STABILITY CONDITIONS AND THE MIRROR SYMMETRY OF K3 SURFACES IN ATTRACTOR BACKGROUNDS

We study the space of stability conditions on K3 surfaces from the perspective of mirror symmetry. This is done in the attractor backgrounds(moduli). We find certain highly non-generic behaviors of marginal stability walls(a key notion in the study of wall crossings)in the space of stability conditions. These correspond via mirror symmetry to some nongeneric behaviors of special Lagrangians in an attractor background. The main results can be understood as a mirror correspondence in a synthesis of the homological mirror conjecture and SYZ mirror conjecture.

P-T stability conditions of methane hydrate in sediment from South China Sea

For reasonable assessment and safe exploitation of marine gas hydrate resource, it is important to determine the stability conditions of gas hydrates in marine sediment. In this paper, the seafloor water sample and sediment sample （saturated with pore water） from Shenhu Area of South China Sea were used to synthesize methane hydrates, and the stability conditions of methane hydrates were investigated by multi-step heating dissociation method. Preliminary experimental results show that the dissociation temperature of methane hydrate both in seafloor water and marine sediment, under any given pressure, is depressed by approximately -1.4 K relative to the pure water system. This phenomenon indicates that hydrate stability in marine sediment is mainly affected by pore water ions.

Stability condition of FAST TCP in high speed network on the basis of control theory

Considering the instability of data transferred existing in high speed network, a new method is proposed for improving the stability using control theory. Under this method, the mathematical model of such a network is established. Stability condition is derived from the mathematical model. Several simulation experiments are performed. The results show that the method can increase the stability of data transferred in terms of the congestion window, queue size, and sending rate of the source.

EIGENVALUE INTEGRAL RELATION AND STABILITY CONDITION FOR A MODE

In this paper,we point out that for a static system the eigenvalue integral relation(iσ)~2I +iσΦ+Σ=0 derived from an eigenequation (?)Ψ=[(iσ)~2(?)_2+(iσ)(?)_1+(?)_0]Ψ(r)=0 only gives the suffi- ciency of condition Σ>0 for the stability of a certain mode,but it can not provide the necessity to the condition in general.Three theorems presented in this paper show that under some conditions, Σ>0 makes the mode stable,while Σ<0 makes the mode unstable.

Experimental studies on the P-T stability conditions and influencing factors of gas hydrate in different systems

The P-T stability conditions of gas hydrate in different systems （i.e., solution, silica sand, and marine sediment） were studied using multi-step decomposition method with our experimental equipment. The effects of different ions with various concentra- tions and sediment grains on the P-T stability conditions of gas hydrate were investigated. The results show that different ions have different influences on the phase equilibrium of gas hydrate. However, the influence of ions is in a similar trend： the larg- er the concentration, the bigger the P-T curve shifts to the left. For the silica sand, the influence of pore capillarity of coarse particles （〉 460 ~tm） can be negligible. The P-T curve measured in coarse silica is in agreement with that in pure water. How- ever, the influence of pore capillarity of fine particles （〈 35 μm） is significant. The maximum reduction value of temperature is 1.5 K for methane hydrate under stable state. The sediment from the South China Sea significantly affects the P-T stability conditions of methane hydrate, with an average reduction value of 1.9 K within the experimental conditions. This is mainly the result of both the pore water salinity and the pore capillarity of sediment. Because the pore water salinity is keeping diluted by the fresh water released from hydrate dissociation, the measured P-T stability points fall on different P-T curves with the de- creasing salinity.

Unified stability condition for particulate and aggregative fluidization—Exploring energy dissipation with direct numerical simulation

Fully resolved simulations of particulate and aggregative fluidization systems are performed suc-cessfully with the so-called combined lattice Boltzmann method and time-driven hard-sphere model （LBM-TDHS）. In this method, the discrete particle phase is described by time-driven hard-sphere model, and the governing equations of the continuous fluid phase are solved with lattice Boltz-mann method. Particle-fluid coupling is implemented by immersed moving boundary method. Time averaged flow structure of the simulated results show the formation of core-annulus structure and sigmoid distribution of voidage in the axial direction, which are typical phenomena in fluidization systems. Combining the results of the simulation, the energy consumption Nst for suspending and transporting solids is calculated from the direct numerical simulation （DNS） of fluidization, and the stability criterion Nst/NT = rain proposed in EMMS/bubbling model is verified numerically. Further-more the numerical results show that the value of Nst/NT in particulate fiuidization is much higher than that in aggregative fluidization, but Nst/NT = rain is effective for both particulate and aggregative fluidization.

A stability condition for turbulence model:From EMMS model to EMMS-based turbulence model

The closure problem of turbulence is still a challenging issue in turbulence modeling. In this work, a stability condition is used to close turbulence. Specifically, we regard single-phase flow as a mixture of turbulent and non-turbulent fluids, separating the structure of turbulence. Subsequently, according to the picture of the turbulent eddy cascade, the energy contained in turbulent flow is decomposed into different parts and then quantified. A turbulence stability condition, similar to the principle of the energy-minimization multi-scale （EMMS） model for gas-solid systems, is formulated to close the dynamic constraint equa- tions of turbulence, allowing the inhomogeneous structural parameters of turbulence to be optimized. We name this model as the ＂EMMS-based turbulence model＂, and use it to construct the corresponding turbulent viscosity coefficient. To validate the EMMS-based turbulence model, it is used to simulate two classical benchmark problems, lid-driven cavity flow and turbulent flow with forced convection in an empty room, The numerical results show that the EMMS-hased turbulence model improves the accuracy of turbulence modeling due to it considers the principle of compromise in competition between viscosity and inertia.

Stability Conditions for Wave Simulation in 3-D Anisotropic Media with the Pseudospectral Method

Simulation of elastic wave propagation has important applications in many areas such as inverse problemand geophysical exploration.In this paper,stability conditions for wave simulation in 3-D anisotropic media with the pseudospectral method are investigated.They can be expressed explicitly by elasticity constants which are easy to be applied in computations.The 3-Dwave simulation for two typical anisotropic media,transversely isotropic media and orthorhombic media,are carried out.The results demonstrate some satisfactory behaviors of the pseudospectral method.

Conditional stability of diatomic molecule driven by a weak laser field

Using a direct perturbation method, we investigate the stability of a diatomic molecule modelled by a weakly laser-driven Morse oscillator. It is shown that stationary state solution of the system is stable in the sense of Lyapunov and the periodical one possesses conditional stability, namely its stability depends on the initial conditions and system parameters. The corresponding sufficient and necessary conditions are established that indicate the stable states associated with some discrete energies. The results reveal how a diatomic molecule can be stabilized or dissociated with a weak laser, and demonstrate that the mathematical conditional stability works in the considered physical system.

Acoustic finite-difference modeling beyond conventional Courant-Friedrichs-Lewy stability limit:Approach based on variable-length temporal and spatial operators

Conventional finite-difference(FD)methods cannot model acoustic wave propagation beyond Courant-Friedrichs-Lewy(CFL)numbers 0.707 and 0.577 for two-dimensional(2D)and three-dimensional(3D)equal spacing cases,respectively,thereby limiting time step selection.Based on the definition of temporal and spatial FD operators,we propose a variable-length temporal and spatial operator strategy to model wave propagation beyond those CFL numbers while preserving accuracy.First,to simulate wave propagation beyond the conventional CFL stability limit,the lengths of the temporal operators are modified to exceed the lengths of the spatial operators for high-velocity zones.Second,to preserve the modeling accuracy,the velocity-dependent lengths of the temporal and spatial operators are adaptively varied.The maximum CFL numbers for the proposed method can reach 1.25 and 1.0 in high velocity contrast 2D and 3D simulation examples,respectively.We demonstrate the effectiveness of our method by modeling wave propagation in simple and complex media.

Stability analysis of traffic flow with extended CACC control models

To further investigate car-following behaviors in the cooperative adaptive cruise control（CACC） strategy,a comprehensive control system which can handle three traffic conditions to guarantee driving efficiency and safety is designed by using three CACC models.In this control system,some vital comprehensive information,such as multiple preceding cars’ speed differences and headway,variable safety distance（VSD） and time-delay effect on the traffic current and the jamming transition have been investigated via analytical or numerical methods.Local and string stability criterion for the velocity control（VC） model and gap control（GC） model are derived via linear stability theory.Numerical simulations are conducted to study the performance of the simulated traffic flow.The simulation results show that the VC model and GC model can improve driving efficiency and suppress traffic congestion.

Stability-driven Structure Evolution:Exploring the Intrinsic Similarity Between Gas-Solid and Gas-Liquid Systems

As the core of the Energy-Minimization Multi-Scale(EMMS) approach,the so-called stability condi-tion has been proposed to reflect the compromise between different dominant mechanisms and believed to be in-dispensable for understanding the complex nature of gas-solid fluidization systems.This approach was recently ex-tended to the study of gas-liquid bubble columns.In this article,we try to analyze the intrinsic similarity between gas-solid and gas-liquid systems by using the EMMS approach.First,the model solution spaces for the two systems are depicted through a unified numerical solution strategy,so that we are able to find three structural hierarchies in the EMMS model for gas-solid systems.This may help to understand the roles of cluster diameter correlation and stability condition.Second,a common characteristic of gas-solid and gas-liquid systems can be found by comparing the model solutions for the two systems,albeit structural parameters and stability criteria are specific in each system:two local minima of the micro-scale energy dissipation emerges simultaneously in the solution space of structure parameters,reflecting the compromise of two different dominant mechanisms.They may share an equal value at a critical condition of operating conditions,and the global minimum may shift from one to the other when the oper-ating condition changes.As a result,structure parameters such as voidage or gas hold-up exhibit a jump change due to this shift,leading to dramatic structure variation and hence regime transition of these systems.This demonstrates that it is the stability condition that drives the structure variation and system evolution,which may be the intrinsic similarity of gas-solid and gas-liquid systems.

THE STABILITY OF DIFFERENCE SCHEMES OF A HIGHER DIMENSIONAL PARABOLIC EQUATION

This paper proposes a new method to improve the stability condition of difference scheme of a parabolic equation. Necessary and sufficient conditions of the stability of this new method are given and proved. Some numerical examples show that this method has some calculation advantages.

Stabilization of Discrete-time 2-D T-S Fuzzy Systems Based on New Relaxed Conditions

This paper is concerned with the problem of stabilization of the Roesser type discrete-time nonlinear 2-D system that plays an important role in many practical applications. First, a discrete-time 2-D T-S fuzzy model is proposed to represent the underlying nonlinear 2-D system. Second, new quadratic stabilization conditions are proposed by applying relaxed quadratic stabilization technique for 2-D case. Third, for sake of further reducing conservatism, new non-quadratic stabilization conditions are also proposed by applying a new parameter-dependent Lyapunov function, matrix transformation technique, and relaxed technique for the underlying discrete-time 2-D T-S fuzzy system. Finally, a numerical example is provided to illustrate the effectiveness of the proposed results.

Convergent robust stabilization conditions for fuzzy chaotic systems based on the edgewise subdivision approach

This paper concerns the problem of stabilizing fuzzy chaotic systems via the viewpoint of the edgewise subdivision approach. Firstly, a new edgewise subdivision algorithm is proposed to implement the simplex edgewise subdivision which divides the overall fuzzy chaotic systems into a lot of sub-systems by a kind of algebraic description. These sub-systems have the same volume and shape characteristics. Secondly, a novel kind of control scheme which switches by the transfer of different operating sub-systems is proposed to achieve convergent stabilization conditions for the underlying controlled fuzzy chaotic systems. Finally, a numerical example is given to demonstrate the validity of the proposed methods.

Dynamic Event-Triggered Fixed-Time Consensus Control and Its Applications to Magnetic Map Construction

This article deals with the consensus problem of multi-agent systems by developing a fixed-time consensus control approach with a dynamic event-triggered rule. First, a new fixedtime stability condition is obtained where the less conservative settling time is given such that the theoretical settling time can well reflect the real consensus time. Second, a dynamic event-triggered rule is designed to decrease the use of chip and network resources where Zeno behaviors can be avoided after consensus is achieved, especially for finite/fixed-time consensus control approaches. Third, in terms of the developed dynamic event-triggered rule, a fixed-time consensus control approach by introducing a new item is proposed to coordinate the multi-agent system to reach consensus. The corresponding stability of the multi-agent system with the proposed control approach and dynamic eventtriggered rule is analyzed based on Lyapunov theory and the fixed-time stability theorem. At last, the effectiveness of the dynamic event-triggered fixed-time consensus control approach is verified by simulations and experiments for the problem of magnetic map construction based on multiple mobile robots.

ON DISPERSION-CONTROLLED PRINCIPLES FOR NON-OSCILLATORY SHOCK-CAPTURING SCHEMES

The role of dispersions in the numerical solutions of hydrodynamic equation systems has been realized for long time.It is only during the last two decades that extensive studies on the dispersion-controlled dissipative(DCD)schemes were reported.The studies have demonstrated that this kind of the schemes is distinct from conventional dissipation-based schemes in which the dispersion term of the modified equation is not considered in scheme construction to avoid nonphysical oscillation occurring in shock wave simulations.The principle of the dispersion controlled aims at removing nonphysical oscillations by making use of dispersion characteristics instead of adding artificial viscosity to dissipate the oscillation as the conventional schemes do.Research progresses on the dispersion- controlled principles are reviewed in this paper,including the exploration of the role of dispersions in numerical simulations,the development of the dispersion-controlled principles,efforts devoted to high-order dispersion-controlled dissipative schemes,the extension to both the finite volume and the finite element methods,scheme verification and solution validation,and comments on several aspects of the schemes from author's viewpoint.

Discussion of Muskingum method parameter X

The parameter X of the Muskingum method is a physical parameter that reflects the flood peak attenuation and hydrograph shape flattening of a diffusion wave in motion. In this paper, the historic process that hydrologists have undergone to find a physical explanation of this parameter is briefly discussed. Based on the fact that the Muskingum method is the second-order accuracy difference solution to the diffusion wave equation, its numerical stability condition is analyzed, and a conclusion is drawn： X ≤ 0.5 is the uniform condition satisfying the demands for its physical meaning and numerical stability. It is also pointed out that the methods that regard the sum of squares of differences between the calculated and observed discharges or stages as the objective function and the routing coefficients C0, C1 and C2 of the Muskingum method as the optimization parameters cannot guarantee the physical meaning of X.

An improved car-following model with consideration of the lateral effect and its feedback control research

A car-following model is presented, in which the effects of non-motor vehicles on adjacent lanes are taken into ac- count. A control signal including the velocity differences between the following vehicle and the target vehicle is introduced according to the feedback control theory. The stability condition for the new model is derived. Numerical simulation is used to demonstrate the advantage of the new model including the control signal; the results are consistent with the analytical ones

Accuracy of the staggered-grid finite-difference method of the acoustic wave equation for marine seismic reflection modeling

Seismic wave modeling is a cornerstone of geophysical data acquisition, processing, and interpretation, for which finite-difference methods are often applied. In this paper, we extend the velocity- pressure formulation of the acoustic wave equation to marine seismic modeling using the staggered-grid finite-difference method. The scheme is developed using a fourth-order spatial and a second-order temporal operator. Then, we define a stability coefficient (SC) and calculate its maximum value under the stability condition. Based on the dispersion relationship, we conduct a detailed dispersion analysis for submarine sediments in terms of the phase and group velocity over a range of angles, stability coefficients, and orders. We also compare the numerical solution with the exact solution for a P-wave line source in a homogeneous submarine model. Additionally, the numerical results determined by a Marmousi2 model with a rugged seafloor indicate that this method is sufficient for modeling complex submarine structures.