On a Quasilinear Degenerate Parabolic Equation from Prandtl Boundary Layer Theory

The equation arising from Prandtl boundary layer theory (e)u/(e)t-(e)/(e)x1(a(u,x,t)(e)u/(e)xi)-fi(x)Diu+c(x,t)u=g(x,t)is considered.The existence of the entropy solution can be proved by BV estimate method.The interesting problem is that,since a(·,x,t) may be degenerate on the boundary,the usual boundary value condition may be overdetermined.Accordingly,only dependent on a partial boundary value condition,the stability of solutions can be expected.This expectation is turned to reality by Kru(z)kov's bi-variables method,a reasonable partial boundary value condition matching up with the equation is found first time.Moreover,if axi(·,x,t)|x∈(e)Ω=a(·,x,t)|x∈(e)Ω=0 and fi(x)|x∈(e)Ω=0,the stability can be proved even without any boundary value condition.

Intercepts allocation for layered defense

One important mission of the strategic defense is to develop an integrated, layered ballistic missile defense system（BMDS）. Considering the problem of assigning limited defense weapons to incoming ballistic missiles, we illustrate how defense weapons, ballistic missiles, kill probability and effectiveness of defense（ED） are interrelated and how to understand this relationship for achieving the best allocation plan. Motivated by the queueing theory, in which the available resources are not sufficient to satisfy the demands placed upon them at all times, the layered deployed defense weapon is modeled as a queueing system to shoot Poisson arrived targets. Simultaneously, examples, of optimum intercepts allocation problems under different constraints are presented. The four theorems determine the allocation rules of intercepts to targets that maximize ED or minimize the cost to achieve a required ED.

Theoretical investigation on shocklets in compressible boundary layers

By the shock relationships, the wavy characteristics and the forming condi-tions of a shock wave are analyzed. The wavy characteristics of an Euler system are stud-ied theoretically. The present research focuses on the wavy characteristics of Tollmien-Schlichting （T-S） waves, the excitation conditions of shocklets in compressible boundary layers, and the viscous effect on shock. The possibility of existence of shocklets in the compressible boundary layer and the physical mechanism of formation are theoretically interpreted.

BUCKLING AND POSTBUCKLING OF LAMINATED THIN CYLINDRICAL SHELLS UNDER HYGROTHERMAL ENVIRONMENTS

The influence of hygrothermal effects on the buckling and postbuckling of composite laminated cylindrical shells subjected to axial compression is investigated using a micro-to-macro-mechanical analytical model. The material properties of the composite are affected hy the variation of temperature and moisture, and are hosed on a micromechanical model of a laminate. The governing equations are based on the classical laminated shell theory, and including hygrothermal effects. The nonlinear prebuckling deformations and initial geometric imperfections of the shell were both taken into account. A boundary layer theory of shell buckling was extended to the case of laminated cylindrical shells under hygrothermal environments, and a singular peturbation technique was employed to determine buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of perfect and imperfect, cross-ply laminated cylindrical shells under different sets of environmental conditions. The influences played by temperature rise, the degree of moisture concentration, fiber volume fraction, shell geometric parameter, total number of plies, stacking sequences and initial geometric imperfections are studied.

Postbuckling of Imperfect Stiffened Cylindrical Shells Under Combined External Liquid Pressure and Axial Compression

posthuckling analysis is presented for the stilTened cylindrical shell of finite length subjected to combined loading of external liquid pressure and axial compression. The formulations are based on a boundary layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, nonlinear large deflections in the postbuckling range and initial geometrical imperfections of the shell. The 'smeared stifl'cner' approach is adopted for the stiffencrs. In the analysis a singular perturbation technique is used (o determine the interactive buckling loads and the postbuckling paths. Numerical examples cover the performance of perfect and imperfect, stringer and ring stiffened cylindrical shells. Typical results arc presented in the dimcnsionless graphical form.

Drag characteristics of power law fluids on an upstream moving surface

The specific problem to be considered here concerns the boundary layer problem of a non-Newtonian fluid on a flat plate in length, whose surface has a constant velocity opposite in the direction to that of the mainstream with Uw 〉〉 U∞, or alternatively when the plate surface velocity is kept fixed but the stream speed is reduced to zero. A theoretical analysis for a boundary layer flow is made and the self-similar equation is determined. Solutions are presented numerically for special power index and the associated transfer behavior is discussed.

POSTBUCKLING OF PRESSURE-LOADED SHEAR DEFORMABLE LAMINATED CYLINDRICAL PANELS

A postbuckling analysis is presented for a shear deformable laminated cylindrical panel of finite length subjected to lateral pressure. The governing equations are based on Reddy's higher order shear deformation shell theory with von Krmn_Donnell_type of kinematic nonlinearity. The nonlinear prebuckling deformations and initial geometric imperfections of the panel are both taken into account. A boundary layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, large deflections in the postbuckling range, and initial geometric imperfections of the shell, is extended to the case of shear deformable laminated cylindrical panels under lateral pressure. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling response of perfect and imperfect, moderately thick, cross_ply laminated cylindrical panels. The effects played by transverse shear deformation, panel geometric parameters, total number of plies, fiber orientation, and initial geometric imperfections are studied.

THERMO-PIEZOELECTRIC EFFECTS ON THE POSTBUCKLING OF AXIALLY-LOADED HYBRID LAMINATED CYLINDRICAL PANELS

A compressive postbuckling analysis is presented for a laminated cylinderical panel with piezoelectric actuators subjected to the combined action of mechanical, electrical and thermal loads. The temperature field considered is assumed to be a uniform distribution over the panel surface and through the panel thickness and the electric field is assumed to be the transverse component E_Z only. The material properties are assumed to be independent of the temperature and the electric field. The governing equations are based on the classical shell theory with von Krmn-Donnell-type of kinematic nonlinearity. The nonlinear prebuckling deformations and initial geometric imperfections of the panel are both taken into account. A boundary layer theory of shell buckling,which includes the effects of nonlinear prebuckling deformations, large deflections in the postbuckling range,and initial geometric imperfections of the shell,is extended to the case of hybrid laminated cylindrical panels of finite length. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the compressive postbuckling behavior of perfect and imperfect, cross-ply laminated cylindrical thin panels with fully covered or embedded piezoelectric actuators under different sets of thermal and electrical loading conditions.The effects played by temperature rise,applied voltage,stacking sequence,the character of in-plane boundary conditions,as well as initial geometric imperfections are studied.

POSTBUCKLING OF IMPERFECT STIFFENED CYLINDRICAL SHELLS UNDER COMBINED EXTERNAL PRESSURE AND HEATING

A postbuckling analysis is presented for a stiffened cylindrical shell of finite length subjected to combined loading of external pressure and a uniform temperature rise. The formulations are based on a boundary layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, nonlinear large deflections in the postbuckling range and initial geometrical imperfections of the shell. The 'smeared stiffener' approach is adopted for the stiffeners. The analysis uses a singular perturbation technique to determine the interactive buckling loads and the postbuckling equilibrium paths. Numerical examples cover the performances of perfect and imperfect, stringer and ring stiffened cylindrical shells. Typical results are presented in dimensionless graphical form.

AN ASYMPTOTIC SOLUTION OF THE NONLINEAR REDUCED WAVE EQUATION

This paper uses the boundary layer theory to obtain an asymptotic solution of the nonlinear educed wave equation. This solution is valid in the secular region where the geometrical optics result fails. However it agrees with the geometrical optics result when the field is away from the secular region. By using this solution the self-focusing length can also be obtained.

Research on Key Issues of Consistency Analysis of Vehicle Steering Characteristics

Given the global lack of effective analysis methods for the impact of design parameter tolerance on performance deviation in the vehicle proof-of-concept stage,it is difficult to decompose performance tolerance to design parameter tolerance.This study proposes a set of consistency analysis methods for vehicle steering performance.The process of consistency analysis and control of automotive performance in the conceptual design phase is proposed for the first time.A vehicle dynamics model is constructed,and the multi-objective optimization software Isight is used to optimize the steering performance of the car.Sensitivity analysis is used to optimize the design performance value.The tolerance interval of the performance is obtained by comparing the original car performance value with the optimized value.With the help of layer-by-layer decomposition theory and interval mathematics,automotive performance tolerance has been decomposed into design parameter tolerance.Through simulation and real vehicle experiments,the validity of the consistency analysis and control method presented in this paper are verified.The decomposition from parameter tolerance to performance tolerance can be achieved at the conceptual design stage.

The crustal fluid evolution and the causes of earthquakes(Ⅲ)

This paper is the third one of a series of three papers on the fluid evolution of the crust upper mantle and the causes of earthquakes. Based on the last two papers, a model of the crustal resistivity structure and the deep seated fluid evolution is presented, and also a seismogeny theory is set up, which is called the potential kinetic energy transformation model. In this model, the crustal deep seated fluid evolution is considered to take the most important effect on the seismogenic process. Taking the Tangshan M 7.8 earthquake of 1976 as an example, the earthquakes occurred in a pull apart rifting basin are analyzed, and finally the crust outgassing in the seismogenic processes is discussed, referring to the here presented theory of seismogeny.

Determination of allowable subgrade frost heave with the pavement roughness index in numerical analysis

Frost heave is an upward swelling of soil during cryogenic conditions in cold regions. It is caused by the accumulation of ice crystals in subgrade soil, which grow upwards when freezing temperatures penetrate into the subgrade. This study establishes the allowable soil subgrade frost heave based on the roughness standard of asphalt pavement in China, and aims to balance the pavement design and frost heave resistance of subgrades in cold regions. We formulated a mechanical model of pavement supported by the boundary conditions of differential frost heave, based on the elastie layered system theory. The differential soil subgrade frost heave was modeled as a sinusoidal function, and the allowable frost heave and the roughness index were modeled as the displacement boundaries for the top and bottom of the pavement structure. Then the allowable frost heave was back-calculated according to the roughness standard. Numerical results show that the allowable frost heave depends on the pavement structure, material properties, the highway grade, and other factors. In order to ensure that the actual soil subgrade frost heave is lower than the allowable frost heave, pavement structures and materials need to be selected and designed carefully. The numerical method proposed here can be applied to establish the frost heave re- sistance of subgrade when the pavement structure and materials are determined.

On the Mechanism of Turbulent Coherent Structure(Ⅰ)──The Physical Model o

In this paper. based on the discussion of properties of the turbulent coherentstructure for smooth boumdary layer. a physical model has been established. The widthof slowly-moving streak line and bursting time of coherent structure expressed bymomentum thickness Reynolds mumber of boundary layer layer have been obtained,whichare in agreement with The experimental data￣[ 3. 4. 5.7 ]

Galerkin-Laguerre Spectral Solution of Self-Similar Boundary Layer Problems

In this work the Laguerre basis for the biharmonic equation introduced by Jie Shen is employed in the spectral solution of self-similar problems of the boundary layer theory.An original Petrov-Galerkin formulation of the Falkner-Skan equation is presented which is based on a judiciously chosen special basis function to capture the asymptotic behaviour of the unknown.A spectral method of remarkable simplicity is obtained for computing Falkner-Skan-Cooke boundary layer flows.The accuracy and efficiency of the Laguerre spectral approximation is illustrated by determining the linear stability of nonseparated and separated flows according to the Orr-Sommerfeld equation.The pentadiagonal matrices representing the derivative operators are explicitly provided in an Appendix to aid an immediate implementation of the spectral solution algorithms.

Layered virtual machine migration algorithm for network resource balancing in cloud computing

Due to the increasing sizes of cloud data centers, the number of virtual machines （VMs） and applications rises quickly. The rapid growth of large scale Internet services re- suits in unbalanced load of network resource. The bandwidth utilization rate of some physical hosts is too high, and this causes network congestion. This paper presents a layered VM migration algorithm （LVMM）. At first, the algorithm will divide the cloud data center into several regions according to the bandwidth utilization rate of the hosts. Then we bal- ance the load of network resource of each region by VM migrations, and ultimately achieve the load balance of net- work resource in the cloud data center. Through simulation experiments in different environments, it is proved that the LVMM algorithm can effectively balance the load of network resource in cloud computing.

Linear stability analysis of interactions between mixing layer and boundary layer flows

The linear instabilities of incompressible confluent mixing layer and boundary layer were analyzed.The mixing layers include wake,shear layer and their combination.The mean velocity profile of confluent flow is taken as a superposition of a hyperbolic and exponential function to model a mixing layer and the Blasius similarity solution for a flat plate boundary layer.The stability equation of confluent flow was solved by using the global numerical method.The unstable modes associated with both the mixing and boundary layers were identified.They are the boundary layer mode,mixing layer mode 1（nearly symmetrical mode）and mode 2（nearly anti-symmetrical mode）.The interactions between the mixing layer stability and the boundary layer stability were examined.As the mixing layer approaches the boundary layer,the neutral curves of the boundary layer mode move to the upper left,the resulting critical Reynolds number decreases,and the growth rate of the most unstable mode increases.The wall tends to stabilize the mixing layer modes at low frequency.In addition,the mode switching behavior of the relative level of the spatial growth rate between the mixing layer mode 1 and mode 2 with the velocity ratio is found to occur at low frequency.

Fabrication of Zn-Ti layered double hydroxide by varying cationic ratio of Ti^(4+) and its application as UV absorbent

ZnTi-layered double hydroxides（LDHs） with varying Zn/Ti ratio have been synthesized by coprecipitation of zinc and titanium salts from homogeneous solution.The obtained ZnTi-LDHs possess high crystallinity and hierarchical structure with improved UV-absorbance property.The UV-vis spectra show that the UV absorbing properties of ZnTi-LDHs is stronger and broader than both MgAl-LDH and ZnAl-LDH due to the existence of Ti.Moreover,the UV absorption property increased with the content of Ti,which can be ascribed to the decrease in the band gap energy,as clearly confirmed by density functional theory calculations.When irradiated by UV rays,the property of the samples with generated free radicals（OH^·and O2^·） was evaluated by means of electron spin resonance（EPR）.ZnTi-LDHs generated a relatively lower active radicals in contrast with TiO2 and ZnO,which implied an increased safety used as sunscreens.Therefore,this work provides a detailed understanding of UV shielding properties of ZnTiLDHs which was unrevealed previously,and demonstrates the expansive application prospects of ZnTiLDHs in the field of sunscreens.

Free vibration of functionally graded sandwich plates in thermal environments

This paper presents an analytical solution for the free vibration of functionally graded material(FGM)sandwich plates in a thermal environment.An equivalentsingle‐layer(ESL)plate theory with four variables is used to obtain the solution.Two types of sandwich plates are examined in this study:one with FGM face sheets and a homogeneous core and the other with an FGM core and homogeneous face sheets.The governing equations of motion are derived based on Hamilton's principle and then solved using the Navier method.The results of natural frequencies of simply supported FGM sandwich plates are compared with the available solutions in the literature.The effects of volume fraction distribution,geometrical parameters,and temperature increments on the free vibration characteristics are discussed in detail.

Observation of specific ion effects in humus aggregation process

Specific ion effects play a vital role in a variety of colloidal and interfacial processes.However,few studies have reported the specific ion effects in the humus aggregation process,which strongly influence the transport and fate of environmental pollutants.In this study,soil humus colloids were prepared and characterized,and the specific ion effects on humus aggregation in electrolyte solutions were investigated at a variety of concentrations and pH values using dynamic light scattering methods.Activation energy(ΔE),which is known to reflect the dynamics and stability of a colloidal system,was used to quantitatively characterize the specific ion effects.The results showed that given ΔE value of 2.48×10^(3) J mol^(-1) at pH 3.0,the electrolyte concentrations were 91.6,58.2,3.8,and 0.8 mmol L^(-1) for Na^(+),K^(+),Mg^(2+),and Ca_(2+),respectively,thus indicating significant specific ion effects in the humus aggregation process.Most importantly,decreasing the electrolyte concentrations increased the differences in the ΔE value between two cation species with the same valence(i.e.,ΔE_(Na)-ΔE_(K) and ΔE_(Mg)-ΔE_(Ca)),while increasing the pH increased the magnitude of ΔE_(Mg)-ΔE_(Ca).However,the classic Derjaguin,Landau,Verwey,and Overbeek(DLVO)theory and the double layer theory,as well as the currently widely used ionic hydration and dispersion effects,failed to predict the experimentally observed increase in the specific ion effects with decreasing electrolyte concentrations in a quantitative sense.These results have implications for the necessity of involving specific ion effects for a better understanding of humus aggregation and interactions in aqueous and soil systems.