Ensemble Behavior Research Articles

Ensemble Force Spectroscopy of a G-Quadruplex Cluster on a Single-Molecule Platform.

Single-molecule methods offer high sensitivities with precisions superior to bulk assays. However, these methods are low in throughput and cannot repetitively interrogate the same cluster of molecular units. In this work, we investigate a tandem array of G-quadruplexes on a single-molecule DNA template with a throughput of at least two orders of magnitude higher than single-molecule force spectroscopy. During mechanical unfolding by optical tweezers, the array of G-quadruplexes experiences identical force, temperature, and ionic conditions, which not only reduce environmental noise but also render unfolding transitions indistinguishable among individual G-quadruplexes. The resultant ensemble behaviors are analyzed by scanning force diagrams, which reveals accurate F1/2 values, where 50% of G-quadruplexes are unfolded. Independent of the number of G-quadruplexes (n > 15) contained in a cluster, F1/2 can effectively evaluate G-quadruplex ligands in a new method called differential scanning forcemetry. When the same G-quadruplex cluster is subject to a series of constant forces in force-jump experiments, unfolding rate constants of G-quadruplexes can be effectively evaluated as a function of force. The high precision demonstrated in all of these measurements reflects the power of repetitive sampling on the same cluster of single-molecule entities under identical conditions. Since biomolecules such as DNA, RNA, and proteins can be conveniently incorporated in a tandem array, we anticipate that this ensemble assay on single-molecule entities (EASE) provides a generic means of ensemble force spectroscopy to amalgamate the accuracy of ensemble measurements with the precision of single-molecule methods.

Critical Dynamics of Strongly Interacting Ensembles in Spin-Exchange-Relaxation-Free Comagnetometers

Spin manipulation and detection of alkali-metal and noble-gas ensembles in spin-exchange-relaxation-free (SERF) comagnetometers are widely used in fundamental physical research, and have potential for inertial navigation. The dynamic behavior of spin ensembles is a vital characteristic that determines the applicability of comagnetometers, which significantly differs from various combinations of alkali-metal and noble-gas species. We comprehensively study the critical dynamics of strongly interacting ensembles in SERF comagnetometers with different species combinations. Different from the self-compensation point, a model of strong coupling point at which the dynamics is nonlinear because two ensembles influence each other strongly is established. We verify it by comparing the transient and steady-state dynamics of K-Rb-${}^{21}\mathrm{Ne}$, K-Rb-${}^{3}\mathrm{He}$, and K-${}^{3}\mathrm{He}$ comagnetometers with various input signals. The K-Rb-${}^{21}\mathrm{Ne}$ comagnetometer has a better potential for bandwidth and sensitivity in inertial measurement. Besides, we propose a critical point where the response rate of coupling spin ensembles is optimal among all polarization, and the critical dynamics is verified experimentally to be in agreement with theoretical simulations. The damping rate and precession frequency at the critical point can be more than 5 times larger than that at typical optimal spin polarization. Enhancement of spin-ensemble coupling strength improves the response rate of SERF comagnetometers and paves the way for efficient manipulation of noble-gas atoms via alkali-metal atoms in quantum information.

Numerical simulation of cold emission in coaxial diode with magnetic isolation

Due to the emergence and active development of new areas of application of powerful and super-powerful microwave vacuum devices, interest in studying the behavior of ensembles of charged particles moving in the interaction space has increased. An example is an electron beam formed in a coaxial diode with magnetic isolation. Numerical simulation of emission in such a diode is traditionally carried out using particle-in-cell methods. They are based on the simultaneous calculation of the equations of motion of particles and the Maxwell’s equations for the electromagnetic field. In the present work, a new computational approach called the point macroparticle method is proposed. In it, the motion of particles is described by the equations of relativistic mechanics, and explicit expressions are written out for fields in a quasi-static approximation. Calculations of the formation of a relativistic electron beam in a coaxial diode with magnetic isolation are performed and a comparison is made with the known theoretical relations for the electron velocity in the beam and for the beam current. Excellent agreement of calculation results with theoretical formulas is obtained.

Generic criterion for explosive synchronization in heterogeneous phase oscillator populations

Ordered and disordered behavior in large ensembles of coupled oscillators map to different functional states in a wide range of applications, e.g., active and resting states in the brain and stable and unstable power grid configurations. For this reason, explosive synchronization transitions, which facilitate fast, abrupt changes between these functional states, has recently seen significant interest from researchers. While previous work has identified properties of complex systems that support explosive synchronization, these investigations have been conducted largely on an ad-hoc basis. Here we provide an exact criterion for explosive synchronization in coupled phase oscillator ensembles by investigating the necessary relationship between dynamical and structural disorder. This result provides a critical step towards untangling the intertwined properties of complex systems responsible for abrupt phase transitions and bistability in biological and engineered systems.

Synchronization in phase-coupled oscillator with attractive–repulsive frequencies

We investigate the synchronization behavior of a simple but quite useful mode of emergent collective behavior in ensembles of interacting dynamical elements, the Kuramoto model with attractive–repulsive frequencies features. Here, we derive a series of phase-locked (PL) states and identify the significant synchronization transition points analytically with exact boundary conditions. A detailed stability study of the model is also presented, as well as the bifurcation of the PL states set. Extremely, we show that these frequencies do not influence the stability of the system model, while the synchronization ability is considerably changed.

Universal scaling limits of the symplectic elliptic Ginibre ensemble

We consider the eigenvalues of symplectic elliptic Ginibre matrices which are known to form a Pfaffian point process whose correlation kernel can be expressed in terms of the skew-orthogonal Hermite polynomials. We derive the scaling limits and the convergence rates of the correlation functions at the real bulk/edge of the spectrum, which in particular establishes the local universality at strong non-Hermiticity. Furthermore, we obtain the subleading corrections of the edge correlation kernels, which depend on the non-Hermiticity parameter contrary to the universal leading term. Our proofs are based on the asymptotic behavior of the complex elliptic Ginibre ensemble due to Lee and Riser as well as on a version of the Christoffel–Darboux identity, a differential equation satisfied by the skew-orthogonal polynomial kernel.

Photothermal behavior for two-dimensional nanoparticle ensembles: Multiple scattering and thermal accumulation effects

Light-assisted micro-nanoscale temperature control in complex nanoparticle network attracts lots of research interests. Many efforts have been put on the optical properties of the nanoparticle networks and only a few investigations on its light-induced thermal behavior was reported. We consider two-dimensional (2D) square-lattice nanoparticle ensemble made of typical metal Ag with a radius of 5 nm. The effect of complex optical coupling and thermal accumulation on the light-induced thermal behavior in plasmonic resonance frequency (around 383 nm) is analyzed by means of the Green\textquotesingle s function approach. Regime borders of both optical coupling and thermal accumulation effects on the photothermal behavior of 2D square-lattice nanoparticle ensemble are figured out clearly and quantitatively. A dimensionless parameter $\varphi$ is defined as the ratio of full temperature increase to that without considering the optical coupling or thermal accumulation to quantify the optical coupling and thermal accumulation effects on photothermal behavior. The more compact the nanoparticle ensemble is, the stronger the optical coupling on thermal behavior is. When the lattice spacing increases to tens of nanoparticle radius, the optical coupling becomes insignificant. When $\varphi \approx 1$ (lattice spacing increases to hundreds of nanoparticle radius), the thermal accumulation effects are weak and can be neglected safely. The polarization-dependent distribution of temperature increase of nanoparticles is observed only in the compact nanoparticle ensemble, while for dilute ensemble, such polarization-dependent temperature increase distribution can not be observed anymore. This work may help for the understanding of the light-induced thermal transport in the 2D particle ensemble.

Performance assessment of ensembles of in situ workflows under resource constraints

SummaryScientific breakthroughs in biomolecular methods and improvements in hardware technology have shifted from a long‐running simulation to a large set of shorter simulations running simultaneously, called an ensemble. In an ensemble, simulations are usually coupled with analyses of data produced by the simulations. In situ methods can be used to analyze large volumes of data generated by scientific simulations at runtime (i.e., simulations and analyses are performed concurrently). In this work, we study the execution of ensemble‐based simulations paired with in situ analyses using in‐memory staging methods. Using an ensemble of molecular dynamics in situ workflows with multiple simulations and analyses, we first show that collecting traditional metrics such as makespan, instructions per cycle, memory usage, or cache miss ratio is not sufficient to characterize complex behaviors of ensembles. We propose a method to evaluate the performance of ensembles of workflows that captures multiple resource usage aspects: resource efficiency, resource allocation, and resource provisioning. Experimental results demonstrate that the proposed method can effectively distinguish the performance of different component placements in an ensemble with up to 32 ensemble members. By evaluating different co‐location scenarios, our proposed performance indicators demonstrate benefits of co‐locating simulation and coupled analyses within a compute node.

PdAg/Ag(111) Surface Alloys: A Highly Efficient Catalyst of Oxygen Reduction Reaction.

In this article, the behavior of various Pd ensembles on the PdAg(111) surfaces was systematically investigated for oxygen reduction reaction (ORR) intermediates using density functional theory (DFT) simulation. The Pd monomer on the PdAg(111) surface (with a Pd subsurface layer) has the best predicted performance, with a higher limiting potential (0.82 V) than Pt(111) (0.80 V). It could be explained by the subsurface coordination, which was also proven by the analysis of electronic properties. In this case, it is necessary to consider the influence of the near-surface layers when modeling the single-atom alloy (SAA) catalyst processes. Another important advantage of PdAg SAA is that atomic-dispersed Pd as adsorption sites can significantly improve the resistance to CO poisoning. Furthermore, by adjusting the Pd ensembles on the catalyst surface, an exciting ORR catalyst combination with predicted activity and high tolerance to CO poisoning can be designed.

Chiral self-assembly of cellulose nanocrystals is driven by crystallite bundles

The transfer of chirality across length-scales is an intriguing and universal natural phenomenon. However, connecting the properties of individual building blocks to the emergent features of their resulting large-scale structure remains a challenge. In this work, we investigate the origins of mesophase chirality in cellulose nanocrystal suspensions, whose self-assembly into chiral photonic films has attracted significant interest. By correlating the ensemble behaviour in suspensions and films with a quantitative morphological analysis of the individual nanoparticles, we reveal an inverse relationship between the cholesteric pitch and the abundance of laterally-bound composite particles. These ‘bundles’ thus act as colloidal chiral dopants, analogous to those used in molecular liquid crystals, providing the missing link in the hierarchical transfer of chirality from the molecular to the colloidal scale.

Single-Molecule Mechanochemical Sensing.

Single-molecule mechanochemical sensing (SMMS) is a novel biosensing technique using mechanical force as a signal transduction mechanism. In the mechanochemical sensing, the chemical binding of an analyte molecule to a sensing template is converted to mechanical signals, such as tensile force, of the template. Since mechanical force can be conveniently monitored by single-molecule tools, such as optical tweezers, magnetic tweezers, or Atomic Force Microscopy, mechanochemical sensing is often carried out at the single molecule level. In traditional format of ensemble sensing, sensitivity can be achieved via chemical or electrical amplifications, which are materials intensive and time-consuming. To address these problems, in 2011, we used the principle of mechanochemical coupling in a single molecular template to detect single nucleotide polymorphism (SNP) in DNA fragments. The single-molecule sensitivity in such SMMS strategy allows to removing complex amplification steps, drastically conserving materials and increasing temporal resolution in the sensing. By placing many probing units throughout a single-molecule sensing template, SMMS can have orders of magnitude better efficiency in the materials usage (i.e., high Atom Economy) with respect to the ensemble biosensing. The SMMS sensing probes also enable topochemical arrangement of different sensing units. By placing these units in a spatiotemporally addressable fashion, single-molecule topochemical sensors have been demonstrated in our lab to detect an expandable set of microRNA targets. Because of the stochastic behavior of single-molecule binding, however, it is challenging for the SMMS to accurately report analyte concentrations in a fixed time window. While multivariate analysis has been shown to rectify background noise due to stochastic nature of single-molecule probes, a template containing an array of sensing units has shown ensemble average behaviors to address the same problem. In this so-called ensemble single-molecule sensing, collective mechanical transitions of many sensing units occur in the SMMS sensing probes, which allows accurate quantification of analytes. For the SMMS to function as a viable sensing approach readily adopted by biosensing communities, the future of the SMMS technique relies on the reduction in the complexity and cost of instrumentation to report mechanical signals. In this account, we first explain the mechanism and main features of the SMMS. We then specify basic elements employed in SMMS. Using DNA as an exemplary SMMS template, we further summarize different types of SMMS which present multiplexing capability and increased throughput. Finally, recent efforts to develop simple and affordable high throughput methods for force generation and measurement are discussed in this Account for potential usage in the mechanochemical sensing.

An approach for constraining mantle viscosities through assimilation of palaeo sea level data into a glacial isostatic adjustment model

Abstract. Glacial isostatic adjustment is largely governed by the rheological properties of the Earth's mantle. Large mass redistributions in the ocean–cryosphere system and the subsequent response of the viscoelastic Earth have led to dramatic sea level changes in the past. This process is ongoing, and in order to understand and predict current and future sea level changes, the knowledge of mantle properties such as viscosity is essential. In this study, we present a method to obtain estimates of mantle viscosities by the assimilation of relative sea level rates of change into a viscoelastic model of the lithosphere and mantle. We set up a particle filter with probabilistic resampling. In an identical twin experiment, we show that mantle viscosities can be recovered in a glacial isostatic adjustment model of a simple three-layer Earth structure consisting of an elastic lithosphere and two mantle layers of different viscosity. We investigate the ensemble behaviour on different parameters in the following three set-ups: (1) global observations data set since last glacial maximum with different ensemble initialisations and observation uncertainties, (2) regional observations from Fennoscandia or Laurentide/Greenland only, and (3) limiting the observation period to 10 ka until the present. We show that the recovery is successful in all cases if the target parameter values are properly sampled by the initial ensemble probability distribution. This even includes cases in which the target viscosity values are located far in the tail of the initial ensemble probability distribution. Experiments show that the method is successful if enough near-field observations are available. This makes it work best for a period after substantial deglaciation until the present when the number of sea level indicators is relatively high.

Chloroaluminate Anion Intercalation in Graphene and Graphite: From Two-Dimensional Devices to Aluminum-Ion Batteries.

A rechargeable aluminum-ion battery based on chloroaluminate electrolytes has received intense attention due to the high abundance and chemical stability of aluminum. However, the fundamental intercalation processes and dynamics in these battery systems remain unresolved. Here, the energetics and dynamics of chloroaluminate ion intercalation in atomically thin single crystal graphite are investigated by fabricating mesoscopic devices for charge transport and operando optical microscopy. These mesoscopic measurements are compared to the high-performance rechargeable Al-based battery consisting of a few-layer graphene-multiwall carbon nanotube composite cathode. These composites exhibit a 60% capacity enhancement over pyrolytic graphite, while an ∼3-fold improvement in overall ion diffusivity is also obtained exhibiting ∼1% of those in atomically thin single crystals. Our results thus establish the distinction between intrinsic and ensemble electrochemical behavior in Al-based batteries and show that engineering ion transport in these devices can yet lead to vast improvements in battery performance.

Creating ground truth for nanocrystal morphology: a fully automated pipeline for unbiased transmission electron microscopy analysis.

Control over colloidal nanocrystal morphology (size, size distribution, and shape) is important for tailoring the functionality of individual nanocrystals and their ensemble behavior. Despite this, traditional methods to quantify nanocrystal morphology are laborious. New developments in automated morphology classification will accelerate these analyses but the assessment of machine learning models is limited by human accuracy for ground truth, causing even unsupervised machine learning models to have inherent bias. Herein, we introduce synthetic image rendering to solve the ground truth problem of nanocrystal morphology classification. By simulating 2D images of nanocrystal shapes via a function of high-dimensional parameter space, we trained a convolutional neural network to link unique morphologies to their simulated parameters, defining nanocrystal morphology quantitatively rather than qualitatively. An automated pipeline then processes, quantitatively defines, and classifies nanocrystal morphology from experimental transmission electron microscopy (TEM) images. Using improved computer vision techniques, 42 650 nanocrystals were identified, assessed, and labeled with quantitative parameters, offering a 600-fold improvement in efficiency over best-practice manual measurements. A classification algorithm was trained with a prediction accuracy of 99.5%, which can successfully analyze a range of concave, convex, and irregular nanocrystal shapes. The resulting pipeline was applied to differentiating two syntheses of nominally cuboidal CsPbBr3 nanocrystals and uniquely classifying binary nickel sulfide nanocrystal phase based on morphology. This pipeline provides a simple, efficient, and unbiased method to quantify nanocrystal morphology and represents a practical route to construct large datasets with an absolute ground truth for training unbiased morphology-based machine learning algorithms.

Monte Carlo Simulations of the Magnetic Behaviour of Iron Oxide Nanoparticle Ensembles: Taking Size Dispersion, Particle Anisotropy, and Dipolar Interactions into Account

Monte Carlo Simulations of the Magnetic Behaviour of Iron Oxide Nanoparticle Ensembles: Taking Size Dispersion, Particle Anisotropy, and Dipolar Interactions into Account

Time-reversal-invariant hexagonal billiards with a point symmetry.

A biparametric family of hexagonal billiards enjoying the C_{3} point symmetry is introduced and numerically investigated. First, the relative measure r(ℓ,θ;t) in a reduced phase space was mapped onto the parameter plane ℓ×θ for discrete time t up to 10^{8} and averaged in tens of randomly chosen initial conditions in each billiard. The resulting phase diagram allowed us to identify fully ergodic systems in the set. It is then shown that the absolute value of the position autocorrelation function decays like |C_{q}(t)|∼t^{-σ}, with 0<σ⩽1 in the hexagons. Following previous examples of irrational triangles, we were able to find billiards for which σ∼1. This is further evidence that, although not chaotic (all Lyapunov exponents are zero), billiards in polygons might exhibit a near strongly mixing dynamics in the ergodic hierarchy. Quantized counterparts with distinct classical properties were also characterized. Spectral properties of singlets and doublets of the quantum billiards were investigated separately well beyond the ground state. As a rule of thumb, for both singlet and doublet sequences, we calculate the first 120000 energy eigenvalues in a given billiard and compute the nearest neighbor spacing distribution p(s), as well as the cumulative spacing function I(s)=∫_{0}^{s}p(s^{'})ds^{'}, by considering the last 20000 eigenvalues only. For billiards with σ∼1, we observe the results predicted for chaotic geometries by Leyvraz, Schmit, and Seligman, namely, a Gaussian unitary ensemble behavior in the degenerate subspectrum, in spite of the presence of time-reversal invariance, and a Gaussian orthogonal ensemble behavior in the singlets subset. For 0<σ<1, formulas for intermediate quantum statistics have been derived for the doublets following previous works by Brody, Berry and Robnik, and Bastistić and Robnik. Different regimes in a given energy spectrum have been identified through the so-called ergodic parameter α=t_{H}/t_{C}, the ratio between the Heisenberg time and the classical diffusive-like transport time, which signals the possibility of quantum dynamical localization when α<1. A good quantitative agreement is found between the appropriate formulas with parameters extracted from the classical phase space and the data from the calculated quantum spectra. A rich variety of standing wave patterns and corresponding Poincaré-Husimi representations in a reduced phase space are reported, including those associated with lattice modes, scarring, and high-frequency localization phenomena.

Analysis of growth cone extension in standardized coordinates highlights self-organization rules during wiring of the Drosophila visual system.

A fascinating question in neuroscience is how ensembles of neurons, originating from different locations, extend to the proper place and by the right time to create precise circuits. Here, we investigate this question in the Drosophila visual system, where photoreceptors re-sort in the lamina to form the crystalline-like neural superposition circuit. The repeated nature of this circuit allowed us to establish a data-driven, standardized coordinate system for quantitative comparison of sparsely perturbed growth cones within and across specimens. Using this common frame of reference, we investigated the extension of the R3 and R4 photoreceptors, which is the only pair of symmetrically arranged photoreceptors with asymmetric target choices. Specifically, we found that extension speeds of the R3 and R4 growth cones are inherent to their cell identities. The ability to parameterize local regularity in tissue organization facilitated the characterization of ensemble cellular behaviors and dissection of mechanisms governing neural circuit formation.

Anisotropic and homogeneous model of heat transfer for self-heating ignition of large ensembles of lithium-ion batteries during storage

Self-heating ignition is a fire hazard in warehouses when stacking large quantities of reactive materials for storage, including lithium-ion batteries. Due to the heavy costs and dangerous fire risks, the thermal behaviour of large-scale LIB ensembles is usually studied by numerical methods. The state-of-the-art self-heating models on LIBs are either too computationally expensive to be applied to the predictions of large LIB ensembles, or capable of large ensemble predictions but missing important heat transfer characteristics like insulation in packaging. Based on four-step kinetics from the literature (Solid electrolyte interphase decomposition, negative-electrolyte reaction, positive-electrolyte reaction, and electrolyte decomposition), we have developed a 3D anisotropic homogeneous (Ani-Hom) transient heat transfer model that can incorporate complex packaging and is numerically affordable for large ensemble predictions based on COMSOL Multiphysics. The effect of packaging insulation is considered by using weight-averaged thermophysical properties and directional thermal conductivities. Lithium Cobalt batteries (LCO) are used as a case study. This Ani-Hom model was verified by comparing a box-scale simulation against an isotropic heterogeneous (Iso-Het) model from the literature. Both the predictions of temperature evolution and the heat generation agreed to within 5%, while the computational time of the Ani-Hom model is one order of magnitude lower than the Iso-Het model. The Ani-Hom model is then applied to LIB ensembles in four possible storage sizes, ranging from a single cell to a rack with around 10 million cells, with different packing configurations and spacing between cells. The model predicts that the presence of packaging insulation promotes self-heating ignition. A rack of this LCO LIBs is predicted to self-ignite at an ambient temperature of 45℃, which indicates that LIBs in a warehouse are vulnerable to fire hazards in warm environments. The presence of defects or abuse will even lower this critical ambient temperature. This work provides insights into the effects of complex insulation and spacing on self-heating ignition of LIBs during storage and contributes to a better understanding which can help mitigate such fires.

The dynamical significance of valley-ridge inflection points

In this paper we demonstrate that valley-ridge inflection (VRI) points of a potential energy surface (PES) have a dynamical influence on the fate of trajectories of the underlying Hamiltonian system. These points have attracted the attention of chemists in the past decades when studying selectivity problems in organic chemical reactions whose energy landscape exhibits a post-transition-state bifurcation in the region between two sequential saddles without an intervening energy minimum. To address the dynamical significance of valley-ridge inflection points, we construct a symmetric potential energy function that allows us to move the location of the VRI point while keeping the locations and energies of the critical points fixed. In this setup, we carry out a parametric study of the dynamical behavior of ensembles of trajectories in terms of the energy of the chemical system and the position of the VRI point. Our analysis reveals that the location of the VRI point controls the fraction of trajectories that recross the high energy saddle region of the PES without entering either of the potential wells that are separated by the low energy saddle.

Evaporation kinetics of a polydisperse ensemble of drops.

A mathematical model of the evaporation of a polydisperse ensemble of drops, with allowance for a nonlinear 'diffusion' term in the kinetic equation for the population density distribution function, is developed. The model describes the interaction of a gas phase with vaporizing drops: it has great potential for application in condensed matter physics, thermophysics and engineering devices (e.g. spray drying, cooling, power engineering). The kinetics of heat transfer between phases is theoretically studied. An analytical solution to the integro-differential equations of the process of droplet evaporation is found in a parametric form. Analytical solutions in the presence and absence of the 'diffusion' term are compared. It is shown that the fluctuations in particle evaporation rates ('diffusion' term in the Fokker-Planck equation) play a decisive role in the evolutionary behaviour of a polydisperse ensemble of vaporizing liquid drops. This article is part of the theme issue 'Transport phenomena in complex systems (part 1)'.