Problems with the ζ-function method

The -function method for evaluating effective actions is applied to an operator containing a potential localized on two parallel planes. This operator is characterized by a continuous spectrum and broken translation invariance. In this case, the -method leads to a divergent volume factor independent of the physical parameters. In a suitable regularization scheme, only the next to leading order term reproduces a physically interesting result.     

Lattice Boltzmann method with the cell-population equilibrium

The central problem of the lattice Boltzmann method （LBM） is to construct a discrete equilibrium. In this paper, a multi-speed 1D cell-model of Boltzmann equation is proposed, in which the cell-population equilibrium, a direct non- negative approximation to the continuous Maxwellian distribution, plays an important part. By applying the explicit one-order Chapman-Enskog distribution, the model reduces the transportation and collision, two basic evolution steps in LBM, to the transportation of the non-equilibrium distribution. Furthermore, 1D dam-break problem is performed and the numerical results agree well with the analytic solutions.     

An analytical method for the electro-acoustic performance of the underwater transducer

A finite element-Helmholtz integral hybrid method has been developed to calculate the electro-acoustic performance of a finite length cylindrical transducer immersed in water. The numerical study concerned with electrical impedances and beam patterns of the transducer is presented. Experimental data are shown to support the numerical study.     

Photoacoustic method for the measurement of the nonlinearity parameter of liquids

I.IntroductionThenonlinearityparameterB/Aisanimportantacousticalparameteroffluids.Hitherto,manytheoreticalandexperimentalstudiesforthedeterminahonofthenon1inearityparamctersof1iquidshavebeenrcported.ThemcthodsfordetCrminationofthenonlinearityparamenterofthe1iquidcanbeseparatedintotwocategories:thermodynamicmethod[llandfinite-amp1itudeacousticwavcmethod.The1attercancseparatedfurtherintoharmonicwavemcthodt2]andpulsemethod.Karabutovetal.[31andBozkhovetaI.[4lusedthepulsedlasertogencratetheplane…     

On the dressing method for the generalised Zakharov–Shabat system

The dressing procedure for the generalised Zakharov–Shabat system is well known for systems, related to sl(N) algebras. We extend the method, constructing explicitly the dressing factors for some systems, related to orthogonal and symplectic Lie algebras. We consider ‘dressed’ fundamental analytical solutions with simple poles at the prescribed eigenvalue points and obtain the corresponding Lax potentials, representing the soliton solutions for some important nonlinear evolution equations.     

Amplitude-difference method in the estimation of ultrasonic attenuation

In this paper a new method of ultrasonic quantitative diagnosis isdiscribed.This method can elminate the effect of system deviation and lessenthe the effect of beam radiation diffraction.In can be spp1ied together withmany kinks of B-scanners.To verify the method,this paper has shown a newmethod to make a tissue phantom and a special apparatus.The results showthat the method is useful in the diagnosis of diffuse liver diseases,tumors andcanccrs.It is also useful in the appraisal of the health and the stages of fetus.     

The generalization of the Boltzmann–Matano method

The phenomenological Boltzmann–Matano (B–M) analysis allows approximating the concentration dependent interdiffusion coefficients related to infinite binary diffusion couple experiments. However, the complete understanding of the phenomenological process related to the Kirkendall plane position coupled with the B–M method is still lacking. A purpose of the present study is to generalize the Boltzmann–Matano analysis and propose a method of estimating the unique intrinsic diffusion coefficients of components from the experimental concentration profile and the positions of Matano and Kirkendall planes in multicomponent systems. The proposed physico-chemical approach is used to approximate the intrinsic diffusivities in a single phase of Ni–Pd binary and Cu–Fe–Ni ternary diffusion couples.     

Track reconstruction using the TSF method for the BESm main drift chamber

We describe the algorithm to reconstruct the charged tracks for BESⅢmain drift chamber at BEPCⅡ,including the track finding and fitting.With a new method of the Track Segment Finder(TSF), the results of present study indicate that the algorithm can reconstruct the charged tracks over a wide range of momentum with high efficiency,while improving the robustness against the background noise in the drift chamber.The overall performances,including spatial resolution,momentum resolution and secondary vertices reconstruction efficiency,etc.satisfy the requirements of BESⅢexperiment.     

A connection between the(G'/G)-expansion method and the truncated Painlevé expansion method and its application to the mKdV equation

Recently the (G'/G)-expansion method was proposed to find the traveling wave solutions of nonlinear evolution equations. This paper shows that the (G'/G)-expansion method is a special form of the truncated Painlevé expansion method by introducing an intermediate expansion method. Then the generalized (G'/G)--(G'/G) expansion method is naturally derived from the standpoint of the nonstandard truncated Painlevé expansion. The application of the generalized method to the mKdV equation shows that it extends the range of exact solutions obtained by using the (G'/G)-expansion method.     

The background field method and the non-linear σ-model

We prove the renormalizability in the background field method of the two-dimensional bosonic non-linear σ-model with an arbitrary riemannian manifold as target space. Particular attention is paid to the question of non-linear renormalization of the quantum fields and its effect on subdivergences. We give an algorithm that allows one to compute to arbitrary loop order.     

A novel method to determine the FOCAL energy range

As the critical dimensions in the semiconductor industryare shrinking, fast and accurate in-situ measurements ofprojection optics aberrations of lithographic tools becomeincreasingly necessary. Focus calibration using alignmentprocedure (FOCAL) [1-4] is an important technique usedfor self-calibration[5-8] of deep-ultraviolet (DUV) litho-graphic tools[9,10]. With this technique, imaging qualityparameters, such as best focus, image tilt, field curva-ture, and so on, can be measured accurately…     

μSR frequency spectra using the maximum entropy method

A novel approach to extracting frequency spectra from transverseSR spectra is presented, based on the maximum entropy method. This has the advantages of ensuring positivity of the frequency spectra, and only deviating from a flat default level where there is statistically significant information present in the data. It allows simultaneous analysis of spectra from multiple detectors with different phases to yield a single frequency spectrum.     

Synchronization of Huygens' clocks and the Poincaré method

We study two models of connected pendulum clocks synchronizing their oscillations, a phenomenon originally observed by Huygens. The oscillation angles are assumed to be small so that the pendulums are modeled by harmonic oscillators, clock escapements are modeled by the van der Pol terms. The mass ratio of the pendulum bobs to their casings is taken as a small parameter. Analytic conditions for existence and stability of synchronization regimes, and analytic expressions for their stable amplitudes and period corrections are derived using the Poincaré theorem on existence of periodic solutions in autonomous quasi-linear systems. The anti-phase regime always exists and is stable under variation of the system parameters. The in-phase regime may exist and be stable, exist and be unstable, or not exist at all depending on parameter values. As the damping in the frame connecting the clocks is increased the in-phase stable amplitude and period are decreasing until the regime first destabilizes and then disappears. The results are most complete for the traditional three degrees of freedom model, where the clock casings and the frame are consolidated into a single mass.     

Applications of F-expansion method to the coupled KdV system

An extended F-expansion method for finding periodic wave solutions of nonlinear evolution equations in mathematical physics is presented, which can be thought of as a concentration of extended Jacobi elliptic function expansion method proposed more recently. By using the homogeneous balance principle and the extended F-expansion, more periodic wave solutions expressed by Jacobi elliptic functions for the coupled KdV equations are derived. In the limit cases, the solitary wave solutions and the other type of travelling wave solutions for the system are also obtained.     

An improved computing method for the image edge detection

The framework of detecting the image edge based on the sub-pixel multi-fractal measure (SPMM) is presented. The measure is defined, which gives the sub-pixel local distribution of the image gradient. The more precise singularity exponent of every pixel can be obtained by performing the SPMM analysis on the image. Using the singularity exponents and the multi-fractal spectrum of the image, the image can be segmented into a series of sets with different singularity exponents, thus the image edge can be detected automatically and easily. The simulation results show that the SPMM has higher quality factor in the image edge detection.     

Explicit multi-symplectic method for the Zakharov—Kuznetsov equation

We propose an explicit multi-symplectic method to solve the two-dimensional Zakharov-Kuznetsov equation. The method combines the multi-symplectic Fourier pseudospectral method for spatial discretization and the Euler method for temporal discretization. It is verified that the proposed method has corresponding discrete multi-symplectic conservation laws. Numerical simulations indicate that the proposed scheme is characterized by excellent conservation.     

Non—equilibrium extrapolation method for velocity and pressure boundary conditions in the lattice Boltzmann method

In this paper, we propose a new approach to implementing boundary conditions in the lattice Boltzmann method (LBM). The basic idea is to decompose the distribution function at the boundary node into its equilibrium and non-equilibrium parts, and then to approximate the non-equilibrium part with a first-order extrapolation of the non-equilibrium part of the distribution at the neighbouring fluid node. Schemes for velocity and pressure boundary conditions are constructed based on this method. The resulting schemes are of second-order accuracy. Numerical tests show that the numerical solutions of the LBM together with the present boundary schemes are in excellent agreement with the analytical solutions. Second-order convergence is also verified from the results. It is also found that the numerical stability of the present schemes is much better than that of the original extrapolation schemes proposed by Chen et al. (1996 Phys. Fluids 8 2527).     

■-dressing method for the complex modified KdV equation

The dressing method based on the 2 × 2 matrix ■-problem is generalized to study the complex modified KdV equation(cmKdV). Through two linear constraint equations, the spatial and time spectral problems related to the cmKdV equation are derived. The gauge equivalence between the cmKdV equation and the Heisenberg chain equation is obtained. Using a recursive operator,a hierarchy of cmKdV with source is proposed. On the basis of the ■-equation, the N-solition solutions of the cmKdV equation are obt...     

A method for improving the performance of MVDR beamforming

I.IntroductionInbeamformingforsonaritisthemostinterestingfunctionthatonecanobtainthctimcwaveformoutputsofthedesiredsignaltobedetectcdwithanimprovcdSignal-to-NoiseplusInterferenceRatio(SNIR).ItiswellknownthatMVDRbeamforminghasoptimumcapabi1i-hesofsignalprotection,interferenccremovalandnoisercduction.NootherbeamformingtochniquecanyicldalargerincreascinSNIR.Itspoweroutputcanbeusedasawavenumberspectrum(bearing)estimation,whoseprecisionorreso1utionisdeterminedprimarilybySignal-to-NoiseRatio…     

Application of the group foliation method to the complex Monge-Ampère equation

We apply the method of group foliation to the complex Monge-Ampère equation (CMA ₂) to establish a regular framework for finding its non-invariant solutions. We employ an infinite symmetry subgroup ofCMA ₂ to produce a foliation of the solution space into orbits of solutions with respect to this group and a corresponding splitting ofCMA ₂ into an automorphic system and a resolvent system. We propose a new approach to group foliation which is based on the commutator algebra of operators of invariant differentiation. This algebra together with its Jacobi identities provides the commutator representation of the resolvent system. Presented by M.B. Sheftel at the DI-CRM Workshop held in Prague, 18–21 June 2000.