Solutions of fourth-order parabolic equation modeling thin film growth

In this paper we study the well-posedness for a fourth-order parabolic equation modeling epitaxial thin film growth. Using Kato's Method [1], [2] and [3] we establish existence, uniqueness and regularity of the solution to the model, in suitable spaces, namelyC⁰([0,T];L^p(Ω)) where  with 1<α<2, n∈N and n≥2. We also show the global existence solution to the nonlinear parabolic equations for small initial data. Our main tools are L_p–L_q-estimates, regularization property of the linear part of e^−tΔ2 and successive approximations. Furthermore, we illustrate the qualitative behavior of the approximate solution through some numerical simulations. The approximate solutions exhibit some favorable absorption properties of the model, which highlight the stabilizing effect of our specific formulation of the source term associated with the upward hopping of atoms. Consequently, the solutions describe well some experimentally observed phenomena, which characterize the growth of thin film such as grain coarsening, island formation and thickness growth.

Dynamics of Gompertzian tumour growth under environmental fluctuations

We investigate the effect of correlated additive and multiplicative Gaussian white noise oil the Gompertzian growth of tumours. Our results are obtained by Solving numerically the time-dependent Fokker-Planck equation (FPE) associated with the stochastic dynamics. In Our numerical approach we have adopted B-spline functions as a truncated basis to expand the approximated eigenfunctions. The eigenfunctions and eigenvalues obtained using this method are used to derive approximate solutions of the dynamics under Study. We perform simulations to analyze various aspects, of the probability distribution. of the tumour cell populations in the transient- and steady-state regimes. More precisely, we are concerned mainly with the behaviour of the relaxation time (tau) to the steady-state distribution as a function of (i) of the correlation strength (lambda) between the additive noise and the multiplicative noise and (ii) as a function of the multiplicative noise intensity (D) and additive noise intensity (alpha). It is observed that both the correlation strength and the intensities of additive and multiplicative noise, affect the relaxation time.

Efficient Processing of Spatial Group Keyword Queries

With the proliferation of geo-positioning and geo-tagging techniques, spatio-textual objects that possess both a geographical location and a textual description are gaining in prevalence, and spatial keyword queries that exploit both location and textual description are gaining in prominence. However, the queries studied so far generally focus on finding individual objects that each satisfy a query rather than finding groups of objects where the objects in a group together satisfy a query.

We define the problem of retrieving a group of spatio-textual objects such that the group's keywords cover the query's keywords and such that the objects are nearest to the query location and have the smallest inter-object distances. Specifically, we study three instantiations of this problem, all of which are NP-hard. We devise exact solutions as well as approximate solutions with provable approximation bounds to the problems. In addition, we solve the problems of retrieving top-k groups of three instantiations, and study a weighted version of the problem that incorporates object weights. We present empirical studies that offer insight into the efficiency of the solutions, as well as the accuracy of the approximate solutions.

Inference in Polytrees with Sets of Probabilities

Inferences in directed acyclic graphs associated with probability intervals and sets of probabilities are NP-hard, even for polytrees. We propose: 1) an improvement on Tessem’s A/R algorithm for inferences on polytrees associated with probability intervals; 2) a new algorithm for approximate inferences based on local search; 3) branch-and-bound algorithms that combine the previous techniques. The first two algorithms produce complementary approximate solutions, while branch-and-bound procedures can generate either exact or approximate solutions. We report improvements on existing techniques for inference with probability sets and intervals, in some cases reducing computational effort by several orders of magnitude.

Approximate Computing with Unreliable Dynamic Memories

Embedded memories account for a large fraction of the overall silicon area and power consumption in modern SoC(s). While embedded memories are typically realized with SRAM, alternative solutions, such as embedded dynamic memories (eDRAM), can provide higher density and/or reduced power consumption. One major challenge that impedes the widespread adoption of eDRAM is that they require frequent refreshes potentially reducing the availability of the memory in periods of high activity and also consuming significant amount of power due to such frequent refreshes. Reducing the refresh rate while on one hand can reduce the power overhead, if not performed in a timely manner, can cause some cells to lose their content potentially resulting in memory errors. In this paper, we consider extending the refresh period of gain-cell based dynamic memories beyond the worst-case point of failure, assuming that the resulting errors can be tolerated when the use-cases are in the domain of inherently error-resilient applications. For example, we observe that for various data mining applications, a large number of memory failures can be accepted with tolerable imprecision in output quality. In particular, our results indicate that by allowing as many as 177 errors in a 16 kB memory, the maximum loss in output quality is 11%. We use this failure limit to study the impact of relaxing reliability constraints on memory availability and retention power for different technologies.

An investigation into the subambient behavior of aqueous mannitol solutions using differential scanning calorimetry, cold stage microscopy, and X-ray diffractometry

The subambient behavior of aqueous mannitol solutions is of considerable relevance to the preparation of freeze dried formulations. In this investigation the properties of 3% w/v mannitol solutions were investigated using differential scanning calorimetry (DSC), cold stage microscopy (CSM), and X-ray diffraction (XRD) to identify the thermal transitions and structural transformations undergone by this system. It was found that on cooling from ambient the system formed ice at circa -20°C while a further exotherm was seen at approximately -30°C. Upon reheating an endotherm was seen at circa -30°C followed immediately by an exotherm at circa -25°C. Temperature cycling indicated that the thermal transitions observed upon reheating were not reversible. Modulated temperature DSC (MTDSC) indicated that the transitions observed upon reheating corresponded to a glass transition immediately followed by recrystallization, XRD data showed that recrystallization was into the ß form. Annealing at -35°C for 40 min prior to cooling and reheating resulted in a maximum enthalpy being observed for the reheating exotherm. It is concluded that on cooling 3% w/v aqueous mannitol solutions an amorphous phase is formed that subsequently recrystallises into the ß form. The study has also shown that DSC, CSM, and XRD are useful complementary techniques for the study of frozen systems

Developing Creative Solutions to the Problems of Children and their Families: Communicative Reason and the use fo Forum Theatre

Building on Habermas’s conceptualisation of modes of reasoning, the authors proposed that an application of critical theory to the present bureaucratised nature of communication between state representatives and welfare recipients (Howe 1992) might open up ways in which social workers could reconceptualise their practice. In a subsequent edition of this journal, three of the present authors introduced the radical theatre of Augusto Boal as a methodology which might provide an expressive route for social workers seeking to build a practice combining the intellectual analysis of critical theory with new ways of working (Spratt et al. 2000). Boal’s method recognises the oppressed status of groups who come to the attention of agents of the state and, through the use of a range of theatrical techniques, introduces strategies to facilitate the conscious recognition of such collective oppressions and develop dialogical ways to address them. In the last paper, the authors presented one such technique, ‘image theatre’, and demonstrated its use with social workers in consciousness raising and developing strategies for collective action.