Evolution Of Order Parameter Research Articles

Disorder trapping by rapidly moving phase interface in an undercooled liquid

Non-equilibrium phenomena such as the disappearance of solute drag, the origin of solute trapping and evolution of disorder trapping occur during fast transformations with originating metastable phases [D.M. Herlach, P.K. Galenko, D. Holland-Moritz, Metastable solids from undrercooled melts (Elsevier, Amsterdam, 2007)]. In the present work, a theoretical investigation of disorder trapping by a rapidly moving phase interface is presented. Using a model of fast phase transformations, a system of governing equations for the diffusion of atoms, and the evolution of both long-range order parameter and phase field variable is formulated. First numerical solutions are carried out for a congruently melting binary alloy system.

Low temperature and high pressure thermoelastic and crystallographic properties of SrZrO3 perovskite in the Pbnm phase

The thermoelastic and structural properties of SrZrO3 perovskite in the Pnma (Pbnm) phase have been studied using neutron powder diffraction at 82 temperatures between 11 K and 406 K at ambient pressure, and at sixteen pressures between 0.07 and 6.7 GPa at ambient temperature. The bulk modulus, derived by fitting the equation of state to a second order Birch-Murnaghan equation-of-state, 157(5) GPa, is in excellent agreement with that deduced in a recent resonant ultrasound investigation. Experimental axial compressional moduli are in agreement with those calculated from the elastic stiffness coefficients derived by ab-initio calculation, although the experimental bulk modulus is significantly softer than that calculated. Following low temperature saturation for temperatures less than 40 K, the unit cell monotonically increases with a predicted high temperature limit in the volume expansivity of ∼2.65 × 10−5 K−1. Axial linear thermal expansion coefficients are found to be in the order αb < αc < αa for all temperatures greater than 20 K with the b axis indicating a weak, low temperature negative expansion coefficient at low temperatures. The thermoelastic properties of SrZrO3 can be approximated by a two-term Debye model for the phonon density of states with Debye temperatures of 238(4) K and 713(6) K derived in a self-consistent manner by simultaneously fitting the isochoric heat capacity and the unit cell volume. Atomic displacement parameters have been fitted to a modified Debye model in which the zero-point term is an additional refinable variable and shows the cations and anions have well separated Debye temperatures, mirroring the need for two Debye-like distributions in the vibrational density of states. The temperature dependence of the crystal structure is presented in terms of the amplitudes of the seven symmetry-adapted basis vectors of the aristotype phase that are consistent with space group Pbnm, thus permitting a direct measure of the order parameter evolution in SrZrO3. The temperature variation of the in-phase tilt, which is lost at the phase transition at 973 K, is consistent with tricritical behaviour, in agreement with published results based on high temperature crystallographic data.

Structural Insights into Solid-to-Solid Phase Transition and Modulated Crystal Formation in Octyl-β-d-Galactoside Crystals.

Despite the significance of synthetic monotailed β-linked galactolipids, for a detailed understanding of natural galactolipids, many aspects of these β-linked galactolipids' crystal structures such as temperature-dependence and hydration characteristics remain inadequately understood. In this manuscript, we demonstrated detailed insight of crystal characteristics of one of the simplest monotailed galactolipids, octyl-β-d-galactoside (MOβ-Gal), using thermal analyses, Fourier-transform infrared spectroscopy (FTIR), powder X-ray diffraction (PXRD) measurements and grazing-incidence wide-angle X-ray diffraction (GI-WAXD) analysis. As a result, it was revealed that the MOβ-Gal anhydrous crystal showed a continuous structural change from the high-symmetry structure to low-symmetry crystal lattice via the strengthened hydrogen bonding interaction as the temperature decreased. In addition, the hemihydrate crystal was found to be in the modulated "ribbon phase". These insights strongly suggest that β-linked galactolipids possess intrinsic characteristics necessary to form a modulated structure even in the crystal state and demonstrate the importance of the presence of tiny amounts of water as cushioning media for preventing order parameter evolution.

Orientational Order of a Lyotropic Chromonic Liquid Crystal Measured by Polarized Raman Spectroscopy.

Lyotropic chromonic liquid crystals are distinct from thermotropic nematics from a fundamental standpoint as the structure of the aggregating columns is a function of both the temperature and concentration. We report on the thermal evolution of orientational order parameters, both the second (=scalar) (⟨P200⟩ (=S)) and fourth (⟨P400⟩) order, of sunset yellow FCF aqueous solutions, measured using polarized Raman spectroscopy for different concentrations. The order parameter increases with the concentration, and their values are high in comparison with those of thermotropic liquid crystals. On the basis of Raman spectroscopy, we provide the strongest evidence yet that the hydrozone tautomer of SSY is the predominant form in aqueous solutions in the isotropic, nematic, and columnar phases, as well as what we believe to be the first measurements of (⟨P400⟩) for this system.

Using gap symmetry and structure to reveal the pairing mechanism in Fe-based superconductors

I review theoretical ideas and implications of experiments for the gap structure and symmetry of the Fe-based superconductors. Unlike any other class of unconventional superconductors, one has in these systems the possibility to tune the interactions by small changes in pressure, doping or disorder. Thus, measurements of order parameter evolution with these parameters should enable a deeper understanding of the underlying interactions. I briefly review the "standard paradigm" for $s$-wave pairing in these systems, and then focus on developments in the past several years which have challenged this picture. I discuss the reasons for the apparent close competition between pairing in s- and d-wave channels, particularly in those systems where one type of Fermi surface pocket -- hole or electron -- is missing. Observation of a transition between $s$- and $d$-wave symmetry, possibly via a time reversal symmetry breaking "$s+id$" state, would provide an importantconfirmation of these ideas. Several proposals for detecting these novel phases are discussed, including the appearance of order parameter collective modes in Raman and optical conductivities. Transitions between two different types of $s$-wave states, involving various combinations of signs on Fermi surface pockets, can also proceed through a ${\cal T}$-breaking "$s+is$" state. I discuss recent work that suggests pairing may take place away from the Fermi level over a surprisingly large energy range, as well as the effect of glide plane symmetry of the Fe-based systems on the superconductivity, including various exotic, time and translational invariance breaking pair states that have been proposed. Finally, I address disorder issues, and the various ways systematic introduction of disorder can (and cannot) be used to extract information on gap symmetry and structure.

Time evolution of entanglement entropy in quenched holographic superconductors

We investigate the dynamical evolution of entanglement entropy in a holographic superconductor model by quenching the source term of the dual charged scalar operator. By access to the full background geometry, the holographic entanglement entropy is calculated for a strip geometry at the AdS boundary. It is found that the entanglement entropy exhibits a robust non-monotonic behaviour in time, independent of the strength of Gaussian quench and the size of the strip: it first displays a small dip, then grows linearly, and finally saturates. In particular, the linear growth velocity of the entanglement entropy has an upper bound for strip with large width; The equilibrium value of the non-local probe at late time shows a power law scaling behaviour with respect to the quench strength; Moreover, the entanglement entropy can uncover the dynamical transition at certain critical quench strength which happens to coincide with the one obtained form the dynamical evolution of scalar order parameter.

Anisotropic phase field solution for morphological evolution and migration of inclusions in piezoelectric films

Based on an anisotropic phase field model, the morphological evolution and migration of inclusions in piezoelectric films under mechanical and electric loads are investigated. An order parameter field is introduced to characterize the evolution of inclusion in piezoelectric film, where the zero contour evolution of order parameter in the phase interface layer between inclusion and matrix film tracks the morphological change and migration of the inclusion driven by coupled mechanical and electric loads. Results show that morphological evolution and migration of inclusion in piezoelectric film is mainly caused by normal stress gradient in the phase interface layer between inclusions and piezoelectric film, and when piezoelectric film appears in a lower resistivity, an additional drive force induced by electron field (electron wind) exerted the piezoelectric film promotes the migration of an inclusion toward the higher electric potential direction. Anisotropic diffusion behavior of interface layer causes asymmetrically morphological evolution of inclusion in piezoelectric film under different loads.

ESR and Optical Study of Photo-Orientation in Azobenzene-Containing Liquid-Crystalline Polymer

We report a comprehensive experimental study of photoinduced processes in azobenzene-containing liquid-crystalline polymer. The kinetic and optical characteristics of the photoisomerization reaction and photo-orientation process have been determined. The spin probe technique has been used to elucidate the details of orientation order and rotational mobility of molecular fragments within the liquid-crystalline polymer. The evolution of orientation order parameters <P2>, <P4>, and <P6> in the course of photoinduced ordering of the material as well as the change of liquid-crystalline domain sizes have been studied quantitatively. The obtained experimental results are compared with the predictions of the existing models of photo-orientation.

Substrate wettability induced alterations in convective heat transfer characteristics in microchannel flows: An order parameter approach

In this paper, we analyze the consequences of substrate wettability on the convective heat transfer characteristics in microchannel flows. However, in sharp contrast to other reported studies, we do not presume a slip-length a priori, but take an explicit accounting of the substrate wettability through an order parameter consideration. The order parameter formalism also allows us to consider co-existences of bulk and interfacial phases and takes the consequent thermo-physical property variations aptly into account. Our results reveal explicit dependence of the heat transfer characteristics, such as the thermal entrance length and the Nusselt number, on the equilibrium contact angle. Further, we present an analysis that theoretically justifies the role of wettability by decomposing the thermophysical properties and flow variables into a base part and a wettability-dependant part, with rigorous justification from a perturbation-based analysis of the order parameter evolution equations. These considerations, along with our simulation predictions, reveal that the effect of substrate wettability on bulk thermal characteristics of microchannel transport is primarily advection-dominated, although a combined advection–diffusion mechanism controls the corresponding interfacial transport in the near-wall regime. Our results bring out an explicit dependence of the heat transfer characteristics on the substrate wettability, and in particular, reveal a trend of decreasing Nusselt number with increasing value of the contact angle.

Study on the Evaluation of Electricity Market Operational Efficiency Based on Synergetic Theory

The operational efficiency of power market is infected by the primary conditions of the market, the regulations of government, the balance of need and supply, the behaviors of participants etc. Owing to the characteristics of dynamic complexity, the evaluation for the operational efficiency of the market should develop a new way rather than the traditional way. Based on the synergetic theory, this paper established a synergetic evolution state equation model of the operational efficiency of power market combining with grey cognate principle. According to the data of the Southern power market of China, the order parameter was conformed and the order parameter evolution equation which reflects the operational situation of the market was constructed. Through this equation, the boundary value of the order parameter which implies the market is in effective was given.

A nonisothermal phase‐field model for the ferromagnetic transition

We propose a model for nonisothermal ferromagnetic phase transition based on a phase field approach, in which the phase parameter is related but not identified with the magnetization. The magnetization is split in a paramagnetic and in a ferromagnetic contribution, dependent on a scalar phase parameter and identically null above the Curie temperature. The dynamics of the magnetization below the Curie temperature is governed by the order parameter evolution equation and by a Landau–Lifshitz type equation for the magnetization vector. In the simple situation of a uniaxial magnet, it is shown how the order parameter dynamics reproduces the hysteresis effect of the magnetization. Copyright © 2012 John Wiley &amp; Sons, Ltd.

Computational Study on Oligomer Formation of Fibril-forming Peptide of α-Synuclein

We have studied the oligomerization of a fibril-forming segment of -Synulcein using a replica exchange molecular dynamics (REMD) simulation. The simulation was performed with trimers and tetramers of a 12 amino acid residue stretch (residues 71-82) of -Synulcein. From extensive REMD simulations, we observed the spontaneous formation of both trimer and tetramer, demonstrating the self-aggregating and fibril-forming properties of the peptides. Secondary structure profile and clustering analysis illustrated that antiparallel -sheet structures are major species corresponding to the global free energy minimum. As the size of the oligomer increases from a dimer to a tetramer, conformational stability is increased. We examined the evolution of simple order parameters and their free energy profiles to identify the process of aggregation. It was found that the degree of aggregation increased as time passed. Tetramer formation was slower than trimer formation and a transition in order parameters was observed, indicating the full development of tetramer conformation which is more stable than that of the trimer. The shape of free energy surface and change of order parameter distributions indicate that the oligomer formation follows a dock-and-lock process.

Nonequilibrium Relaxation and Critical Aging for Driven Ising Lattice Gases

We employ MonteCarlo simulations to study the nonequilibrium relaxation of driven Ising lattice gases in two dimensions. Whereas the temporal scaling of the density autocorrelation function in the nonequilibrium steady state does not allow a precise measurement of the critical exponents, these can be accurately determined from the aging scaling of the two-time autocorrelations and the order parameter evolution following a quench to the critical point. We obtain excellent agreement with renormalization group predictions based on the standard Langevin representation of driven Ising lattice gases.

A dynamical theory of nucleation for colloids and macromolecules

A general theory of nucleation for colloids and macromolecules in solution is formulated within the context of fluctuating hydrodynamics. A formalism for the determination of nucleation pathways is developed and stochastic differential equations for the evolution of order parameters are given. The conditions under which the elements of classical nucleation theory are recovered are determined. The theory provides a justification and extension of more heuristic equilibrium approaches based solely on the free energy. It is illustrated by application to the low-concentration/high-concentration transition in globular proteins, where a novel two-step mechanism is identified, where the first step involves the formation of long-wavelength density fluctuations, and the second step is the actual nucleation event occurring within the fluctuation.

Dynamics of Boolean Networks: An Exact Solution

The dynamics of Boolean networks (BN) with quenched disorder and thermal noise is studied via the generating functional method. A general formulation, suitable for BN with any distribution of Boolean functions, is developed. It provides exact solutions and insight into the evolution of order parameters and properties of the stationary states, which are inaccessible via existing methodology. We identify cases where the commonly used annealed approximation is valid and others where it breaks down. Broader links between BN and general Boolean formulas are highlighted.

Magnetic phase diagram of multiferroicMnWO4 probed by ultrasound

The magnetic phase diagram of multiferroicMnWO4 is studied in magnetic fields up to 60 T using sound velocity and soundattenuation measurements. Anomalies are observed at temperaturesTN1 = 7.6 K,TN2 = 12.6 Kand TN3 = 13.6 K that separate commensurate antiferromagnetic (AF1) to helical AF2 and commensurateAF3 to paramagnetic phases, respectively. The anomalies are significantlydifferent and shed light on the spin–phonon coupling and evolution of thevarious order parameters in this multiferroic material. For temperatures belowTN2 pronounced field hysteresis effects are also observed in the sound velocity, indicatingfield-induced transformations. In the temperature dependence of the attenuation weobserve anomalies distinctively different from the usual maxima related to relaxationeffects. They are attributed to the combination of dispersion effects due to domain wallsand the discontinuously changing sound velocity. In total, six different magnetic phases, atvarious temperatures and fields including a novel high-field phase, are revealed andanalyzed.

A fast–slow dynamical systems theory for the Kuramoto type phase model

We present a fast–slow dynamical systems theory for the Kuramoto type phase model. When the order parameters are frozen, the fast system consists of independent oscillator equations, whereas the slow system describes the evolution of order parameters. We average out the slow system over the fast manifold to derive a weak form of an amplitude–angle coupled system for the evolution of Kuramotoʼs order parameters. This yields the slow evolution of order parameters to be constant values which gives a rigorous proof to Kuramotoʼs original assumption in his self-consistent mean-field theory.

Application of Synergetic Neural Network in Online Writeprint Identification

Abstract Synergetic neural network (SNN) associates synergetics with artificial neural network, it can rigorously deal with the behavior of network in the mathematical theory, and have the advantage of fast learning, short pattern recalling time and so on. In this paper, a pattern recognition method based on the self-adaptive attention parameters presented on the basis of analyzing the key technology of SNN, and the advanced algorithm will be employed in the online writeprint identification, the key point of this algorithm is that it can correct initial mis-identified patterns through measuring similarity between the prototype pattern and the testing pattern in the evolution of order parameters. Experimental results show that the advanced SNN has better performance and robustness than the SNN based on balanced attention parameters. Further, the network’s self-learning ability and recognition performance is greatly improved by using advanced SNN.

Relaxation to thermal equilibrium in the self-gravitating sheet model

We revisit the issue of relaxation to thermal equilibrium in the so-called ‘sheet model’,i.e. particles in one dimension interacting by attractive forces independent of theirseparation. We show that this relaxation may be very clearly detected and characterized byfollowing the evolution of order parameters defined by appropriately normalized momentsof the phase space distribution which probe its entanglement in space and velocitycoordinates. For a class of quasi-stationary states which result from the violentrelaxation of rectangular waterbag initial conditions, characterized by their virial ratioR0, weshow that relaxation occurs on a timescale which (i) scales approximately linearly in the particle numberN and (ii) also shows astrong dependence on R0, with quasi-stationary states from colder initial conditions relaxing much more rapidly.The temporal evolution of the order parameter may be well described by a stretchedexponential function. We study finally the correlation of the relaxation times with theamplitude of fluctuations in the relaxing quasi-stationary states, as well as the relationbetween temporal and ensemble averages.

Self-assembly of nanocomponents into composite structures: Derivation and simulation of Langevin equations

The kinetics of the self-assembly of nanocomponents into a virus, nanocapsule, or other composite structure is analyzed via a multiscale approach. The objective is to achieve predictability and to preserve key atomic-scale features that underlie the formation and stability of the composite structures. We start with an all-atom description, the Liouville equation, and the order parameters characterizing nanoscale features of the system. An equation of Smoluchowski type for the stochastic dynamics of the order parameters is derived from the Liouville equation via a multiscale perturbation technique. The self-assembly of composite structures from nanocomponents with internal atomic structure is analyzed and growth rates are derived. Applications include the assembly of a viral capsid from capsomers, a ribosome from its major subunits, and composite materials from fibers and nanoparticles. Our approach overcomes errors in other coarse-graining methods, which neglect the influence of the nanoscale configuration on the atomistic fluctuations. We account for the effect of order parameters on the statistics of the atomistic fluctuations, which contribute to the entropic and average forces driving order parameter evolution. This approach enables an efficient algorithm for computer simulation of self-assembly, whereas other methods severely limit the timestep due to the separation of diffusional and complexing characteristic times. Given that our approach does not require recalibration with each new application, it provides a way to estimate assembly rates and thereby facilitate the discovery of self-assembly pathways and kinetic dead-end structures.