Spatial distribution order parameter prediction of collective system using graph network

In the past few decades, the study of collective motion phase transition process has made great progress. It is also important for the description of the spatial distribution of particles. In this work, we propose a new order parameter φ to quantify the degree of order in the spatial distribution of particles. The results show that the spatial distribution order parameter can effectively describe the transition from a disorderly moving phase to a phase with a coherent motion of the particle distribution and the same conclusion could be obtained for systems with different sizes. Furthermore, we develop a powerful molecular dynamic graph network(MDGNet) model to realize the long-term prediction of the self-propelled collective system solely from the initial particle positions and movement angles. Employing this model, we successfully predict the order parameters of the specified time step. And the model can also be applied to analyze other types of complex systems with local interactions.

SPECTRUM DISTRIBUTION OF THE SEDOND ORDER GENERALIZED DISTRIBUTED PARAMETER SYSTEMS

Spectrum distribution of the second order generalized distributed parameter system was discussed via the functional analysis and operator theory in Hilbert space. The solutions of the problem and the constructive expression of the solutions are given by the generalized inverse one of bounded linear operator. This is theoretically important for studying the stabilization and asymptotic stability of the second order generalized distributed parameter system.

CONSTITUTIVE EQUATION WITH ORDERED PARAMETERS FOR VISCOELASTIC MATERIAL CONTAINING DEFECTS

Based on the experimental results of local temperature field formed in the evolution period of defects, the defect field is defined by this internal temperature field. The evolutionary processes of statistically correlative meso-scopic defects are analysed with the growth rate and nucleation rate of the meso-defect, and it is deemed that the dynamic failure process of the viscoelastic material with defects can be quantitatively described by the normal method of the procedure of heat wave transmission. The defect field is regarded as a complex system of the union of the real sets and null sets, its main characteristics depending on the stratum hypothesis about the activities of the subsystems of the highest stratum described by ordered parameters. The fluctuation of ordered parameters is demonstrated by means of the projection operator method. The constitutive equation with ordered parameters for the meso-defect evolutionary state of viscoelastic material with defects is deduced from the nonlinear rheological dynamic approach, and its solution is obtained.

A tentative model for the explanation of B?th law using the order parameter of seismicity in natural time

Using the order parameter of seismicity defined in natural time, we suggest a simple model for the expla- nation of Bath law, according to which a mainshock differs in magnitude from its largest aftershock by approximately 1.2 regardless of the mainshock magnitude. In addition, the validity of Bath law is studied in the Global Centroid Moment Tensor catalogue by using two different aftershock definitions. It is found that the mean of this difference, when considering all the pairs mainshock-largest aftershock, does not markedly differ from 1.2 and the corresponding distributions do not depend on the mainshock＇s magnitude threshold in a statistically significant manner. Finally, the analysis of the cumulative distribution functions provides evidence in favour of the proposed model.

A novel approach to topological defects in a vector order parameter system

Based on Duan＇s topological current theory,we propose a novel approach to study the topological properties of topological defects in a two-dimensional complex vector order parameter system.This method shows explicitly the fine topological structure of defects.The branch processes of defects in the vector order parameter system have also been investigated with this method.

Temperature dependence of ratio between dielectric anisotropy and order parameter in fluorinated nematic liquid crystals

Temperature dependence of ratio between dielectric anisotropy and order parameter of fluorinated nematic liquid crystal is investigated by using a semi-empirical molecular orbital package that can accurately calculate an angle between molecular dipole moment and long axis. We optimize the molecular conformations with three semi-empirical Hamiltonians AM1, PM3 and PM5, and then make a comparison between computational results and experimental measurements. It is shown that the results obtained from AM1 method are in good agreement with the measurements. The present study offers an applicable method to predict the dielectric properties of liquid crystal material.

Order parameters and synchronization of FitzHugh-Nagumo small-world networks

This paper numerically investigates the order parameter and synchronisation in the small world connected FitzHugh-Nagumo excitable systems. The simulations show that the order parameter continuously decreases with increasing D, the quality of the synchronisation worsens for large noise intensity. As the coupling intensity goes up, the quality of the synchronisation worsens, and it finds that the larger rewiring probability becomes the larger order parameter. It obtains the complete phase diagram for a wide range of values of noise intensity D and control parameter g.

Universal order-parameter and quantum phase transition for two-dimensional q-state quantum Potts model

We investigate quantum phase transitions for q-state quantum Potts models(q=2,3,4)on a square lattice and for the Ising model on a honeycomb lattice by using the infinite projected entangled-pair state algorithm with a simplified updating scheme.We extend the universal order parameter to a two-dimensional lattice system,which allows us to explore quantum phase transitions with symmetry-broken order for any translation-invariant quantum lattice system of the symmetry group G.The universal order parameter is zero in the symmetric phase,and it ranges from zero to unity in the symmetry-broken phase.The ground-state fidelity per lattice site is computed,and a pinch point is identified on the fidelity surface near the critical point.The results offer another example highlighting the connection between(i)critical points for a quantum many-body system undergoing a quantum phase-transition and(ii)pinch points on a fidelity surface.In addition,we discuss three quantum coherence measures:the quantum Jensen–Shannon divergence,the relative entropy of coherence,and the l1norm of coherence,which are singular at the critical point,thereby identifying quantum phase transitions.

Polarizabilities and Orientational Order Parameter in N-(p-n-Ethoxybenzylidene)- p-n-Alkoxy Anilines, 2O.Om LC Compounds

n.m, n.Om, nO.m and nO.Om compounds play an important role in the fundamental and applied aspects. As a part of our systematic studies of the above homologous series regarding the synthesis, characterization and phase transition studies, here the authors report the polarizabilities and orientational order parameter, S in N-(p-n-ethoxybenzylidene)-p-n-alkoxy anilines, 2O.Om with m = 3 to 10 liquid crystalline compounds except with m = 5 which has been already published. The rest of the compounds exhibit the nematic LC phase except with m = 10 which shows the smectic-C phase along the nematic phase which is originally not detected by Godzwon et al. But the author’s observations with TM and differential scanning calorimeter have shown the existence on SmC phase in addition to nematic phase. Further, SmC is clarified using the histogram technique whose details are given below and are published elsewhere. The orientstonal order parameter, S is estimated using different methods and compared with the value obtained from birefringence, δn = (ne – no) where no field model is used. It is observed in these compounds case as in other LC compounds Vuks isotropic model is favored compared to that of anisotropic model proposed by Neugebauer.

On the Cosmic Evolution of the Quantum Vacuum Using Two Variable G Models and Winterberg’s Thesis

We work within a Winterberg framework where space, i.e., the vacuum, consists of a two component superfluid/super-solid made up of a vast assembly (sea) of positive and negative mass Planck particles, called planckions. These material particles interact indirectly, and have very strong restoring forces keeping them a finite distance apart from each other within their respective species. Because of their mass compensating effect, the vacuum appears massless, charge-less, without pressure, net energy density or entropy. In addition, we consider two varying G models, where G, is Newton’s constant, and G-1, increases with an increase in cosmological time. We argue that there are at least two competing models for the quantum vacuum within such a framework. The first follows a strict extension of Winterberg’s model. This leads to nonsensible results, if G increases, going back in cosmological time, as the length scale inherent in such a model will not scale properly. The second model introduces a different length scale, which does scale properly, but keeps the mass of the Planck particle as, ± the Planck mass. Moreover we establish a connection between ordinary matter, dark matter, and dark energy, where all three mass densities within the Friedman equation must be interpreted as residual vacuum energies, which only surface, once aggregate matter has formed, at relatively low CMB temperatures. The symmetry of the vacuum will be shown to be broken, because of the different scaling laws, beginning with the formation of elementary particles. Much like waves on an ocean where positive and negative planckion mass densities effectively cancel each other out and form a zero vacuum energy density/zero vacuum pressure surface, these positive mass densities are very small perturbations (anomalies) about the mean. This greatly alleviates, i.e., minimizes the cosmological constant problem, a long standing problem associated with the vacuum.

Microscopic phase-field simulation of L1_2 and D0_(22) phases during the early precipitation process of Ni-Cr-Al alloys

The influence of temperature on the precipitation mechanism and sequence of L 12 and D022 phases during the early precipitation process of a Ni-15.Sat%Cr-14at%Al alloy was simulated based on the microscopic phase-field model. In the range from 873 to 1373 K, the precipitation mechanism transformed from spinodal decomposition to non-classic nucleation and growth; the incubation period prolonged gradually with increasing temperature. The volume fraction of L12 phases increased and that of D022 phases decreased. D022 phases disappeared at 1373 K, and finally single-phase L12 phases were formed.

Microscopic Phase-field Simulation of Competition Mechanism Between Ll_2 and D0_(22) Structure in Ni-Cr-Al Alloy

Simulations are performed on temporal evolution of atom morphology and ordering parameters of Ni-14.5 Cr-16.5 Al alloy during early precipitation process at different temperatures based on microscopic phase-field theory; the relationship between precipitation sequence and mechanism of L12 and D022 structure and precipitation temperature are illuminated. The nonstoichiometric ordered L12 phases appear first with congruent ordering＋spinodal decomposition mechanism which is then followed by precipitation of D022 phases at ordering domain boundaries of L12 phases by spinodal decomposition mechanism at 1073 K and 1223 K. The nonstoichiometric L12 phases transform to stoichiometric ordering phases gradually. The incubation period of L12 and D022 phases is shorter at 1073 K than that 1223 K, and growth speed is higher at 1073 K. At 1373 K, L12 and D022 phases appear simultaneously by non-classical nucleation and growth mechanism. After that the particles of D022 phases diminish and disappear gradually; L12 phases grow and single L12 phases are remained at last.

Microscopic phase-field simulation for nucleation incubation time of Ni_(75)Al_xV_(25-x)alloy

With the microscopic phase-field dynamic model, the effects of temperature and concentration on the nucleation incubation time of Ni75AlxV25-x alloy were studied and the relation between the incubation time and precipitation mechanism was investigated by using the atomic occupation probability picture and average order parameter curve. The simulation results demonstrate that there exists the incubation time for different precipitation mechanisms~ such as non-classical nucleation, the mixed style of non-classical nucleation and spinodal decomposition, and spinodal ordering; and the incubation time shortens in turn for the three kinds of mechanisms. With the increase of Al content of Ni75AlxV25-x alloy, the incubation time of Llz phases shortens continuously and that of DOzz phases is prolonged. The effects of temperature on the incubation time of Llz and DOzz phases are accordant, i.e. the incuba- tion time is greatly prolonged with the temperature rising.

Quantum theory-based physical model of the human body in TCM

In the study,a quantum resonant cavity model based on wave-particle duality was proposed for the explanation of the dynamic processes of essence,vigor,and spirit in the human body in traditional Chinese medicine(TCM).It is assumed that there is a macro human order parameter(wave function),and its dynamics are governed by a macro potential field reflecting influences from heaven,earth,and society,and satisfy the generalized Schrodinger equation.This proposed model was applied in the study to interpret basic concepts of human body in TCM,with an aim to unfold the TCM development in the future.

HOSVD-based LPV modeling and mixed robust H_2/H_∞ control design for air-breathing hypersonic vehicle

This paper focuses on synthesizing a mixed robust H_2/H_∞ linear parameter varying（LPV） controller for the longitudinal motion of an air-breathing hypersonic vehicle via a high order singular value decomposition（HOSVD） approach.The design of hypersonic flight control systems is highly challenging due to the enormous complexity of the vehicle dynamics and the presence of significant uncertainties.Motivated by recent results on both LPV control and tensor-product（TP） model transformation approach,the velocity and altitude tracking control problems for the air-breathing hypersonic vehicle is reduced to that of a state feedback stabilizing controller design for a polytopic LPV system with guaranteed performances.The controller implementation is converted into a convex optimization problem with parameterdependent linear matrix inequalities（LMIs） constraints,which is intuitively tractable using LMI control toolbox.Finally,numerical simulation results demonstrate the effectiveness of the proposed approach.

STUDY ON THE POLING PROPERTIES OF NONLINEAR OPTICAL ACTIVE DERIVATIVE OF POLY (p-HYDROXYSTYRENE):(PS)O-DCV

In this paper, the poling properties of (PS)O-DCV, a derivative of poly (p-hydroxystyrene ), was reported. The investigations showed that the thermochromism correction, which was neglected in the literatures, should be considered in the measurements of order parameter of poled films with electrochromism technique Here, another linear optical method, IR and polarized IR spectra for characterizing of poled films was suggested first time. The bulk second nonlinear optical coefficient d_(33) of poled films could be estimated by measured order parameter semi-qualitatively.

Glassy behaviour of random field Ising spins on Bethe lattice in external magnetic field

The thermodynamics and the phase diagram of random field Ising model （RFIM） on Bethe lattice are studied by using a replica trick. This lattice is placed in an external magnetic field （B）. A Gaussian distribution of random field （hi） with zero mean and variance （hi2 = H2RF is considered. The free-energy （F）, the magnetization （M） and the order parameter （q） are investigated for several values of coordination number （z）. The phase diagram shows several interesting behaviours and presents tricritical point at critical temperature Tc = J/k and when HRF = 0 for finite z. The free-energy （F） values increase as T increases for different intensities of random field （HRE） and finite z. The internal energy （U） has a similar behaviour to that obtained from the Monte Carlo simulations. The ground state of magnetization decreases as the intensity of random field HRF increases, The ferromagnetic （FM） paramagnetic （PM） phase boundary is clearly observed only when z →∞. While FM PM-spin glass （SG） phase boundaries are present for finite z. The magnetic susceptibility （X） shows a sharp cusp at Tc in a small random field for finite z and rounded different peaks on increasing HRF.

Phase Transitions Induced by Top-Priority of Randomization

We study the characteristics of phase transition to take the top-priority of randomization in the rules of NaSch model （i.e. noise-first model） into account via computing the relaxation time and the order parameter. The scaling exponents of the relaxation time and the scaling relation of order parameter, respectively, are obtained.

Dynamic crossover in [VIO^(2+)][Tf_(2)N-]_(2) ionic liquid

Ionic liquids usually behave as fragile liquids,and the temperature dependence of their dynamic properties obeys supper-Arrhenius law.In this work,a dynamic crossover is observed in([VIO^(2+)][Tf_(2)N-]_(2)) ionic liquid at the temperature of 240-800 K.The diffusion coefficient does not obey a single Arrhenius law or a Vogel-Fulcher-Tammann(VFT) relation,but can be well fitted by three Arrhenius laws or a combination of a VFT relation and an Arrhenius law.The origin of the dynamic crossover is analyzed from correlation,structure,and thermodynamics.Ion gets a stronger backward correlation at a lower temperature,as shown by the fractal dimension of the random walk.The temperature dependence function of fractal dimension,heterogeneity order parameter,and thermodynamic data can be separated into three regions similar to that observed in the diffusion coefficient.The two crossover temperatures observed in the three types of data are almost the same as that in diffusion coefficient fitted by three Arrhenius laws.The results indicate that the dynamic crossover of[VIO2+][Tf2 N-]2 is attributed to the heterogeneous structure when it undergoes cooling.

Orientation in Nematic Liquid Crystals Doped with Orange Dyes and Effect of Carbon Nanoparticles

Some properties of nematic liquid crystal E7 doped with two disperse orange dyes used together and effect of addition of carbon nanoparticles （single walled carbon nanotube or fullerene C60） on them were studied. Two dyes （disperse orange 11 and 13） having high solubility and order parameter were used as co-dopants. A notable increase in order parameter was obtained comparing to that of liquid crystal doped with single dye. When carbon nanoparticles were used as dopant, a decrease in order parameter was observed at low temperatures while it increased at high temperatures. When applied voltage changed, the order parameter abruptly increased in its threshold value and saturated in higher voltages as expected. An appreciable change in textures was not observed with addition of dopants. This addition gave rise to an increase in nematic-isotropic phase transition temperatures compared with that of pure liquid crystal.