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.

Optimum fifth order Stokes wave theory

This Paper improves the existing fifth order Stokes wave theory by using least Square method, and givesthe optimum result in the meaning of minimum error Squares to satisfy the free surface boundary conditions, and thewave profile can be adjusted according to the measured data. This paper also gives a simplified method for derivingthe parameters of the existing fifth order Stokes wave.

THE DISPLACEMENT WAVE THEORY OF BLOOD VESSEL

On the basis of the medical and mechanical analysis and explanations in this paper the visco-elastic simply supported beam model is proposed to treat the displacement wave of the blood vessels. The relationships between the displacement wave and blood vessel elasticity as well as the viscous dissipation of the blood and blood vessel are obtained. The corresponding relations of such kinds of pulses in the traditional Chinese medicine as smooth pulse, surface pulse and deep pulse to the displacement waves of blood vessels are also found. The computational results are in good agreement with those acquired in the experiments with ultrasonic wave.

Interpretation of living tissue's temperature oscillations by thermal wave theory

The fact that the temperature of living tissue may respond oscillatorily to externalheating has been a classical difficulty in the field of bioheat transfer for a long time.Roemer et al. have carefully discussed this in their serial articles, but experiments did notsupport their conclusions, Tharp et al. have artificially made a time-delay differential equs-tion to describe this phenomenon, but their model is short of a strict theoretical founda-

Study on pile drivability with one dimensional wave propagation theory

Pile drivability is a key problem during the stage of design and construction installation of pile foundations. The solution to the one dimensional wave equation was used to determine the impact force at the top of a concrete pile for a given ram mass, cushion stiffness, and pile impedance. The kinematic equation of pile toe was established and solved based on wave equation theory. The movements of the pile top and pile toe were presented, which clearly showed the dynamic displacement, including rebound and penetration of pile top and toe. A parametric study was made with a full range of practical values of ram weight, cushion stiffness, dropheight, and pile impedance. Suggestions for optimizing the parameters were also presented. Comparisons between the results obtained by the present solution and in-situ measurements indicated the reliability and validity of the method.

BASIC EQUATIONS AND WAVE THEORY OF GAS-LIQUID TWO-PHASE TRANSIENT FLOW

This paper systematically discussed the equations for two-phase transient flow and pressure wave and interfacial wave. The behaviour of basic equations was analyzed. The formulas for the wave speed of the pressure wave and the interfacial wave were derived. It was proved that various mathematical models can be uniformed by the integrating model and various wave speed formulas can be uniformed by the universal formula derived. The basic equations for the separated flow model are ill-conditioned because of the unreasonable neglect of the pressure differences between the phases and interfaces. Drift flux model can improve the accuracy if some additional equations are provided. The basic equations for homogeneous flow model are well-conditioned and they can be used in two-phase transient flow, especially in the cases of no velocity slips between various phases fluid.

A discussion on the double wave theory and its applications to description of radiation atoms

The double wave theory (DWT), sometimes called the“non_statistical quantum mechanics” by its proposer, describes the state of each single particle in an ensemble with two wave functions which have a parameter corresponding to the particle. However the basic postulates of the DWT show that this theory can hardly describe any quantum rules of the microscopic world. In the double wave descriptions, the wave feature of the behavior of microscopic particles and the discontinuity characteristic of energy almost disappear. The discussions on several problems of the radiation atoms made by the DWT's proposer on the basis of this theory are either mathematically incorrect or inconsistent with experiments and the usual theory.

THE APPLICATION OF COKELET'S WAVE THEORY IN THE CALCULATION OF WAVE-CURRENT FIELD

By using Cokelet's wave theory,the limiting wave height and the relative wave angular frequency in wave-current field were calculated in this paper.It is indicated by numeri- cal calculation that if the water depth is not too small,the result given by authors'calculation are very close to the results of limiting wave height by Dalrymple(1975)and to the data of rel- ative wave angular frequency by linear wave theory;but if water depth is rather small,there are some discrepancy,

Study of algorithms of new slender ship theory of wave resistance

In this paper, Noblesse's New Slender-Ship Wave-Making Theory was investigated numerically. Detailed expressions of zeroth and lst order wave resistance have been derived and calculation programs have also been compiled. In the single and double integral terms of Green function, the kernel function of wave resistance expression, special function expansion method and Chebyshev polynomials approach have been adopted respectively, which greatly simplify the calculation and increase the convergence speed.

Failure analysis of polycrystalline diamond compact cutters for breaking rock by bending waves theory

The breakage mechanism of the polycrystalline diamond compact(PDC) cutters was analyzed by the energy theory of bending waves. The cutting tests of granite block were conducted on a multifunctional testing device by using the cutter at three kinds of negative fore angles of 30°, 45° and 60°. The results show that, when the edge of the PDC layer is broken, the layer of tungsten cobalt is broken a little under the angle of 30°, while the layer of tungsten cobalt is broken continuously under the angle of 60°, their maximum depths are about 2 and 7 mm respectively in the two cases. The eccentric distance mainly depends on the negative fore angle of the cutter. When the cutter thrusts into the rock under an attack angle of 60°, the energy of bending waves reaches the maximum since the eccentric distance is the maximum. So the damage of cutter is the most serious. This test result is consistent with the conclusion of theoretical analysis well. The eccentric distance from the axial line of cutter to the point of action between the rock and cutter has great effect on the breakage of the cutter. Thus during the process of cutting, the eccentric distance should be reduced to improve the service life of PDC cutters.

Derivation of Multiverse from Universal Wave Function Interpretation of String Theory

The multiverse is a hypothesis created to solve certain problems in cosmology. Currently, this scheme is still largely ad hoc, rather than derived from fundamental laws and principles. Because of this, the predictive power of this theory is rather limited. Furthermore, there are concerns that this theory will make it impossible to calculate some measured quantities, such as the masses of quarks and the electron. In this paper, we will show that a new development in string theory, the universal wave function interpretation of string theory, provides a way to derive the mathematical expression of the multiverse. We will demonstrate that the Weyl invariance existing in string theory indicates that our observed universe is a projection from a hologram. We will present how the laws of physics can be derived from this fact. Furthermore, we suggest it may also provide a way to calculate the masses of fundamental particles such as quarks and the electron.

Inflation Scheme Derived from Universal Wave Function Interpretation of String Theory

Inflation is the most commonly accepted theory in cosmology to explain why the universe appears flat, homogeneous, and isotropic, as well as the origin of the large-scale structure of the cosmos and why no magnetic monopoles have been detected. However, so far, the origin of the inflation epoch and what is the hypothetical field, the inflation, giving rise to inflation, remains unknown. String theory is one of the promising candidates for the grand unification theory. Grand unification theory is to use one mathematic formula to describe everything. In this work, we study the inflation scheme in a new development in string theory, UWFIST （universal wave function interpretation of string theory）. We show that from UWFIST we can derive from the fundamental theory that the long-range vibration is the possible candidate of inflation. We estimate the vacuum energy created by the long-range vibration and show that it can indeed drive the inflation.

High-Frequency Guided Wave Scattering by a Partly Through-Thickness Hole Based on 3D Theory

We present a theoretical investigation of the scattering of high frequency S0 Lamb mode from a circular blind hole defect in a plate based on the 3D theory. The SO wave is incident at the frequency above the A1 mode cut-off frequency, in which the popular approximate plate theories are inapplicable. Due to the non-symmetric blind hole defect, the scattered fields will contain higher order converted modes in addition to the fundamental SO and AO modes. The far-field scattering amplitudes of various propagating Lamb modes for different hole sizes are inspected. The results are compared with those of lower frequencies and some different phenomena are found. Two-dimensional Fourier transform （2DFT） results of transient scattered Lamb and SH wave signals agree well with the analytical dispersion curves, which check the validity of the solutions from another point of view.

Suppression of Wave-Excited Vibration of Offshore Platform by Use of Tuned Liquid Dampers

This paper describes experimental and theoretical investigations of Tuned Liquid Damper (TLD) characteristics for suppressing the wave-excited structural vibration. The structural model for the experiments is scaled according to a full size offshore platform by matching their dynamic properties. Rectangular TLDs of different sizes with partially filled liquid are examined. By observing the performance and behavior of TLDs through laboratory experiments, the Study investigates the influence of a number of parameters, including container size, container shape, frequency ratio, and incident wave characteristics. In an analytical study, a mathematical model that describes the nonlinear behavior of liquid in TLD and the interaction of TLD and structure is prerequisite. The validity of the model is evaluated and simulating results can reasonably match the corresponding experimental results.

Oblique Water Wave Scattering by Bottom Undulation in a Two-layer Fluid Flowing Through a Channel

The problem of oblique wave （internal wave） propagation over a small deformation in a channel flow consisting of two layers was considered. The upper fluid was assumed to be bounded above by a rigid lid, which is an approximation for the free surface, and the lower one was bounded below by an impermeable bottom surface having a small deformation; the channel was unbounded in the horizontal directions. Assuming irrotational motion, the perturbation technique was employed to calculate the first-order corrections of the velocity potential in the two fluids by using Green＇s integral theorem suitably with the introduction of appropriate Green＇s functions. Those functions help in calculating the reflection and transmission coefficients in terms of integrals involving the shape ftmction c（x） representing the bottom deformation. Three-dimensional linear water wave theory was utilized for formulating the relevant boundary value problem. Two special examples of bottom deformation were considered to validate the results. Consideration of a patch of sinusoidal ripples （having the same wave number） shows that the reflection coefficient is an oscillatory function of the ratio of twice the x-component of the wave number to the ripple wave number. When this ratio approaches one, the theory predicts a resonant interaction between the bed and the interface, and the reflection coefficient becomes a multiple of the number of ripples. High reflection of incident wave energy occurs if this number is large. Similar results were observed for a patch of sinusoidal ripples having different wave numbers. It was also observed that for small angles of incidence, the reflected energy is greater compared to other angles of incidence up to π/ 4. These theoretical observations are supported by graphical results.

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.

Lateral wave-field stacking of seismic Fresnel zones for the generalized-offset case

To unify different seismic geometries, the concept of generalized offset is defined and the expressions for Fresnel zones of different order on a plane are presented. Based on wave theory, the equation of the lateral wave-field stacking for generalized-offset Fresnel zones is derived. For zero and nonzero offsets, the lateral stacking amplitude of diffraction bins of different sizes is analyzed by referring to the shape of the Fresnel zones of different order. The results suggest the following. First, the contribution of diffraction bins to wave- field stacking is related to the offset, surface relief, interface dip, the depth of the shot point to the reflection interface, the observational geometry, and the size of the interference stacking region. Second, the first-order Fresnel zone is the main constructive interference, and its contribution to the reflection amplitude is slightly smaller than half the contribution of all Fresnel zones. Finally, when the size of the diffraction bin is smaller than the first- order Fresnel zone, the larger the size of the diffraction bin, the larger is the amplitude of the receiver, even in the nonzero offset-case.

Theoretical and numerical investigation of HF elastic wave propagation in two-dimensional periodic beam lattices

The elastic wave propagation phenomena in two-dimensional periodic beam lattices are studied by using the Bloch wave transform. The numerical modeling is applied to the hexagonal and the rectangular beam lattices, in which, both the in-plane （with respect to the lattice plane） and out-of-plane waves are considered. The dispersion relations are obtained by calculating the Bloch eigenfrequencies and eigenmodes. The frequency bandgaps are observed and the influence of the elastic and geometric properties of the primitive cell on the bandgaps is studied. By analyzing the phase and the group velocities of the Bloch wave modes, the anisotropic behaviors and the dispersive characteristics of the hexagonal beam lattice with respect to the wave prop- agation are highlighted in high frequency domains. One im- portant result presented herein is the comparison between the first Bloch wave modes to the membrane and bend- ing/transverse shear wave modes of the classical equivalent homogenized orthotropic plate model of the hexagonal beam lattice. It is shown that, in low frequency ranges, the homog- enized plate model can correctly represent both the in-plane and out-of-plane dynamic behaviors of the beam lattice, its frequency validity domain can be precisely evaluated thanks to the Bloch modal analysis. As another important and original result, we have highlighted the existence of the retro- propagating Bloch wave modes with a negative group veloc- ity, and of the corresponding ＂retro-propagating＂ frequency bands.

Third-Order Stokes Wave Solutions of the Free Surface Capillary- Gravity Wave and the Interfacial Internal Wave

Based on the Stokes wave theory, the capillary-gravity wave and the interfacial internal wave in two-layer constant depth＇s fluid system are investigated. The fluids are assumed to be incompressible, inviscid and irrotational. The third-order Stokes wave solutions are given by using a perturbation method. The results indicate that the third-order solutions depend on the surface tension, the density and the depth of each layer. As expected, the first-order solutions are the linear theoretical results （the small amplitude wave theoretical results）. The second-order and the third-order solutions describe the nonlinear modification and the nonlinear interactions. The nonlinear impact appears not only in the n （n〉~2） times＇ high frequency components, but also in the low frequency components. It is also noted that the wave velocity depends on the wave number, depth, wave amplitude and surface tension.

Undulatory Theory with Paraconsistent Logic (Part II): Schrödinger Equation and Probability Representation

Part I of this study proved that the Paraconsistent Annotated Logic using two values (PAL2v), known as the Paraquantum Logic (PQL), can represent the quantum by a model comprising two wave functions obtained from interference phenomena in the 2W (two-wave) region of Young’s experiment (double slit). With this model represented in one spatial dimension, we studied in the Lattice of the PQL, with their values represented in the set of complex numbers, the state vector of unitary module and its correspondence with the two wave functions. Based on these considerations, we applied the PQL model for obtaining Paraquantum logical states ψ related to energy levels, following the principles of the wave theory through SchrÖdinger’s equation. We also applied the probability theory and Bonferroni’s inequality for demonstrating that quantum wave functions, represented by evidence degrees, are probabilistic functions studied in the PQL Lattice, confirming that the final Paraquantum Logic Model is well suited to studies involving aspects of the wave-particle theory. This approach of quantum theory using Paraconsistent logic allows the interpretation of various phenomena of Quantum Mechanics, so it is quite promising for creating efficient models in the physical analysis and quantum computing processes.