Integral Transformation Method Research Articles

Slippage solution of gas pressure distribution in process of landfill gas seepage

A mathematical model of landfill gas migration was established under presumption of the effect of gas slippage. The slippage solutions to the nonlinear mathematical model were accomplished by the perturbation and integral transformation method. The distribution law of gas pressure in landfill site was presented under the conditions of considering and neglecting slippage effect. Sensitivity of the model input parameters was analyzed. The model solutions were compared to observation values. Results show that gas slippage effect has a large impact on gas pressure distribution. Landfill gas pressure and pressure gradient considering slippage effect is lower than that neglecting slippage effect, with reasonable agreement between model solution and measured data. It makes clear that the difference between considering and neglecting slippage effect is obvious and the effects of coupling cannot be ignored. The theoretical basis is provided for engineering design of security control and decision making of gas exploitation in landfill site. The solutions give scientific foundation to analyzing well test data in the process of low-permeability oil gas reservoir exploitation.

Stress Concentration in Microstructural Elements of Viscoelastic Composite Materials

We present solution of the problem of estimating the stress concentration in the constituents (matrix and inclusions) of a multiconstituent viscoelastic composite material, depending on the shape of inclusions, properties of the matrix and the whole composite. The matrix material is isotropic and viscoelastic. A wide range of properties of inclusions (e.g., pores, solid and viscous particles) is considered. To solve this problem, we use the method of integral transformations.

πphotoproduction on the deuteron via Δ-excitation using the Lorentz Integral Transform

The Lorentz Integral Transform method (LIT) is extended to pion photoproduction in the $\Delta$-resonance region. The main focus lies on the solution of the conceptual difficulties which arise if energy dependent operators for nucleon resonance excitations are considered. In order to demonstrate the applicability of our approach, we calculate the inclusive cross section for $\pi^0$-photoproduction off the deuteron within a simple pure resonance model.

Shallow Prismatic Shell in a Nonuniform Temperature Field

We study the thermal stressed state of a shallow prismatic shell composed of two flat elements. The analytic solutions of the problems of heat conduction and thermoelasticity are obtained by the method of finite integral transformations in the form of double series. The distributions of forces and moments along the coordinate lines are analyzed for different angles of inflection of the shell.

Electromagnetic break-up of nuclei with A = 3 ÷ 7

This talk contains a short review of some of the progresses made in the last three years in the calculations of electromagnetic cross sections of light nuclei up to A=7. Since many of them have been possible thanks to the use of the Lorentz Integral Transform (LIT) method, both for inclusive and exclusive reactions, I will first make a few remarks on the method, stressing its essential points and then show results for different nuclei. One of the interesting outcomes is e.g. the appearing of typical collective motion features from ab initio six-body calculations. When a comparison with available experimental data is attempted, it is rather disappointing to realize that low-energy data are old, incomplete and not accurate enough to disantangle interesting efforts, showing the need of a major experimental program in this direction, together with more theoretical efforts to implement modern realistic forces in continuum calculations of A⩾ 4 systems.

Electromagnetic break-up of nuclei with A = 3 ÷ 7

This talk contains a short review of some of the progresses made in the last three years in the calculations of electromagnetic cross sections of light nuclei up to A=7. Since many of them have been possible thanks to the use of the Lorentz Integral Transform (LIT) method, both for inclusive and exclusive reactions, I will first make a few remarks on the method, stressing its essential points and then show results for different nuclei. One of the interesting outcomes is e.g. the appearing of typical collective motion features from ab initio six-body calculations. When a comparison with available experimental data is attempted, it is rather disappointing to realize that low-energy data are old, incomplete and not accurate enough to disantangle interesting efforts, showing the need of a major experimental program in this direction, together with more theoretical efforts to implement modern realistic forces in continuum calculations of A⩾ 4 systems.

Integral transformation method for sedimentation behaviours of aggregates: Part I. α-Cyclodextrin/poly(ethyrene glycol)/water system

We tried to investigate concentration profiles of colloidal particles diffusing and settling down in aqueous media with a digital image processing and an integral transformation method. We proposed this method as an original one in previous papers. The definition of the method is shown as: I(t)=∫i(t,τ)×D(τ) dt , where I( t), i( t, τ) and D( τ) are phenomenological (response), elementary and distribution functions, respectively. The distributions of the characteristic length of concentration profiles were given by this method based on digital graphical image data. We have applied this method to sedimentation behaviours of α-cyclodextrin (α-CD)/poly(ethylene glycol) (PEG)/water systems. The obtained distribution curves of aggregates between CD–PEG complexes were changed as a function of time. In this paper, we could discuss also about relaxation times, τ sed for a sedimentation equilibrium of latex particles at various temperatures. We will briefly discuss about the different sedimentation behaviours between latex particles and CD–PEG complexes.

Effect ofP-wave interaction inHe6andLi6photoabsorption

The total photoabsorption cross sections of six-body nuclei are calculated including complete final state interaction via the Lorentz Integral Transform method. The effect of nucleon-nucleon central P-wave forces is investigated. Comparing to results with central potentials containg S-wave forces only one finds considerably more strength in the low-energy cross sections and a rather strong improvement in comparison with experimental data, in particular for 6Li.

A Mathematical Model of Geonavigation in Horizontal Well-boring Control Systems

A mathematical model for determination of the layer boundaries in the horizontal well-boring systems was considered, and a method to resolve it on the basis of the A.N. Tikhonov variational algorithms of determination of the extremal was proposed. The direct problem was solved by the combined method of integral transformations and integral equations.

Stoneley wave generation by an external seismic point source in an infinite fluid-filled borehole embedded in a transversely isotropic formation: Basic relationships

The method of integral transformations is used to obtain a long-wave solution to the problem of tube wave excitation by an external point source in an infinite fluid-filled borehole embedded in a transversely isotropic formation. The external field that occurs in the formation gives rise to waves in the borehole fluid. The waves generated in the borehole include the lowest mode of the Stoneley wave (tube wave), which is the borehole eigenmode, and the qP-and qSV-waves. It is shown that the Stoneley wave is determined by the contributions of two poles in the complex plane of horizontal slowness. According to the asymptotic solution, the Stoneley wave can be described by one of three different waveforms depending on the relationship between the elastic parameters of the surrounding anisotropic formation and the borehole fluid. An analysis of the results of calculations shows that the shape and polarity of the Stoneley wave strongly depend on the sign of the nonellipticity parameter of the elastic medium, which offers a possibility of estimating the anisotropy of the borehole environment from observations of the waveform of the Stoneley wave.

Mathematical problems in the integral-transformation method of dynamic crack

In the investigation on fracture mechanics, the potential function was introduced, and the moving differential equation was constructed. By making Laplace and Fourier transformation as well as sine and cosine transformation to moving differential equations and various responses, the dual equation which is constructed from boundary conditions lastly was solved. This method of investigating dynamic crack has become a more systematic one that is used widely. Some problems are encountered when the dynamic crack is studied. After the large investigation on the problems, it is discovered that during the process of mathematic derivation, the method is short of precision, and the derived results in this method are accidental and have no credibility. A model for example is taken to explain the problems existing in initial deriving process of the integral-transformation method of dynamic crack.

The non-stationary freefield response for a moving load with a random amplitude

This paper presents a stochastic solution procedure for the calculation of the non-stationary freefield response due to a moving load with a random amplitude. In this case, a non-stationary autocorrelation function and a time-dependent spectral density are required to characterize the response at a fixed point in the freefield. The non-stationary solution is derived from the solution in the case of a moving load with a deterministic amplitude. It is shown how the deterministic solution can be calculated in an efficient way by means of integral transformation methods if the problem geometry exhibits a translational invariance in the direction of the moving load. A key ingredient is the transfer function between the source and the receiver that represents the fundamental response in the freefield due to an impulse load at a fixed location. The solution in the case of a moving load with a random amplitude is formulated in terms of the double forward Fourier transform of the non-stationary autocorrelation function. The solution procedure is illustrated with an example where the non-stationary autocorrelation function and the time-dependent standard deviation of the freefield response are computed for a moving harmonic load with a random phase shift. The results are compared with the response in the deterministic case.

GPS fault detection and exclusion using moving average filters

A new approach based on the moving average (MA) is proposed to perform satellite failure detection and exclusion (FDE). By taking the average of the last few sums of the squares of the GPS range residual errors, the MA filter is applied to speed up failure detection. The detection threshold cannot be obtained directly because the cumulative distribution of a random process with an MA filter is unknown. Therefore, the Markov chain approach is applied to resolve the threshold. In addition, variations in the number of visible satellites may cause problems in data fusion. The probability integral transformation (PIT) method is adopted to overcome this. After a satellite failure is detected, the multivariate MA filter is used to reduce the incorrect exclusion rate (IER) by taking the average of the last few parity vectors. Simulation results show that, in comparison with the conventional least-squares-residuals method, the MA filter demonstrates higher performance in detecting small failures and a similar level of performance in detecting large failures. Moreover, simulation results also verify that the proposed method has lower IER than the conventional parity space method.

Fluid-solid coupling mathematical model of contaminant transport in unsaturated zone and its asymptotical solution

The process of contaminant transport is a problem of multicomponent and multiphase flow in unsaturated zone. Under the presupposition that gas existence affects water transport, a coupled mathematical model of contaminant transport in unsaturated zone has been established based on fluid-solid interaction mechanics theory. The asymptotical solutions to the nonlinear coupling mathematical model were accomplished by the perturbation and integral transformation method. The distribution law of pore pressure, pore water velocity and contaminant concentration in unsaturated zone has been presented under the conditions of with coupling and without coupling gas phase. An example problem was used to provide a quantitative verification and validation of the model. The asymptotical solution was compared with Faust model solution. The comparison results show reasonable agreement between asymptotical solution and Faust solution, and the gas effect and media deformation has a large impact on the contaminant transport. The theoretical basis is provided for forecasting contaminant transport and the determination of the relationship among pressure-saturation-permeability in laboratory.

Efficient Method for Lorentz Integral Transforms of Reaction Cross Sections

The Lorentz Integral Transform (LIT) method is reformulated via the Lanczos algorithm both for inclusive and exclusive reactions. The new technique is tested for the total photoabsorption cross section of 3H and 4He. Due to the rapid convergence of the algorithm one has a decrease in cpu time by two orders of magnitude, but at the same time an excellent agreement with the results of a conventional LIT calculation. The present work opens up the possibility of ab initio calculations for inclusive and exclusive processes for A greater equal 6 with inclusion of complete final state interactions.

Modelling the input–output behaviour of piezoelectric structural health monitoring systemsfor composite plates

This paper investigates the input–output characteristics of structural health monitoringsystems for composite plates based on permanently attached piezoelectric transmitter andsensor elements. Using dynamic piezoelectricity theory and a multiple integral transformmethod to describe the propagating and scattered flexural waves an electro-mechanicalmodel for simulating the voltage input–output transfer function for circular piezoelectrictransmitters and sensors adhesively attached to an orthotropic composite plate isdeveloped. The method enables the characterization of all three physical processes, i.e.wave generation, wave propagation and wave reception. The influence of transducer, plateand attached electrical circuit characteristics on the voltage output behaviourof the system is examined through numerical calculations, both in frequencyand the time domain. The results show that the input–output behaviour of thesystem is not properly predicted by the transducers’ properties alone. Couplingeffects between the transducers and the tested structure have to be taken intoaccount, and adding backing materials to the piezoelectric elements can significantlyimprove the sensitivity of the system. It is shown that in order to achieve maximumsensitivity, particular piezoelectric transmitters and sensors need to be designedaccording to the structure to be monitored and the specific frequency regime ofinterest.

Analysis on the cohesive stress at half infinite crack tip

The nonlinear fracture behavior of quasi-brittle materials is closely related with the cohesive force distribution of fracture process zone at crack tip. Based on fracture character of quasi-brittle materials, a mechanical analysis model of half infinite crack with cohesive stress is presented. A pair of integral equations is established according to the superposition principle of crack opening displacement in solids, and the fictitious adhesive stress is unknown function. The properties of integral equations are analyzed, and the series function expression of cohesive stress is certified. By means of the data of actual crack opening displacement, two approaches to gain the cohesive stress distribution are proposed through resolving algebra equation. They are the integral transformation method for continuous displacement of actual crack opening, and the least square method for the discrete data of crack opening displacement. The calculation examples of two approaches and associated discussions are given.

Amplitude-Energy Characteristics of Tsunami Waves for Various Types of Seismic Sources Generating Them

We perform a comparative analysis of the amplitude-energy characteristics of tsunami waves caused by seismic sources of four types. For the description of tsunami waves, we use linear equations of long waves. The deformations of the bottom of the ocean are found from the solution of a problem of elasticity theory for a half space regarded as a model of the lithosphere. The investigation is based on the analytic solutions obtained by the method of integral transformations.

THE DYNAMIC RESPONSE OF A ROTATING SHAFT SUBJECT TO AN AXIALLY MOVING AND ROTATING LOAD

The dynamic response of a rotating shaft subject to an axially, constant-velocity, moving and rotating load is investigated. The dynamic behaviour of future, high-speed linear bearings is studied. Shafts used in linear bearing applications are typically slender. Therefore, Rayleigh beam theory is used to model the rotating shaft. Modal analysis and integral transformation methods are employed to develop analytical expressions for the transient response of a shaft with simply supported boundary conditions. Numerical results are presented, discussed and compared with some available solutions. As shown in the paper, by changing model parameters, it is possible to describe dynamic behaviour of different types of linear bearings and other mechanical elements.

Transform methods—what can they contribute to (computational) dynamics?

In comparison to FEM or to time step procedures integral transform methods (ITM) have a very restricted domain for application. Under the condition however, that they can be used at all, they lead to a deeper understanding of the physical nature of the problem, they may allow to ameliorate existing computational techniques and they can be used to develop new approaches “on their own right”. The paper shows examples for illustration. After a short introduction of different well known transform techniques and respective operations in the original and the transformed domains, it deals with signal processing: In a first example different possibilities for the interpretation of time dependent signals in the original domain, in a Fourier or in a wavelet transformed domain are compared. After that the usefulness of ITM is illustrated in regard of reliability questions. It is shown that typical characteristics known for time depending signals exist in a comparable, however more general, manner also in regard of spatial relations for problems of half space dynamics. ITM does not only allow interpretations but –– e.g. for the half space dynamics –– it leads also to very efficient solution techniques, particularly for moving loads. It can be used also for the development of auxiliary techniques for FEM or BEM approaches. Finally also in stochastic dynamics it is applicable with great advantages.