Yes / The existing analytical solutions of dam-break flow do not consider simultaneously the effects of wet downstream bottom and bed slope on the dam-break wave propagation. In this study, a new analytical solution for the shallow-water equations (SWE) is developed to remove this limitation to simulate the wave caused by an instantaneous dam-break. The approach adopts the method of characteristics and has been applied to simulate the dam-break flows with different downstream water depths and slopes. The analytical solutions have been compared with predictions by the lattice Boltzmann method and the agreement is good. Although the proposed analytical solution treats an idealized case, it is nonetheless suitable for assessing the robustness and accuracy of numerical models based on the SWE without the frictional slope. / The National Key Research and Development Program of China (Grant No: 2018YFC1505000), National Natural Science Foundation of China (Grant Nos: 51879179; 51579166) and Sichuan Science and Technology Program (No. 2019JDTD0007); Open Fund from the State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University (SKHL1809). .

Yes / Physics-based skin deformation methods can greatly improve the realism of character animation, but require non-trivial training, intensive manual intervention, and heavy numerical calculations. Due to these limitations, it is generally time-consuming to implement them, and difficult to achieve a high runtime efficiency. In order to tackle the above limitations caused by numerical calculations of physics-based skin deformation, we propose a simple and efficient analytical approach for physics-based skin deformations. Specifically, we (1) employ Fourier series to convert 3D mesh models into continuous parametric representations through a conversion algorithm, which largely reduces data size and computing time but still keeps high realism, (2) introduce a partial differential equation (PDE)-based skin deformation model and successfully obtain the first analytical solution to physics-based skin deformations which overcomes the limitations of numerical calculations. Our approach is easy to use, highly efficient, and capable to create physically realistic skin deformations. / This research is supported by the PDE-GIR project which has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement (No.778035), the National Natural Science Foundation of China (Grant No.51475394), and Innovate UK (Knowledge Transfer Partnerships KTP.010860). Shaojun Bian is also supported by Chinese Scholar Council. Xiaogang Jin is supported by the Key Research and Development Program of Zhejiang Province (No.2018C01090) and the National Natural Science Foundation of China (No.61732015).

Yes / We provide multi-factor real option models (and quasi-analytical solutions) for equipment capital budgeting under uncertainty, when there is either unexpected, or anticipated, or uncertain (volatile) technological progress. We calculate the threshold level of revenues and operating costs using the incumbent equipment that would justify replacement. Replacement is deferred for lower revenue thresholds. If progress is anticipated or highly uncertain, alert financial managers should wait longer before replacing equipment. Replacement deferral increases with decreases in the expected correlation between revenue and operating costs, and with increases in the revenue and/or operating cost volatility. Uncertain technological progress increases the real option value of waiting. The best approach for equipment suppliers is to reduce the expected revenue and/or cost volatility, and/or reduce the expected uncertainty of technological innovations, since then an incentive exists for the early replacement of old equipment when a technologically advanced version is launched.

The main goal of this work is to determine values of elastic constants of orthotropic, transversely isotropic and cubic materials through indentation tests on thin layers bonded to rigid substrates. Accordingly, we first use the Stroh formalism to provide an analytical solution for generalized plane strain deformations of a linear elastic anisotropic layer bonded to a rigid substrate, and indented by a rigid cylindrical indenter. The mixed boundary-value problem is challenging since the deformed indented surface of the layer contacting the rigid cylinder is unknown a priori, and is to be determined as a part of the solution of the problem. For a rigid parabolic prismatic indenter contacting either an isotropic layer or an orthotropic layer, the computed solution is found to compare well with solutions available in the literature. Parametric studies have been conducted to delimit the length and the thickness of the layer for which the derived relation between the axial load and the indentation depth is valid. We then derive an expression relating the axial load, the indentation depth, and the elastic constants of an orthotropic material. This relation is specialized to a cubic material (e.g., an FCC single crystal). By using results of three virtual (i.e., numerical) indentation tests on the same specimen oriented differently, we compute values of the elastic moduli, and show that they agree well with their expected values. The technique can be extended to other anisotropic materials. We review the literature on relations between deformations at the atomic level and stresses and strains defined at the continuum level. These are then used to compare stress and strain distributions in mechanical tests performed on atomic systems and their equivalent continuum structures. Whereas averaged stresses and strains defined in terms of the overall deformations of the atomic system match well with those derived from the continuum description of the body, their local spatial distributions differ. / Ph. D.

No description available.

No description available.

Vazamentos em tubos pressurizados geram ondas acústicas que se propagam através das paredes destes tubos, as quais podem ser captadas por acelerômetros ou por sensores de emissão acústica. O conhecimento de como estas paredes podem vibrar, ou de outro modo como as ondas acústicas se propagam neste meio, é fundamental em um processo de detecção e localização da fonte de vazamento. Neste trabalho, foi implementado um modelo analítico, através das equações de movimento da casca cilíndrica, com o objetivo de entender o comportamento da superfície do tubo em função de uma excitação pontual. Como a superfície cilíndrica é um meio fechado na direção circunferencial, ondas que iniciaram sua jornada, a partir de uma fonte pontual sobre a superfície, se encontrarão com outras que já completaram a volta na casca cilíndrica, tanto no sentido horário como no anti-horário, gerando interferências construtivas e destrutivas. Após um tempo suficiente, uma estacionariedade é atingida, criando pontos de picos e vales na superfície da casca, os quais podem ser visualizadas através de uma representação gráfica do modelo analítico criado. Os resultados teóricos foram comprovados através de medidas realizadas em uma bancada de testes composta de um tubo de aço terminado em caixa de areia, simulando a condição de tubo infinito. Para proceder à localização da fonte pontual sobre a superfície, adotou-se o processo de solução inversa, ou seja, conhecidos os sinais dos sensores dispostos na superfície do tubo, determina-se através do modelo teórico onde a fonte que gerou estes sinais pode estar. / Leaks in pressurized tubes generate acoustic waves that propagate through the walls of these tubes, which can be captured by accelerometers or by acoustic emission sensors. The knowledge of how these walls can vibrate, or in another way, how these acoustic waves propagate in this material is fundamental in the detection and localization process of the leak source. In this work an analytic model was implemented, through the motion equations of a cylindrical shell, with the objective to understand the behavior of the tube surface excited by a point source. Since the cylindrical surface has a closed pattern in the circumferential direction, waves that are beginning their trajectory will meet with another that has already completed the turn over the cylindrical shell, in the clockwise direction as well as in the counter clockwise direction, generating constructive and destructive interferences. After enough time of propagation, peaks and valleys in the shell surface are formed, which can be visualized through a graphic representation of the analytic solution created. The theoretical results were proven through measures accomplished in an experimental setup composed of a steel tube finished in sand box, simulating the condition of infinite tube. To determine the location of the point source on the surface, the process of inverse solution was adopted, that is to say, known the signals of the sensor disposed in the tube surface, it is determined through the theoretical model where the source that generated these signals can be.

Vazamentos em tubos pressurizados geram ondas acústicas que se propagam através das paredes destes tubos, as quais podem ser captadas por acelerômetros ou por sensores de emissão acústica. O conhecimento de como estas paredes podem vibrar, ou de outro modo como as ondas acústicas se propagam neste meio, é fundamental em um processo de detecção e localização da fonte de vazamento. Neste trabalho, foi implementado um modelo analítico, através das equações de movimento da casca cilíndrica, com o objetivo de entender o comportamento da superfície do tubo em função de uma excitação pontual. Como a superfície cilíndrica é um meio fechado na direção circunferencial, ondas que iniciaram sua jornada, a partir de uma fonte pontual sobre a superfície, se encontrarão com outras que já completaram a volta na casca cilíndrica, tanto no sentido horário como no anti-horário, gerando interferências construtivas e destrutivas. Após um tempo suficiente, uma estacionariedade é atingida, criando pontos de picos e vales na superfície da casca, os quais podem ser visualizadas através de uma representação gráfica do modelo analítico criado. Os resultados teóricos foram comprovados através de medidas realizadas em uma bancada de testes composta de um tubo de aço terminado em caixa de areia, simulando a condição de tubo infinito. Para proceder à localização da fonte pontual sobre a superfície, adotou-se o processo de solução inversa, ou seja, conhecidos os sinais dos sensores dispostos na superfície do tubo, determina-se através do modelo teórico onde a fonte que gerou estes sinais pode estar. / Leaks in pressurized tubes generate acoustic waves that propagate through the walls of these tubes, which can be captured by accelerometers or by acoustic emission sensors. The knowledge of how these walls can vibrate, or in another way, how these acoustic waves propagate in this material is fundamental in the detection and localization process of the leak source. In this work an analytic model was implemented, through the motion equations of a cylindrical shell, with the objective to understand the behavior of the tube surface excited by a point source. Since the cylindrical surface has a closed pattern in the circumferential direction, waves that are beginning their trajectory will meet with another that has already completed the turn over the cylindrical shell, in the clockwise direction as well as in the counter clockwise direction, generating constructive and destructive interferences. After enough time of propagation, peaks and valleys in the shell surface are formed, which can be visualized through a graphic representation of the analytic solution created. The theoretical results were proven through measures accomplished in an experimental setup composed of a steel tube finished in sand box, simulating the condition of infinite tube. To determine the location of the point source on the surface, the process of inverse solution was adopted, that is to say, known the signals of the sensor disposed in the tube surface, it is determined through the theoretical model where the source that generated these signals can be.

O objetivo deste trabalho e a modelagem matem atica da propagaçãao do poluente mercúrio na agua. O modelo bidimensional consiste na drenagem da agua atrav es de um canal, onde o poluente (mercúrio) entra. O modelo consiste em um conjunto de equaçõoes diferenciais parciais: as equações para a conservação da massa, a quantidade de movimento, e a concentração das espécies, sujeitas a condições iniciais e de contorno apropriadas. Estas equações foram discretizadas pelo método de diferenças finitas centrais, gerando sistemas lineares que foram resolvidos pelo método de Gauss-Seidel e a convergência foi acelerada usando a técnica de sobre-relaxações SOR. A an alise da consistência e estabilidade da equação de concentração foi feita. Além disso, a solução analítica da equação de concentração, que e uma equação diferencial parcial bidimensional não homogênea com uma condição de contorno não homogênea, foi obtida com a transformada de Laplace. Os resultados obtidos a partir do modelo numérico e da solução analítica foram comparados e apresentam concordância razoável. / The goal of this work is the mathematical modeling of the spreading of the polluting mercury in the water. The two-dimensional model consists of water drainage through a canal, where the pollutant (mercury) enters. The model consists of a set of partial di erential equations: the equations for the conservation of the mass, the momentum, and the concentration of the species, subject to appropriate initial and boundary conditions. These equations were discretized by the method of central nite di erences, generating linear systems, which were solved by the Gauss-Seidel method and convergence was accelerated using the over-relaxation SOR technique. The analysis of the consistency and stability of the concentration equation was made. Furthermore, the analytical solution of the concentration equation, which is a two-dimensional non-homogeneous partial di erential equation with one nonhomogeneous contour condition, was obtained using Laplace transform. The results obtained from the numerical model and the analytical solution were compared and presented reasonable agreement.

Most combustion machines feature internal flows with very high energy densities. If a small fraction of the total energy contained in the flow is diverted into oscillations, large mechanical or thermal loads on the structure can be the result, which are potentially devastating if not predicted correctly. This is particularly the case for lightweight high performing devices like rockets. The problem is commonly known as "Combustion Instability". Several mechanisms have been identified in the past that link the flow field to the acoustics inside a combustion chamber and thereby drive or dampen oscillations, one of them being vortex shedding. The interaction between the highly sheared flow behind an obstacle and longitudinal acoustic oscillations inside a solid rocket booster is investigated both analytically and experimentally.The analytical approach is developed based on modeling of the second order acoustic energy. The energy model is applied to the specific flow conditions just downstream of a single baffle protruding into the flow. The mean flow profile is assumed to be of the form of a hyperbolic tangent, the unsteady acoustic velocities are assumed to be sinusoidally oscillating. Solutions for the unsteady rotational velocities and the unsteady vorticity are derived. The resulting flow field is utilized in stability calculations for a simplified two-dimensional axial-symmetric geometry. This yields to linear growth rates of the (longitudinal) oscillation modes. The growth rates are functions of the chamber geometry, the mean flow properties and the properties of the shear layer created by the flow restriction.A cold flow experiment is designed, tested and performed in order to validate the analytical findings. Flow is injected radially into a tube with acoustic closed-closed end conditions. A single baffle is installed in the tube, the axial position of the baffle is varied as well as its inner diameter. Frequency spectra of pressure oscillations are recorded. The experimental data is then compared qualitatively to the analytical growth rates. Those longitudinal Normal Modes, which feature the highest theoretical growth rates, are expected to be most prominent in the experimental data. This behavior is clearly observable.