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.

Some New Features of Linear Theory for Describing Non-linear Diffusion

The non-linear flux equation, the non-linear Fokker-Planck equation （or Smoluchowski equation）, and the non-linear Langiven equation are the basic equations for describing particle diffusion in non-ideal system subjected to time-dependent external fields. Nevertheless, the exact solution of those equations is still a challenge because of their inherent complexity of the non-linear mathematics. Li et al. found that, based on the defined apparent variables, the nonlinear Fokker-Planck equation and the non-linear flux equation could be transformed to linear forms under the condition of strong friction limit or loeal equilibrium assumption. In this paper, some new features of the theory were found： （i） The linear flux equation for describing non-linear diffusion can be obtained from the irreversible thermodynamic theory; （ii） The linear non-steady state diffusion equation for describing non-linear diffusion of the non-steady state, which was described by the non-linear Fokker-Planek equation, can be derived more consistently from the microscopic molecular statistical theory; （iii） In the theory, the non-linear Langiven equation also bears a linear form; （iv） For some special cases, e.g. diffusion in a periodic total potential system, the local equilibrium assumption or the strong friction limit is not required in establishing the linear theory for describing non-linear diffusion, so the linear theory may be important in the study of Brown motor.

Initial pre-stress finding procedure and structural performance research for Levy cable dome based on linear adjustment theory

The cable-strut structural system is statically and kinematically indeterminate. The initial pre-stress is a key factor for determining the shape and load carrying capacity. A new numerical algorithm is presented herein for the initial pre-stress finding procedure of complete cable-strut assembly. This method is based on the linear adjustment theory and does not take into account the material behavior. By using this method,the initial pre-stress of the multi self-stress modes can be found easily and the cal-culation process is simplified and efficient also. Finally,the initial pre-stress and structural performances of a particular Levy cable dome are analyzed comprehensively. The algorithm has proven to be efficient and correct,and the numerical results are valuable for practical design of Levy cable dome.

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.

Initial Pre-stress Finding and Structural Behaviors Analysis of Cable Net Based on Linear Adjustment Theory

The tensile cable-strut structure is a self-equilibrate pre-stressed system.The initial pre-stress cal- culation is the fundamental structural analysis.A new numerical procedure was developed.The force density method is the cornerstone of analytical formula,and then introduced into linear adjustment theory;the least square least norm solution,the optimized initial pre-stress,is yielded.The initial pre-stress and structural performances of a particular single-layer saddle-shaped cable-net structure were analyzed with the developed method,which is proved to be efficient and correct.The modal analyses were performed with respect to various pre-stress levels.Finally,the structural performances were investigated comprehensively.

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.

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.

Ion Dynamics in Concentrated Electrolyte Solutions:Relating Equilibrium Fluctuations of the Ions to Transport Properties in Battery Cells

In recent years,the interest in the development of highly concentrated electrolyte solutions for battery applications has increased enormously.Such electrolyte solutions are typically characterized by a low flammability,a high thermal and electrochemical stability and by the formation of a stable solid electrolyte interphase(SEI)in contact to electrode materials.However,the classification of concentrated electrolyte solutions in terms of the classical scheme"strong"or"weak"has been controversially discussed in the literature.In this paper,a comprehensive theoretical framework is presented for a more general classification,which is based on a comparison of charge transport and mass transport.By combining the Onsager transport formalism with linear response theory,center-of-mass fluctuations and collective translational dipole fluctuations of the ions in equilibrium are related to transport properties in a lithium-ion battery cell,namely mass transport,charge transport and Li^(+)transport under anion-blocking conditions.The relevance of the classification approach is substantiated by showing that i)it is straightforward to classify highly concentrated electrolytes and that ii)both fast charge transport and fast mass transport are indispensable for achieving fast Li^(+)transport under anion-blocking conditions.

Linear stability of plane creeping Couette flow for Burgers fluid

It is well known that plane creeping Couette flow of UCM and Oldroy-B fluids are linearly stable. However, for Burges fluid, which includes UCM and Oldroyd-B fluids as special cases, unstable modes are detected in the present work. The wave speed, critical parameters and perturbation mode are studied for neutral waves. Energy analysis shows that the sustaining of perturbation energy in Poiseuille flow and Couette flow is completely different. At low Reynolds number limit, analytical solutions are obtained for simpli- fied perturbation equations. The essential difference between Burgers fluid and Oldroyd-B fluid is revealed to be the fact that neutral mode exists only in the former.

Fuzzy linear model for production optimization of mining systems with multiple entities

Planning and production optimization within multiple mines or several work sites （entities） mining systems by using fuzzy linear programming （LP） was studied. LP is the most commonly used operations research methods in mining engineering. After the introductory review of properties and limitations of applying LP, short reviews of the general settings of deterministic and fuzzy LP models are presented. With the purpose of comparative analysis, the application of both LP models is presented using the example of the Bauxite Basin Niksic with five mines. After the assessment, LP is an efficient mathematical modeling tool in production planning and solving many other single-criteria optimization problems of mining engineering. After the comparison of advantages and deficiencies of both deterministic and fuzzy LP models, the conclusion presents benefits of the fuzzy LP model but is also stating that seeking the optimal plan of production means to accomplish the overall analysis that will encompass the LP model approaches.

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.

Linear stability analysis of supersonic axisymmetric jets

Stabilities of supersonic jets are examined with different velocities, momentum thicknesses, and core temperatures. Amplification rates of instability waves at inlet are evaluated by linear stability theory （LST）. It is found that increased velocity and core temperature would increase amplification rates substantially and such influence varies for different azimuthal wavenumbers. The most unstable modes in thin momentum thickness cases usually have higher frequencies and azimuthal wavenumbers. Mode switching is observed for low azimuthal wavenumbers, but it appears merely in high velocity cases. In addition, the results provided by linear parabolized stability equations show that the mean-flow divergence affects the spatial evolution of instability waves greatly. The most amplified instability waves globally are sometimes found to be different from that given by LST.

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.

Frequency responses of immersing tunnel element under wave actions

The immersion of large-scale tunnel elements is one of the most important working procedures in the construction of an underwater immersed tunnel. To investigate the dynamic characteristics of tunnel element in the process of immersion, based on the twin-barge immersing operation method, the frequency-domain analysis of the tunnel element motions under wave actions was made. The linear wave diffraction theory and the three-dimensional source distribution method were applied to calculate the wave loads and motion responses of the tunnel element under different incident wave conditions. In the study, movement of the two barges in the water was assumed to be small and was ignored. Cable tension was computed by the static method. On the basis of the above theories, a computer program was made, and two cases were taken to check the validity of the program. The results showed that wave loads acting on the immersed tunnel element are relatively large near the water surface, and they decrease with the increase of immersing depth of the tunnel element. Wave loads first increase, then decrease, with the increase of wave period. The motion responses of the tunnel element are also generally large near the water surface and decrease as the immersing depth increases.

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.