Experimental and Modelling Analysis on the Moisture Induced Failures in Flip Chip on Flex Interconnections with Anisotropic Conductive Film

This paper reports the investigations into the moisture induced failures in flip-chip-on-flex interconnections with anisotropic conductive films (ACF). Both experimental and modeling methods were applied. In the experiments, the contact resistance was used as a quality indicator and was measured continuously during the accelerated tests (autoclave tests). The temperature, relative humidity and the pressure were set at 121°C, 100%RH, 1atm respectively. The contact resistance of the ACF joints increased during the tests and nearly 25% of the joints were found to be open after 168 hours' testing time. Visible conduction gaps between the adhesive and substrate pads were observed. Cracks at the adhesive/flex interface were also found. It is believed that the swelling effect of the adhesive and the water penetration along the adhesive/flex interface are the main causes of this contact degradation. Another finding from the experimental work was that the ACF interconnections that had undergone the reflow treatment were more sensitive to the moisture and showed worse reliability during the tests. For a better understanding of the experimental results, 3D finite element (FE) models were built and a macro-micro modeling method was used to determine the moisture diffusion and moisture-induced stresses inside the ACF joints. Modeling results are consistent with the findings in the experimental work.

Stochastic Analysis of Saltwater Intrusion in Heterogeneous Aquifers using Local Average Subdivision

This study investigates the effects of ground heterogeneity, considering permeability as a random variable, on an intruding SW wedge using Monte Carlo simulations. Random permeability fields were generated, using the method of Local Average Subdivision (LAS), based on a lognormal probability density function. The LAS method allows the creation of spatially correlated random fields, generated using coefficients of variation (COV) and horizontal and vertical scales of fluctuation (SOF). The numerical modelling code SUTRA was employed to solve the coupled flow and transport problem. The well-defined 2D dispersive Henry problem was used as the test case for the method. The intruding SW wedge is defined by two key parameters, the toe penetration length (TL) and the width of mixing zone (WMZ). These parameters were compared to the results of a homogeneous case simulated using effective permeability values. The simulation results revealed: (1) an increase in COV resulted in a seaward movement of TL; (2) the WMZ extended with increasing COV; (3) a general increase in horizontal and vertical SOF produced a seaward movement of TL, with the WMZ increasing slightly; (4) as the anisotropic ratio increased the TL intruded further inland and the WMZ reduced in size. The results show that for large values of COV, effective permeability parameters are inadequate at reproducing the effects of heterogeneity on SW intrusion.

Stochastic analysis of seepage under water-retaining structures

This paper investigated the problem of confined flow under dams and water retaining structuresusing stochastic modelling. The approach advocated in the study combined a finite elementsmethod based on the equation governing the dynamics of incompressible fluid flow through aporous medium with a random field generator that generates random hydraulic conductivity basedon lognormal probability distribution. The resulting model was then used to analyse confined flowunder a hydraulic structure. Cases for a structure provided with cutoff wall and when the wall didnot exist were both tested. Various statistical parameters that reflected different degrees ofheterogeneity were examined and the changes in the mean seepage flow, the mean uplift forceand the mean exit gradient observed under the structure were analysed. Results reveal that underheterogeneous conditions, the reduction made by the sheetpile in the uplift force and exit hydraulicgradient may be underestimated when deterministic solutions are used.

Stochastic processes and their applications semi-markov analysis of some inventory and queuing problems

This thesis analyses certain problems in Inventories and Queues. There are many situations in real-life where we encounter models as described in this thesis. It analyses in depth various models which can be applied to production, storag¢, telephone traffic, road traffic, economics, business administration, serving of customers, operations of particle counters and others. Certain models described here is not a complete representation of the true situation in all its complexity, but a simplified version amenable to analysis. While discussing the models, we show how a dependence structure can be suitably introduced in some problems of Inventories and Queues. Continuous review, single commodity inventory systems with Markov dependence structure introduced in the demand quantities, replenishment quantities and reordering levels are considered separately. Lead time is assumed to be zero in these models. An inventory model involving random lead time is also considered (Chapter-4). Further finite capacity single server queueing systems with single/bulk arrival, single/bulk services are also discussed. In some models the server is assumed to go on vacation (Chapters 7 and 8). In chapters 5 and 6 a sort of dependence is introduced in the service pattern in some queuing models.

Probability Theory. Stochastic Processes And Their Applications Probabilistic Analysis Of Some Queueing And Inventory Models

In this thesis we attempt to make a probabilistic analysis of some physically realizable, though complex, storage and queueing models. It is essentially a mathematical study of the stochastic processes underlying these models. Our aim is to have an improved understanding of the behaviour of such models, that may widen their applicability. Different inventory systems with randon1 lead times, vacation to the server, bulk demands, varying ordering levels, etc. are considered. Also we study some finite and infinite capacity queueing systems with bulk service and vacation to the server and obtain the transient solution in certain cases. Each chapter in the thesis is provided with self introduction and some important references

Introduction. Stochastic physics and climate modelling

Finite computing resources limit the spatial resolution of state-of-the-art global climate simulations to hundreds of kilometres. In neither the atmosphere nor the ocean are small-scale processes such as convection, clouds and ocean eddies properly represented. Climate simulations are known to depend, sometimes quite strongly, on the resulting bulk-formula representation of unresolved processes. Stochastic physics schemes within weather and climate models have the potential to represent the dynamical effects of unresolved scales in ways which conventional bulk-formula representations are incapable of so doing. The application of stochastic physics to climate modelling is a rapidly advancing, important and innovative topic. The latest research findings are gathered together in the Theme Issue for which this paper serves as the introduction.

Easier analysis and better reporting : modelling ordinal data in mathematics education research

This article presents an examination of the use of Rasch modelling in a major research project, 'Improving Middle Years Mathematics and Science' (IMYMS). It is unarguable that it is important to take students' perceptions, or views, into account when planning learning and teaching for them. The IMYMS student perceptions survey is an attempt to make visible these student viewpoints, and report them in a way that is accessible to teachers and researchers involved in the project. The project involves four clusters of schools from urban and regions of Victoria to investigate the role of mathematics and science knowledge and subject cultures in mediating change processes in the middle years of schooling. There are five secondary and twenty-eight primary schools. The project has generated both qualitative and quantitative data, with much of the qualitative data being ordinal in nature. Reporting the results of analyses for a range of audiences necessitates careful, well-designed report formats. Some useful new report formats based on Rasch modeling -the Modified Variable Map, the Ordinal Map, the Threshold Map, and the Annotated Ordinal Map - are illustrated using data from the IMYMS project. The Rasch analysis and the derived reporting formats avoid the pitfalls that exist when working with ordinal data and provide insights into the respondents' views about their experiences in schools unavailable by other approaches.

Forming behaviour analysis and constitutive modelling of Ti-6Al-4V at room temperature.

 A constitutive model was proposed in this thesis and a promising approach for accurate prediction of forming behaviour of high strength titanium alloy sheet metal forming at room temperature is presented. Outcomes showed a potential solution of cold roll forming of this material for aerospace and automotive structural applications.

Non-Markovian stochastic processes and their applications: from anomalous diffusion to time series analysis

This work provides a forward step in the study and comprehension of the relationships between stochastic processes and a certain class of integral-partial differential equation, which can be used in order to model anomalous diffusion and transport in statistical physics. In the first part, we brought the reader through the fundamental notions of probability and stochastic processes, stochastic integration and stochastic differential equations as well. In particular, within the study of H-sssi processes, we focused on fractional Brownian motion (fBm) and its discrete-time increment process, the fractional Gaussian noise (fGn), which provide examples of non-Markovian Gaussian processes. The fGn, together with stationary FARIMA processes, is widely used in the modeling and estimation of long-memory, or long-range dependence (LRD). Time series manifesting long-range dependence, are often observed in nature especially in physics, meteorology, climatology, but also in hydrology, geophysics, economy and many others. We deepely studied LRD, giving many real data examples, providing statistical analysis and introducing parametric methods of estimation. Then, we introduced the theory of fractional integrals and derivatives, which indeed turns out to be very appropriate for studying and modeling systems with long-memory properties. After having introduced the basics concepts, we provided many examples and applications. For instance, we investigated the relaxation equation with distributed order time-fractional derivatives, which describes models characterized by a strong memory component and can be used to model relaxation in complex systems, which deviates from the classical exponential Debye pattern. Then, we focused in the study of generalizations of the standard diffusion equation, by passing through the preliminary study of the fractional forward drift equation. Such generalizations have been obtained by using fractional integrals and derivatives of distributed orders. In order to find a connection between the anomalous diffusion described by these equations and the long-range dependence, we introduced and studied the generalized grey Brownian motion (ggBm), which is actually a parametric class of H-sssi processes, which have indeed marginal probability density function evolving in time according to a partial integro-differential equation of fractional type. The ggBm is of course Non-Markovian. All around the work, we have remarked many times that, starting from a master equation of a probability density function f(x,t), it is always possible to define an equivalence class of stochastic processes with the same marginal density function f(x,t). All these processes provide suitable stochastic models for the starting equation. Studying the ggBm, we just focused on a subclass made up of processes with stationary increments. The ggBm has been defined canonically in the so called grey noise space. However, we have been able to provide a characterization notwithstanding the underline probability space. We also pointed out that that the generalized grey Brownian motion is a direct generalization of a Gaussian process and in particular it generalizes Brownain motion and fractional Brownain motion as well. Finally, we introduced and analyzed a more general class of diffusion type equations related to certain non-Markovian stochastic processes. We started from the forward drift equation, which have been made non-local in time by the introduction of a suitable chosen memory kernel K(t). The resulting non-Markovian equation has been interpreted in a natural way as the evolution equation of the marginal density function of a random time process l(t). We then consider the subordinated process Y(t)=X(l(t)) where X(t) is a Markovian diffusion. The corresponding time-evolution of the marginal density function of Y(t) is governed by a non-Markovian Fokker-Planck equation which involves the same memory kernel K(t). We developed several applications and derived the exact solutions. Moreover, we considered different stochastic models for the given equations, providing path simulations.