Dynamic Scaling Law Research Articles

Phase Separation Dynamics for a Polymer Blend Compatibilized by Protein-like Copolymers: A Monte Carlo Simulation

We use Monte Carlo simulation based on the bond fluctuation model to investigate how adding ≈4.92% protein-like copolymer (PLC) to an immiscible binary polymer blend affects the dynamics of phase separation. PLCs slow down effectively the process of phase separation in binary blends by migrating to the biphasic interface between the immiscible homopolymers, thereby reducing the interfacial tension. The ability of PLCs to retard effectively the process of phase separation depends sensitively on the interaction energy between the PLCs and homopolymers and the PLC chain length. PLCs compatibilize the binary blend more effectively with increasing attractive interaction between the PLC blocks and homopolymers. Nominal improvement in compatibilization of the binary blend is achieved with increasing PLC chain length. The growth of phase-separated domains follows a dynamical scaling law for both the binary blend and PLC compatibilized ternary blend in the late stages of phase separation. The universal scaling functions are nearly independent of the interaction energy and PLC chain length. Thus, the phase-separated domains grow with dynamical self-similarity irrespective of the type of PLC added to the binary blend, although the type of PLC significantly alters the growth rate of the phase-separated domains.

Cluster-cluster aggregations of superparamagnetic particles in a rotational magnetic field

We investigate the cluster-cluster aggregations of superparamagnetic particles in a rotational magnetic field numerically by the Brownian dynamics method, focusing on the cases of ϕ = 0.01 and 0.03 and Ma = 0, 0.001, 0.01, and 0.1, where ϕ is the area fraction of superparamagnetic particles and Ma is the Mason number, i.e., the ratio of viscous drag to magnetic force acting on a magnetic particle. We clarify the effect of ϕ and Ma on the cluster-cluster aggregation process from the point of view of dynamic scaling law.

Acousto-spinodal decomposition of compressible polymer solutions: Early stage analysis

The structure and dynamics of early stage kinetics of pressure-induced phase separation of compressible polymer solutions via spinodal decomposition is analyzed using a linear Euler-Cahn-Hilliard model and the modified Sanchez Lacombe equation of state. The integrated density wave and Cahn-Hilliard equations combine the kinetic and structural characteristics of spinodal decomposition with density waves arising from pressure-induced couplings. When mass transfer rate is slower that acoustic waves, concentration gradients generate density waves that cycle back into the spinodal decomposition dynamics, resulting in oscillatory demixing. The wave attenuation increases with increasing mass transfer rates eventually leading to nonoscillatory spinodal demixing. The novel aspects of acousto-spinodal decomposition arise from the coexistence of stable oscillatory density dynamics and the unstable monotonic concentration dynamics. Scaling laws for structure and dynamics indicate deviations from incompressible behavior, with a significant slowing down of demixing due to couplings with density waves. Partial structure factors for density and density-concentration reflect the oscillatory nature of acousto-spinodal modes at lower wave vectors, while the single maximum at a constant wave vector reflects the presence of a dominant mode in the linear regime. The computed total structure factor is in qualitative agreement with experimental data for a similar polymer solution.

Systematic perturbation approach for a dynamical scaling law in a kinetically constrainedspin model

The dynamical behaviours of a kinetically constrained spin model (Fredrickson–Andersenmodel) on a Bethe lattice are investigated by a perturbation analysis that provides exactfinal states above the nonergodic transition point. It is observed that the time-dependentsolutions of the derived dynamical systems obtained by the perturbation analysis becomesystematically closer to the results obtained by Monte Carlo simulations as the order ofthe perturbation series is increased. This systematic perturbation analysis alsoclarifies the existence of a dynamical scaling law, which provides an implication fora universal relation between a size scale and a timescale near the nonergodictransition.

Distinguishing magnetic blocking and surface spin-glass freezing in nickel ferrite nanoparticles

Nickel ferrite nanoparticles dispersed in SiO2 matrix have been synthesized by sol-gel method. Structural analysis has been performed by using x-ray diffraction and transmission electron microscopy. Magnetic properties have been investigated by using superconducting quantum interference device magnetometry. In addition to the average blocking temperature peak at TB=120 K measured by a zero field cooled temperature scan of the dc susceptibility, an additional hump near 15 K is observed. Temperature dependent out-of-phase ac susceptibility shows the same features: one broad peak at high temperature and a second narrow peak at low temperature. The high temperature peak corresponds to magnetic blocking of individual nanoparticles, while the low temperature peak is attributed to surface spin-glass freezing which becomes dominant for decreasing particle diameter. To prove the dynamics of the spin (dis)order in both regimes of freezing and blocking, the frequency dependent ac susceptibility is investigated under a biasing dc field. The frequency shift in the “frozen” low-temperature ac susceptibility peak is fitted to a dynamic scaling law with a critical exponent zv=7.5, which indicates a spin-glass phase. Exchange bias is turned on at low temperature which signifies the existence of a strong core-shell interaction. Aging and memory effects are further unique fingerprints of a spin-glass freezing on the surface of isolated magnetic nanoparticles.

Polarization dynamics of polar nano-regions in Sr0.5Ba0.5Nb2O6 doped with combinations of Ce and Cr

Vugmeister’s model (Phys Rev B 2006;73:174117) of relaxors has been extended and proven to be applicable to the polarization dynamics of PNRs in Sr0.5Ba0.5Nb2O6 (SBN50) doped with combinations of Ce and Cr. In this extended model, the distribution function in describing the real part of the complex permittivity can be scaled in terms of the activated dynamic scaling law rather than Vogel–Fulcher law for the uniaxial relaxor of SBN50. In the non-dispersion region below Td (Burns temperature), mean-field theory is applicable. In the dispersion region, the activated dynamic scaling law has been shown to be valid in predicting the relationship between the frequency of the AC probing field and the maximum temperature. The dependence of the values of the critical exponent, θν (where ν is the exponent of the correlation length and θ is the “violation of hyperscaling” exponent) on the random fields induced by dopants is plausibly explained.

Navier-Stokes hydrodynamics of thermal collapse in a freely cooling granular gas

We show that, in dimension higher than one, heat diffusion and viscosity cannot arrest thermal collapse in a freely evolving dilute granular gas, even in the absence of gravity. Thermal collapse involves a finite-time blowup of the gas density. It was predicted earlier in ideal, Euler hydrodynamics of dilute granular gases in the absence of gravity, and in nonideal, Navier-Stokes granular hydrodynamics in the presence of gravity. We determine, analytically and numerically, the dynamic scaling laws that characterize the gas flow close to collapse. We also investigate bifurcations of a freely evolving dilute granular gas in circular and wedge-shaped containers. Our results imply that, in general, thermal collapse can only be arrested when the gas density becomes comparable with the close-packing density of grains. This provides a natural explanation to the formation of densely packed clusters of particles in a variety of initially dilute granular flows.

Global Structure and Shape of NH4Cl Dendritic Crystals in Quasi-Two-Dimensional Growth

We experimentally study the statistical properties of sidebranching NH 4 Cl dendritic crystals in quasi-two-dimensional growth at low supersaturation. The number density profile of the sidebranches satisfies a simple dynamic scaling law. The average height of the active branches exhibits a power law with exponent 0.86 as a function of time, which is consistent with the envelope of active branches as a function of distance from the stem tip. The average interval of active branches also increases in a power law with the distance from the stem tip.

Polymer Light-Emitting Diode Interlayers’ Formation Studied by Current-Sensing Atomic Force Microscopy and Scaling Laws

This work describes the use of current-sensing atomic force microscopy and dynamic scaling laws to characterize the surface morphologies of polymer light-emitting diode interlayers formed by poly(9,9-dioctylfluorene), PFO, on top of poly(3,4-ethylene dioxythiophene) doped with poly(styrene sulfonic acid), PEDOT:PSS. Two types of PFO differing in molecular weight are compared. Surface current maps and calculated energy gaps of PEDOT:PSS evidence surface segregation of the two components of the blend, being PEDOT preferentially located in the surface valleys. Upon formation of PFO interlayers, an overall current decrease occurs, with this decrease being more pronounced for the interlayer based on PFO with higher molecular weight. It is observed that, under the preparation conditions used, neither of the two PFO samples leads to full coverage of the surface. The submonolayer nature of these interlayers has allowed us to establish that PFO chains are preferentially deposited in the valleys of the PEDOT:PSS su...

Dual structures of chaos and turbulence, and their dynamic scaling laws

The decay form of the time correlation function Un(t) of a state variable un(t) with a small wave number kn has been shown to take the algebraic decay 1/{1+(gammanat)2} in the initial regime t<taun(gamma) and the exponential decay alphane exp(-gammanet) in the final regime t>taun(gamma), where taun(gamma) denotes the decay time of the memory function Gamman(t). This dual structure of Un(t) is generated by the deterministic short orbits in the initial regime and the stochastic long orbits in the final regime, thus giving the outstanding features of chaos and turbulence. The kn dependence of gammana, alphane, and gammane is obtained for the chaotic Kuramoto-Sivashinsky equation, and it is shown that if kn is sufficiently small, then the dual structure of Un(t) obeys a hydrodynamic scaling law in the final regime t>tau(gamma) with scaling exponent z=2 and a dynamic scaling law in the initial regime t<taun(gamma) with scaling exponent z=1. If kn is increased so that the decay time taun(u) of Un(t) becomes equal to the decay time taun(gamma), then the decay form of Un(t) becomes the power-law decay t-3/2 in the final regime.

Universal scaling in a strongly interacting Rydberg gas

We study a gas of ultracold atoms resonantly driven into a strongly interacting Rydberg state. The long-distance behavior of the spatially frozen effective pseudospin system is determined by a set of dimensionless parameters, and we find that the experimental data exhibit algebraic scaling laws for the excitation dynamics and the saturation of Rydberg excitation. Mean-field calculations as well as numerical simulations provide an excellent agreement with the experimental finding and are evidence for universality in a strongly interacting frozen Rydberg gas.

Viscoelasticity of entangled λ-phage DNA solutions

The viscoelastic moduli of lambda-phage DNA through the entanglement transition were obtained with particle tracking microrheology. With increasing frequency, the viscous loss modulus first increases, then levels off, and eventually increases again. Concurrently, the elastic storage modulus monotonously increases and eventually levels off to a constant high frequency plateau value. Once the DNA molecules become entangled at about ten times the overlap concentration, the elastic storage modulus becomes larger than the viscous loss modulus in an intermediate frequency range. The number of entanglements per chain is obtained from the plateau value of the elasticity modulus. The longest, global relaxation time pertaining to the motion of the DNA molecules is obtained from the low shear viscosity as well as from the lowest crossover frequency of the viscous loss and elastic storage moduli. The concentration dependencies of the low shear viscosity, the number of entanglements per chain, and the relaxation time agree with the relevant scaling laws for reptation dynamics of entangled polyelectrolytes in an excess of simple, low molecular weight salt with screened electrostatic interactions.

Modeling fluvial incision and transient landscape evolution: Influence of dynamic channel adjustment

Channel geometry exerts a fundamental control on fluvial processes. Recent work has shown that bedrock channel width depends on a number of parameters, including channel slope, and is not solely a function of drainage area as is commonly assumed. The present work represents the first attempt to investigate the consequences of dynamic, gradient‐sensitive channel adjustment for drainage‐basin evolution. We use the Channel‐Hillslope Integrated Landscape Development (CHILD) model to analyze the response of a catchment to a given tectonic perturbation, using, as a template, the topography of a well‐documented catchment in the footwall of an active normal fault in the Apennines (Italy) that is known to be undergoing a transient response to tectonic forcing. We show that the observed transient response can be reproduced to first order with a simple detachment‐limited fluvial incision law. Transient landscape is characterized by gentler gradients and a shorter response time when dynamic channel adjustment is allowed. The differences in predicted channel geometry between the static case (width dependent solely on upstream area) and dynamic case (width dependent on both drainage area and channel slope) lead to contrasting landscape morphologies when integrated at the scale of a whole catchment, particularly in presence of strong tilting and/or pronounced slip‐rate acceleration. Our results emphasize the importance of channel width in controlling fluvial processes and landscape evolution. They stress the need for using a dynamic hydraulic scaling law when modeling landscape evolution, particularly when the relative uplift field is nonuniform.

Experimental and theoretical study of dynamical hysteresis and scaling laws in the polarization switching of vertical-cavity surface-emitting lasers

We study experimentally the role of the bias current sweep rate in measurements of polarization switching (PS) of vertical-cavity surface-emitting lasers. We find that the size of the hysteresis cycle of the PS for increasing and decreasing current follows a power-law relationship with the speed of the current ramp. A similar relation is found for the laser turn-on. Numerical calculations based on the spin-flip model are in good agreement with the observations. We also show that the PS points and the power-law exponents depend critically on the noise level included in the simulations.

Kinetic roughening of magnetic flux penetration in MgB2 thin films

Time-resolved magneto-optical studies are performed on MgB2 thin film samples grown by in situ pulsed laser deposition and in situ reactive deposition technique. The latter reveal dendritic avalanche-free flux penetration. The kinetic roughening of magnetic flux penetration is studied for applied ac current. Dynamic scaling laws determined for both static field and ac current are consistent with the directed percolation depinning model, placing the vortex dynamics in MgB2 in the same universality class as YBCO and Nb.

Mathematical formulation to predict the harmonics of the superconducting Large Hadron Collider magnets. II. Dynamic field changes and scaling laws

A superconducting particle accelerator like the LHC (Large Hadron Collider) at CERN, can only be controlled well if the effects of the magnetic field multipoles on the beam are compensated. The demands on a control system solely based on beam feedback may be too high for the requirements to be reached at the specified bandwidth and accuracy. Therefore, we designed a suitable field description for the LHC (FIDEL) as part of the machine control baseline to act as a feed-forward magnetic field prediction system. FIDEL consists of a physical and empirical parametric field model based on magnetic measurements at warm and in cryogenic conditions. The performance of FIDEL is particularly critical at injection when the field decays, and in the initial part of the acceleration when the field snaps back. These dynamic components are both current and time dependent and are not reproducible from cycle to cycle since they also depend on the magnet powering history. In this paper a qualitative and quantitative description of the dynamic field behavior substantiated by a set of scaling laws is presented.

Self-Organization of Vortex Line Length Distribution in Dilute Quantum Turbulence

There has been an exponential growth of interest in scale-free structure of quantum turbulence in recent years. Recent studies revealed that the vortex length distribution (VLD), meaning the size distribution of the vortices, in decaying quantum turbulence at zero temperature obeys a power law. This power law is very important because it means that there is a kind of self-similarity in quantum turbulence during the decay. Unfortunately, however, there has been no practical study that answers the important question; why can the quantum turbulence acquire power law VLD? In this paper, we first propose that the nature of quantized vortices allows us to describe the decay of quantum turbulence with a simple model without loosing physical validity. This simple model well reproduces the observed power law and suggests that the emergence of power law VLD is a consequence of two mechanisms; Richardson cascade and dynamical scaling law of vortex dynamics.

Cluster relaxation dynamics in liquids and solids near the glass-transformation temperature

The structural relaxation in glass-forming materials is studied near the glass transformation temperature Tg indicated by the heat capacity maximum. The late-time asymptote of the Kohlrausch–Williams–Watts form of the relaxation function is rationalized via the mesoscopic-scale correlated regions in terms of the Debye-type clusters following the dynamic scaling law. It is repeatedly shown that regardless of underlying microscopic realizations in glass formers with site disorder the structural relaxation is driven by local random fields, described via the directed random walks model. The relaxation space dimension ds=3 at Tg is suggested for relaxing units of fractal dimension df=5∕2 for quadrupolar-glass clusters in ortho–parahydrogen mixtures, that is compared with entangled-chain clusters in polymers (df=1) and solid-like clusters relaxing in supercooled molecular liquids (with ds=6 and df=3). The relaxation dynamics of orientational-glass clusters in plastic crystals is attributed to the model of continuous-time random walks in space ds=6. As a by-product, the expansivity in polymers, molecular liquids, and networks is predicted.

Spreading of a water droplet on a vertically aligned Si nanorod array surface

The dynamics of spreading of a water drop on a vertically aligned Si nanorod array surface is studied with a fast charge coupled device camera. Four dynamic spreading regimes are identified, with a precursor rim advancing ahead of the contact line. The diameters of the precursor rim Dp, the precursor length δ, and the contact line Dc obey dynamic scaling laws, Dc,p∝tnc,p∕2, with nc≈0.216 and np≈0.272, and δ≈t1∕2. The exponents do not vary significantly with the nanorod height and are consistent with the dynamic spreading behavior on a rough or porous surface.

Critical slowing down in the single crystalline relaxor SBN75

The dielectric susceptibility of strontium-barium niobate, Sr0.75Ba0.25Nb2O6, reveals strong relaxor behaviour. It is shown that the relationship between the frequency of the ac probing field and the temperature, at which the real part of the susceptibility passes through a maximum, satisfactorily follows the activated dynamic scaling law predicted for the random-field Ising model. Applicability of a power law as suggested by the dynamic scaling theory is discussed.