Comparison of Linear Level I Green-Naghdi Theory with Linear Wave Theory for Prediction of Hydroelastic Responses of VLFS

Very Large Floating Structures (VLFS) have drawn considerable attention recently due to their potential significance in the exploitation of ocean resources and in the utilization of ocean space. Efficient and accurate estimation of their hydroelastic responses to waves is very important for the design. Recently, an efficient numerical algorithm was developed by Ertekin and Kim (1999). However, in their analysis, the linear Level I Green-Naghdi (GN) theory is employed to describe fluid dynamics instead of the conventional linear wave (LW) theory of finite water depth. They claimed that this linear level I GN theory provided better predictions of the hydroelastic responses of VLFS than the linear wave theory. In this paper, a detailed derivation is given in the conventional linear wave theory framework with the same quantity as used in the linear level I GN theory framework. This allows a critical comparison between the linear wave theory and the linear level I GN theory. It is found that the linear level I GN theory can be regarded as an approximation to the linear wave theory of finite water depth. The consequences of the differences between these two theories in the predicted hydroelastic responses are studied quantitatively. And it is found that the linear level I GN theory is not superior to the linear wave theory. Finally, various factors affecting the hydroelastic response of VLFS are studied with the implemented algorithm.

Book Review “Fabrikant,V.I.Contact and Crack Problems in Linear Theory of Elasticity,Bentham Science Publishers,Sharjah,UAE(2010)”

As suggested by the title, this extensive book is concerned with crack and contact prob- lems in linear elasticity. However, in general, it is intended for a wide audience ranging from engineers to mathematical physicists. Indeed, numerous problems of both academic and tech- nological interest in electro-magnetics, acoustics, solid and fluid dynamics, etc. are actually related to each other and governed by the same mixed boundary value problems from a unified mathematical standpoint

NEW POINTSOF VIEW ON THE NONLOCAL FIELD THEORY AND THEIR APPLICATIONS TO THE FRACTURE MECHANICS( Ⅲ) ——RE_DISCUSS THE LINEAR THEORY OF NONLOCAL ELASTICITY

In this paper, it is proven that the balance equation of energy is the first integral of the balance equation of momentum in the linear theory of nonlocal elasticity. In other words, the balance equation of energy is not an independent one. It is also proven that the residual of nonlocal body force identically equals zero. This makes the transform formula of the nonlocal residual of energy much simpler. The linear nonlocal constitutive equations of elastic bodies are deduced in details, and a new formula to calculate the antisymmetric stress is given.

Dynamic electron transport theory for multiprobe mesoscopic structures

Using the linear response theory and random phase approximation, we develop a general dynamic electron transport theory for multiprobe mesoscopic structures in an arbitrarily time-dependent external field. In this case, the responses of the dynamic current, charge and internal potential to the external fields can be determined self-consistently. Without loss of generality, charge （current） conservation and gauge invariance under a potential shift are satisfied. As an example, we employ a quantum wire with a single barrier to discuss the response of the internal potential.

On plane Λ-fractional linear elasticity theory

Non-local plane elasticity problems are discussed in the context of Λ-fractional linear elasticity theory. Adapting the Λ-fractional derivative along with the Λ-fractional space, where geometry and mechanics are valid in the conventional way, non-local plane elasticity problems are solved with the help of biharmonic functions. Then, the results are transferred into the initial plane.Applications are presented to homogeneous and the fractional beam bending problem.

Lattice dynamics properties of chalcopyrite ZnSnP_2:Density-functional calculations by using a linear response theory

We present a first-principles study of the structural,dielectric,and lattice dynamical properties for chalcopyrite semiconductor ZnSnP2.The structural properties are calculated using a plane-wave pseudopotential method of densityfunctional theory.A linear response theory is used to derive Born effective charge tensors for each atom,dielectric constants in low and high frequency limits,and phonon frequencies.We calculate all zone-center phonon modes,identify Raman and infrared active modes,and report LO-TO splitting of the infrared modes.The results show an excellent agreement with experiment and propose several predictive behaviors.

Studies on the Quantitative Structure-activity Relationship of Substituted Biphenyls by Density Function Theory (DFT)

Geometrical configurations of 16 substituted biphenyls were computed at the B3LYP/6-311G^＊＊ level with Gaussian 98 program. Based on linear solvation energy theory, lgKow as well as the structural and thermodynamic parameters obtained at this level was taken as theoretical descriptors, and corresponding equation predicting the toxicity of Daphnia magna （-lgEC5o） was thus obtained, in which three parameters were contained, i.e., n-octanol/water partition coefficients （lgKow）, dipole moment of the molecules（ μ） and entropy （S°）. For this equation, R^2 = 0.9582, q^2 = 0.8921 and SD = 0.102. The absolute t-scores of three variables are larger than the standard one in the confidence range of 95%, which confirms the creditability and stability of this model.

A General(k,n)Threshold Secret Image Sharing Construction Based on Matrix Theory

Shamir proposed a classic polynomial-based secret sharing(SS)scheme,which is also widely applied in secret image sharing(SIS).However,the following researchers paid more attention to the development of properties,such as lossless recovery,rather than the principle of Shamir’s polynomial-based SS scheme.In this paper,we introduce matrix theory to analyze Shamir’s polynomial-based scheme as well as propose a general(k,n)threshold SIS construction based on matrix theory.Besides,it is proved that Shamir’s polynomial-based SS scheme is a special case of our construction method.Both experimental results and analyses are given to demonstrate the effectiveness of the proposed construction method.

Scalings for the Alfvén-cyclotron instability in a bi-kappa plasma

The particle velocity distribution in space plasma usually exhibits a non-Maxwellian high-energy tail that can be well modeled by kappa distributions.In this study,we focus on the growth rates of the Alfvén-cyclotron instability driven by ion temperature anisotropy in a kappa plasma.By solving the kinetic linear dispersion equation,we explore the sensitivity of growth rates to the spectral indexκof a bi-kappa distribution under different plasma conditions,including a variety of plasma beta β_(hp) and temperature anisotropy A_(hp) values of hot protons.Furthermore,a concise,analytic scaling formula is derived that relates the dimensionless maximum growth rate to three independent variables:the spectral index and the plasma beta and temperature anisotropy of hot protons.Our results show that as theκ-value increases,the instability bandwidth narrows and the maximum growth rate increases significantly.For higherβ_(hp)and A_(hp)′the maximum instability undergoes a sharp increase as well.When our fits of dimensionless maximum growth rates are compared with solutions to kinetic linear dispersion theory,the results generally exhibit good agreement between them.Especially under the circumstances of largeκ-values and highβ_(hp)and A_(hp)′the scalings of maximum growth rates primarily accurately model the numerical solutions.Our analytic expressions can readily be used in large-scale models of the Earth’s magnetosphere to understand wave generation due to the Alfvén-cyclotron instability.

Effect of local wall temperature on hypersonic boundary layer stability and transition

Wall temperature significantly affects stability and receptivity of the boundary layer. Changing the wall temperature locally may therefore be an effective laminar flow control technique. However, the situation is complicated when the wall temperature distribution is nonuniform, and researchers have experimentally found that local wall cooling may delay the onset of transition. We attempt to clarify the physical mechanisms whereby the local wall temperature affects the transition and the stability of a hypersonic boundary layer. A numerical investigation of the disturbance evolution in a Mach-6 sharp cone boundary layer with local wall heating or cooling is conducted. Direct numerical simulation(DNS) is performed for the single-frequency and broadband disturbance evolution caused by random forcing. We vary the local wall temperature and the location of heating/cooling, and then use the eNmethod to estimate the transition onset. Our results show that local wall cooling amplifies high-frequency unstable waves while stabilizing low-frequency unstable waves, with local heating amplifying all unstable waves locally. The disturbance amplitude and second-mode peak frequency obtained by DNS agree well with the previous experimental results. Local cooling/heating has a dual effect on the stability of the hypersonic boundary layer. For local cooling, while it effectively inhibits the growth of the low-frequency unstable waves that dominate the transition downstream, it also further destabilizes the downstream flow. In addition, while upstream cooling can delay the transition, excessive cooling may promote it;local heating always slightly promotes the transition.Finally, recommendations are given for practical engineering applications based on the present results.

Extend ethylene aromatization single-event kinetic modeling with physical and chemical descriptor based on ZSM-5 catalyst

The ethylene aromatization is critical for the methanol to aromatics and light alkane dehydroaromatization process.The single-event microkinetic(SEMK)model combining the linear free energy theory and solid acid distribution concept were established and extend for the ethylene aromatization process,which can reduce the kinetic parameters and simplify the reaction network by comparison with the SEMK model including subtype elementary steps based on the type of carbenium ions.Further introducing deactivation parametersφinto the model and applying the linear free energy model to the deactivation experimental data,the obtained deactivation parametersφindicate that the carbon deposition precursors have the greatest impact on reducing the reaction rate of single-molecular reactions and the smallest impact on the hydrogen transfer reaction.Meanwhile,according to the change of reaction enthalpy,effect of carbenium ion structure on methylation,ethylation,cyclization and endo-βscission was investigated by introducing linear free energy concept into the SEMK model.The effect of different acid strengths on elementary steps was investigated based on the acid strength distribution model,it was found that the methylation and oligomerization reactions,the ali-βscission reaction,endo-βscission reaction and the cyclization reaction were more sensitive to strong acidity sites.The physisorption and chemisorption heat are separated from the protonation heat in the linear free energy kinetic model and the acid strength distribution kinetic model,and the absolute values of the obtained physisorption and chemisorption heat increase with the carbon number of carbenium ions.Furthermore,the parameters of the acid strength distribution kinetic model were applied to propane dehydroaromatization on H-ZSM-5 and the ethane dehydroaromatization on Zn/ZSM-5 to confirm the independence of parameters in the SEMK model with the similar reaction network.

Statistical Distribution of Surface Slope in A 3-D Ocean Wave Field

A joint probability density function (PDF) for surface slopes in two arbitrary directions is derived on the basis of Longuet Higgins's linear model for three-dimensionol (3-D) random wave field. and the correlation moments of surface slopes. as parameters in the PDF, are expressed in terms of directional spectrum of ocean waves. So long as the directional spectrum model is given, these parameters are determined. Since the directional spectrum models proposed so far are mostly parameterized by the wind speed and fetch, this allows for substituting these parameters with thc wind speed and fetch. As an example, the wind speed and fetch are taken to be 14 m ' s and 200 km, and the Hasselmann and Donclan directional spectra are, respectively, use to compute these parameters. Some novel results a reobtained. One of the increasing interesting results is that the variances of surface slope in downwind and cross-wind directions determined by the Donclan directional spectra are close to those measured by Cox and Munk (1954). Some discussions are made on these results.

Quantitative Correlation of Chromatographic Retention and Acute Toxicity for Alkyl(1-phenylsulfonyl) Cycloalkane Carboxylates and Their Structural Parameters by DFT

Twenty eight alkyl(1-phenylsulfonyl) cycloalkane carboxylates were computed at the B3LYP/6-31G* level. Based on linear solvation energy theory, two quantitative correlation equations of the molecular structures of alkyl(1-phenylsulfonyl) cycloalkane carboxylate com- pounds to their chromatographic retention (capacity factor lgKW) and the toxicity for photo- bacterium phosphoreum (–lgEC50) were developed by using the molecular structural parameters as theoretical descriptors (r2 = 0.9501, 0.9488). The two quantitative correlation equations were consequently cross validated by leave-one-out (LOO) validation method with q2 of 0.9113 and 0.9281, respectively. The result showed that the two equations achieved in this work by B3LYP/6-31G* are both more advantageous than those from AM1, and can be used to predict the lgKW and –lgEC50 of congeneric organics.

Studies on the Quantitative Structure-activity Relationship of Toxicity of Chlorophenol Serial Compounds in the ab initio Methods and Substitutive Position of Chlorine Atom (N_(PCS))

20 Quantum chemical parameters of chlorophenol compounds were fully optimized by using B3LYP method on both 6-31G^＊ and 6-311G^＊ basis sets. These structural parameters are taken as theoretical descriptors, and the experimental data of 20 compounds＇ aquatic photogen toxicity（-lgEC50） are used to perform stepwise regression in order to obtain two predicted -lgEC50 correlation models whose correlation coefficients R^2 are respectively 0.9186 and 0.9567. In addition, parameters of chlorine atom＇s substitutive positions and their correlations （NPCs） are taken as descriptors to obtain another predicted -lgEC50 model with the correlation coefficient R2 of 0.9444. Correlation degree of each independent variable in the three models is verified by using variance inflation factors （VIF） and t value. In the cross-validation method, cross-validation coefficients q^2 of 3 models are respectively 0.8748, 0.9119 and 0.8993, which indicates that the relativity and prediction ability of this model are superior to those of the model obtained by topological and BLYP methods.

Verification of parabolized stability equations for its application to compressible boundary layers

Parabolized stability equations （PSE） were used to study the evolution of disturbances in compressible boundary layers. The results were compared with those obtained by direct numerical simulations （DNS）, to check if the results from PSE method were reliable or not. The results of comparison showed that no matter for subsonic or supersonic boundary layers, results from both the PSE and DNS method agreed with each other reasonably well, and the agreement between temperatures was better than those between velocities. In addition, linear PSE was used to calculate the neutral curve for small amplitude disturbances in a supersonic boundary layer. Compared with those obtained by linear stability theory （LST）, the situation was similar to those for incom- pressible boundary layer.

Vertical variations of wave-induced radiation stress tensor

The distributions of the wave-induced radiation stress tensor over depth are studied by us- ing the linear wave theory, which are divided into three regions, i. e., above the mean water level, be- low the wave trough level, and between these two levels. The computational expressions of the wave-in- duced radiation stress tensor at the arbitrary wave angle are established by means of the Eulerian coordi- nate transformation, and the asymptotic forms for deep and shallow water are also presented. The verti- cal variations of a 30°incident wave-induced radiation stress tensor in deep water, intermediate water and shallow water are calculated respectively. The following conclusions are obtained from computations. The wave-induced radiation stress tensor below the wave trough level is induced by the water wave parti- cle velocities only, whereas both the water wave particle velocities and the wave pressure contribute to the tensor above the wave trough level. The vertical variations of the wave-induced radiation stress ten- sor are influenced substantially by the velocity component in the direction of wave propagation. The dis- tributions of the wave-induced radiation stress tensor over depth are nonuiniform and the proportion of the tensor below the wave trough level becomes considerable in the shallow water. From the water surface to the seabed, the reversed variations occur for the predominant tensor components.

Stability analysis method considering non-parallelism:EPSE method and its application

The e-N method is widely used in transition prediction. The amplitude growth rate used in the e-N method is usually provided by the linear stability theory （LST） based on the local parallel hypothesis. Considering the non-parallelism effect, the parabolized stability equation （PSE） method lacks local characteristic of stability analysis. In this paper, a local stability analysis method considering non-parallelism is proposed, termed as EPSE since it may be considered as an expansion of the PSE method. The EPSE considers variation of the shape function in the streamwise direction. Its local characteristic is convenient for stability analysis. This paper uses the EPSE in a strong non-parallel flow and mode exchange problem. The results agree well with the PSE and the direct numerical simulation （DNS）. In addition, it is found that the growth rate is related to the normalized method in the non-parallel flow. Different results can be obtained using different normalized methods. Therefore, the normalized method must be consistent.

QSPR Studies on lgK_(ow) and lgK_(oc) of Fluorobenzenes and Property Parameters Based on HF and DFT Calculations

Quantum chemistry parameters of 22 fluorobenzenes were computed at six levels using Hartree-Fock and DFT methods. Based on the experimental data of n-octanol/water partition coefficient （lgKow）, a three-parameter （dipole moments （μ）, zero point energy （ZPE） and free energy （G°）） quantitative correlation equation that can predict IgKow was developed using structural and thermodynamic parameters as theoretical descriptors. Similarly, based on experimental data of soil organic carbon sorption coefficient （lgKoc）, the other three-parameter （the most negative atomic net charge of molecule （q^-）, dipole moments （μ） and molecular volume （Vi）） quantitative correlation equation that can predict lgKoc was given. Quantitative correlation equations based on B3LYP/6- 311 G^＊＊ calculation were validated by VIF （variance inflation factors） and t-test and used to predict IgKow and lgKoc of a series of compounds. The result showed that the correlation and prediction ability of lgKoc equations based on three levels of HF/STO-3G, B3LYP/6-31 G^＊ and B3LYP/6- 311G^＊＊ are all more advantageous than those based on AMI.

Quantitative Correlation of the Acute Toxicity of Phenylthio-carboxylates with Their Structural and Thermodynamic Parameters by DFT Calculation

Phenylthio-carboxylates were computed at the B3LYP/6-31G* level with DFT method. Based on linear solvation energy theory, the structural parameters were firstly taken as theoretical descriptors, and the corresponding linear solvation energy relationship (LSER) equation (r = 0.8989) to the toxicity of photobacterium phosphoreum (–lgEC50) was thus obtained. Then the structural and thermodynamic parameters were taken as theoretical descriptors, and as a result the other corresponding correlation equation (r = 0.9274) relating to –lgEC50 was provided. The two equations achieved in this work by B3LYP/6-31G* are both more advantageous than that from AM1.

Application of Arnoldi method to boundary layer instability

The Arnoldi method is applied to boundary layer instability, and a finite difference method is employed to avoid the limit of the finite element method. This modus operandi is verified by three comparison cases, i.e., comparison with linear stability theory（LST） for two-dimensional（2D） disturbance on one-dimensional（1D） basic flow, comparison with LST for three-dimensional（3D） disturbance on 1D basic flow, and comparison with Floquet theory for 3D disturbance on 2D basic flow. Then it is applied to secondary instability analysis on the streaky boundary layer under spanwise-localized free-stream turbulence（FST）. Three unstable modes are found, i.e., an inner mode at a high-speed center streak, a sinuous type outer mode at a low-speed center streak, and a sinuous type outer mode at low-speed side streaks. All these modes are much more unstable than Tollmien–Schlichting（TS） waves, implying the dominant contribution of secondary instability in bypass transition. The modes at strong center streak are more unstable than those at weak side streaks, so the center streak is ‘dangerous＇ in secondary instability.