162 research outputs found
Improving Stability Prediction in Peripheral Milling of Al7075T6
Chatter is an old enemy to machinists but, even today, is far from being defeated. Current requirements around aerospace components call for stronger and thinner workpieces which are more prone to vibrations. This study presents the stability analysis for a single degree of freedom down-milling operation in a thin-walled workpiece. The stability charts were computed by means of the enhanced multistage homotopy perturbation (EMHP) method, which includes the helix angle but also, most importantly, the runout and cutting speed effects. Our experimental validation shows the importance of this kind of analysis through a comparison with a common analysis without them, especially when machining aluminum alloys. The proposed analysis demands more computation time, since it includes the calculation of cutting forces for each combination of axial depth of cut and spindle speed. This EMHP algorithm is compared with the semi-discretization, Chebyshev collocation, and full-discretization methods in terms of convergence and computation efficiency, and ultimately proves to be the most efficient method among the ones studied.The authors wish to acknowledge the financial support received from HAZITEK program, from the Department of Economic Development and Infrastructures of the Basque Government and from FEDER funds. Additional support was provided by the Tecnologico de Monterrey, through the Research Group in Nanomaterials and Devices Design
Doctor of Philosophy
dissertationWe first study the inverse problem of recovering a complex Schro ?dinger potential from a discrete set of measurements of the solution to the Schro ?dinger equation using different source terms. We solve this problem by generalizing the inverse Born series method to nonlinear mappings between Banach spaces. In this general setting, we show convergence and stability of inverse Born series follow from a single problem- specific bound. We show this bound for the inverse Schro ?dinger problem, and study numerically an application of this inverse problem to transient hydraulic tomography. Additionally, we develop a family of iterative methods based on truncated inverse Born series that are akin to iterative methods based on truncated Taylor series. Next, we study the inverse problem of imaging scatterers in a homogeneous medium when only intensities of wavefields can be measured. Classic imaging meth- ods, such as Kirchhoff migration, rely on phase information contained in full waveform data and thus cannot be used directly with intensity-only data. In situations where scattered wavefields are small compared to the incident wavefields, we can form and solve a linear least squares problem to recover a projection (on a known subspace) of full waveform data from intensity data. We show that for sufficiently high frequencies, this projection gives a Kirchhoff image asymptotically equivalent to the Kirchhoff image obtained from full waveform data. We also generalize this imaging method to using stochastic incident fields with autocorrelation measurements. Finally, we study a mathematical model of grain growth in polycrystalline mate- rials. We review a simplified 1D grain growth model and an entropy-based theory for the evolution of an important statistic harvested from this model, the GBCD. The theory suggests the GBCD evolves according to a Fokker-Planck equation, which we validate numerically. We derive methods to estimate times from the GBCD, thus fitting it to Fokker-Planck time scales. This allows for direct comparisons of the GBCD with the Fokker-Planck solution, where we find qualitative agreement. We alsofind an energy dissipation identity which Fokker-Planck solutions must satisfy. We verify the GBCD satisfies this identity both qualitatively and quantitatively, further validating the Fokker-Planck model of GBCD evolution
The solar wind structures associated with cosmic ray decreases and particle acceleration in 1978-1982
The time histories of particles in the energy range 1 MeV to 1 GeV at times of all greater than 3 percent cosmic ray decreases in the years 1978 to 1982 are studied. Essentially all 59 of the decreases commenced at or before the passages of interplanetary shocks, the majority of which accelerated energetic particles. We use the intensity-time profiles of the energetic particles to separate the cosmic ray decreases into four classes which we subsequently associate with four types of solar wind structures. Decreases in class 1 (15 events) and class 2 (26 events) can be associated with shocks which are driven by energetic coronal mass ejections. For class 1 events the ejecta is detected at 1 AU whereas this is not the case for class 2 events. The shock must therefore play a dominant role in producing the depression of cosmic rays in class 2 events. In all class 1 and 2 events (which comprise 69 percent of the total) the departure time of the ejection from the sun (and hence the location) can be determined from the rapid onset of energetic particles several days before the shock passage at Earth. The class 1 events originate from within 50 deg of central meridian. Class 3 events (10 decreases) can be attributed to less energetic ejections which are directed towards the Earth. In these events the ejecta is more important than the shock in causing a depression in the cosmic ray intensity. The remaining events (14 percent of the total) can be attributed to corotating streams which have ejecta material embedded in them
The Parallel One-way Hash Function Based on Chebyshev-Halley Methods with Variable Parameter
In this paper a parallel Hash algorithm construction based on the Chebyshev Halley methods with variable parameters is proposed and analyzed. The two core characteristics of the recommended algorithm are parallel processing mode and chaotic behaviors. Moreover in this paper, an algorithm for one way hash function construction based on chaos theory is introduced. The proposed algorithm contains variable parameters dynamically obtained from the position index of the corresponding message blocks. Theoretical analysis and computer simulation indicate that the algorithm can assure all performance requirements of hash function in an efficient and flexible style and secure against birthday attacks or meet-in-the-middle attacks, which is good choice for data integrity or authentication
Classe de métodos Chebyshev-Halley inexata livre de tensores com convergência cúbica para resolução de sistemas não lineares e um estudo sobre o raio de convergência
Resumo: Esta tese introduz dois novos resultados sobre a Classe Chebyshev-Halley para resolução de sistemas não-lineares. Os métodos dessa classe possuem convergência cúbica, tendo portanto uma taxa de convergência superior a do método de Newton. Em contrapartida, esses métodos são mais caros computacionalmente, por necessitarem de derivadas de segunda ordem. O primeiro resultado apresentado _e um resultado teórico. Introduzimos um novo raio de convergência para a Classe Chebyshev-Halley, ou seja, mostramos que dado qualquer ponto inicial pertencente à uma bola centrada em uma solução com o novo raio, a sequência gerada por qualquer método da Classe Chebyshev-Halley é bem definida e converge para a respectiva solução com taxa de convergência cúbica. Comparamos com o raio utilizado na prova de convergência dada no livro Numerische Losung Nichtlinearer Gleichungen [70] para os métodos Halley, Chebyshev e Super-Halley, através de alguns exemplos. As comparações apresentadas sugerem perspectivas futuras, tais como determinar o raio ótimo de convergência. O segundo resultado apresentado é a introdução de uma nova classe de métodos, chamada Classe Chebyshev-Halley Inexata livre de tensores, cujo objetivo _e baratear o custo computacional da Classe Chebyshev-Halley, no que tange o uso da derivada de segunda ordem e a resolução de dois sistemas lineares. A grosso modo, não utilizamos informações de derivada de segunda ordem e os dois sistemas lineares, necessários para a obtenção do passo, podem ser resolvidos de maneira inexata. Além de apresentar a prova de convergência, mostramos que, dependendo das hipóteses, os métodos dessa classe podem ter taxa de convergência superlinear, quadrática, superquadrática e cúbica. Mostramos também que essas hipóteses são bastante razoáveis. Porém, comparações numéricas são apresentadas, mostrando uma melhoria significativa quando se usa a estratégia inexata livre de tensores, proposta nesta tese, nos métodos clássicos da Classe Chebyshev-Halley
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