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161.
In this article we carry on the study of the fundamental category (Goubault and Raussen, Dihomotopy as a tool in state space
analysis. In: Rajsbaum, S. (ed.) LATIN 2002: Theoretical Informatics. Lecture Notes in Computer Science, vol. 2286, Cancun,
Mexico, pp. 16–37, Springer, Berlin Heidelberg New York, 2002; Goubault, Homology, Homotopy Appl., 5(2): 95–136, 2003) of a partially ordered topological space (Nachbin, Topology and Order, Van Nostrand, Princeton, 1965; Johnstone, Stone Spaces, Cambridge University Press, Cambridge, MA, 1982), as arising in e.g. concurrency theory (Fajstrup et al., Theor. Comp. Sci. 357: 241–278, 2006), initiated in (Fajstrup et al., APCS, 12(1): 81–108, 2004). The “algebra” of dipaths modulo dihomotopy (the fundamental category) of such a po-space is essentially finite in a number
of situations. We give new definitions of the component category that are more tractable than the one of Fajstrup et al. (APCS,
12(1): 81–108, 2004), as well as give definitions of future and past component categories, related to the past and future models of Grandis (Theory
Appl. Categ., 15(4): 95–146, 2005). The component category is defined as a category of fractions, but it can be shown to be equivalent to a quotient category,
much easier to portray. A van Kampen theorem is known to be available on fundamental categories (Grandis, Cahiers Topologie
Géom. Différentielle Catég., 44: 281–316, 2003; Goubault, Homology, Homotopy Appl., 5(2): 95–136, 2003), we show in this paper a similar theorem for component categories (conjectured in Fajstrup et al. (APCS, 12(1): 81–108,
2004). This proves useful for inductively computing the component category in some circumstances, for instance, in the case of
simple PV mutual exclusion models (Goubault and Haucourt, A practical application of geometric semantics to static analysis
of concurrent programs. In: Abadi, M., de Alfaro, L. (eds.) CONCUR 2005 – Concurrency Theory: 16th International Conference,
San Francisco, USA, August 23–26. Lecture Notes in Computer Science, vol. 3653, pp. 503–517, Springer, Berlin Heidelberg New
York, 2005), corresponding to partially ordered subspaces of R
n
minus isothetic hyperrectangles. In this last case again, we conjecture (and give some hints) that component categories enjoy
some nice adjunction relations directly with the fundamental category.
相似文献
162.
Xin Li 《Advances in Computational Mathematics》2008,29(4):393-413
Approximate solutions of boundary value problems of homogeneous modified Helmholtz equations on the unit ball are explicitly
constructed by the method of fundamental solutions (MFS) with the order of approximation provided. Hyperinterpolation is used
to find particular solutions of non-homogeneous equations, and the rate of convergence of solving boundary value problems
of non-homogeneous equations is derived. Numerical examples are shown to demonstrate the efficiency of the methods.
相似文献
163.
Sohrab Behnia Amin Jafari Farzan Ghalichi Ashkan Bonabi 《Central European Journal of Physics》2008,6(2):211-222
In this paper, the finite-element method (FEM) simulation of ultrasound brain surgery is presented. The overheating problem
of the post-target bone, which is one of the limiting factors for a successful ultrasound brain surgery, is considered. In
order to decrease bone heating, precise choices of frequency, focal pressure, and scanning path are needed. The effect of
variations in the mentioned scanning parameters is studied by means of the FEM. The resulting pressure and temperature distributions
of a transdural ultrasound brain surgery are simulated by employing the FEM for solving the Helmholtz and bioheat equations
in the context of a two-dimensional MRI-based brain model. Our results show that for a suitable value of the frequency, an
increase in focal pressure leads to a decrease in the required duration of the treatment and is associated with less heating
of the surrounding normal tissue. In addition, it is shown that at a threshold focal pressure, the target temperature reaches
toxic levels whereas the temperature rise in the bone is minimal. Wave reflections from sinus cavities, which result in constructive
interference with the incoming waves, are one of the reasons for overheating of the bone and can be avoided by choosing a
suitable scanning path.
相似文献
164.
A thermodynamic framework for a mixture of two liquids 总被引:1,自引:0,他引:1
In this study, we extend a thermodynamic framework that has been used with some success for describing the response of a variety of single constituent continua. Using the thermodynamic framework, we obtain a model for the mixture of two compressible fluids that has a much simpler structure than the model obtained earlier within the context of mixture theory. We also investigate the response of a mixture of two fluids that is constrained to have a constant volume, using the same thermodynamic framework. 相似文献
165.
166.
针对管道内低频噪声难以抑制的问题,本文基于亥姆霍兹共振腔(HR)阵列吸声板和穿孔管消声器组合,设计了一种复合式宽带消声器。首先利用有限元法仿真分析传统穿孔管消声器,发现中低频消声能力较差,通过嵌入HR阵列吸声板吸收中低频噪声。采用仿真与实验的方式研究吸声板的声学性能:在400-1000 Hz频段内的平均吸声系数达到了0.88。然后对复合式消声器进行数值模拟及3D打印阻抗管实验测试对比:复合式消声器在400-1718Hz频率范围内的平均传递损失为18.15 dB ,最终实现了管道内全频带噪声有效控制。 相似文献
167.
Margarida Mendes Lopes Rita Pardini Sofia Tirabassi 《Mathematische Nachrichten》2023,296(10):4739-4744
Kawamata has shown that the quasi-Albanese map of a quasi-projective variety with log-irregularity equal to the dimension and log-Kodaira dimension 0 is birational. In this note, we show that under these hypotheses the quasi-Albanese map is proper in codimension 1 as conjectured by Iitaka. 相似文献
168.
采用PDE灵敏度滤波器可以消除连续体结构拓扑优化结果存在的棋盘格现象、数值不稳定等问题,且PDE灵敏度滤波器的实质是具有Neumann边界条件的Helmholtz偏微分方程.针对大规模PDE灵敏度滤波器的求解问题,有限元分析得到其代数方程,分别采用共轭梯度算法、多重网格算法和多重网格预处理共轭梯度算法对代数方程进行求解,并且研究精度、过滤半径以及网格数量对拓扑优化效率的影响.结果表明:与共轭梯度算法和多重网格算法相比,多重网格预处理共轭梯度算法迭代次数最少,运行时间最短,极大地提高了拓扑优化效率. 相似文献
169.
170.
Two iterative solutions of the Helmholtz equation for a scalar field in above a rough surface that admits the Dirichlet boundary condition are derived. The bases for the two iterative methods are two different boundary integral equations that represent the solution. The first integral equation is classified as a Fredholm integral equation of the first kind. The second is classified as a Fredholm integral equation of the second kind. This classification suggests that it is easier to find stable solution methods to the second equation. In both methods, the boundary integral was separated into a major part which is easy to calculate and a local residual part. The major part is a convolution and thus can be calculated using FFT in complexity O(N log N), where N is the number of surface points in which the surface height and its first derivatives together with the incoming wave and its normal derivative are all known. The residual element of the equations can be approximated efficiently only for surfaces where their amplitude is less than the wavelength of the incoming wave. The iterative schemes were tested numerically against a reference solution in order to examine the applicability range, the error estimation and the stability of the schemes. All tests supported the superiority of the second method. In particular the error estimation and stability tests indicated good performance for surfaces with slope up to 1. Yet, being an equation in the scattered field alone, makes the first method useful as a benchmark solution in its domain of applicability. 相似文献