Given the set of square matrices M ⊂ Mn+m(C) that keep the subspace W = Cnx{0} ⊂ C invariant, we obtain the implicit form of a miniversal deformation of a matrix a ∈ M, and we compute it explicitely when this matrix is marked (this is, if there is a permutation matrix p ∈ Mn+m(C) such that p−1ap is a Jordan matrix). We derive some applications to tackle the classical Carlson problem.

Chip-packaging interaction is becoming a critical reliability issue for Cu/low k chips during package assembly. With the traditional TEOS interlevel dielectric being replaced by much weaker low k dielectrics, packaging induced interfacial delamination in low k interconnects has been widely observed, raising serious reliability concerns for Cu/low k chips. In a flip-chip package, the thermal def...

Detailed three-dimensional finite element analysis was carried out for area-array solder-bumped flip-chip packages. The analysis enabled determinations of accurate three-dimensional effects on stress distributions as well as local fracture behaviors under thermal load. The 3D analysis also estimated thermal fatigue life of solder bumps. Since dimensions of various components span more than thre...

[1] The deformation, stirring processes and transport structures for a series of numerical models of plume formation in axisymmetric spherical shell are examined to better understand the development of lateral heterogeneity in mantle plumes. In our models we find that under a wide range of conditions the surrounding material is heated and entrained. This indicates that plume sampling the ambien...

S U M M A R Y Continuum models are used to investigate the large-scale deformation associated with the subduction of aseismic ridges. Formulated in the horizontal plane using thin viscous sheet theory, these models measure the horizontal transmission of stress through the arc lithosphere accompanying ridge subduction. Modelling was used to compare the Tonga arc and Louisville ridge collision wi...

Second-order shear deformation theory (SSDT) is employed to analyze vibration of temperature-dependent solar functionally graded plates (SFGP’s). Power law material properties and linear steady-state thermal loads are assumed to be graded along the thickness. Two different types of SFGP’s such as ZrO2/Ti-6Al-4V and Si3N4/SUS304 are considered. Uniform, linear, nonlinear, heat-flux and sinusoida...

In this study, a method of computer model calibration, which was proposed by Kennedy & O’Hagan 2001, is applied to quantify the uncertainty arising in the inverse material identification of the solder joint in the microelectronics package subject to a thermal cycle based on the Bayesian framework. A mathematical example is considered to illustrate the concept and the procedure of the calibratio...

The mechanical properties of microscopic particles have been a heated research object for it takes the deformation of micro-beads in the microfluidic environment into account. Sufficient knowledge on mechanical properties of micro-beads would lead to better device design and application for cell mechanics, tissue engineering, etc. The physical properties of alginate beads were examined both in ...

Seth’s transition theory is applied to the problems of thickness variation parameter in a thin rotating disc by finite deformation. Neither the yield criterion nor the associated flow rule is assumed here. The results obtained here are applicable to compressible materials. If the additional condition of incompressibility is imposed, then the expression for stresses corresponds to those arising ...

In the present article, buckling analysis of functionally graded annular thin and moderately thick plates under mechanical and thermal loads is investigated. The equilibrium and stability equations of the plate are obtained based on both classical and first order shear deformation plate theories. By using an analytical method, the coupled stability equations are converted to independent equatio...