Approximate Analytical Solutions for a Class of Laminar Boundary-Layer Equations

A simple and efficient approximate analytical technique is presented to obtain solutions to a class of two-point boundary value similarity problems in fluid mechanics. This technique is based on the decomposition method which yields a genera/analytic solution in the form of a convergent infinite series with easily computable terms. Comparative study is carried out to show the accuracy and effectiveness of the technique.     

Solutions of Heat-Like and Wave-Like Equations with Variable Coefficients by Means of the Homotopy Analysis Method

We employ the homotopy analysis method （HAM） to obtain approximate analytical solutions to the heat-like and wave-like equations. The HAM contains the auxiliary parameter h, which provides a convenient way of controlling the convergence region of series solutions. The analysis is accompanied by several linear and nonlinear heat-like and wave-like equations with initial boundary value problems. The results obtained prove that HAM is very effective and simple with less error than the Adomian decomposition method and the variational iteration method.     

A Simple Method for Measuring Tensile Force with Piezoelectric Patch

We propose a simple method for monitoring the axial tensile and compressive force in a structure by using a piezoelectric patch with the piezoelectric impedance based measurement. A simple approximate equation for estimating the tensile force in two different conditions, which can be calculated easily if the naturM frequencies in two different states are measuredt is explained in detail. On another front, the natural frequency can be very easily measured by a piezoelectric element by bonding it on the measuring subject structure, because its electric impedance of piezoelement is related to the structural mechanical impedance. Furthermore, an experiment for measuring a tensile force in a simple supported beam is carried out for validating the proposed method. The results show a good accuracy in estimating the tensile force variation by the natural frequency change measured from the piezoelement.     

Antiferromagnetism in a doped spin-Peierls model: Classical and quantum behaviors

We investigate the sequential cracking of thin brittle coatings attached adhesively to substrates. The focus of our study are uniaxial tensile loading conditions, where we monitor the behavior in a continuous picture and the coating strength follows a two-parameter Weibull distribution. For fracture well under way we derive an approximate analytical expression for the distribution of fragment lengths. We recover that the distribution scales with the average fragment length and that is a power function of the applied strain , i.e. , where depends on the distribution of the strength of the coating and on the adhesive's nonlinearity. Furthermore we compare our approximate analytical expression with numerical solutions and with simulations' findings. Received 16 February 2000     

Emissvity of metallic microcontoured surfaces

In this paper, we study the diffraction of electromagnetic radiation by a periodic micro-rough surface separating vacuum from a metal with a finite conductivity. We submit the integral method to the surface impedance boundary condition. Thus the numerical implementation is greatly reduced. We compare the numerical emissivities obtained by this approach to those we have calculated through the rigorous multilayer modal method. This enables us to show that the mentioned approximate method has two regions of validity: one corresponding to fairly flat surfaces and the other to very deep surfaces. It is well known that both the Kirchhoff approximation and the constant flat boundary impedance approximation are also valid for fairly flat surfaces. Our investigation aims also to establish whether these two approximate methods lead to the same results, and whether the integral method submitted to the surface impedance condition has a larger domain of validity. Concerning deep surfaces with a period smaller than the wavelength, we introduce the homogenization process in order to study its accuracy.Finally, this work permitted to identify three different regimes depending on the surface slopes: the simple scattering regime, the homogenization regime and the intermediate regime. For the latter, if the period is in the order of the wavelength, then we will show that the emissivity can be exalted.     

Self-Trapping of Two Bose-Einstein Condensates with a Coupling Drive

We present an approximate analytical solution to the population imbalance of two-component Bose-Einstein condensate with the coupling drive. The dependence of the time evolution of self-trapping upon the radio frequency wave, the Rabi coupling frequency, the initial atom number and relative phase between two condensates are investigated. The lower radio frequency wave, the same atom number and initial relative phase between condensates are beneficial to observe the self-trapping.     

Nonlinear adaptive synchronization rule for identification of a large amount of parameters in dynamical models

The existing adaptive synchronization technique based on the stability theory and invariance principle of dynamical systems, though theoretically proved to be valid for parameters identification in specific models, is always showing slow convergence rate and even failed in practice when the number of parameters becomes large. Here, for parameters update, a novel nonlinear adaptive rule is proposed to accelerate the rate. Its feasibility is validated by analytical arguments as well as by specific parameters identification in the Lotka-Volterra model with multiple species. Two adjustable factors in this rule influence the identification accuracy, which means that a proper choice of these factors leads to an optimal performance of this rule. In addition, a feasible method for avoiding the occurrence of the approximate linear dependence among terms with parameters on the synchronized manifold is also proposed.     

Casimir Energy in Hartle--Hawking State

We calculate the Casimir effect at finite temperature in Minkowski spacetime by using statistical method, the approximate expressions of the Casimir effect in the low and high temperature limits are also discussed. Then employing some general properties of the renormalized stress tensor, we obtain the Casimir energy stress tensor in Hattie-Hawking state.     

Continued-fraction expansion of eigenvalues of generalized evolution operators in terms of periodic orbits

A new expansion scheme to evaluate the eigenvalues of the generalized evolution operator (Frobenius-Perron operator)H _q relevant to the fluctuation spectrum and poles of the order-q power spectrum is proposed. The partition function is computed in terms of unstable periodic orbits and then used in a finite pole approximation of the continued fraction expansion for the evolution operator. A solvable example is presented and the approximate and exact results are compared; good agreement is found.     

A model for the propagation of nonlinear dispersive strain waves in a solid with defect clusters

A model for the propagation of nonlinear dispersive one-dimensional longitudinal strain waves in an isotropic solid with quadratic nonlinearity of elastic continuum is developed with taking into account the interaction with atomic defect clusters. The governing nonlinear dispersive-dissipative equation describing the evolution of longitudinal strain waves is derived. An approximate solution of the model equation was derived which describes asymmetrical distortion of geometry of the solitary strain wave due to the interaction between the strain field and the field of clusters. The contributions of the finiteness of the relaxation times of cluster-induced atomic defects to the linear elastic modulus and the lattice dissipation and dispersion parameters are determined. The amplitudes and width of the nonlinear waves depend on the elastic constants and on the properties of the defect subsystem (atomic defects, clusters) in the medium. The explicit expression is received for the sound velocity dependence upon the fractional cluster volume, which is in good agreement with experiment. The critical value of cluster volume fraction for the influence on the strain wave propagation is determined.     

Orbital effect of a magnetic field on two-leg Hubbard ladder

By setting up the relevant recursion relations and by doing exact and approximate calculations, we show that there is no critical dimension in a self-avoiding random walk on a simplex fractal. Received: 6 April 1998 / Revised: 4 August 1998 / Accepted: 26 August 1998     

Perturbation Analysis on Guided Waves in a Fluid-Filled Borehole Surrounded by a Cubic Crystal Anisotropic Medium

The perturbation method is employed to analyse the guided waves in a borehole surrounded by a cubic crystal medium for the first time. The cubic crystal medium is regarded as a reference unperturbed isotropic state added to the perturbation. The dispersion characteristics of Stoneley wave, pseudo-Rayleigh wave, flexural wave, and screw wave are investigated in detail. It is found that dispersion of the guided waves excited by monopole and dipole sources does not depend on the azimuth of the source, whereas the dispersion of screw wave excited by quadrupole source is significantly related to the azimuth of the source. Screw waves propagated along different azimuth in the borehole can be split. This is different from screw waves in transversely isotropic media （hexagonal crystal）, which have been widely studied.     

Dissociative attachment of an electron to a molecule: kinetic theory

Test particles interact with a medium by means of a bimolecular reversible chemical reaction. Two species are assumed to be much more numerous so that they are distributed according to fixed distributions: Maxwellians and Dirac's deltas. Equilibrium and its stability are investigated in the first case. For the second case, a system is constructed, in view of an approximate solution.     

Coupling of Acoustical Plane p-Wave to a Cased Borehole

Theoretical and numerical study on the coupling acoustic field of the plane p-wave to a cased borehole is carried out. The medium outside the cased borehole is modeled as the porous medium. The scattering field characteristics in the cased borehole are investigated when a plane fast p-wave is incident in tilt to the cased borehole from the porous medium. The scattering fields inside and outside the cased borehole are analyzed and deduced by Biot＇s theory under the boundary conditions on each interface, and they are numerically studied. It is found that the scattering field has strong resonant characteristics and there exists a series of resonant frequencies and peaks. The effects of the frequency, radii of each interface, incident angle, porosity, and other parameters on the resonant acoustic field have been investigated in detail in the fast and slow formations respectively. The resonant characteristics of the scattering field are also analyzed from the physical sense.     

Hadron spectrum in a two-colour baryon-rich medium

The hadron spectrum of SU(2)$\mathrm{SU}(2)$ lattice gauge theory with two flavours of Wilson quark is studied on an ⁸³×16$8^3\times 16$ lattice using all-to-all propagators, with particular emphasis on the dependence on quark chemical potential μ. As μ is increased from zero the diquark states with non-zero baryon number B   respond as expected, while states with B=0$B=0$ remain unaffected, until the onset of non-zero baryon density at μ=mπ/2$\mu =m_{\pi }/2$. Post onset the pi-meson mass increases in accordance with chiral perturbation theory while the rho becomes lighter. In the diquark sector a Goldstone state associated with a superfluid ground state can be identified. A further consequence of superfluidity is an approximate degeneracy between mesons and baryons with the same spacetime and isospin quantum numbers. Finally we find tentative evidence for the binding of states with kaon quantum numbers within the baryonic medium.     

Phononic band structure in a two-dimensional hybrid triangular graphite lattice

The propagation of acoustic wave in a two-dimensional phononic crystal of a hybrid triangular graphite array is investigated by the plane wave expansion (PWE) method. Our numerical results show that the location and width of the band gaps can be tuned by altering the radii of scatters at different positions.     

Thickness Determination for a Two-Layered Composite of a Film and a Plate by Low-Frequency Ultrasound

We present an ultrasonic method for determining the thickness of a composite consisting of a soft thin film attached to a hard plate substrate, by resonance spectra in the low frequency region, The interrogating waves can be incident only to the two-layered composite from the substrate side. The reflection spectra are obtained by FFT analysis of the compressive pulsed echoes from the composite, and the thicknesses of the film and the substrate are simultaneously inversed by the simulated annealing method from the resonant frequencies knowing other acoustical parameters in prior. The sensitivity of the method to individual thickness, its convergence and stability against experimental noises are studied, Experiment with interrogating wavelength 4 times larger than the film thickness in a sample of a polymer film （0.054mm） on an aluminium plate （6.24mm） verifies the validity of the method. The average relative errors in the measurement of the thicknesses of the film and the substrate are found to be -4.1% and -0.62%, respectively.     

A fractal model for heat transfer of nanofluids by convection in a pool

Based on the fractal distribution of nanoparticles, a fractal model for heat transfer of nanofluids is presented in the Letter. Considering heat convection between nanoparticles and liquids due to the Brownian motion of nanoparticles in fluids, the formula of calculating heat flux of nanofluids by convection is given. The proposed model is expressed as a function of the average size of nanoparticle, concentration of nanoparticle, fractal dimension of nanoparticle, temperature and properties of fluids. It is shown that the fractal model is effectual according to a good agreement between the model predictions and experimental data.     

Determination of Thermal Conductivity of Liquids by a Multi-Point Laser Pump Method

As an advanced optical method, a multi-point pump method is presented for measurements of thermo-physical properties of liquids. Meanwhile, based on the laser-induced thermal grating method, a new theory model is presented and used to analyse the thermal effects caused by the multi-point laser pump, by which the thermal conductivity of liquids can be obtained. The results of some typical liquids, such as water, ethanol and acetone, are presented and are consistent with those of acknowledged values, demonstrating that the multi-point method is simple and useful for characterizing thermal properties of liquids.     

Guided Waves in a Multi-Layered Cylindrical Elastic Solid Medium

We investigate the guided waves in a multi-layered cylindrical elastic solid medium. The dispersion function of guided waves is usually complex and the dispersion curves of all modes are not conveniently obtained. Here we present an effective method to obtain the dispersion curves of all modes. First, the dispersion function of the guided waves is transformed into a real function. The dispersion curves are then calculated for all the modes of the guided waves by the bisection method. The modes with the orders n = 0, 1, and 2 are analysed in two- and three-layer media. The existence condition of Stoneley wave is discussed. The modes of the guided waves are also investigated in a two-layer medium, in which the velocity of shear wave in the outer layer is less than that in the inner layer.