it is possible to integrate analytically at least half of the integration variables prior to setting up the particular Monte Carlo calculation of interest, in some cases more. Proper accounting of invariant phase space structures shows that the system's dynamics is reducible into composite stable and unstable degrees of freedom. Stable degrees of freedom behave locally in the reduced dimensional phase space exactly as an analogous integrable system would. Classification of the unstable degrees of freedom is dependent upon the degree of chaos present in the dynamics. The techniques for deriving the requisite canonical coordinate transformations are developed and shown to block diagonalize the stability matrix into irreducible parts. In doing so, it is demonstrated how to reduce the amount of sampling directions necessary in a Monte Carlo simulation. The technique is illustrated by calculating return probabilities and expectation values for different dynamical regimes of a two-degrees-of-freedom coupled quartic oscillator within a classical Wigner method framework.

Low-dimensional criticality embedded in high-dimensional awake brain dynamics.

Whether cortical neurons operate in a strongly or weakly correlated dynamical regime determines fundamental information processing capabilities and has fueled decades of debate. We offer a resolution of this debate; we show that two important dynamical regimes, typically considered incompatible, can coexist in the same local cortical circuit by separating them into two different subspaces. In awake mouse motor cortex, we find a low-dimensional subspace with large fluctuations consistent with criticality-a dynamical regime with moderate correlations and multi-scale information capacity and transmission. Orthogonal to this critical subspace, we find a high-dimensional subspace containing a desynchronized dynamical regime, which may optimize input discrimination. The critical subspace is apparent only at long timescales, which explains discrepancies among some previous studies. Using a computational model, we show that the emergence of a low-dimensional critical subspace at large timescales agrees with established theory of critical dynamics. Our results suggest that the cortex leverages its high dimensionality to multiplex dynamical regimes across different subspaces.

Evolving division of labor in a response threshold model

The response threshold model explains the emergence of division of labor (i.e., task specialization) in an unstructured population by assuming that the individuals have different propensities to work on different tasks. The incentive to attend to a particular task increases when the task is left unattended and decreases when individuals work on it. Here we derive mean-field equations for the stimulus dynamics and show that they exhibit complex attractors through period-doubling bifurcation cascades when the noise disrupting the thresholds is small. In addition, we show how the fixed threshold can be set to ensure specialization in both the transient and equilibrium regimes of the stimulus dynamics. However, a complete explanation of the emergence of division of labor requires that we address the question of where the threshold variation comes from, starting from a homogeneous population. We then study a structured population scenario, where the population is divided into a large number of independent groups of equal size, and the fitness of a group is proportional to the weighted mean work performed on the tasks during a fixed period of time. Using a winner-take-all strategy to model group competition and assuming an initial homogeneous metapopulation, we find that a substantial fraction of workers specialize in each task, without the need to penalize task switching.

Executive Approval Dynamics in Presidential and Parliamentary Democratic Regimes

Does the type of democratic regime matter for public evaluations of leaders? We argue two characteristics intrinsic to presidential and parliamentary regimes lead to divergent patterns of executive approval. For presidents, direct elections foster more personal leader-voter linkages; for prime ministers, dependence on the legislature for survival contributes to more institutionalized party systems. These two mechanisms should generate higher approval at the outset of a term—larger honeymoons— for presidents than for prime ministers, but also more rapid decline. Analyses of data from 40 countries produce evidence consistent with these constitutionally-based distinctions. Yet we uncover important within-regime differences. Within presidential systems, approval patterns vary along with paths to power—first-election versus re-election, and elected versus unelected. Within parliamentarism, honeymoons are greater for prime ministers overseeing single-party majoritarian governments. Study findings advance long-standing debates about the relative merits of presidential and parliamentary systems—particularly the tradeoff between democratic responsiveness and stability.

Experimental study of the shear behavior of concrete-rock interfaces under static and dynamic loading in the context of low confinement stress

Modified static and dynamic shear tests are introduced to study the shear behavior of concrete-rock interfaces under static and dynamic loading in the context of low confinement stresses. Static and dynamic shear tests of concrete-sandstone and concrete-granite interfaces are performed using these techniques. Three levels of interface roughness are considered: smooth, bush-hammered, and rough rock surfaces. The results of these tests show that in both static and dynamic regimes, the shear evolution of concrete-rock interfaces can be described according to three successive stages: the shear stress accumulation, the shear slip, and the residual shear stress stage. The main parameters driving the shear process are the concrete-rock bonds, the interface roughness, and the residual friction. However, unlike in the static shear evolution, in the dynamic shear evolution, the concrete-rock bonds and the roughness seem active in the shear stress accumulation stage. Furthermore, the correlation between the shear strength and the normal stress is stronger in static than dynamic conditions. The significance of the normal stress on the dynamic shear strength appears more important in rough concrete-granite interfaces than in the other two interfaces. Lastly, the dynamic peak shear strengths of all the interfaces tested are three to four times higher than their static counterparts.

Strain rate-dependent behavior of cold-sprayed additively manufactured Al–Al[formula omitted]O[formula omitted] composites: Micromechanical modeling and experimentation

Metal matrix composites (MMCs) fabricated by cold spray additive manufacturing (CSAM) are increasingly gaining attention as structural materials due to their rapid production and scalability. Herein, the failure behavior of CSAM Al–Al2O3 composites under quasi-static and dynamic compression was studied by an experimentally informed/validated 3D microstructure-based finite element (FE) model. The debonding mechanism was found to grow at a higher rate consequently dampening the particle cracking mechanism when the strain rate rises to dynamic regimes. The stress-bearing capacity of the particles plays a key role in enhancing the flow stress and elongation at failure of the CSAM composite under high strain rates due to the lower propensity of particle cracking. Eventually, the model was exercised to study the microscale failure progression in the material under elevated temperatures. For the first time in the literature, this study informs on the correlation between the microscale failure mechanisms and the mechanical performance of CSAM MMCs at the macro scale across strain rates and temperatures whose outcomes are applicable to the design of next-generation materials with a tailored performance.

Impacts of Quaternary Climatic Changes on the Diversification of Riverine Cichlids in the Lower Congo River.

Climatic and geomorphological changes during the Quaternary period impacted global patterns of speciation and diversification across a wide range of taxa, but few studies have examined these effects on African riverine fish. The lower Congo River is an excellent natural laboratory for understanding complex speciation and population diversification processes, as it is hydrologically extremely dynamic and recognized as a continental hotspot of diversity harboring many narrowly endemic species. A previous study using genome-wide SNP data highlighted the importance of dynamic hydrological regimes to the diversification and speciation in lower Congo River cichlids. However, historical climate and hydrological changes (e.g., reduced river discharge during extended dry periods) have likely also influenced ichthyofaunal diversification processes in this system. The lower Congo River offers a unique opportunity to study climate-driven changes in river discharge, given the massive volume of water from the entire Congo basin flowing through this short stretch of the river. Here, we, for the first time, investigate the impacts of paleoclimatic factors on ichthyofaunal diversification in this system by inferring divergence times and modeling patterns of gene flow in four endemic lamprologine cichlids, including the blind cichlid, Lamprologus lethops. Our results suggest that Quaternary climate changes associated with river discharge fluctuations may have impacted the diversification of species along the system and the emergence of cryptophthalmic phenotype in some endemic species. Our study, using reduced representation sequencing (2RADseq), indicates that the lower Congo River lamprologines emerged during the Early-Middle Pleistocene transition, characterized as one of the earth's major climatic transformation periods. Modeling results suggest that gene flow across populations and between species was not constant but occurred in temporally constrained pulses. We show that these results correlate with glacial-interglacial fluctuations. The current hyper-diverse fish assemblages of the lower Congo River riverscape likely reflect the synergistic effects of multiple drivers fueling complex evolutionary processes through time.

Seeking a quantum advantage with trapped-ion quantum simulations of condensed-phase chemical dynamics.

Simulating the quantum dynamics of molecules in the condensed phase represents a longstanding challenge in chemistry. Trapped-ion quantum systems may serve as a platform for the analog-quantum simulation of chemical dynamics that is beyond the reach of current classical-digital simulation. To identify a 'quantum advantage' for these simulations, performance analysis of both analog-quantum simulation on noisy hardware and classical-digital algorithms is needed. In this Review, we make a comparison between a noisy analog trapped-ion simulator and a few choice classical-digital methods on simulating the dynamics of a model molecular Hamiltonian with linear vibronic coupling. We describe several simple Hamiltonians that are commonly used to model molecular systems, which can be simulated with existing or emerging trapped-ion hardware. These Hamiltonians may serve as stepping stones towards the use of trapped-ion simulators for systems beyond the reach of classical-digital methods. Finally, we identify dynamical regimes in which classical-digital simulations seem to have the weakest performance with respect to analog-quantum simulations. These regimes may provide the lowest hanging fruit to make the most of potential quantum advantages.

Learning spiking neuronal networks with artificial neural networks: neural oscillations.

First-principles-based modelings have been extremely successful in providing crucial insights and predictions for complex biological functions and phenomena. However, they can be hard to build and expensive to simulate for complex living systems. On the other hand, modern data-driven methods thrive at modeling many types of high-dimensional and noisy data. Still, the training and interpretation of these data-driven models remain challenging. Here, we combine the two types of methods to model stochastic neuronal network oscillations. Specifically, we develop a class of artificial neural networks to provide faithful surrogates to the high-dimensional, nonlinear oscillatory dynamics produced by a spiking neuronal network model. Furthermore, when the training data set is enlarged within a range of parameter choices, the artificial neural networks become generalizable to these parameters, covering cases in distinctly different dynamical regimes. In all, our work opens a new avenue for modeling complex neuronal network dynamics with artificial neural networks.

Maximum entropy network states for coalescence processes

Complex network states are characterized by the interplay between system’s structure and dynamics. One way to represent such states is by means of network density matrices, whose von Neumann entropy characterizes the number of distinct microstates compatible with given topology and dynamical evolution. In this Letter, we propose a maximum entropy principle to characterize network states for systems with heterogeneous, generally correlated, connectivity patterns and non-trivial dynamics. We focus on three distinct coalescence processes, widely encountered in the analysis of empirical interconnected systems, and characterize their entropy and transitions between distinct dynamical regimes across distinct temporal scales. Our framework allows one to study the statistical physics of systems that aggregate, such as in transportation infrastructures serving the same geographic area, or correlate, such as inter-brain synchrony arising in organisms that socially interact, and active matter that swarm or synchronize.

Estimating dynamic treatment regimes for ordinal outcomes with household interference: Application in household smoking cessation.

The focus of precision medicine is on decision support, often in the form of dynamic treatment regimes, which are sequences of decision rules. At each decision point, the decision rules determine the next treatment according to the patient's baseline characteristics, the information on treatments and responses accrued by that point, and the patient's current health status, including symptom severity and other measures. However, dynamic treatment regime estimation with ordinal outcomes is rarely studied, and rarer still in the context of interference - where one patient's treatment may affect another's outcome. In this paper, we introduce the weighted proportional odds model: a regression based, approximate doubly-robust approach to single-stage dynamic treatment regime estimation for ordinal outcomes. This method also accounts for the possibility of interference between individuals sharing a household through the use of covariate balancing weights derived from joint propensity scores. Examining different types of balancing weights, we verify the approximate double robustness of weighted proportional odds model with our adjusted weights via simulation studies. We further extend weighted proportional odds model to multi-stage dynamic treatment regime estimation with household interference, namely dynamic weighted proportional odds model. Lastly, we demonstrate our proposed methodology in the analysis of longitudinal survey data from the Population Assessment of Tobacco and Health study, which motivates this work. Furthermore, considering interference, we provide optimal treatment strategies for households to achieve smoking cessation of the pair in the household.

Conformal diagrams for stationary and dynamical strong-field hyperboloidal slices

Conformal Carter–Penrose diagrams are used for the visualization of hyperboloidal slices, which are smooth spacelike slices reaching null infinity. The focus is on the Schwarzschild black hole geometry in spherical symmetry, whose Penrose diagrams are introduced in a pedagogical way. The stationary regime involves time-independent slices. In this case, different options are given for integrating the height function—the main ingredient for constructing hyperboloidal foliations. The dynamical regime considers slices changing in time, which are evolved together with the spacetime using the eikonal equation. It includes the relaxation of hyperboloidal Schwarzschild trumpet slices and the collapse of a massless scalar field into a black hole, for which Penrose diagrams are presented.

Recovering Quasi-Biennial Oscillations from Chaos

Abstract The Quasi-Biennial Oscillation (QBO) is understood to result from wave-mean-flow interactions, but the reasons for its relative stability remain a subject of ongoing debate. In addition, consensus has yet to be reached regarding the respective roles of different equatorial wave types in shaping the QBO’s characteristics. Here we employ Holton-Lindzen-Plumb’s quasilinear model to shed light on the robustness of periodic behavior in the presence of multiple wave forcings. A comprehensive examination of the various dynamical regimes in this model reveals that increased vertical wave propagation at higher altitudes favors periodicity. In the case of single standing wave forcing, enhanced vertical propagation is controlled by the wave attenuation length scale. The occurrence of non-periodic states at high forcing amplitudes is explained by the excitation of high vertical unstable modes. Increasing the attenuation length scale prevents the emergence of such modes. When multiple wave forcing is considered, the mean flow generated by a dominant primary wave facilitates greater vertical propagation of a perturbation wave. Raising the altitude where most of the wave damping occurs favors periodicity by preventing the development of secondary jets responsible for the aperiodic behavior. This mechanism underscores the potential role of internal gravity waves in supporting the periodicity of a QBO primarily driven by planetary waves.

Thermalization of long range Ising model in different dynamical regimes: A full counting statistics approach

We study the thermalization of the transverse field Ising chain with a power law decaying interaction \sim 1/r^{\alpha}∼1/rα following a global quantum quench of the transverse field in two different dynamical regimes. The thermalization behavior is quantified by comparing the full probability distribution function (PDF) of the evolving states with the corresponding thermal state given by the canonical Gibbs ensemble (CGE). To this end, we used the matrix product state (MPS)-based Time Dependent Variational Principle (TDVP) algorithm to simulate both real time evolution following a global quantum quench and the finite temperature density operator. We observe that thermalization is strongly suppressed in the region with strong confinement for all interaction strengths \alphaα, whereas thermalization occurs in the region with weak confinement.