On parabolic equations with a small parameter

A singularly perturbed parabolic equation with a nonlinear right-hand side of a special form is examined. A numerical analytical study of such equations is performed.     

Infinite-dimensional linear groups with restrictions on subgroups that are not soluble <Emphasis Type="Italic">A</Emphasis><Subscript>3</Subscript>-groups

We are concerned with infinite-dimensional locally soluble linear groups of infinite central dimension that are not soluble A₃-groups and all of whose proper subgroups, which are not soluble A₃-groups, have finite central dimension. The structure of groups in this class is described. The case of infinite-dimensional locally nilpotent linear groups satisfying the specified conditions is treated separately. A similar problem is solved for infinite-dimensional locally soluble linear groups of infinite fundamental dimension that are not soluble A₃-groups and all of whose proper subgroups, which are not soluble A₃-groups, have finite fundamental dimension. __________ Translated from Algebra i Logika, Vol. 46, No. 5, pp. 548–559, September–October, 2007.     

Mathematical modelling and analytical solution for workpiece temperature in grinding

This paper deals with modelling the workpiece temperature field produced during the grinding process. The proposed model is given in terms of a two-dimensional boundary-value problem where the interdependence among the grinding wheel, the workpiece and the coolant is described by two variable functions in the boundary condition. An explicit integral form solution is constructed using the Laplace and Fourier transforms and the Green’s function method.     

浅水中污染物扩散的自适应有限元分析法

介绍浅水中污染物扩散分析中的有限元法.分析包括两个部分:1)流场速度、水面高度的计算;2)根据扩散模型计算污染物浓度场.联合使用了自适应网格技术以期提高解的精度,同时减少计算时间和计算机内存的消耗.通过几个有已知解的实例验证了有限元公式和计算机程序.最后,使用这种联合方法分析泰国Chao Phraya河附近海湾中的污染物扩散.     

Comment on “The Free Will Theorem”

In a recent paper Conway and Kochen, Found. Phys. 36, 2006, claim to have established that theories of the Ghirardi-Rimini-Weber (RW) type, i.e., of spontaneous wave function collapse, cannot be made relativistic. On the other hand, relativistic GRW-type theories have already been presented, in my recent paper, J. Stat. Phys. 125, 2006, and by Dowker and Henson, J. Stat. Phys. 115, 2004. Here, I elucidate why these are not excluded by the arguments of Conway and Kochen.      

A novel specimen for investigating the mechanical behavior of elastomers under multiaxial loading conditions

In this paper we describe the design and manufacture of an axial-torsion test specimen, and provide relationships needed when conducting stress-strain characterization experiments with the specimen. The specimen is a short hollow cylinder of rubber bonded between two steel mounting rings, in which simultaneous axial and shear strains are produced via independently controlled axial and twist displacements. We present calculations for the strain-displacement and stress-load relationships, and strain energy density. These relationships have been established and validated via a combination of analytical and experimental techniques, and finite element analysis. We have investigated the extent and effects of strain and stress field non-uniformity in the test specimen. The specimen design is sufficiently simple that a closed-form expression for the strain-displacement relationship has been successfully developed.     

“Slow” active control of combustion instabilities by modification of liquid fuel spray properties

This paper describes an experimental investigation of the feasibility of using “slow” active control approaches, which “instantaneously” change liquid fuel spray properties, to suppress combustion instabilities. The objective of this control approach was to break up the feedback between the combustion process heat release and combustor pressure oscillations that drive the instability by changing the characteristics of the combustion process (e.g., the characteristic combustion time). To demonstrate the feasibility of such control, this study used a proprietary fuel injector (Nanomiser^TM), which can vary its fuel spray properties, to investigate the dependence of acoustics–combustion process coupling, i.e., the driving of combustion instabilities, upon the fuel spray properties. This study showed that by changing the spray characteristics it is possible to significantly damp combustion instabilities. Furthermore, using combustion zone chemiluminescence distributions, which were obtained by Abel’s deconvolution synchronized with measured acoustic data, it has been shown that the instabilities were mostly driven midway between the combustor centerline and wall, a short distance downstream from the flame holder, where the mean axial flow velocity is approximately zero in the vortex near the flame holder. The results of this study strongly suggest that a “slow” active control system that employs controllable fuel injectors could be effectively used to prevent the onset of detrimental combustion instabilities.     

A numerical experimental study of inverse preconditioning for the parallel iterative solution to 3D finite element flow equations

Integration of the subsurface flow equation by finite elements (FE) in space and finite differences (FD) in time requires the repeated solution to sparse symmetric positive definite systems of linear equations. Iterative techniques based on preconditioned conjugate gradients (PCG) are one of the most attractive tool to solve the problem on sequential computers. A present challenge is to make PCG attractive in a parallel computing environment as well. To this aim a key factor is the development of an efficient parallel preconditioner. FSAI (factorized sparse approximate inverse) and enlarged FSAI relying on the approximate inverse of the coefficient matrix appears to be a most promising parallel preconditioner. In the present paper PCG using FSAI, diagonal and pARMS (parallel algebraic recursive multilevel solvers) preconditioners is implemented on the IBM SP4/512 and CLX/768 supercomputers with up to 32 processors to solve underground flow problems of a large size. The results show that FSAI may allow for a parallel relative efficiency larger than 50% on the largest problems with p=32 processors. Moreover, FSAI turns out to be significantly less expensive and more robust than pARMS. Finally, it is shown that for p in the upper range may be much improved if PCG–FSAI is implemented on CLX.     

等腰三角形Mindlin板的自由振动分析

提出了一种新方法来对基于 Mindlin剪切变形理论的等腰三角形板进行自由振动分析 .此方法采用了一种新的基函数并利用 pb-2 Rayleigh-Ritz边界函数得到了一种新型的 Ritz方法 .这种方法的有效性通过收敛性和对比性分析得到了证实 .数值结果表明此方法相当精确有效 .