Narrow Results

The mutual information method has demonstrated to be very useful for deriving the potential order parameter of a system. Although the method suggests some constraints which help to define this quantity, there is still some freedom in the definition. The method then results inefficient for cases where we have order parameters with a large number of constants in the expansion, which happens when we have many degenerate vacuums. Here, we introduce some additional constraints based on the existence of broken symmetries, which help us to reduce the arbitrariness in the definitions of the order parameter in the proposed mutual information method.

The order parameters and synchronization are numerically investigated in the time delay small-world connected FitzHugh–Nagumo excitable systems. The simulations show that the order parameter continuously decreases with increasing D, the quality of the synchronization worsens for large noise intensity. As the coupling intensity goes up, the quality of the synchronization worsens also, and find that the larger rewiring probability becomes, the larger-order parameter. At the same time, the order parameter goes up, the time delay declines. We obtained the complete phase diagram for a wide range of values of noise intensity D and control parameter g.

The density profiles and corresponding order parameters of the hard ellipsoids confined between two hard walls and also in contact with a single hard wall are studied using the density functional theory (DFT). The hypernetted-chain (HNC) approximation is used to write excess grand potential of the system with respect to the bulk value. To simplify the calculations, we use restricted orientation model (ROM) for the orientation of ellipsoids to find the density profiles and order parameters. DFT shows that there is a uniaxial–biaxial (U–B) phase transition near a single hard wall and also between two hard walls for a fluid consisting of uniaxial hard ellipsoidal particles with finite elongation.

We present the latest data of the c-axis bicrystal twist Josephson junctions experiments of Liet al. and of the artificial and recent natural cross-whisker junction experiments on Bi₂Sr₂CaCu₂O_8+δ (Bi2212) of Takano et al. and Latyshev et al., respectively. These combined experiments provide strong evidence for a dominant s-wave order parameter and for strongly incoherent c-axis quasiparticle tunneling in Bi2212 for T≤T_c.

Critical phenomena in systems which have a joint multicritical and Lifshitz-point-like behavior are investigated. An expression for the upper critical dimension of such systems is found. A condition of the variational scale invariance of the considered model is specified. If the space dimension coincides with the upper critical dimension, then the critical behavior of the fluctuation correction to the heat capacity is similar to that of the heat capacity without order parameter modulation.

A polaronic model of superconductivity in doped fulleride systems is presented. The normal and anomalous one-particle Green's functions are derived for a system with strong electron phonon coupling. The study of collapse of the electron band and the phonon vacuum is presented within the mean-field approximation. Self-consistent equation for the superconductivity order parameter (Δ) is derived using Green's fucntion technique and following Lang and Firsov transformations.

Expressions for specific heat, density of states, free energy and critical field based on this model have been derived. The theory is applied to explain the experimental results in the systems K₃C₆₀ and Rb₃C₆₀. These results are in good agreement with the available experimental data.

The interfacial properties of hydrate and its ambient play an important role in hydrate technique. In this paper, the molecular characteristics of H₂O in hydrate/ice/liquid water mixture system are investigated based on molecular dynamics (MD) simulations. The structure I (sI) methane hydrate is partially heated to obtain the studied system. The properties including hydrogen bond, radial distribution function (RDF) and F3 order parameter (tetrahedral coordinated parameter of H₂O) indicate that there is little difference of water structure in the hydrate region and ice/liquid water mixture region. The F4 order parameter (parameter based on H–O–O–H torsion angles of H₂O) could be used to distinguish the different region. The value of F4 experiences the continuous change at interface between mixture region and hydrate region.

Fluctuation effects at first-order phase transitions driven by changes of other-than-temperature factors like pressure, concentration or external fields are investigated by perturbation theory. The results for the fluctuation contributions to the order parameter, the internal energy and the free energy at pre-transitional states near spinodal points of first-order phase transitions are presented to the first-nonvanishing order of the expansion parameters of the theory.

In this paper, the synchronization between spatially distributed power plants and their supported consumers is studied, where the case of Kuramoto-like model power grids connected to an external permanent magnet synchronous motor (PMSM) is taken as an example. We focus on the dependence of the synchronization on the coupling coefficient. To quantitatively study the synchronization degree, we introduce the order parameter and the frequency deviation to measure the synchronization of the coupled system. It is found that as the external coupling coefficient is increased, the distributed power grids and the loading system become more and more synchronized in space, and the complete synchronization appears at a particular value of external coupling coefficient. Our results may provide a useful tip for analyzing the synchronous ability of distributed power grids.

The effect of magnetic fluctuations on the free energy, the order parameter profile and the latent heat at the equilibrium point of the first order phase transition to superconducting state in thin films of type I superconductors is considered. The possibility for an experimental observation of the fluctuation change of the order of the superconducting phase transition is briefly discussed. Numerical data for the order parameter jump and the latent heat of Al films are presented.

We show that the suppression of light scattering off a Bose Einstein Condensate is equivalent to the Landau argument for superfluidity and thus is a consequence of the Principle of Superfluidity. The superfluid ground state of a BEC contains nonseparable, nontrivial correlations between the bosons that make up the system, i.e., it is entangled. The correlations in the ground state entangle the bosons into a coherent state for the lowest energy state. The entanglement is so extreme that the bosons that make up the system cannot be excited at long wavenumbers. Their existence at low energies is impossible. Only quantum sound can be excited, i.e. the excitations are Bogolyubov quasiparticles which do not resemble free bosons whatsoever at low energies. This means that the system is superfluid by the Landau argument and the superfluidity is ultimately the reason for suppressed scattering at low wavelengths.

The new types of nonlinear localized state of generalized order parameter in the three-layered structure of band antiferromagnets with congruent sections of the Fermi surface are obtained. The nonlinear effects inside the narrow plane defects between the layers representing the local magnetization in the direction of polarization of the spin density wave are described by the nonlinear source function. The variation of the Ginsburg–Landau functional near the Lifshitz point leads to nonlinear Schrödinger equation (NSE) with cubic nonlinear terms and self-consistent nonlinear potential modeling the plane defects. The dispersion equations of two type stationary nonlinear localized states are derived. The solutions of dispersion equations in explicit analytical form in dependence on characteristics of plane defects and the distance between them are found and analyzed. The localized states of order parameter existing only near the plane defects with nonlinear response are obtained.

A series of identities of correlation functions K(n₁, n₂, …, n_N) are given in the nearest-particle system. The above correlation identities are applied to the one-dimensional contact process. The decoupling induced by a renewal measure yields the first approximation: for the critical value and for the order parameter, which makes a rigorous bound as proved by Holley and Liggett. Furthermore, introducing a new decoupling procedure, improved estimations of and are calculated.

The long-term mean-field dynamics of coupled underdamped Duffing oscillators driven by an external periodic signal with Gaussian noise is investigated. A Boltzmann-type $H$-theorem is proved for the associated nonlinear Fokker–Planck equation to ensure that the system can always be relaxed to one of the stationary states as time is long enough. Based on a general framework of the linear response theory, the linear dynamical susceptibility of the system order parameter is explicitly deduced. With the spectral amplification factor as a quantifying index, calculation by the method of moments discloses that both mono-peak and double-peak resonance might appear, and that noise can greatly signify the peak of the resonance curve of the coupled underdamped system as compared with a single-element bistable system. Then, with the input signals taken from laboratory experiments, further observations show that the mean-field coupled stochastic resonance system can amplify the periodic input signal. Also, it reveals that for some driving frequencies, the optimal stochastic resonance parameter and the critical bifurcation parameter have a close relationship. Moreover, it is found that the damping coefficient can also give rise to nontrivial nonmonotonic behaviors of the resonance curve, and the resultant resonant peak attains its maximal height if the noise intensity or the coupling strength takes the critical value. The new findings reveal the role of the order parameter in a coupled system of chaotic oscillators.

We consider an Individual-Based Model for self-rotating particles interacting through local alignment and investigate its macroscopic limit. This model describes self-propelled particles moving in the plane and trying to synchronize their rotation motion with their neighbors. It combines the Kuramoto model of synchronization and the Vicsek model of swarm formation. We study the mean-field kinetic and hydrodynamic limits of this system within two different scalings. In the small angular velocity regime, the resulting model is a slight modification of the "Self-Organized Hydrodynamic" model which has been previously introduced by the first author. In the large angular velocity case, a new type of hydrodynamic model is obtained. A preliminary study of the linearized stability is proposed.

The synchronous dynamics of many limit-cycle oscillators can be described by phase models. The Kuramoto model serves as a prototype model for phase synchronization and has been extensively studied in the last 40 years. In this paper, we deal with the complete synchronization problem of the Kuramoto model with frustrations on a complete graph. We study the robustness of complete synchronization with respect to the network structure and the interaction frustrations, and provide sufficient frameworks leading to the complete synchronization, in which all frequency differences of oscillators tend to zero asymptotically. For a uniform frustration and unit capacity, we extend the applicable range of initial configurations for the complete synchronization to be distributed on larger arcs than a half circle by analyzing the detailed dynamics of the order parameters. This improves the earlier results [S.-Y. Ha, H. Kim and J. Park, Remarks on the complete frequency synchronization of Kuramoto oscillators, Nonlinearity28 (2015) 1441–1462; Z. Li and S.-Y. Ha, Uniqueness and well-ordering of emergent phase-locked states for the Kuramoto model with frustration and inertia, Math. Models Methods Appl. Sci.26 (2016) 357–382.] which can be applicable only for initial configurations confined in a half circle.

The mesoscopic dynamic simulation (MesoDyn) has been carried out to investigate the phase structure and the aggregate properties of triblock copolymers (ethylene oxide)₃₇ (propylene oxide)₅₆ (ethylene oxide)₃₇ (P105) in aqueous solution. A Gaussian chain model is successfully built according to the equivalent chain method and the Flory–Huggins interaction parameters, χ, used for determining the repulsions between different chain segments are computed. Simulation results show that P105 can form several microstructures including spherical micelles, ellipsoid micellar cluster, worm-like micelles, defective bicontinuous phase, and bicontinuous phase with increasing concentration. A special transition phase structure of P105 is found in the spherical micellar region. The dynamic evolution processes of spherical micelles are investigated by observing the induction time before phase separation and the changing of isosurface during phase separation. The influence of P105 concentration on the density of micelles at equilibrium state is also discussed, which shows that the increase of P105 concentration will lead to the decrease of micelles' amount. Two kinds of growth mechanisms during phase separation are discussed by MesoDyn simulation.

A density functional theory (DFT) based multi-step simulation method is used to characterize the detailed molecular structure and inter/intra- molecular interactions of two benchmark liquid crystals (LC) 5CB, 8CB and a novel tri-biphenyl ring bent core LC material. The method uses hybrid DFT at the B3LYP/6-31G* level to obtain molecular structure and Raman data. These results are fed to a crystal packing simulation to find possible crystal structures. A pico-second quantum mechanics/molecular mechanics (QM/MM) simulation model is built for the selected structures with lower overall energy as well as optimal density. The stabilized crystal structures are then extended into a super cell, heated and simulated using a mixed force field and nano-second molecular dynamics (MD). The described simulation process sequence provides predictions of molecular Raman spectrum, LC density, isotropic depolarization ratio, ratio of differential polarizability, order parameters, molecular structures, and rotating Raman spectrum of the different mesophases. The Raman spectra, order parameters and depolarization ratios all agree well with existing experimental and previous simulation results. The study of the novel tri-biphenyl ring bent core LC system shows that the ratio of differential polarizability depends on intra-molecular interactions. The findings presented in this manuscript contribute to the on-going efforts to establish links between LC molecular structures and their properties, including optical behavior.

The cell is the basic functional and biological unit of life, and a complex system that contains a huge number of molecular components. How can we quantify the macroscopic state of a cell from the microscopic information of these molecular components? This is a fundamental question to increase the understanding of the human body. The recent maturation of single-cell RNA sequencing (scRNA-seq) technologies has allowed researchers to gain information on the transcriptomes of individual cells. Although considerable progress has been made in terms of cell-type clustering over the past few years, there is no strong consensus about how to define a cell state from scRNA-seq data. Here, we present single-cell entropy (scEntropy) as an order parameter for cellular transcriptome profiles from scRNA-seq data. scEntropy is a straightforward parameter with which to define the intrinsic transcriptional state of a cell that can provide a quantity to measure the developmental process and to distinguish different cell types. The proposed scEntropy followed by Gaussian mixture model (scEGMM) provides a coherent method of cell-type classification that is simple, includes no parameters or clustering and is comparable to existing machine learning-based methods in benchmarking studies. The results of cell-type classification based on scEGMM are robust and easy to biologically interpret.

The purpose of this work is in development of the model that allows to investigate the conformations of macromolecules near the interface “dielectric-metal” depending on the conditions of formation of the polymer coating. In the modified model of “sticky tape”, one part of macromolecule is anchored to the metal surface while the other can be elongated due to effective mean (molecular) field of dipolar type formed by free ends of other chains. The dynamic Monte-Carlo method for Langmuir’s model is used for calculation of adhesion force taking into account the interaction energy of monomers with the metal surface. It is shown that conformation of polymer chain is defined by temperature conditions of its formation. The obtained results are confirmed by the data of production tests on polymer coatings in JSC “Severstal”.