Dynamic Scaling Analysis Research Articles

Dynamics of polarization reversal in neodymium-doped PMN-PT ceramic

In this investigation, we present a comparative dynamic scaling analysis of switching and non-switching loops for PMN-PT ceramic and its neodymium-doped counterpart. The results demonstrate that both the samples exhibit similar scaling relations at high fields, suggesting that their distinct piezoelectric behaviour primarily stems from their polarization dynamics at low fields. For E<4kV/cm, the switching polarization for PMN-PT and Nd:PMN-PT follows the scaling relations: <ASW>=1.65*E5.89f−0.27 and <ASW>=34.5*E3.4f−0.2, respectively. On the other hand, non-switching polarization for the two samples follows the relations: <ASW>=2.26*E4.28f−0.15 and <ASW>=65.9*E1.95f−0.05, respectively. These scaling relations suggest that switching as well as non-switching polarization for Nd:PMN-PT respond faster to changing applied field as compared to their PMN-PT counterparts. We argue that the proportionality constants in two scaling relations have significant effect on the electromechanical behaviour of piezoceramics and should be evaluated in forthcoming dynamic scaling investigations. The kinetics of domain reversal, investigated using the Kolmogorov-Avrami-Ishibashi (KAI) model, suggest that the crystallographic domains in both the samples exhibit nucleation limited-switching (NLS) behaviour. We believe that our work will stimulate investigations on other piezoelectrics to corelate their functional response with the underlying dynamics and kinetics of polarization rotation.

Steric repulsion introduced by loop constraints modulates the microphase separation of chromatins.

Within the confines of a densely populated cell nucleus, chromatin undergoes intricate folding, forming loops, domains, and compartments under the governance of topological constraints and phase separation. This coordinated process inevitably introduces interference between different folding strategies. In this study, we model interphase chromatins as block copolymers with hetero-hierarchical loops within a confined system. Employing dissipative particle dynamics simulations and scaling analysis, we aim to explain how the structure and distribution of loop domains modulate the microphase separation of chromatins. Our results highlight the correlation between the microphase separation of the copolymer and the length, heterogeneity, and hierarchically nested levels of the loop domains. This correlation arises from steric repulsion intrinsic to loop domains. The steric repulsion induces variations in chain stiffness (including local orientation correlations and the persistence length), thereby influencing the degree of phase separation. Through simulations of block copolymers with distinct groups of hetero-hierarchical loop anchors, we successfully reproduce changes in phase separation across diverse cell lines, under fixed interaction parameters. These findings, in qualitative alignment with Hi-C data, suggest that the variations of loop constraints alone possess the capacity to regulate higher-order structures and the gene expressions of interphase chromatins.

Dynamical Scaling Analysis for ±J Ising Model in Three Dimensions

The ±J Ising model in three dimensions is investigated using dynamical scaling analysis for a nonequilibrium relaxation process. The spin-glass (SG) transition is analyzed under an assumed dynamical exponent z proposed for the scaling analysis of the SG transition. To estimate dynamical exponent z precisely, we introduce an extrapolation scheme for the asymptotic value of the logarithmic derivative of the dynamical Binder parameter. We obtain the phase diagram in the temperature–concentration (p–T) space, as well as the p-dependence of critical exponents γ, ν, and z. For the static exponents of the SG transition, the universality is strongly indicated numerically along the whole region of the paramagnetic (PM)–SG phase boundary. A remarkable crossover behavior is observed for estimations of critical exponents at the boundary close to the multicritical point (MCP) of PM–ferromagnetic (FM)–SG phases. In addition, the dynamical assumption for z resulting from the slow relaxation in the SG region disappears in the FM region, and the crossover between them occurs around the Nishimori Line.

Plaster and magnets: Modelling magnetic fabric development in magma intrusions using scaled analogue experiments

Understanding magma behaviour during emplacement within the crust is vital for understanding the dynamic processes occurring in volcanic systems. However, linking the static record of magma flow to its dynamic origin is challenging, particularly as macroscopic indicators of magma flow are often not observed, absent and/or have been modified after emplacement. Anisotropy of magnetic susceptibility (AMS) has been used as an important tool in field studies to infer magma flow direction, using the magnetic fabric as a record of the magma intrusion dynamics and to identify magma source regions. Here, we describe a new method to explore magnetic fabric development in magma intrusions and lava flows using scaled analogue laboratory experiments. Coloured mixtures of Plaster of Paris (the magma analogue) seeded with magnetite particles were loaded concentrically into a piston and injected through a central port in the base of a box filled with compacted fine-grained wheat flour (the crust analogue). This created a series of interconnected sheet and tube-like ‘magma’ intrusions which eventually breached the surface to feed a model ‘lava flow’. Once solidified, the intrusions were excavated and sampled for AMS, with the results showing that magnetic fabrics were preserved. A new dynamic scaling analysis shows the plaster mixture represents the intrusion of dacite magma into the shallow crust. These models provide proof-of-concept that this new methodology and scaling analysis can be used to explore AMS development in viscous (dacite) magma intrusions in nature, with the potential for direct comparison with field-based indicators of magma flow dynamics.

Characterizing the seismic response of a molten salt nuclear reactor

AbstractOne Generation IV nuclear reactor, which uses a fluoride salt as a coolant, graphite reflector blocks as a moderator, and circulating buoyant TRISO pebbles as fuel is at an advanced stage of development. To characterize the seismic behavior of components of this reactor, validate numerical models for analysis, and develop recommendations for design, a set of earthquake‐simulator experiments on a scaled model of the reactor vessel and its internals was executed on a six‐degree‐of‐freedom earthquake simulator. The model was seismically isolated at its base using two types of spherical sliding bearings. The scaled model involved representations of the prototype reactor vessel, core barrel, reflector blocks, coolant, and spherical fuel pebbles. The material and geometric properties of different test components were selected based on a dynamic similitude scaling analysis and an approximate length scale of 0.4. Four sets of three‐component earthquake motions were used as inputs for testing. Instrumentation on the test specimen recorded the dynamic responses of the outer vessel, core barrel, and reflector‐block assembly, the hydrodynamic responses (sloshing and hydrodynamic pressure) of the liquid coolant, pebble consolidation under earthquake shaking, and the behavior of the isolation systems. This paper describes the design of the experiments and presents key results from the tests. The dynamic responses of the outer vessel, core barrel, and the reflector blocks revealed that the components responded as a unit for the intense shaking used in the experiments. The sloshing response of the fluid in a thin annulus near the perimeter of the vessel was heavily damped. The change in the packing fraction of the pebble bed under repeated, intense 3D earthquake shaking was less than 3%. Seismically isolating the vessel substantially reduced demands on its internal components.

Dynamic multi-dimensional scaling of 30+ year evolution of Chinese urban systems: Patterns and performance

Understanding the co-evolution and organizational dynamics of urban properties (i.e., urban scaling) is the science base for pursuing synergies toward sustainable cities and society. The generalization of urban scaling theory yet requires more studies from various developmental regimes and across time. Here, we extend the universality proposition by exploring the evolution of longitudinal and transversal scaling of Chinese urban attributes between 1987 and 2018 using a global artificial impervious area (GAIA) remotely sensed dataset, harmonized night light data (NTL), and socioeconomic data, and revealed agreements and disagreements with theories. The superlinear relationship of urban area and population often considered as an indicator of wasting land resources (challenging the universality theory βc = 2/3), is in fact the powerful impetus (capital raising) behind the concurrent superlinear expansion of socio-economic metabolisms (e.g., GDP, total wage) in a rapidly urbanizing country that has not yet reached equilibrium. Similarly, infrastructural variables associated with public services, such as hospitals and educational institutions, exhibited some deviations as well and were scaled linearly. However, the temporal narrowing of spatial deviations, such as the decline in urban land diseconomies of scale and the stabilization of economic output, clearly indicates the Chinese government's effort in charting urban systems toward balanced and sustainable development across the country. More importantly, the transversal sublinear scaling of areal-based socio-economic variables was inconsistent with the theoretical concept of increasing returns to scale, thus validating the view that a single measurement cannot unravel the intricate web of diverse urban attributes and urbanization. Our dynamic urban scaling analysis across space and through time in China provides new insights into the evolving nexus of urbanization, socioeconomic development, and national policies.

Two-parameter dynamical scaling analysis of single-phase natural circulation in a simple rectangular loop based on dilation transformation

Two-parameter dynamical scaling analysis of single-phase natural circulation in a simple rectangular loop based on dilation transformation

Formulation of Chromatin Mobility as a Function of Nuclear Size during C. elegans Embryogenesis Using Polymer Physics Theories.

During early embryogenesis of the nematode, Caenorhabditis elegans, the chromatin motion markedly decreases. Despite its biological implications, the underlying mechanism for this transition was unclear. By combining theory and experiment, we analyze the mean-square displacement (MSD) of the chromatin loci, and demonstrate that MSD-vs-time relationships in various nuclei collapse into a single master curve by normalizing them with the mesh size and the corresponding time scale. This enables us to identify the onset of the entangled dynamics with the size of tube diameter of chromatin polymer in the C. elegans embryo. Our dynamical scaling analysis predicts the transition between unentangled and entangled dynamics of chromatin polymers, the quantitative formula for MSD as a function of nuclear size and timescale, and provides testable hypotheses on chromatin mobility in other cell types and species.

Hydrodynamics and transport in the long-range-interacting φ 4 chain

We present a simulation study of the one-dimensional φ 4 lattice theory with long-range interactions decaying as an inverse power r −(1+σ) of the intersite distance r, σ > 0. We consider the cases of single and double-well local potentials with both attractive and repulsive couplings. The double-well, attractive case displays a phase transition for 0 < σ ⩽ 1 analogous to the Ising model with long-range ferromagnetic interactions. A dynamical scaling analysis of both energy structure factors and excess energy correlations shows that the effective hydrodynamics is diffusive for σ > 1 and anomalous for 0 < σ < 1, where fluctuations propagate superdiffusively. We argue that this is accounted for by a fractional diffusion process and we compare the results with an effective model of energy transport based on Lévy flights. Remarkably, this result is fairly insensitive on the phase transition. Nonequilibrium simulations with an applied thermal gradient are in quantitative agreement with the above scenario.

Dimensional crossover for universal scaling far from equilibrium

We perform a dynamical finite-size scaling analysis of a nonequilibrium Bose gas which is confined in the transverse plane. Varying the transverse size, we establish a dimensional crossover for universal scaling properties far from equilibrium. Our results suggest that some aspects of the dynamical universal behavior of anisotropic systems can be classified in terms of fractional spatial dimensions. We discuss our findings in view of recent experimental results with quasi one-dimensional setups of quenched ultracold quantum gases.

Invasion front dynamics of interactive populations in environments with barriers

Invading populations normally comprise different subpopulations that interact while trying to overcome existing barriers against their way to occupy new areas. However, the majority of studies so far only consider single or multiple population invasion into areas where there is no resistance against the invasion. Here, we developed a model to study how cooperative/competitive populations invade in the presence of a physical barrier that should be degraded during the invasion. For one dimensional (1D) environment, we found that a Langevin equation as dX/dt=V_ft+sqrt{D_f}eta (t) describing invasion front position. We then obtained how V_f and D_f depend on population interactions and environmental barrier intensity. In two dimensional (2D) environment, for the average interface position movements we found a Langevin equation as dH/dt=V_Ht+sqrt{D_H}eta (t). Similar to the 1D case, we calculate how V_H and D_H respond to population interaction and environmental barrier intensity. Finally, the study of invasion front morphology through dynamic scaling analysis showed that growth exponent, beta, depends on both population interaction and environmental barrier intensity. Saturated interface width, W_{sat}, versus width of the 2D environment (L) also exhibits scaling behavior. Our findings show revealed that competition among subpopulations leads to more rough invasion fronts. Considering the wide range of shreds of evidence for clonal diversity in cancer cell populations, our findings suggest that interactions between such diverse populations can potentially participate in the irregularities of tumor border.

On the physics of transient ejection from bubble bursting

Using a dynamical scaling analysis of the flow variables and their evolution due to bubble bursting, here we predict the size and speed of ejected droplets for the whole range of experimental Ohnesorge and Bond numbers where ejection occurs. The transient ejection, which requires the backfire of a vortex ring inside the liquid to preserve physical symmetry, shows a delicate balance between inertia, surface tension and viscous forces around a critical Ohnesorge number, akin to an apparent singularity. Like in other natural phenomena, this balance makes the process extremely sensitive to initial conditions. Our model generalizes or displaces other recently proposed ones, impacting on, for instance, the statistical description of sea spray.

Possible Evidence for Berezinskii-Kosterlitz-Thouless Transition in Ba(Fe0.914Co0.086)2As2 Crystals.

In this study, we measure the in-plane transport properties of high-quality Ba(Fe0.914Co0.086)2As2 single crystals. Signatures of vortex unbinding Berezinskii–Kosterlitz–Thouless (BKT) transition are shown from both the conventional approach and the Fisher–Fisher–Huse dynamic scaling analysis, in which a characteristic Nelson–Kosterlitz jump is demonstrated. We also observe a non-Hall transverse signal exactly at the superconducting transition, which is explained in terms of guided motion of unbound vortices.

The dynamical system scaling analysis for single-phase integral test facilities

Recently, the dynamical system scaling (DSS) method was developed based on the similarity of trajectories. However, there is still a need to investigate the applicability of the DSS two-affine method in the design of integral test facilities. In this study, the DSS two-affine method was employed to perform the scaling analysis for single-phase integral test facilities, and similarity laws were obtained at the system, component, and process levels. The DSS ω-strain method was employed in the models with same properties, and the main parameter ratios are the same as those of the traditional reduced-height scaling method. Moreover, the models with reduced enthalpy difference were designed by the identify method. Transient simulations were performed using RELAP5/MOD3.4. The results show that all models are well scaled. A preliminary conclusion that the DSS method of λA≠1 is not suitable for the scaling of single-phase natural circulation in the design of integral test facilities.

Tailoring Antifouling Properties of Nanocarriers via Entropic Collision of Polymer Grafting.

Polymer graftings (PGs) are widely employed in antifouling surfaces and drug delivery systems to regulate the interaction with a foreign environment. Through molecular dynamics simulations and scaling theory analysis, we investigate the physical antifouling properties of PGs via their collision behaviors. Compared with mushroom-like PGs with low grafting density, we find brush-like PGs with high grafting density could generate large deformation-induced entropic repulsive force during a collision, revealing a microscopic mechanism for the hop motions of polymer-grafted nanoparticles for drug delivery observed in experiment. In addition, the collision elasticity of PGs is found to decay with the collision velocity by a power law, i.e., a concise dynamic scaling despite the complex process involved, which is beyond expectation. These results elucidate the dynamic interacting mechanism of PGs, which are of immediate interest for a fundamental understanding of the antifouling performance of PGs and the rational design of PG-coated nanoparticles in nanomedicine for drug delivery.

Elasticity of jammed packings of sticky disks

Numerous soft materials jam into an amorphous solid at high packing fraction. This non-equilibrium phase transition is best understood in the context of a model system in which particles repel elastically when they overlap. Recently, however, it was shown that introducing any finite amount of attraction between particles changes the universality class of the transition. The properties of this new ``sticky jamming'' class remain almost entirely unexplored. We use molecular dynamics simulations and scaling analysis to determine the shear modulus, bulk modulus, and coordination of marginal solids close to the sticky jamming point. In each case, the behavior of the system departs sharply and qualitatively from the purely repulsive case.

Spin-glass behavior inCo3Mn3(O2BO3)2ludwigite with weak disorder

X-ray diffraction, magnetization, ac susceptibility, and specific heat have been measured on high-quality single crystals of ${\mathrm{Co}}_{3}{\mathrm{Mn}}_{3}{({\mathrm{O}}_{2}{\mathrm{BO}}_{3})}_{2}$ ludwigite. Different from previously studied ludwigites, this compound is characterized by the existence two low-dimensional subunits each containing a unique ion. The subsystem formed by ions at sites 3-1-3, known as a three-legged ladder (3LL), contains only divalent Co ions, while the 3LL formed by ions at sites 4-2-4 contains both divalent and trivalent Mn ions. Although there is only a weak disorder caused by a very small amount of Mn at sites 1, the experimental results evidence the existence of a low-temperature spin-glass phase. A dynamic scaling analysis of ac susceptibility data according to conventional critical slowing down results in a spin-glass phase-transition temperature ${T}_{g}=31.9$ K and a dynamic exponent $z\ensuremath{\nu}=7.05$. The temperature dependence of heat capacity has a linear contribution with the coefficient $\ensuremath{\gamma}=21.9$ mJ/(mol ${\mathrm{K}}^{2}$), which shows that this compound has the highest degree of magnetic disorder among ludwigites, corroborating the spin-glass state at low temperatures. The origin of this state is discussed, taking into account the particular structure of each subunit and the competition between the different exchange interactions involved.

Dynamical scaling analysis of symmetry breaking for the antiferromagnetic triangular Heisenberg model in a uniform magnetic field

Phase transitions for the two-dimensional antiferromagnetic triangular Heisenberg model in a uniform field are primarily analyzed using dynamical scaling analysis. The system has ${Z}_{3}$ and $O(2)$ symmetries. The transition temperatures and types of transition are investigated using the relaxation of order parameters and the asymptotic behaviors of relaxation time around transition temperatures. In the low-field range, the order parameters for the ${Z}_{3}$ and $O(2)$ symmetries exhibit the behavior typical of a second-order transition and Kosterlitz-Thouless (KT) transition, respectively, with distinct transition temperatures. In the high-field range, an order parameter for the ${Z}_{3}$ symmetry exhibits the behavior of a second-order transition, while another order parameter related to the components perpendicular to the field demonstrates that the relaxation time diverges with an asymptotic form, indicating a second-order transition rather than a KT transition. These transition temperatures are estimated to be close. Critical exponents for these two order parameters are estimated separately by calculating the relaxation of fluctuations in the high-field range. It was confirmed that the critical exponents for both of these order parameters change continuously as a function of field, and they are distinct from each other.

Dynamical scaling analysis on critical universality class for fully frustrated XY models in two dimensions

Critical properties of the fully frustrated XY models on square and triangular lattices are investigated by means of the nonequilibrium relaxation (NER) method. We examine the validity of the conclusion on the universality class of the chiral transition previously obtained by the NER method, in which that belongs to a non-Ising-type one. To clarify it, we analyze the NER of fluctuations for longer Monte Carlo steps on lager lattices than those performed previously. The calculation is made at the chiral transition temperatures estimated carefully by the use of recently improved dynamical scaling analysis. The result indicates that the asymptotic behavior of the time-dependent exponents, which should converge to the critical exponents, show the same tendency as those obtained previously in shorter times. We also apply the improved dynamical scaling analysis to the estimation of Kosterlitz-Thouless (KT) transitions and confirm the existence of the double transitions for the chiral and KT phases with more reliable estimations.

Relaxation Time Spectrum and Dynamics of Stretched Polymer Chain in Dilute θ Solution: Implicit Solvent Model versus Explicit Solvent Model

AbstractRelaxation dynamics of a single stretched polymer chain after releasing the two fixed ends in dilute solutions are investigated by using implicit solvent and explicit solvent molecular dynamic simulations. The phase diagram of polymer in explicit solvent solution is determined, and the θ point is estimated by the form factor of the polymer chain. The relaxation time spectrum is obtained by the inverse Laplace transform of length–time decay curves of the relaxation process. The dependencies of the longest relaxation time in the spectrum on the chain length are compared with the scaling prediction of the Rouse model and the Zimm model of flexible chains. In this paper, it is confirmed that the dynamical scaling analysis of theoretical models are in good agreement with the simulation models in all range of polymerization degree of chain studied. The coarse‐grained explicit solvent simulation model of polymer chain in dilute solution developed in this paper can be a good numerical model for the future study of the dynamics process of macromolecules with hydrodynamic interactions in solutions.