Dynamic Crossover Research Articles

Viscoelastic necking dynamics between attractive microgels

HypothesisMicrogels can deform and interpenetrate and display colloid/polymer duality. The effective interaction of microgels in the collapsed state is governed by the interplay of polymer–solvent interfacial tension and bulk elasticity. A connecting neck is shown to mediate microgel interaction, but its temporal evolution has not been addressed. We hypothesize that the necking dynamics of attractive microgels exhibits liquid-like or solid-like behavior over different time and length scales. ExperimentsWe simulate the merging and pinching of attractive microgels with different crosslinking densities in explicit solvent using dissipative particle dynamics. The temporal coalescence dynamics of microgels is investigated and compared with simple liquid and polymeric droplets. We model the neck growth on long time scales using Maxwell model of polymer relaxation and compare the theoretical prediction with simulation data. The mechanical strength of the neck is characterized systematically via simulated pinch-off of microgels by steered molecular dynamics. FindingsWe evidence a crossover in the coalescence dynamics reflecting the viscoelastic signature of microgels. In contrast to the common knowledge that viscoelastic materials respond elastically on short time scales, the early expansion of the microgel neck exhibits a linear behavior, similar to the viscous coalescence of liquid droplets. However, the late regime with arrested dynamics resembles sintering of solid particles. Through an analytical model relating microgel dynamics to neck growth, we show that the long-term behavior is governed by stress relaxation of the polymers in the neck region and predict an exponential decay in the rate of growth, which agrees favorably with the simulation. Different from coalescence, the thread thinning in microgel breakup primarily highlights its polymeric characteristics.

Structure and Dynamic Properties of a Glycerol-Betaine Deep Eutectic Solvent: When Does a DES Become an Aqueous Solution?

Deep eutectic solvents (DESs) are an emerging class of green solvents with a wide spectrum of potential applications whose properties may be further tailored through the addition of water. Here, we study, through molecular dynamics, the influence of water on the properties of a betaine-glycerol-water (B:G:W) DES (1:2:ζ; ζ = 0 to 100), aiming at getting insight into the structural and dynamic crossover between a DES and an aqueous solution. The density, shear viscosity, and diffusion coefficients are found to exhibit a non-linear dependence of ζ, similar to that observed for the solvation layers' composition. Each Gly and Bet are replaced, respectively, by ∼3 and ∼5 water molecules, with the highest rates of depletion being found for Gly around Bet and Gly around Gly. Above ζ = 7 (70 mol %; 29.5 wt %), a major structural transformation occurs, with the complete disruption of the second Bet-Gly solvation layer and the formation of a new second layer at a shorter distance, accompanied by a sudden change in the rate of increase of the components' diffusion. Nonetheless, opposite to other DES, our results indicate a smooth crossover between a DES and an aqueous solution.

New paradigm for configurational entropy in glass-forming systems

We show that on cooling towards glass transition configurational entropy exhibits more significant changes than predicted by classic relation. A universal formula according to Kauzmann temperature {T}_{K} is given: S={S}_{0}{t}^{n}, where t=left(T-{T}_{K}right)/T. The exponent n is hypothetically linked to dominated local symmetry. Such a behaviour is coupled to previtreous evolution of heat capacity Delta {C}_{P}^{config.}left(Tright)=left(nC/Tright){left(1-{T}_{K}/Tright)}^{n-1} associated with finite temperature singularity. These lead to generalised VFT relation, for which the basic equation is retrieved. For many glass-formers, basic VFT equation may have only an effective meaning. A universal-like reliability of the Stickel operator analysis for detecting dynamic crossover phenomenon is also questioned. Notably, distortions-sensitive and derivative-based analysis focused on previtreous changes of configurational entropy and heat capacity for glycerol, ethanol and liquid crystal is applied.

Dynamical crossover behavior in the relaxation of quenched quantum many-body systems

A crossover between different power-law relaxation behaviors of many-body periodically driven integrable systems has come to light in recent years. We demonstrate using integrable quantum systems, that similar kinds of dynamical transitions may also occur in the relaxation of such systems following a sudden quench. Particularly, we observe two distinct power-law relaxation behaviors following a sudden quench in the integrable XY model, depending upon whether the quenched Hamiltonian lies in the commensurate or the incommensurate phase. The relaxation behavior for quenches at and near the boundary line, called the disorder line (DL), separating these phases is also characterized. The relaxation at the DL shows a new scaling exponent previously unexplored. The transitions occur through a crossover from the commensurate/incommensurate scaling behavior to the DL scaling behavior. The crossover time diverges like a power law as the parameters of the final quenched Hamiltonian approach the DL. The transitions are also observed to be robust under weak integrability breaking perturbations but disappear following strongly chaotic quenches.

Gene Selection and Classification of scRNA-seq Data Combining Information Gain Ratio and Genetic Algorithm with Dynamic Crossover

Single-cell RNA sequencing (scRNA-seq) is emerging as a promising technology. There exist a huge number of genes in a scRNA-seq data. However, some genes are high quality genes, and some are noises and irrelevant genes because of unspecific technology reasons. These noises and irrelevant genes may have a strong influence on downstream data analyses, such as a cell classification, gene function analysis, and cancer biomarker detection. Therefore, it is very significant to obviate these irrelevant genes and choose high quality genes by gene selection methods. In this study, a novel gene selection and classification method is presented by combining the information gain ratio and the genetic algorithm with dynamic crossover (abbreviated as IGRDCGA). The information gain ratio (IGR) is employed to eliminate irrelevant genes roughly and obtain a preliminary gene subset, and then the genetic algorithm with a dynamic crossover (DCGA) is utilized to choose high quality genes finely from the preliminary gene subset. The main difference between the IGRDCGA and the existing methods is that the DCGA and IGR are integrated first and used to select genes from scRNA-seq data. We conduct the IGRDCGA and several competing methods on some real-world scRNA-seq datasets. The obtained results demonstrate that the IGRDCGA can choose high quality genes effectively and efficiently and outperforms the other several competing methods in terms of both the dimensionality reduction and the classification accuracy.

Active Brownian motion with speed fluctuations in arbitrary dimensions: exact calculation of moments and dynamical crossovers

We consider the motion of an active Brownian particle with speed fluctuations in d-dimensions in the presence of both translational and orientational diffusion. We use an Ornstein–Uhlenbeck process for active speed generation. Using a Laplace transform approach, we describe and use a Fokker–Planck equation-based method to evaluate the exact time dependence of all relevant dynamical moments. We present explicit calculations of several such moments and compare our analytical predictions against numerical simulations to demonstrate and analyze the dynamical crossovers, determined by the orientational persistence of activity, speed fluctuation and relaxation. The kurtosis of displacement shows positive and negative deviations from a Gaussian behavior at intermediate times depending on the dominance of speed and orientational fluctuations, respectively.

Using coherent X-rays to follow dynamics in amorphous ices.

Amorphous solid water plays an important role in our overall understanding of water's phase diagram. X-ray scattering is an important tool for characterising the different states of water, and modern storage ring and XFEL facilities have opened up new pathways to simultaneously study structure and dynamics. Here, X-ray photon correlation spectroscopy (XPCS) was used to study the dynamics of high-density amorphous (HDA) ice upon heating. We follow the structural transition from HDA to low-density amorphous (LDA) ice, by using wide-angle X-ray scattering (WAXS), for different heating rates. We used a new type of sample preparation, which allowed us to study μm-sized ice layers rather than powdered bulk samples. The study focuses on the non-equilibrium dynamics during fast heating, spontaneous transformation and crystallization. Performing the XPCS study at ultra-small angle (USAXS) geometry allows us to characterize the transition dynamics at length scales ranging from 60 nm-800 nm. For the HDA-LDA transition we observe a clear separation in three dynamical regimes, which show different dynamical crossovers at different length scales. The crystallization from LDA, instead, is observed to appear homogenously throughout the studied length scales.

Dynamic Crossover in Metallic Glass Melt Detected by Nmr

Dynamic Crossover in Metallic Glass Melt Detected by Nmr

Bi-objective optimization of identical parallel machine scheduling with flexible maintenance and job release times

This paper investigates an identical parallel machine scheduling problem with flexible maintenance and job release times and attempts to optimize two objectives: the minimization of the makespan and total tardiness simultaneously. A mixed-integer programming (MIP) model for solving small-scale instances is presented first, and then a modified NSGA-Ⅱ (M-NSGA-Ⅱ) algorithm is constructed for solving medium- and large-scale instances by incorporating several strategies. These strategies include: (ⅰ) the proposal of a decoding method based on dynamic programming, (ⅱ) the design of dynamic probability crossover and mutation operators, and (ⅲ) the presentation of neighborhood search method. The parameters of the proposed algorithm are optimized by the Taguchi method. Three scales of problems, including 52 instances, are generated to compare the performance of different optimization methods. The computational results demonstrate that the M-NSGA-Ⅱ algorithm obviously outperforms the original NSGA-II algorithm when solving medium- and large-scale instances, although the time taken to solve the instances is slightly longer.

Probing the Dynamic Crossover in Liquid Ga

Probing the Dynamic Crossover in Liquid Ga

Machine learning glass caging order parameters with an artificial nested neural network.

Around a glass transition, the dynamics of a supercooled liquid dramatically slow down, exhibited by caging of particles, while the structural changes remain subtle. Alternative to recent machine learning studies searching for structural predictors of glassy dynamics, here we propose to learn directly particle caging features defined purely according to dynamics. We focus on three transitions in a simulated hard sphere glass model, the melting of ultra-stable glasses, the Gardner transition and the liquid to ordinary glass transition. Implementing the machine learning algorithm based on a two-level nested neural network, we attain not only appropriate caging order parameters for all three transitions, but also a phase classification for input samples. A finite-size scaling analysis of the phase classification results identifies the order of melting (first) and Gardner (second) transitions. A false positive is avoided, as the liquid to glass transition is indicated as a crossover, rather than a phase transition with a well-defined transition point. This study paves the way to a generic approach for learning dynamical features in glassy systems, with a minimum requirement of system-specific knowledge.

Temperature-dependent anomalous energy transport in finite-length quasi-one-dimensional MoS2 : Crossover from phonons to solitons

Anomalous energy transport is a widely investigated character in one-dimensional lattice and both phonons and solitons are candidate energy carriers responsible for the thermal conductivity divergence before their mean-free paths. However, it was long believed the contribution of solitons could be neglected even close to the melting point in a real crystalline solid. In this paper, we show that a crossover of wave-packet dynamics, from a phonon- to a soliton-dominated state, occurs in a quasi-one-dimensional molybdenum disulfide $({\mathrm{MoS}}_{2})$ sheet at high temperatures far below its melting point by nonequilibrium and equilibrium molecular dynamics simulations. Divergent sound speed variation and the corresponding heat capacity peaks are observed in the transition-temperature region that is related to a second-order phase transition. We also find that its anomalous energy transport falls into a universality class with thermal conductivity divergence exponent $\ensuremath{\alpha}=2/5$ at a finite length scale within 2000 nm when solitons are excited above 600 K, and the scaling relations derived from the L\'evy walk of energy carriers is fulfilled as $\ensuremath{\alpha}=2\ensuremath{-}1/\ensuremath{\gamma}=\ensuremath{\beta}\ensuremath{-}1$ in the soliton-dominated state above 1800 K. Our results reveal the peculiar solitonlike contribution to thermal conduction at high temperatures in the low-dimensional crystalline solids.

Non-Markovian dynamics control of spin-1/2 system interacting with magnets

The unavoidable interaction of an open quantum system with its surrounding environment may follow non-Markovian dynamics behavior, which causes its memory effects to play a key role in many quantum technologies. In this work, we first consider the dynamics control of a spin-1/2 system that simultaneously interacts with two magnets. Subsequently, we study in detail the evolution of a classically driven spin-1/2 system that is coupled with a magnet. Two dynamical crossovers of the spin system, namely, from Markovian dynamics to non-Markovian dynamics and from no-speedup evolution to speedup evolution, can be controlled in these two models. Slightly different from the previous quantum speedup scenarios with controllable non-Markovianity, the stronger non-Markovianity does not necessarily lead to the quantum speedup dynamics process of the spin system in our spin-magnet schemes.

Water Thermodynamics and Its Effects on the Protein Stability and Activity

We discuss a phenomenon regarding water that was until recently a subject of scientific interest: i.e., the dynamical crossover, from the fragile to strong glass forming material, for both bulk and protein hydration water. Such crossover is characterized by a temperature TL in which significant dynamical changes like the decoupling (or the violation of the Stokes-Einstein relation) of homologous transport parameters, e.g., the density relaxation time τ and the viscosity η, occur in the system. On this respect we considered the dynamic properties of water-protein systems. More precisely, we focused our study on proteins and their hydration water, as far as bulk and confined water. In order to clarify the effects of the water dynamical crossover on the protein properties we considered and discussed in a comparative way previous and new experimental data, obtained from different techniques and molecular dynamic simulation (MD). We pointed out the reasons for different dynamical findings from the use of different experimental techniques.

Driven-dissipative Ising model: Dynamical crossover at weak dissipation

Driven quantum systems coupled to an environment typically exhibit effectively thermal behavior with relaxational dynamics near criticality. However, a different qualitative behavior might be expected in the weakly dissipative limit due to the competition between coherent dynamics and weak dissipation. In this work, we investigate a driven-dissipative infinite-range Ising model in the presence of individual atomic dissipation, a model that emerges from the paradigmatic open Dicke model in the large-detuning limit. We show that the system undergoes a dynamical crossover from relaxational dynamics, with a characteristic dynamical exponent , to underdamped critical dynamics governed by the exponent in the weakly dissipative regime; a behavior that is markedly distinct from that of equilibrium. Finally, utilizing an exact diagrammatic representation, we demonstrate that the dynamical crossover to underdamped criticality is not an artifact of the mean-field nature of the model and persists even in the presence of short-range perturbations.

Long-Range Static and Dynamic Previtreous Effects in Supercooled Squalene—Impact of Strong Electric Field

This article presents evidence for the long-range previtreous changes of two static properties: the dielectric constant (ε) and its strong electric field related counterpart, the nonlinear dielectric effect (NDE). Important evidence is provided for the functional characterizations of ε(T) temperature changes by the ‘Mossotti Catastrophe’ formula, as well as for the NDE vs. T evolution by the relations resembling those developed for critical liquids. The analysis of the dynamic properties, based on the activation energy index, excluded the Vogel–Fulcher–Tammann (VFT) relation as a validated tool for portraying the evolution of the primary relaxation time. This result questions the commonly applied ‘Stickel operator’ routine as the most reliable tool for determining the dynamic crossover temperature. In particular, the strong electric field radically affects the distribution of the relaxation times, the form of the evolution of the primary relaxation time, and the fragility. The results obtained in this paper support the concept of a possible semi-continuous phase transition hidden below Tg. The studies were carried out in supercooled squalene, a material with an extremely low electric conductivity, a strongly elongated molecule, and which is vitally important for biology and medicine related issues.

Theory of Transient Localization, Activated Dynamics, and a Macromolecular Glass Transition in Ring Polymer Liquids.

We construct a segmental scale force level theory for the center-of-mass diffusion constant and corresponding relaxation time for globally compact unconcatenated ring polymer solutions and melts (degree of polymerization N). The approach is based on slowly decaying macromolecular scale intermolecular force dynamic correlations as the origin of their unusual dynamics. Unentangled Rouse, weakly caged, and activated regimes are predicted. The barrier of the activated regime scales linearly with N and as a power law of concentration, which drives a kinetic glass transition on the radius-of-gyration scale. The values of N at the two dynamic crossovers (Rouse to weakly caged, weakly caged to activated) are proportional, with nonuniversality entering mainly via macromolecular volume fraction and dimensionless compressibility. Quantitative comparisons with simulation data reveal good agreement. Aspects of intermediate time dynamics are analyzed, and predictions are made for the conditions required to observe a macromolecular glass transition in the laboratory and on the computer.

Prediction of Chaotic Time Series Based on BEN-AGA Model

Aiming at the prediction problem of chaotic time series, this paper proposes a brain emotional network combined with an adaptive genetic algorithm (BEN-AGA) model to predict chaotic time series. First, we improve the emotional brain learning (BEL) model using the activation function to change the two linear structures the amygdala and the orbitofrontal cortex into the nonlinear structure, and then we establish the brain emotional network (BEN) model. The brain emotional network model has stronger nonlinear calculation ability and generalization ability. Next, we use the adaptive genetic algorithm to optimize the parameters of the brain emotional network model. The weights to be optimized in the model are coded as chromosomes. We design the dynamic crossover probability and mutation probability to control the crossover process and the mutation process, and the optimal parameters are selected through the fitness function to evaluate the chromosome. In this way, we increase the approximation capability of the model and increase the calculation speed of the model. Finally, we reconstruct the phase space of the observation sequence based on the short-term predictability of the chaotic time series; then we establish a brain emotional network model and optimize its parameters with an adaptive genetic algorithm and perform a single-step prediction on the optimized model to obtain the prediction error. The model proposed in this paper is applied to the prediction of Rossler chaotic time series and sunspot chaotic time series. The experimental results verify the effectiveness of the BEN-AGA model and show that this model has higher prediction accuracy and more stability than other methods.

Pattern formation of quantum Kelvin-Helmholtz instability in binary superfluids

We study theoretically nonlinear dynamics induced by shear-flow instability in segregated two-component Bose-Einstein condensates in terms of the Weber number, defined by extending the past theory on the Kelvin-Helmholtz instability in classical fluids. Numerical simulations of the Gross-Pitaevskii equations demonstrate that dynamics of pattern formation is well characterized by the Weber number $We$, clarifying the microscopic aspects unique to the quantum fluid system. For $We \lesssim 1$, the Kelvin-Helmholtz instability induces flutter-finger patterns of the interface and quantized vortices are generated at the tip of the fingers. The associated nonlinear dynamics exhibits a universal behavior with respect to $We$. When $We \gtrsim 1$ in which the interface thickness is larger than the wavelength of the interface mode, the nonlinear dynamics is effectively initiated by the counter-superflow instability. In a strongly segregated regime and a large relative velocity, the instability causes transient zipper pattern formation instead of generating vortices due to the lack of enough circulation to form a quantized vortex per a finger. While, in a weakly segregating regime and a small relative velocity, the instability leads to sealskin pattern in the overlapping region, in which the frictional relaxation of the superflow cannot be explained only by the homogeneous counter-superflow instability. We discuss the details of the linear and nonlinear characteristics of this dynamical crossover from small to large Weber numbers, where microscopic properties of the interface become important for the large Weber number.

Theory of the effect of external stress on the activated dynamics and transport of dilute penetrants in supercooled liquids and glasses.

We generalize the self-consistent cooperative hopping theory for a dilute spherical penetrant or tracer activated dynamics in dense metastable hard sphere fluids and glasses to address the effect of external stress, the consequences of which are systematically established as a function of matrix packing fraction and penetrant-to-matrix size ratio. All relaxation processes speed up under stress, but the difference between the penetrant and matrix hopping (alpha relaxation) times decreases significantly with stress corresponding to less time scale decoupling. A dynamic crossover occurs at a critical "slaving onset" stress beyond which the matrix activated hopping relaxation time controls the penetrant hopping time. This characteristic stress increases (decreases) exponentially with packing fraction (size ratio) and can be well below the absolute yield stress of the matrix. Below the slaving onset, the penetrant hopping time is predicted to vary exponentially with stress, differing from the power law dependence of the pure matrix alpha time due to system-specificity of the stress-induced changes in the penetrant local cage and elastic barriers. An exponential growth of the penetrant alpha relaxation time with size ratio under stress is predicted, and at a fixed matrix packing fraction, the exponential relation between penetrant hopping time and stress for different size ratios can be collapsed onto a master curve. Direct connections between the short- and long-time activated penetrant dynamics and between the penetrant (or matrix) alpha relaxation time and matrix thermodynamic dimensionless compressibility are also predicted. The presented results should be testable in future experiments and simulations.