Apresentamos alguns métodos numéricos para a resolução das equações hiperbólicas que regem problemas de transporte de cargas elétricas em isolantes, aplicando-os a quatro problemas específicos: injeção de corrente por um contato ôhmico em uma amostra com voltagem constante aplicada; transporte de um pulso de cargas através de uma amostra em circuito aberto; transporte de um pulso de cargas através de uma amostra submetida a uma diferença de potencial constante (tempo de vôo); e, finalmente, descarga termo-estimulada em circuito aberto. Empregamos, basicamente, dois tipos de métodos: características e diferenças finitas. Concluímos que, quando as descontinuidades são importantes, é mais conveniente usar o método das características; porém, quando não houver descontinuidades ou se estas não forem importantes, alguns métodos de diferenças finitas podem ser utilizados com boa precisão e menores tempos de computação do que aqueles gastos pelos métodos das características. / Numeral methods for solving partial differential equations of the hiperbolic type, governing some problems of transport of electric charge in dielectrics are presented and then applied to four specific problems: injection of charge via an ohmic contact into a sample with a constant applied voltage; transport of a pulse of charge through a sample in the open circuit mode; transport of a pulse of charge through a sample subjected to a constant voltage; and finally, thermally stimulated discharge in open circuit. Essentially two kinds of methods are employed: the method of characteristics and finite-difference methods. It is concluded that when discontinuities are important, the method of characteristics is the most convenient; otherwise, appropriate finite-difference schemes can be used with sufficient precision and less time expenses in computers.

Landslides cause significant damage to property and human lives throughout the world. Rainfall is the most common triggering factor for the occurrence of landslides. This dissertation presents two novel methodologies for assessment of rainfall-triggered shallow landslide hazard. The first method focuses on using remotely sensed soil moisture and soil surface properties in developing a framework for real-time regional scale landslide hazard assessment while the second method is a deterministic approach to landslide hazard assessment of the specific sites identified during first assessment. In the latter approach, landslide inducing transient seepage in soil during rainfall and its effect on slope stability are modeled using numerical analysis. Traditionally, the prediction of rainfall-triggered landslides has been performed using pre-determined rainfall intensity-duration thresholds. However, it is the infiltration of rainwater into soil slopes which leads to an increase of porewater pressure and destruction of matric suction that causes a reduction in soil shear strength and slope instability. Hence, soil moisture, pore pressure and infiltration properties of soil must be direct inputs to reliable landslide hazard assessment methods. In-situ measurement of pore pressure for real-time landslide hazard assessment is an expensive endeavor and thus, the use of more practical remote sensing of soil moisture is constantly sought. In past studies, a statistical framework for regional scale landslide hazard assessment using remotely sensed soil moisture has not been developed. Thus, the first major objective of this study is to develop a framework for using downscaled remotely sensed soil moisture available on a daily basis to monitor locations that are highly susceptible to rainfall- triggered shallow landslides, using a well-structured assessment procedure. Downscaled soil moisture, the relevant geotechnical properties of saturated hydraulic conductivity and soil type, and the conditioning factors of elevation, slope, and distance to roads are used to develop an improved logistic regression model to predict the soil slide hazard of soil slopes using data from two geographically different regions. A soil moisture downscaling model with a proven superior prediction accuracy than the downscaling models that have been used in previous landslide studies is employed in this study. Furthermore, this model provides satisfactory classification accuracy and performs better than the alternative water drainage-based indices that are conventionally used to quantify the effect that elevated soil moisture has upon the soil sliding. Furthermore, the downscaling of soil moisture content is shown to improve the prediction accuracy. Finally, a technique that can determine the threshold probability for identifying locations with a high soil slide hazard is proposed. On the other hand, many deterministic methods based on analytical and numerical methodologies have been developed in the past to model the effects of infiltration and subsequent transient seepage during rainfall on the stability of natural and manmade slopes. However, the effects of continuous interplay between surface and subsurface water flows on slope stability is seldom considered in the above-mentioned numerical and analytical models. Furthermore, the existing seepage models are based on the Richards equation, which is derived using Darcy’s law, under a pseudo-steady state assumption. Thus, the inertial components of flow have not been incorporated typically in modeling the flow of water through the subsurface. Hence, the second objective of this study is to develop a numerical model which has the capability to model surface, subsurface and infiltration water flows based on a unified approach, employing fundamental fluid dynamics, to assess slope stability during rainfall-induced transient seepage conditions. The developed model is based on the Navier-Stokes equations, which possess the capability to model surface, subsurface and infiltration water flows in a unified manner. The extended Mohr-Coulomb criterion is used in evaluating the shear strength reduction due to infiltration. Finally, the effect of soil hydraulic conductivity on slope stability is examined. The interplay between surface and subsurface water flows is observed to have a significant impact on slope stability, especially at low hydraulic conductivity values. The developed numerical model facilitates site-specific calibration with respect to saturated hydraulic conductivity, remotely sensed soil moisture content and rainfall intensity to predict landslide inducing subsurface pore pressure variations in real time.

In mammalian hearts, initiation of the heartbeat occurs in a region of specialised pacemaker cells known as the sinoatrial node (SAN). The SAN is a highly complex spatially distributed structure which displays considerable cellular heterogeneity and is subject to complex electrotonic interactions with the surrounding atrial tissue. In this study, biophysically detailed ionic models of central and peripheral SAN pacemaker cells are described. These models are able to accurately reproduce experimental recordings of the membrane potential from central and peripheral SAN tissue. These models are used to investigate frequency synchronisation of electrically coupled cardiac pacemaker cells. Based on simulation results presented, it is proposed that cellular heterogeneity in the SAN plays an important role in achieving rhythm coordination and possibly contributes to the efficient activation of the surrounding atrial myocardium. This represents an important, previously unexplored, mechanism underlying pacemaker synchronisation and cardiac activation in vivo. A spatial-gradient model of action potential heterogeneity within the SAN is then formulated using a large-scale least squares optimisation technique. This model accurately reproduces the smooth spatial variation in action potential characteristics observed in the SAN. One and two dimensional models of the intact SAN are then formulated and three proposed models of SAN heterogeneity are investigated: 1) the discrete-region model, in which the SAN consists of a compact central region surrounded by a region of transitional pacemaker cells, 2) the gradient model, in which cells of the SAN exhibit a smooth variation in properties from the centre to the periphery of the SAN, and 3) the mosaic model, in which SAN and atrial cells are scattered throughout the SAN region with the proportion of atrial cells increasing towards the periphery. Simulation results suggest that the gradient model achieves frequency entrainment more easily than the other models of SAN heterogeneity. The gradient model also reproduces action potential waveshapes and a site of earliest activation consistent with experimental observations in the intact SAN. It is therefore proposed that the gradient model of SAN heterogeneity represents the most plausible model of SAN organisation.

A hybrid FEM/FDM algorithm for particle migration of quasi-steady flow in concentrated suspension materials is proposed in this study. This hybrid FEM/FDM algorithm in which the planar variables, such as pressure field, are described in terms of finite element method, and gapwise variables of temperature, density concentration and time derivatives are expressed by finite difference method. The particle concentration inhomogeneities can be predicted, which is ignored by the existing injection molding simulation packages. Simulation results indicated that powder concentration variation could be significant in practical processing in PIM. / Singapore-MIT Alliance (SMA)

Liquid sloshing with unrestrained free surface in a moving container is associated with various engineering problems, such as tankers on highways, liquid oscillations in large storage tanks caused by earthquakes, sloshing of liquid cargo in ocean-going vessels, and the motion of liquid fuel in aircraft and spacecraft. The purpose of this study is to develop a three-dimensional (3D) numerical wave tank with or without internal structures to investigate the mechanism of liquid sloshing and the interaction between the fluid and internal structures. The developed 3D time-independent finite difference method is applied on solving liquid sloshing in tanks with or without the influence of baffles under the ground motion of six-degrees of freedom. The 3D Navier-Stokes equations were solved and transformed to a tank-fixed coordinate system, and the fully nonlinear kinematic and dynamic free surface boundary conditions for fluid sloshing in a rectangular tank with a square base were considered. The fluid is assumed incompressible in this study. The complicated interaction in the vicinity of the fluid-structure interface was solved by implementing one dimensional ghost cell approach and the stretching grid technique near the fluid-structure boundaries were used to catch the detailed evolution of local flow field. A PC-cluster was established by linking several single computers to reduce the computational times due to the implementation of the 3D numerical model. The Message Passing Interface (MPI) parallel language and MPICH2 software were utilized to code the computer codes and to carry out the circumstance of parallel computation, respectively. The developed numerical scheme was verified by rigorous benchmark tests. Not only the reported analytical, numerical and experimental studies were compared with the present numerical results, the experimental investigation was also involved in the present work to further validate the accuracy of the numerical scheme. All the benchmark tests of this study showed excellent accuracy of the developed numerical scheme. For a tank without internal structures, the coupled motions of surge and sway are simulated with various excitation angles, excitation frequencies and water depths. The characteristics of sloshing waves are dissected in terms of the classification of sloshing wave types, sloshing amplitude, beating phenomenon, sloshing-induced forces and energy transfer of sloshing waves. Six types of sloshing waves, named single-directional, diagonal, square-like, swirling-like, swirling and irregular waves, were found and classified in the present study and the occurrence of these waves are tightly in connection with the excitation frequency of the tank. The effect of excitation angle on the characteristics of sloshing waves is explored and discussed, especially for swirling waves. The spectral analyses of sloshing displacement of various sloshing waves are examined and a clear evidence of the correlation between sloshing wave patterns and resonant modes of sloshing waves are demonstrated. The mechanism of switching direction of swirling waves is discussed by investigating the situation of circulatory flow, the instantaneous free surface, the gravitational effect and the instantaneous direction of external forcing. The coupling effects of heave, surge and sway motions were also included in this study and the result showed an unstable influence of heave motion on the kinematic and dynamic characteristics of sloshing waves when the vertical excitation frequency of the tank is twice as large as the fundamental natural frequency. Except irregular waves, the other types of sloshing waves are converted into swirling waves due to the effect of heave motion. The study related to tuned liquid damper (TLD) in 2D and 3D tanks were considered. A comprehensive investigation for a 2D tank with vertically tank bottom-mounted baffles (baffled tank) are demonstrated and discussed with respect to the influence of baffle height on the natural mode of the tank, the evolution of vortices and vortex shedding phenomenon, the relationship between the vortex shedding frequency and the excitation frequency of the tank, the vortex size generated in the vicinity of the baffle tip, the interaction of vortices inside the tank. The baffle height shows a significant influence on the shift of the first natural frequency of the baffled tank and the liquid depth also plays an important part in determining this influence. In other words, the shift of the first natural mode due to various baffle height is varied with water depths. The design of two baffles separated by 0.2 times the tank breadth is an efficient tool to not only reduce the sloshing amplitude but switch the first natural frequency of the tank. The sloshing displacement is affected distinctly by different numbers of baffles mounted vertically on the tank bottom. The more baffles mounted onto the tank bottom, the smaller the sloshing displacement is presented in both the transient and steady-state periods. The processes of the evolution of vortices near the baffle tip are categorized into four phases: the formation of separated shear layer and generation of vortices, the formation of a vertical jet and shedding of vortices, the interaction between shedding vortices and sloshing flow (the generation of snaky flow) and the interaction between snaky flow and sloshing waves. Vortex shedding phenomenon due to stronger vertical jets occurs when the excitation frequency is close to the first natural mode of the baffled tank. The size of the vortex generated near the baffle tip is discussed and the vortex size is closely correlated with the baffle height. Two types of 3D tuned liquid dampers, a vertically tank bottom-mounted baffle and a vertical plate, are discussed for a tank under coupled surge-sway motions. The wave types of diagonal and single-directional waves switch to the swirling type due to the influence of the baffle. The phenomenon of square-like waves or irregular waves coexisting with swirling waves is found in the baffled tank under diagonal excitation. The baffle and the vertical plate mounted parallel to the east (west) wall of the tank can effectively reduce the sloshing amplitude when the excitation angle is between 0 degree and 10 degree and the corresponding sloshing displacement in the sway (z) direction becomes more dominant with the increase of the excitation angle. The shift of the first natural mode of the baffled tank due to various baffle heights in the x direction is dominated in this design of baffled tank. The length of the plate can cause a significant influence on not only the variation of the natural frequencies but the type of the sloshing waves. The influence of the vertical plate on the irregular waves is insignificant and several peaks appear in the spectral analysis of the sloshing displacement for the irregular waves and the numbers of peaks are more than that of the baffled tank.

In geothermal reservoirs and unconventional gas reservoirs with very low matrix permeability, fractures are the main routes of fluid flow and heat transport, so the fracture permeability change is important. In fact, reservoir development under this circumstance relies on generation and stimulation of a fracture network. This thesis presents numerical simulation of the response of a fractured rock to injection and extraction considering the role of poro-thermoelasticity and joint deformation. Fluid flow and heat transport in the fracture are treated using a finite difference method while the fracture and rock matrix deformation are determined using the displacement discontinuity method (DDM). The fractures response to fluid injection and extraction is affected both by the induced stresses as well as by the initial far-field stress. The latter is accounted for using the non-equilibrium condition, i.e., relaxing the assumption that the rock joints are in equilibrium with the in-situ stress state. The fully coupled DDM simulation has been used to carry out several case studies to model the fracture response under different injection/extractions, in-situ stresses, joint geometries and properties, for both equilibrium and non-equilibrium conditions. The following observations are made: i) Fluid injection increases the pressure causing the joint to open. For non-isothermal injection, cooling increases the fracture aperture drastically by inducing tensile stresses. Higher fracture aperture means higher conductivity. ii) In a single fracture under constant anisotropic in-situ stress (non-equilibrium condition), permanent shear slip is encountered on all fracture segments when the shear strength is overcome by shear stress in response to fluid injection. With cooling operation, the fracture segments in the vicinity of the injection point are opened due to cooling-induced tensile stress and injection pressure, and all the fracture segments experience slip. iii) Fluid pressure in fractures increases in response to compression. The fluid compressibility and joint stiffness play a role. iv) When there are injection and extraction in fractured reservoirs, the cooler fluid flows through the fracture channels from the injection point to extraction well extracting heat from the warmer reservoir matrix. As the matrix cools, the resulting thermal stress increases the fracture apertures and thus increases the fracture conductivity. v) Injection decreases the amount of effective stress due to pressure increase in fracture and matrix near a well. In contrast, extraction increases the amount of effective stress due to pressure drop in fracture and matrix.

This thesis analyses the governing equation of elastic wave propagation by the finite difference method , and considered absorbing boundary condition and the material damping to simulate behavior of wave propagation. Otherwise, we combined with the mechanics of the soil pore water pressure raised by shear stress effected repeatedly and the soil property is changed by water pressure effected to simulate physical phenomenon in half-space, and probe into the soil liquefaction process during different force types. Using the developed numerical wave propagation model probe into reducing vibration by dug trench and filler trench, and analyzed data by 1/3 octave band method. This thesis discuss with reducing vibration effect by different trench disposed¡Bdifferent filler material property, complex filler, and extending the force source pile length.

No description available.

Recently the computational speed and the functions of the numerical methods are advancing rapidly. It is the future trend that using the computational fluid dynamics (CFD) to perform simulation for making up the experimental deficiency, reducing the risk, improving the quality of the product, and saving the cost of research and development. A two-dimensional simulation was employed to study the melt/air and melt/solid interface shapes of the miniature molten zone formed in the laser-heated pedestal growth (LHPG) system. Using non-orthogonal body-fitting grid system with control-volume finite difference method, the interface shape can be determined both efficiently and accurately. During stable growth, the dependence of the molten-zone length and shape on the heating CO2 laser is examined in detail under both the maximum and the minimum allowed powers with various growth speeds. The effect of gravity for the miniature molten zone is also simulated, which reveals the possibility for a horizontally oriented LHPG system. Such a horizontal system is good for the growth of long crystal fibers. After comparing with the shape of the molten zone in terms of the experiment and the analysis of the simulation shown as above. Heat transfer and fluid flow in the LHPG system are analyzed near the deformed interfaces. The global thermal distributions of the crystal fiber, the melt, and the source rod are described by temperature and its axial gradient within length of ~10 mm. As compared with the growth of bulk crystal of several centimeters in dimension, natural convection drops six orders in magnitude due to smaller melt volume; therefore, conduction rather than convection determines the temperature distribution in the molten zone. Moreover, thermocapillary convection rather than mass-transfer convection becomes dominant. The symmetry and mass flow rate of double eddy pattern are significantly influenced by the molten-zone shape due to the diameter reduction and the large surface-tension-temperature coefficient in the order of 10-4~10-3. According to the analysis shown as above, the results could be further extended for the analysis of the concentration profile and study of horizontal growth.

Disertacijoje išnagrinėta trečiosios eilės vienmatė pseudoparabolinė lygtis su dviejų tipų nelokaliosiomis sąlygomis. Šiems uždaviniams spręsti sudarytos skirtuminės schemos, kurių stabilumas tiriamas, taikant skirtuminių operatorių su nelokaliosiomis sąlygomis spektro struktūrą. Trečiosios eilės vienmatėms ir dvimatėms pseudoparabolinėms lygtims su integralinėmis sąlygomis sudarytos ir išnagrinėtos padidinto tikslumo skirtuminės schemos. Išnagrinėta dvimatė pseudoparabolinė lygtis su nelokaliosiomis integralinėmis sąlygomis viena koordinačių kryptimi. Tokiam uždaviniui spręsti pritaikytas ir išnagrinėtas lokaliai vienmatis metodas, ištirtos šio metodo stabilumo sąlygos. Taip pat išnagrinėtos: trisluoksnės skirtuminės schemos vienmatei pseudoparabolinei lygčiai su įvairiomis, taip pat ir nelokaliosiomis, sąlygomis; trisluoksnių išreikštinių skirtuminių schemų stabilumo sąlygos. / The thesis analyzes the third-order one-dimensional pseudoparabolic equations with two types of nonlocal conditions. The stability of difference schemes for this problem was studied using the analysis of the spectrum structure of a difference operator with nonlocal conditions. The analysis of the increased accuracy difference schemes for third-order one-dimensional and two-dimensional pseudoparabolic equations with integral conditions has been made. The thesis considers a two-dimensional pseudoparabolic equation with nonlocal integral conditions in one coordinate direction. This problem was solved by a locally one-dimensional method. The stability of a difference scheme has been investigated based on the spectrum structure. The doctoral disertation investigates three-layer difference schemes for one-dimensional pseudoparabolic equations with various, including nonlocal, conditions. Also, the conditions for the stability of three-layer explicit difference schemes have been explored.