A variational conjugate gradient method for determining the fluid velocity of a slow viscous flow

The problem considered is that of determining the fluid velocity for linear hydrostatics Stokes flow of slow viscous fluids from measured velocity and fluid stress force on a part of the boundary of a bounded domain. A variational conjugate gradient iterative procedure is proposed based on solving a series of mixed well-posed boundary value problems for the Stokes operator and its adjoint. In order to stabilize the Cauchy problem, the iterations are ceased according to an optimal order discrepancy principle stopping criterion. Numerical results obtained using the boundary element method confirm that the procedure produces a convergent and stable numerical solution.

N-dimensional electron in an anharmonic potential:the large-N limit

We show that the energy levels predicted by a frac(1, N)-expansion method for an N-dimensional electron in an anharmonic potential are always lower than the exact energy levels but monotonically converge toward their exact eigenstates for higher ordered corrections. The technique allows a systematic approach for quantum many body problems in a confined potential and explains the remarkable agreement of such approximate theories when compared with numerical results.

Methyl chloride purification for the silicone industry

This study experimentally investigated methyl chloride (MeCl) purification method using an inhouse designed and built volumetric adsorption/desorption rig. MeCl is an essential raw material in the manufacture of silicone however all technical grades of MeCl contain concentrations (0.2 - 1.0 % wt) of dimethyl ether (DME) which poison the process. The project industrial partner had previously exhausted numerous separation methods, which all have been deemed not suitable for various reasons. Therefore, adsorption/desorption separation was proposed in this study as a potential solution with less economic and environmental impact. Pure component adsorption/desorption was carried out for DME and MeCl on six different adsorbents namely: zeolite molecular sieves (types 4 Å and 5 Å); silica gels (35-70 mesh, amorphous precipitated, and 35-60 mesh) and granular activated carbon (type 8-12 mesh). Subsequent binary gas mixture adsorption in batch and continuous mode was carried out on both zeolites and all three silica gels following thermal pre-treatment in vacuum. The adsorbents were tested as received and after being subjected to different thermal and vacuum pre-treatment conditions. The various adsorption studies were carried out at low pressure and temperature ranges of 0.5 - 3.5 atm and 20 - 100 °C. All adsorbents were characterised using Brunauer Emmett Teller (BET), thermogravimetric analysis (TGA), scanning electron microscopy (SEM) and energy dispersive x-ray analysis (EDXA) to investigate their physical and chemical properties. The well-known helium (He) expansion method was used to determine the empty manifold and adsorption cell (AC) regions and respective void volumes for the different adsorbents. The amounts adsorbed were determined using Ideal gas laws via the differential pressure method. The heat of adsorption for the various adsorbate-adsorbent (A-S) interactions was calculated using a new calorimetric method based on direct temperature measurements inside the AC. Further adsorption analysis included use of various empirical and kinetic models to determine and understand the behaviour of the respective interactions. The gas purification behaviour was investigated using gas chromatography and mass spectroscopy (GC-MC) analysis. Binary gas mixture samples were syringed from the manifold iii and AC outlet before and after adsorption/desorption analysis through manual sample injections into the GC-MS to detect and quantify the presence of DME and ultimately observe for methyl chloride purification. Convincing gas purification behaviour was confirmed using two different GC columns, thus giving more confidence on the measurement reliability. From the single pure component adsorption of DME and MeCl on the as received zeolite 4A subjected to 1 h vacuum pre-treatment, both gases exhibited pseudo second order adsorption kinetics with DME exhibiting a rate constant nearly double that of MeCl thus suggesting a faster rate of adsorption. From the adsorption isotherm classification both DME and MeCl exhibited Type II and I adsorption isotherm classifications, respectively. The strength of bonding was confirmed by the differential heat of adsorption measurement, which was found to be 23.30 and 10.21 kJ mol-1 for DME and MeCl, respectively. The former is believed to adsorb heterogeneously through hydrogen bonding whilst MeCl adsorbs homogenously via van der Waal’s (VDW) forces. Single pure component adsorption on as received zeolite 5A, silica gels (35-70, amorphous precipitated and 35-60) resulted in similar adsorption/desorption behaviour in similar quantities (mol kg-1). The adsorption isotherms for DME and MeCl on zeolite 5A, silica gels (35-70, amorphous precipitated and 35-60) and activated carbon 8-12 exhibited Type I classifications, respectively. Experiments on zeolite 5A indicated that DME adsorbed stronger, faster and with a slightly stronger strength of interaction than MeCl but in lesser quantities. On the silica gels adsorbents, DME exhibited a slightly greater adsorption capacity whilst adsorbing at a similar rate and strength of interaction compared to MeCl. On the activated carbon adsorbent, MeCl exhibited the greater adsorption capacity at a faster rate but with similar heats of adsorption. The effect of prolonged vacuum (15 h), thermal pre-treatment (150 °C) and extended equilibrium time (15 min) were investigated for the adsorption behaviour of DME and MeCl on both zeolites 4A and 5A, respectively. Compared to adsorption on as received adsorbents subjected to 1 h vacuum the adsorption capacities for DME and MeCl were found to increase by 1.95 % and 20.37 % on zeolite 4A and by 4.52 % and 6.69 % on zeolite 5A, respectively. In addition the empirical and kinetic models and differential heats of adsorption resulted in more definitive fitting curves and trends due to the true equilibrium position of the adsorbate with the adsorbent. Batch binary mixture adsorption on thermally and vacuum pre-treated zeolite 4A demonstrated purification behaviour of all adsorbents used for MeCl streams containing DME impurities, with a concentration as low as 0.66 vol. %. The GC-MS analysis showed no DME detection for the tested concentration mixtures at the AC outlet after 15 or 30 min, whereas MeCl was detectable in measurable amounts. Similar behaviour was also observed when carrying out adsorption in continuous mode. On the other hand, similar studies on the other adsorbents did not show such favourable MeCl purification behaviour. Overall this study investigated a wide range of adsorbents (zeolites, silica gels and activated carbon) and demonstrated for the first time potential to purify MeCl streams containing DME impurities using adsorption/desorption separation under different adsorbent pre-treatment and adsorption operating conditions. The study also revealed for the first time the adsorption isotherms, empirical and kinetic models and heats of adsorption for the respective adsorbentsurface (A-S) interactions. In conclusion, this study has shown strong evidence to propose zeolite 4A for adsorptive purification of MeCl. It is believed that with a technical grade MeCl stream competitive yet simultaneous co-adsorption of DME and MeCl occurs with evidence of molecular sieiving effects whereby the larger DME molecules are unable to penetrate through the adsorbent bed whereas the smaller MeCl molecules diffuse through resulting in a purified MeCl stream at the AC outlet. Ultimately, further studies are recommended for increased adsorption capacities by considering wider operating conditions, e.g. different adsorbent thermal and vacuum pre-treatment and adsorbing at temperatures closer to the boiling point of the gases and different conditions of pressure and temperature.

A variational method and approximations of a Cauchy problem for elliptic equations

A Cauchy problem for general elliptic second-order linear partial differential equations in which the Dirichlet data in H½(?1 ? ?3) is assumed available on a larger part of the boundary ? of the bounded domain O than the boundary portion ?1 on which the Neumann data is prescribed, is investigated using a conjugate gradient method. We obtain an approximation to the solution of the Cauchy problem by minimizing a certain discrete functional and interpolating using the finite diference or boundary element method. The minimization involves solving equations obtained by discretising mixed boundary value problems for the same operator and its adjoint. It is proved that the solution of the discretised optimization problem converges to the continuous one, as the mesh size tends to zero. Numerical results are presented and discussed.

A variational method for identifying a spacewise-dependent heat source

The inverse problem of determining a spacewise-dependent heat source for the parabolic heat equation using the usual conditions of the direct problem and information from one supplementary temperature measurement at a given instant of time is studied. This spacewise-dependent temperature measurement ensures that this inverse problem has a unique solution, but the solution is unstable and hence the problem is ill-posed. We propose a variational conjugate gradient-type iterative algorithm for the stable reconstruction of the heat source based on a sequence of well-posed direct problems for the parabolic heat equation which are solved at each iteration step using the boundary element method. The instability is overcome by stopping the iterative procedure at the first iteration for which the discrepancy principle is satisfied. Numerical results are presented which have the input measured data perturbed by increasing amounts of random noise. The numerical results show that the proposed procedure yields stable and accurate numerical approximations after only a few iterations.

A variational approach to learning curves

We combine the replica approach from statistical physics with a variational approach to analyze learning curves analytically. We apply the method to Gaussian process regression. As a main result we derive approximative relations between empirical error measures, the generalization error and the posterior variance.

A basis function approach to Bayesian inference in diffusion processes

In this paper, we present a framework for Bayesian inference in continuous-time diffusion processes. The new method is directly related to the recently proposed variational Gaussian Process approximation (VGPA) approach to Bayesian smoothing of partially observed diffusions. By adopting a basis function expansion (BF-VGPA), both the time-dependent control parameters of the approximate GP process and its moment equations are projected onto a lower-dimensional subspace. This allows us both to reduce the computational complexity and to eliminate the time discretisation used in the previous algorithm. The new algorithm is tested on an Ornstein-Uhlenbeck process. Our preliminary results show that BF-VGPA algorithm provides a reasonably accurate state estimation using a small number of basis functions.

A comparison of variational and Markov chain Monte Carlo methods for inference in partially observed stochastic dynamic systems

In recent work we have developed a novel variational inference method for partially observed systems governed by stochastic differential equations. In this paper we provide a comparison of the Variational Gaussian Process Smoother with an exact solution computed using a Hybrid Monte Carlo approach to path sampling, applied to a stochastic double well potential model. It is demonstrated that the variational smoother provides us a very accurate estimate of mean path while conditional variance is slightly underestimated. We conclude with some remarks as to the advantages and disadvantages of the variational smoother. © 2008 Springer Science + Business Media LLC.

Variational inference for Student-t MLP models

This paper presents a novel methodology to infer parameters of probabilistic models whose output noise is a Student-t distribution. The method is an extension of earlier work for models that are linear in parameters to nonlinear multi-layer perceptrons (MLPs). We used an EM algorithm combined with variational approximation, the evidence procedure, and an optimisation algorithm. The technique was tested on two regression applications. The first one is a synthetic dataset and the second is gas forward contract prices data from the UK energy market. The results showed that forecasting accuracy is significantly improved by using Student-t noise models.

Data assimilation for precipitation nowcasting using Bayesian inference

This work introduces a new variational Bayes data assimilation method for the stochastic estimation of precipitation dynamics using radar observations for short term probabilistic forecasting (nowcasting). A previously developed spatial rainfall model based on the decomposition of the observed precipitation field using a basis function expansion captures the precipitation intensity from radar images as a set of ‘rain cells’. The prior distributions for the basis function parameters are carefully chosen to have a conjugate structure for the precipitation field model to allow a novel variational Bayes method to be applied to estimate the posterior distributions in closed form, based on solving an optimisation problem, in a spirit similar to 3D VAR analysis, but seeking approximations to the posterior distribution rather than simply the most probable state. A hierarchical Kalman filter is used to estimate the advection field based on the assimilated precipitation fields at two times. The model is applied to tracking precipitation dynamics in a realistic setting, using UK Met Office radar data from both a summer convective event and a winter frontal event. The performance of the model is assessed both traditionally and using probabilistic measures of fit based on ROC curves. The model is shown to provide very good assimilation characteristics, and promising forecast skill. Improvements to the forecasting scheme are discussed

Variational Markov Chain Monte Carlo for Bayesian smoothing of non-linear niffusions

In this paper we develop set of novel Markov chain Monte Carlo algorithms for Bayesian smoothing of partially observed non-linear diffusion processes. The sampling algorithms developed herein use a deterministic approximation to the posterior distribution over paths as the proposal distribution for a mixture of an independence and a random walk sampler. The approximating distribution is sampled by simulating an optimized time-dependent linear diffusion process derived from the recently developed variational Gaussian process approximation method. Flexible blocking strategies are introduced to further improve mixing, and thus the efficiency, of the sampling algorithms. The algorithms are tested on two diffusion processes: one with double-well potential drift and another with SINE drift. The new algorithm's accuracy and efficiency is compared with state-of-the-art hybrid Monte Carlo based path sampling. It is shown that in practical, finite sample, applications the algorithm is accurate except in the presence of large observation errors and low observation densities, which lead to a multi-modal structure in the posterior distribution over paths. More importantly, the variational approximation assisted sampling algorithm outperforms hybrid Monte Carlo in terms of computational efficiency, except when the diffusion process is densely observed with small errors in which case both algorithms are equally efficient.

LRD : Latent Relation Discovery for vector space expansion and information retrieval

In this paper, we propose a text mining method called LRD (latent relation discovery), which extends the traditional vector space model of document representation in order to improve information retrieval (IR) on documents and document clustering. Our LRD method extracts terms and entities, such as person, organization, or project names, and discovers relationships between them by taking into account their co-occurrence in textual corpora. Given a target entity, LRD discovers other entities closely related to the target effectively and efficiently. With respect to such relatedness, a measure of relation strength between entities is defined. LRD uses relation strength to enhance the vector space model, and uses the enhanced vector space model for query based IR on documents and clustering documents in order to discover complex relationships among terms and entities. Our experiments on a standard dataset for query based IR shows that our LRD method performed significantly better than traditional vector space model and other five standard statistical methods for vector expansion.

Bed expansion:extending correlations for fluidized beds with inserts to open fluidized beds

Bed expansion occurs during the operation of gas-fluidized beds and is influenced by particle properties, gas properties and distributor characteristics. It has a significant bearing on heat and mass transfer phenomena within the bed. A method of predicting bed expansion behavior from other fluidizing parameters would be a useful tool in the design process, dispensing with the need for small-scale trials. This study builds on previous work on fluidized beds with vertical inserts to produce a correlation that links a modified particle terminal velocity, minimum fluidizing velocity and distributor characteristics with bed voidage in the relationship with P as the pitch between holes in the perforated distributor plate. © 2007 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Internet search:subdivision-based interactive query expansion and the soft semantic web

The expansion of the Internet has made the task of searching a crucial one. Internet users, however, have to make a great effort in order to formulate a search query that returns the required results. Many methods have been devised to assist in this task by helping the users modify their query to give better results. In this paper we propose an interactive method for query expansion. It is based on the observation that documents are often found to contain terms with high information content, which can summarise their subject matter. We present experimental results, which demonstrate that our approach significantly shortens the time required in order to accomplish a certain task by performing web searches.

A potentially scalable method for the harvesting of hMSCs from microcarriers

The use of hMSCs for allogeneic therapies requiring lot sizes of billions of cells will necessitate large-scale culture techniques such as the expansion of cells on microcarriers in bioreactors. Whilst much research investigating hMSC culture on microcarriers has focused on growth, much less involves their harvesting for passaging or as a step towards cryopreservation and storage. A successful new harvesting method has recently been outlined for cells grown on SoloHill microcarriers in a 5L bioreactor [1]. Here, this new method is set out in detail, harvesting being defined as a two-step process involving cell 'detachment' from the microcarriers' surface followed by the 'separation' of the two entities. The new detachment method is based on theoretical concepts originally developed for secondary nucleation due to agitation. Based on this theory, it is suggested that a short period (here 7min) of intense agitation in the presence of a suitable enzyme should detach the cells from the relatively large microcarriers. In addition, once detached, the cells should not be damaged because they are smaller than the Kolmogorov microscale. Detachment was then successfully achieved for hMSCs from two different donors using microcarrier/cell suspensions up to 100mL in a spinner flask. In both cases, harvesting was completed by separating cells from microcarriers using a Steriflip® vacuum filter. The overall harvesting efficiency was >95% and after harvesting, the cells maintained all the attributes expected of hMSC cells. The underlying theoretical concepts suggest that the method is scalable and this aspect is discussed too. © 2014 The Authors.