The First Five Years of a Phase Theory for Complex Systems and Networks

In this paper,we review the development of a phase theory for systems and networks in its first five years,represented by a trilogy:Matrix phases and their properties;The MIMO LTI system phase response,its physical interpretations,the small phase theorem,and the sectored real lemma;The synchronization of a multi-agent network using phase alignment.Towards the end,we also summarize a list of ongoing research on the phase theory and speculate what will happen in the next five years.

Comparative study on phase transition behaviors of fractional molecular field theory and random-site Ising model

Fractional molecular field theory(FMFT)is a phenomenological theory that describes phase transitions in crystals with randomly distributed components,such as the relaxor-ferroelectrics and spin glasses.In order to verify the feasibility of this theory,this paper fits it to the Monte Carlo simulations of specific heat and susceptibility versus temperature of two-dimensional(2D)random-site Ising model(2D-RSIM).The results indicate that the FMFT deviates from the 2D-RSIM significantly.The main reason for the deviation is that the 2D-RSIM is a typical system of component random distribution,where the real order parameter is spatially heterogeneous and has no symmetry of space translation,but the basic assumption of FMFT means that the parameter is spatially uniform and has symmetry of space translation.

Investigations of phase transition, elastic and thermodynamic properties of GaP by using the density functional theory

The phase transition of gallium phosphide （GAP） from zinc-blende （ZB） to a rocksalt （RS） structure is investigated by the plane-wave pseudopotential density functional theory （DFT）. Lattice constant a0, elastic constants cij, bulk modulus B0 and the pressure derivative of bulk modulus B0 are calculated. The results are in good agreement with numerous experimental and theoretical data. From the usual condition of equal enthalpies, the phase transition from the ZB to the RS structure occurs at 21.9 GPa, which is close to the experimental value of 22.0 GPa. The elastic properties of GaP with the ZB structure in a pressure range from 0 GPa to 21.9 GPa and those of the RS structure in a pressure range of pressures from 21.9 GPa to 40 GPa are obtained. According to the quasi-harmonic Debye model, in which the phononic effects are considered, the normalized volume V/Vo, the Debye temperature 8, the heat capacity Cv and the thermal expansion coefficient a are also discussed in a pressure range from 0 CPa to 40 GPa and a temperature range from 0 K to 1500 K.

OSCILLATION FREQUENCY THEORY OF A PIEZOELECTRIC SENSOR INLIQUID PHASE WITH TWO SEPARATED－ELECTRODES

In this paper, an oscillation frequency equation for a pizoelectric sensor with two separated-electrodes is theoretically derived and experimentally verified. The correlatione of the oscillation frequency and the liquid properties are investigated.

Quantitative feedback theory and zero phase error tracking control combined robust control for radar truck leveling simulator

Radar leveling system is the key equipment for improving the radar mobility and survival capability. A combined quantitative feedback theory (QFT) controller is designed for the radar truck leveling simulator in this paper, which suffers from strong nonlinearities and system parameter uncertainties. QFT can reduce the plant uncertainties and stabilize the system, but it fails to obtain high-precision tracking. This drawback can be solved by a robust QFT control scheme based on zero phase error tracking control (ZPETC) compensation. The combined controller not only possesses high robustness, but greatly improves the system performance. To verify the effiectiveness and the potential of the proposed controller, a series of experiments have been carried out. Experimental results have demonstrated its robustness against a large range of parameters variation and high tracking precision performance, as well as its capability of restraining the load coupling among channels. The combined QFT controller can drive the radar truck leveling platform accurately, quickly and stably.

Nonlinear Kinetic Theory and Pulse Interactions in Phase Transition

The kinetics of nucleation of phase transition is a phenomenal theory.Some new technologies of preparation of nanomaterials,for example,by shock wave and by electropulsing,are pulse interactions.Based on the known nonlinear theories of phase transition,the nonlinear kinetics of phase transition is discussed,and a soliton-like model is proposed. This mathematical method can not only explain the basic characteristics of pulse interactions and suddenness of phase transition, and possesses a consistency of mechanism for nucleation and growth.

APPLICATION OF MOLECULAR ORBITAL THEORY TO ANALYSIS OF PHASE STABILITY FOR ALLOYS

The critical _d vahues ( _ ) of the γ/(γ+σ).γ/(γ+μ) and γ/(γ+γ') phase boundaries in some ternar alloy phase diagrams at various temperatures are calculated by averaging the _d values of sererai selected characteristic points at the phase boundaries.Approxmate equations for the temperature dependence of the critical _d of γ/(γ+σ).γ/(γ+μ) and γ/(γ+γ') phase boundaries are established.The accuracy of the analysis is discussed in detail. It is found for the first time that the average value of the bond order _ at the phase boundaries ts also approximatelr a constant and therefore a critical average bond order _ like - can be introduced for the analysts of phase stability

Orbital Phase Theory and the Diastereoselectivity of Some Organic Reactions

The orbital phase refers to the relationship between orbitals that originates from their wave character. We show here that the orbital phase essentially determines the diastereoselectivity of the following three organic reactions. 1) Torquoselectivity of the electrocyclicring-opening reaction of 3-substituted cyclobutenes;2) Contradictory torquoselectivity of the retro-Nazarov reaction;3) Diastereoselectivity in electrophilic addition to substituted ethylenes.

A Back Look on the Binary Phase Diagrams of Metals from the Mass Action Law and the Coexistence Theory of Metallic Melts

According to the mass action law and the coexistence theory of metallic melts, the mass action concentrations of Cu-Mg, Bi-Tl and Ni-Al melts involving compound formation have been calculated. The calculated results show that, except the ultimate case of pure element, when two elements are present in the melts, all structural units (atoms and molecules) without exception will be present in the melts, i.e., their concentrations may change from great to small, but they will not vanish into nothing, and only under such conditions, the calculated results both agree with practice and obey the law of mass action. In view of that over considerable wide composition range, the activities of both elements of the three solid binary alloys mentioned above have been measured, this seems in contradiction with the present relevant phase diagrams, in which the structural units are determined by composition range, so the latter needs further investigation and consideration.

Phase diagrams in mixed spin-3/2 and spin-2 Ising system with two alternative layers within the effective-field theory

The phase diagrams in the mixed spin-3/2 and spin-2 Ising system with two alternative layers on a honeycomb lattice are investigated and discussed by the use of the effective-field theory with correlations. The interaction of the nearest-neighbour spins of each layer is taken to be positive （ferromagnetic interaction） and the interaction of the adjacent spins of the nearest-neighbour layers is considered to be either positive or negative （ferromagnetic or antiferromagnetic interaction）. The temperature dependence of the layer magnetizations of the system is examined to characterize the nature （continuous or discontinuous） of the phase transitions and obtain the phase transition temperatures. The system exhibits both second- and first-order phase transitions besides triple point （TP）, critical end point （E）, multicritical point （A）, isolated critical point （C） and reentrant behaviour depending on the interaction parameters. We have also studied the temperature dependence of the total magnetization to find the compensation points, as well as to determine the type of behaviour, and N-type behaviour in Neel classification nomenclature existing in the system. The phase diagrams are constructed in eight different planes and it is found that the system also presents the compensation phenomena depending on the sign of the bilinear exchange interactions.

Study on the Phase Equilibria of Hard Core Asakura-Oosawa Fluids with Renormalization-group Theory

An analytical equation of state (EOS) for hard core Asakura-Oosawa (AO) fluid is established by combining the AO potential, the first-order perturbation theory and the radial distribution function (RDF) for the hard sphere fluid.The phase equilibria are studied by using the renormalization-group (RG) theory. The obtained results agree well with the simulation data. Investigation shows that the attractive range parameter plays an important role in the phase equilibria for AO fluid.

Light-Front Hamiltonian, Path Integral and BRST Formulations of the Chern-Simons-Higgs Theory in the Broken Symmetry Phase

In the present work we study the Hamiltonian, path integral and BRST formulations of the Chern-Simons-Higgs theory in two-space one-time dimensions, in the so-called broken symmetry phase of the Higgs potential (where the phase φ(xμ) of the complex matter field Φ(xμ) carries the charge degree of freedom of the complex matter field and is akin to the Goldstone boson) on the light-front (i.e., on the hyperplanes defined by the fixed light-cone time). The theory is seen to possess a set of first-class constraints and the local vector gauge symmetry. The theory being gauge-invariant is quantized under appropriate gauge-fixing conditions. The explicit Hamiltonian and path integral quantization is achieved under the above light-cone gauges. The Heisenberg equations of motion of the system are derived for the physical degrees of freedom of the system. Finally the BRST quantization of the system is achieved under appropriate BRST gauge-fixing, where the BRST symmetry is maintained even under the BRST light-cone gauge-fixing.

Pairing phase transition in the odd-A nuclei: identification and classification

Research on the pairing phase transition in the odd-A nucleus ^(161)Dy is based on a sophisticated blend of the covariant density functional theory and the shell-model-like approach.It has been observed that variations in thermodynamic quantities at the critical temperature do not exclusively align with pairing phase transitions.The presence of an S-shaped heat capacity curve,often interpreted as an indicator of such transitions,does not offer a definitive confirmation.Additional factors,including the blocking effect,can modify the heat capacity curve and impede the transition process.The pairing phase transition in ^(161)Dy,which occurs approximately from 0.7 to 1.0 MeV,is unequivocally characterized as a first-order transition.Furthermore,the analysis of the impact of varying strengths of pairing correlations on these transitions reveals a nonlinear relationship,thereby adding complexity to the transition dynamics.

Durable hierarchical phosphorus‐doped biphase MoS_(2)electrocatalysts with enhanced H^(*)adsorption

Phase engineering is an efficient strategy for enhancing the kinetics of electrocatalytic reactions.Herein,phase engineering was employed to prepare high‐performance phosphorous‐doped biphase(1T/2H)MoS_(2)(P‐BMS)nanoflakes for hydrogen evolution reaction(HER).The doping of MoS_(2)with P atoms modifies its electronic structure and optimizes its electrocatalytic reaction kinetics,which significantly enhances its electrical conductivity and structural stability,which are verified by various characterization tools,including X‐ray photoelectron spectroscopy,high‐resolution transmission electron microscopy,X‐ray absorption near‐edge spectroscopy,and extended X‐ray absorption fine structure.Moreover,the hierarchically formed flakes of P‐BMS provide numerous catalytic surface‐active sites,which remarkably enhance its HER activity.The optimized P‐BMS electrocatalysts exhibit low overpotentials(60 and 72 mV at 10 mA cm^(−2))in H_(2)SO_(4)(0.5 M)and KOH(1.0 M),respectively.The mechanism of improving the HER activity of the material was systematically studied using density functional theory calculations and various electrochemical characterization techniques.This study has shown that phase engineering is a promising strategy for enhancing the H*adsorption of metal sulfides.

Bayesian Decision Theory and its Applications in Early Phase Clinical Trails

Bayes'theorem is named after the Reverend Thomas Bayes who proposed the idea in the 18th century[1].It has been adapted by scientists for many different applications.One of the applications is clinical trials,where decisions are guided by clinical expertise as well as by data,especially in early phases.This paper reviews Bayes' theorem,decision theory and their applications in clinical trials.

Phase-Space Areas of the Body Motion in the Solar System Deduced from the Bohr-Sommerfeld Atomic Theory and Approximate Invariance of Their Ratios for the Pairs of Planets and Satellites

Energy-time and momentum-position phase spaces defined by the electron orbits in the hydrogen-like atom exhibit special properties of equivalence. It is demonstrated that equivalence of the same kind can be obtained for the phase-space areas defined by the orbit pairs of planets, or satellites, which compose the solar system. In the choice of the examined areas it is useful to be guided by the Bohr-Sommerfeld atomic theory.

INTERNET TRAFFIC DATA FLOW FORECAST BY RBF NEURAL NETWORK BASED ON PHASE SPACE RECONSTRUCTION

Characteristics of the Internet traffic data flow are studied based on the chaos theory. A phase space that is isometric with the network dynamic system is reconstructed by using the single variable time series of a network flow. Some parameters, such as the correlative dimension and the Lyapunov exponent are calculated, and the chaos characteristic is proved to exist in Internet traffic data flows. A neural network model is construct- ed based on radial basis function （RBF） to forecast actual Internet traffic data flow. Simulation results show that, compared with other forecasts of the forward-feedback neural network, the forecast of the RBF neural network based on the chaos theory has faster learning capacity and higher forecasting accuracy.

Phase field method simulation of faceted dendrite growth with arbitrary symmetries

A numerical simulation based on a regularized phase field model is developed to describe faceted dendrite growth morphology. The effects of mesh grid, anisotropy, supersaturation and fold symmetry on dendrite growth morphology were investigated, respectively. These results indicate that the nucleus grows into a hexagonal symmetry faceted dendrite. When the mesh grid is above 640×640, the size has no much effect on the shape. With the increase in the anisotropy value, the tip velocities of faceted dendrite increase and reach a balance value, and then decrease gradually. With the increase in the supersaturation value, crystal evolves from circle to the developed faceted dendrite morphology. Based on the Wulff theory and faceted symmetry morphology diagram, the proposed model was proved to be effective, and it can be generalized to arbitrary crystal symmetries.

QFT control based on zero phase error compensation for flight simulator

To improve the robustness of high-precision servo systems, quantitative feedback theory （QFT） which aims to achieve a desired robust design over a specified region of plant uncertainty is proposed. The robust design problem can be solved using QFT but it fails to guarantee a high precision tracking. This problem is solved by a robust digital QFT control scheme based on zero phase error （ZPE） feed forward compensation. This scheme consists of two parts： a QFT controller in the closed-loop system and a ZPE feed-forward compensator. Digital QFT controller is designed to overcome the uncertainties in the system. Digital ZPE feed forward controller is used to improve the tracking precision. Simulation and real-time examples for flight simulator servo system indicate that this control scheme can guarantee both high robust performance and high position tracking precision.

Large System Analysis of Downlink C-RAN with Phase Noise and Fronthaul Compression

This paper studies the effect of phase noise and fronthaul compression on a downlink cloud radio access network(C-RAN), where several remote radio heads(RRHs) are coordinated to communicate with users by a baseband unit(BBU) on the cloud server. In the system, the baseband signals are precoded at BBU, and then compressed before being transmitted to RRHs through capacity-limited fronthaul links which results in the compressive quantization noise. We assume the regularized zero-forcing precoding is performed with an imperfect channel state information and a compression strategy is applied at BBU. The effect of phase noise arising from nonideal local oscillators both at RRHs and users is considered. We propose an approximate expression for the downlink ergodic sum-rate of considered C-RAN utilizing large dimensional random matrix theory in the large-system regime. From simulation results, the accuracy of the approximate expression is validated, and the effect of phase noise and fronthaul compression can be analyzed theoretically based on the approximate expression.