EFFECTIVE DYNAMICS OF A COUPLED MICROSCOPIC-MACROSCOPIC STOCHASTIC SYSTEM

A conceptual model for microscopic-macroscopic slow-fast stochastic systems is considered. A dynamical reduction procedure is presented in order to extract effective dynamics for this kind of systems. Under appropriate assumptions, the effective system is shown to approximate the original system, in the sense of a probabilistic convergence.

Experimental and theoretical study on the dynamic effective stress of loaded gassy coal during gas release

In the process of mining coalbed methane(CBM),an unsteady state often arises due to the rapid extraction,release and pressure relief of CBM.In this case,the effective stress of coal changes dynamically,affecting the stability of the gassy coal seam.In this paper,gas release tests of gassy coal under conventional triaxial compression were performed,and the dynamic effective stress(DES)during gas release was obtained indirectly based on a constitutive equation and deformation of coal.The results show that the maximum increases in DES caused by the release of free gas and adsorbed gas under the stress of 1.1 MPa were 0.811 and 5.418 MPa,respectively,which seriously affected the stress state of the coal.During the gas release,the free gas pressure and the adsorbed gas volume were the parameters that directly affected the DES and showed a positive linear relationship with the DES with an intercept of zero.The DES of the coal sample increased exponentially with time,which was determined by the contents of free and adsorbed gas.Based on the experimental results and theoretical analysis,an effective stress model was obtained for loaded gassy coal during gas release.The results of verification indicated accuracy greater than 99%.

Dynamics of Quantum State and Effective Hamiltonian with Vector Differential Form of Motion Method

Effective Hamiltonians in periodically driven systems have received widespread attention for realization of novel quantum phases, non-equilibrium phase transition, and Majorana mode. Recently, the study of effective Hamiltonian using various methods has gained great interest. We consider a vector differential equation of motion to derive the effective Hamiltonian for any periodically driven two-level system, and the dynamics of the spin vector are an evolution under the Bloch sphere. Here, we investigate the properties of this equation and show that a sudden change of the effective Hamiltonian is expected. Furthermore, we present several exact relations, whose expressions are independent of the different starting points. Moreover, we deduce the effective Hamiltonian from the high-frequency limit, which approximately equals the results in previous studies. Our results show that the vector differential equation of motion is not affected by a convergence problem, and thus, can be used to numerically investigate the effective models in any periodic modulating system. Finally, we anticipate that the proposed method can be applied to experimental platforms that require time-periodic modulation, such as ultracold atoms and optical lattices.

Theoretical study on dynamic effective electroelastic properties of random piezoelectric composites with aligned inhomogeneities

The closed-form solutions of the dynamic problem of heterogeneous piezoelectric materials are formulated by introducing polarizations into a reference medium and using the generalized reciprocity theorem.These solutions can be reduced to the ones of an elastodynamic problem.Based on the effective medium method,these closedform solutions can be used to establish the self-consistent equations about the frequencydependent effective parameters,which can be numerically solved by iteration.Theoretical predictions are compared with the experimental results,and good agreement can be found.Furthermore,the analyses on the effects of microstructure and wavelength on the effective properties,resonance frequencies,and attenuation are also presented,which may provide some guidance for the microstructure design and analysis of piezoelectric composites.

A Method of Evaluating the Effectiveness of a Hydraulic Oscillator in Horizontal Wells

Bent-housing motor is the most widely used directional drilling tool,but it often encounters the problem of high friction when sliding drilling in horizontal wells.In this paper,a mathematical model is proposed to simulate slide drilling with a friction reduction tool of axial vibration.A term called dynamic effective tractoring force(DETF)is defined and used to evaluate friction reduction effectiveness.The factors influencing the DETF are studied,and the tool placement optimization problem is investigated.The studyfinds that the drilling rate of penetration(ROP)can lower the DETF but does not change the trend of the DETF curve.To effectively work,the shock tool stiffness must be greater than some critical value.For the case study,the best oscillating frequency is within 15∼20 Hz.The reflection of the vibration at the bit boundary can intensify or weaken the friction reduction effec-tiveness,depending on the distance between the hydraulic oscillator and the bit.The optimal placement position corresponds to the plateau stage of the DETF curve.The reliability of the method is verified by thefield tests.The proposed method can provide a design and use guide to hydraulic oscillators and improve friction reduction effectiveness in horizontal wells.

Flatness Control Based on Dynamic Effective Matrix for Cold Strip Mills

Steel strips are the main of steel products and flatness is an important quality indicator of steel strips. Flatness control is the key and highly difficult technique of strip mills. The bottle-neck restricting the improvement of flatness control techniques is that the research on flatness theories and control mathematic models is not in accordance with the requirement of technique developments. To build a simple, rapid and accurate explicit formulation control model has become an urgent need for the development of flatness control technique. This paper puts forward the conception of dynamic effective matrix based on the effective matrix method for flatness control proposed by the authors under the consideration of the influence of the change of parameters in roiling processes on the effective matrix, and the concept is validated by industrial productions. Three methods of the effective matrix generation are induced： the calculation method based on the flatness prediction model; the calculation method based on the data excavation in rolling processes and the direct calculation method based on the network model. A fuzzy neural network effective matrix model is built based on the clusters, and then the network structure is optimized and the high-speed-calculation problem of the dynamic effective matrix is solved. The flatness control scheme for cold strip mills is proposed based on the dynamic effective matrix. On stand 5 of the 1 220 mm five-stand 4-high cold strip tandem mill, the industrial experiment with the control methods of tilting roll and bending roll is done by the control scheme of the static effective matrix and the dynamic effective matrix, respectively. The experiment result proves that the control effect of the dynamic effective matrix is much better than that of the static effective matrix. This paper proposes a new idea and method for the dynamic flatness control in the rolling processes of cold strip mills and develops the theory and model of the flatness control effective matrix method.

DYNAMIC EFFECTIVE SHEAR STRENGTH OF SATURATED SAND

The dynamic effective shear strength of saturated sand under cyclic loading is discussed in this paper.The discussion includes the transient time depen- dency behaviors based on the analysis of the results obtained in conventional cyclic triaxial tests and cyclic torsional shear triaxial tests.It has been found that the dy- namic effective shear strength is composed of effective frictional resistance and viscous resistance,which are characterized by the strain rate dependent feature of strength magnitude,the coupling of consolidation stress with cyclic stress and the dependency of time needed to make the soil strength sufficiently mobilized,and can also be ex- pressed by the extended Mohr-Coulomb's law.The two strength parameters of the dynamic effective internal frictional angle φd and the dynamic viscosity coefficient η are determined.The former is unvaried for different number of cyclic loading,dy- namic stress form and consolidation stress ratio.And the later is unvaried for the different dynamic shear strain rate γt developed during the sand liquefaction,but increases with the increase of initial density of sand.The generalization of dynamic effective stress strength criterion in the 3-dimensional effective stress space is studied in detail for the purpose of its practical use.

Blood Lead Dynamics of Lead-Exposed Pregnant Women and Its Effects on Fetus Development

The dynamics of blood lead (Pb-B) and blood zinc protoporphyrin (ZPP-B) of women in early pregnancy and parturient women with lead exposure and the effects on fetus development were investigated. Pb-B of lead-exposed women was high: 0.984 μmol/L (20.38 μg/dl) and ZPP was 84.52μg/dl. Cord blood Pb-B was 0.896 μmol/L(18.56μg/dl)and cord blood ZPP was 69.24μg/dl. In the control group, Pb-B was 0.261μmol/L(5.41μg/dl), ZPP-B, 37.59 μg/dl, cord blood, Pb-B 0.34 μmol/L (7.93 μg/dl), and cord ZPP-B 49.0μg/dl. There was a significant correlation between blood lead and blood ZPP, maternal Pb-B and cord Pb-B, maternal Pb-B and cord ZPP-B. The significance of the consistency of high level Pb-B and the effects on fetus development is discussed.

Combined Effect of Classical Chaos and Quantum Resonance on Entanglement Dynamics

We use linear entropy of an exact quantum state to study the entanglement between internal electronic states and external motional states for a two-level atom held in an amplitude-modulated and tilted optical lattice. Starting from an unentangled initial state associated with the regular ＇island＇ of classical phase space, it is demonstrated that the quantum resonance leads to entanglement generation, the chaotic parameter region results in the increase of the generation speed, and the symmetries of the initial probability distribution determine the final degree of entanglement. The entangled initial states are associated with the classical ＇chaotic sea＇, which do not affect the final entanglement degree for the same initial symmetry. The results may be useful in engineering quantum dynamics for quantum information processing.

Dynamical Evolution of an Effective Two-Level System with PT Symmetry

We investigate the dynamics of parity-and time-reversal（PT） symmetric two-energy-level atoms in the presence of two optical and one radio-frequency fields. The strength and relative phase of fields can drive the system from the unbroken to the broken PT symmetric regions. Compared with the Hermitian model, Rabi-type oscillation is still observed, and the oscillation characteristics are also adjusted by the strength and relative phase in the region of the unbroken symmetry. At the exception point, the oscillation breaks down. To better understand the underlying properties we study the effective Bloch dynamics and find that the emergence of the PT components of the fixed points is the feature of the PT symmetry breaking and the projections in the x–y plane can be controlled with high flexibility compared with the standard two-level system with the PT symmetry. It helps to study the dynamic behavior of the complex PT symmetric model.

Application of Auto-regressive Linear Model in Understanding the Effect of Climate on Malaria Vectors Dynamics in the Three Gorges Reservoir

It is important to understand the dynamics of malaria vectors in implementing malaria control strategies. Six villages were selected from different sections in the Three Gorges Reservoir fc,r exploring the relationship between the climatic ｜：actors and its malaria vector density from 1997 to 2007 using the auto-regressive linear model regressi^n method. The result indicated that both temperature and precipitation were better modeled as quadratic rather than linearly related to the density of Anopheles sinensis.

The Roles of Low-level Jets in “21·7” Henan Extremely Persistent Heavy Rainfall Event

An extremely heavy rainfall event lasting from 17 to 22 July 2021 occurred in Henan Province of China, with accumulated precipitation of more than 1000 mm over a 6-day period that exceeded its mean annual precipitation. The present study examines the roles of persistent low-level jets(LLJs) in maintaining the precipitation using surface station observations and reanalysis datasets. The LLJs triggered strong ascending motions and carried moisture mainly from the outflow of Typhoon In-fa(2021). The varying directions of the LLJs well corresponded to the meridional shifts of the rainfall. The precipitation rate reached a maximum during 20-21 July as the LLJs strengthened and expanded vertically into double LLJs, including synoptic-weather-system-related LLJs(SLLJs) at 850–700 hPa and boundary-layer jets(BLJs)at ~950 hPa. The coupling of the SLLJ and BLJ provided strong mid-and low-level convergence on 20 July, whereas the SLLJ produced mid-level divergence at its entrance that coupled with low-level convergence at the terminus of the BLJ on21 July. The formation mechanisms of the two types of LLJs are further examined. The SLLJs and the low-pressure vortex(or inverted trough) varied synchronously as a whole and were affected by the southwestward movement of the WPSH in the rainiest period. The persistent large total pressure gradient force at low levels also maintained the strength of low-level geostrophic winds, thus sustaining the BLJs on the synoptic scale. The results based on a Du-Rotunno 1D model show that the Blackadar and Holton mechanisms jointly governed the BLJ dynamics on the diurnal scale.

Splash Zone Dynamic Analysis of A Suspended Semi-Submerged Subsea Module for Irregular Waves

Experimental and numerical studies on the dynamic cable tension of a subsea module during semi-submerged hoisting tests are performed. The experiments are carried out in irregular waves and the time-domain numerical simulations are conducted using the software “Simulation of Marine Operations”. The numerical formulation is validated through a comparison with experimental test measurements. The effects of the significant wave height, spectral peak period,and wave direction on the dynamic effect in the main sling and sub-slings are then investigated numerically. The relationship between the wave parameters and the dynamic effect is identified in the time and frequency domains,enabling the allowable sea states to be partially specified. The extreme dynamic effects in all slings under different wave conditions are estimated by using cumulative distribution functions of the Gumbel distribution. The results show that it is reasonable to model a complex subsea module via slender elements and depth-dependent coefficients in simulations of offshore operations. Lowering operations are safer if the wave height is 1 m and the wave period is larger than 8 s because the wave steepness is sufficient for the maximum possible dynamic effect to remain below 0.9. The dynamic tension may decrease when the wave direction is approximately 150°. It is dangerous for subsea modules to encounter lateral waves while entering the water because large overloads and underloads in the extreme dynamic tension may cause snap loads to occur and the slings to become slack.

Pore water pressure increment model for saturated Nanjing fine sand subject to cyclic loading

Three groups of dynamic triaxial tests were performed for saturated Nanjing fine sand subjected to uniform cyclic loading. The tested curves of the excess pore water pressure （EPWP） ratio variation with the ratio of the number of cycles are provided. The concept of the EPWP increment ratio is introduced and two new concepts of the effective dynamic shear stress ratio and the log decrement of effective stress are defined. It is found that the development of the EPWP increment ratio can be divided into three stages： descending, stable and ascending. Furthermore, at the stable and ascending stages, a satisfactory linear relationship is obtained between the accumulative EPWP increment ratio and natural logarithm of the effective dynamic shear stress ratio. Accordingly, the EPWP increment ratio at the number of cycles N has been deduced that is proportional to the log decrement of effective stress at the cycle number N-l, but is independent of the cyclic stress amplitude. Based on the analysis, a new EPWP increment model for saturated Nanjing fine sand is developed from tested data fitting, which provides a better prediction of the curves of EPWP generation, the number of cycles required for initial liquefaction and the liquefaction resistance.

Modified Saint-Venant equations for flow simulation in tidal rivers

Flow in tidal rivers periodically propagates upstream or downstream under tidal influence. Hydrodynamic models based on the Saint-Venant equations （the SVN model） are extensively used to model tidal rivers. A force-corrected term expressed as the combination of flow velocity and the change rate of the tidal fevel was developed to represent tidal effects in the SVN model. A momentum equation incorporating with the corrected term was derived based on Newton＇s second law. By combing the modified momentum equation with the continuity equation, an improved SVN model for tidal rivers （the ISVN model） was constructed. The simulation of a tidal reach of the Qiantang River shows that the ISVN model performs better than the SVN model. It indicates that the corrected force derived for tidal effects is reasonable; the ISVN model provides an appropriate enhancement of the SVN model for flow simulation of tidal rivers.

CAPTURE EFFECT OF ELECTRORHEOLOGICAL SUSPENSIONS IN FLOW FIELD

According to the results of experiments and theoretical analysis, a phenomenon called ＂capture effect＂ is put forward, which could be used to describe the particles dynamic behavior of electrorheological （ER） suspensions. Then a ＂structure-force＂ mathematical model is established to explain this effect based on electrostatic energy density equation. The analysis results show that the dynamic coupling process of ER suspensions under an external electric filed is the function not only of the electric intensity, but also of the dielectric properties and the structure form.

A lattice Boltzmann exploration of two-phase displacement in 2D porous media under various pressure boundary conditions

While experimental designs developed in recent decades have contributed to research on dynamic nonequilibrium effects in transient two-phase flow in porous media,this problem has been seldom investigated using direct numerical simulation(DNS).Only a few studies have sought to numerically solve Navier—Stokes equations with level-set(LS)or volume-of-fluid(VoF)methods,each of which has constraints in terms of meniscus dynamics for various flow velocities in the control volume(CV)domain.The Shan—Chen multiphase multicomponent lattice Boltzmann method(SC-LBM)has a fundamental mechanism to separate immiscible fluid phases in the density domain without these limitations.Therefore,this study applied it to explore two-phase displacement in a single representative elementary volume(REV)of two-dimensional(2D)porous media.As a continuation of a previous investigation into one-step inflow/outflow in 2D porous media,this work seeks to identify dynamic nonequilibrium effects on capillary pressure—saturation relationship(P_(c)—S)for quasi-steady-state flow and multistep inflow/outflow under various pressure boundary conditions.The simulation outcomes show that P_(c),S and specific interfacial area(a_(nw))had multistep-wise dynamic effects corresponding to the multistep-wise pressure boundary conditions.With finer adjustments to the increase in pressure over more steps,dynamic nonequilibrium effects were significantly alleviated and even finally disappeared to achieve quasisteady-state inflow/outflow conditions.Furthermore,triangular wave-formed pressure boundary conditions were applied in different periods to investigate dynamic nonequilibrium effects for hysteretical Pc—S.The results showed overshoot and undershoot of P_(c)to S in loops of the nonequilibrium hysteresis.In addition,the flow regimes of multistep-wise dynamic effects were analyzed in terms of Reynolds and capillary numbers(Re and Ca).The analysis of REV-scale flow regimes showed higher Re(1<Re<10)for more significant dynamic nonequilibrium effects.This indicates that inertia is critical for transient twophase flow in porous media under dynamic nonequilibrium conditions.

Earth's deformation due to the dynamical perturbations of the fluid outer core

The elasto-gravitational deformation response of the Earths solid parts to the perturbations of the pressure and gravity on the core-mantle boundary (CMB) and the solid inner core boundary (ICB), due to the dynamical behaviors of the fluid outer core (FOC), is discussed. The internal load Love numbers, which are formulized in a general form in this study, are employed to describe the Earths deformation. The preliminary reference Earth model (PREM) is used as an example to calculate the internal load Love numbers on the Earths surface, CMB and ICB, respectively. The characteristics of the Earths deformation variation with the depth and the perturbation periods on the boundaries of the FOC are also investigated. The numerical results indicate that the internal load Love numbers decrease quickly with the increasing degree of the spherical harmonics of the displacement and depend strongly on the perturbation frequencies, especially on the high frequencies. The results, obtained in this work, can be used to construct the boundary conditions for the core dynamics of the long-period oscillations of the Earths fluid outer core.

Determination of dynamic capillary effect on two-phase flow in porous media: A perspective from various methods

The relationship between capillary pressure and saturation plays a critical role in the characterization of two-phase flow and transport in aquifers and oil reservoirs. This relationship is usually determined under the static condition, where capillary pressure is the only function of saturation. However,considerable experiments have suggested that the dependence of capillary pressure on desaturation rate is under the dynamic condition. Thus, a more general description of capillary pressure that includes dynamic capillary effect has been approved widely. A comprehensive understanding of the dynamic capillary effect is needed for the investigation of the two-phase flow in porous media by various methods. In general, dynamic capillary effect in porous media can be studied through the laboratory experiment, pore-to macro-scale modeling, and artificial neural network. Here, main principle and research procedures of each method are reviewed in detail. Then, research progress, disadvantages and advantages are discussed, respectively. In addition, upscaling study from pore-to macro-scale are introduced, which explains the difference between laboratory experiment and pore-scale modeling. At last, several future perspectives and recommendations for optimal solution of dynamic capillary effect are presented.