Local and global error models to improve uncertainty quantification

In groundwater applications, Monte Carlo methods are employed to model the uncertainty on geological parameters. However, their brute-force application becomes computationally prohibitive for highly detailed geological descriptions, complex physical processes, and a large number of realizations. The Distance Kernel Method (DKM) overcomes this issue by clustering the realizations in a multidimensional space based on the flow responses obtained by means of an approximate (computationally cheaper) model; then, the uncertainty is estimated from the exact responses that are computed only for one representative realization per cluster (the medoid). Usually, DKM is employed to decrease the size of the sample of realizations that are considered to estimate the uncertainty. We propose to use the information from the approximate responses for uncertainty quantification. The subset of exact solutions provided by DKM is then employed to construct an error model and correct the potential bias of the approximate model. Two error models are devised that both employ the difference between approximate and exact medoid solutions, but differ in the way medoid errors are interpolated to correct the whole set of realizations. The Local Error Model rests upon the clustering defined by DKM and can be seen as a natural way to account for intra-cluster variability; the Global Error Model employs a linear interpolation of all medoid errors regardless of the cluster to which the single realization belongs. These error models are evaluated for an idealized pollution problem in which the uncertainty of the breakthrough curve needs to be estimated. For this numerical test case, we demonstrate that the error models improve the uncertainty quantification provided by the DKM algorithm and are effective in correcting the bias of the estimate computed solely from the MsFV results. The framework presented here is not specific to the methods considered and can be applied to other combinations of approximate models and techniques to select a subset of realizations

Comparison between molecular dynamics abd Monte Carlo simulations of an ordering process in a binary alloy

Ordering in a binary alloy is studied by means of a molecular-dynamics (MD) algorithm which allows to reach the domain growth regime. Results are compared with Monte Carlo simulations using a realistic vacancy-atom (MC-VA) mechanism. At low temperatures fast growth with a dynamical exponent x>1/2 is found for MD and MC-VA. The study of a nonequilibrium ordering process with the two methods shows the importance of the nonhomogeneity of the excitations in the system for determining its macroscopic kinetics.

Statistics of transverse mode turn-on dynamics in VCSEL's

The turn-on process of a multimode VCSEL is investigated from a statistical point of view. Special attention is paid to quantities such as time jitter and bit error rate. The single-mode performance of VCSEL¿s during current modulation is compared to that of edge-emitting lasers.

Clarifying the Quadrennial Needs Study Process, December 1993

The Quadrennial Needs Study was developed to assist in the identification of highway needs and the distribution of road funds in Iowa among the various highway entities. During the period 1978 to 1990, the process has seen large shifts in needs and associated funding distribution in individual counties with no apparent reasons. This study investigated the reasons for such shifts. The study identified program inputs that can result in major shifts in needs either up or down from minor changes in the input values. The areas of concern were identified as the condition ratings for roads and structures, traffic volume and mix counts, and the assignment of construction cost areas. Eight counties exhibiting the large shifts (greater than 30%) in needs over time were used to test the sensitivity of the variables. A ninth county was used as the base line for the study. Recommendations are identified for improvements in the process of data collection in the areas of road and structure condition--rating, traffic, and in the assignment of construction cost areas. Advice is also offered in how to account for changes in jurisdiction between successive studies. Maintenance cost area assignment and levels of maintenance service are identified as requiring additional detailed research.

Development of a Model for the Ice Scraping Process, October 1996

A laboratory study has been conducted with two aims in mind. The first goal was to develop a description of how a cutting edge scrapes ice from the road surface. The second goal was to investigate the extent, if any, to which serrated blades were better than un-serrated or "classical" blades at ice removal. The tests were conducted in the Ice Research Laboratory at the Iowa Institute of Hydraulic Research of the University of Iowa. A specialized testing machine, with a hydraulic ram capable of attaining scraping velocities of up to 30 m.p.h. was used in the testing. In order to determine the ice scraping process, the effects of scraping velocity, ice thickness, and blade geometry on the ice scraping forces were determined. Higher ice thickness lead to greater ice chipping (as opposed to pulverization at lower thicknesses) and thus lower loads. Behavior was observed at higher velocities. The study of blade geometry included the effect of rake angle, clearance angle, and flat width. The latter were found to be particularly important in developing a clear picture of the scraping process. As clearance angle decreases and flat width increases, the scraping loads show a marked increase, due to the need to re-compress pulverized ice fragments. The effect of serrations was to decrease the scraping forces. However, for the coarsest serrated blades (with the widest teeth and gaps) the quantity of ice removed was significantly less than for a classical blade. Finer serrations appear to be able to match the ice removal of classical blades at lower scraping loads. Thus, one of the recommendations of this study is to examine the use of serrated blades in the field. Preliminary work (by Nixon and Potter, 1996) suggests such work will be fruitful. A second and perhaps more challenging result of the study is that chipping of ice is more preferable to pulverization of the ice. How such chipping can be forced to occur is at present an open question.

Evaluation of Hot Mix Asphalt Moisture Sensitivity Using the Nottingham Asphalt Test Equipment, July 2005

Moisture sensitivity of Hot Mix Asphalt (HMA) mixtures, generally called stripping, is a major form of distress in asphalt concrete pavement. It is characterized by the loss of adhesive bond between the asphalt binder and the aggregate (a failure of the bonding of the binder to the aggregate) or by a softening of the cohesive bonds within the asphalt binder (a failure within the binder itself), both of which are due to the action of loading under traffic in the presence of moisture. The evaluation of HMA moisture sensitivity has been divided into two categories: visual inspection test and mechanical test. However, most of them have been developed in pre-Superpave mix design. This research was undertaken to develop a protocol for evaluating the moisture sensitivity potential of HMA mixtures using the Nottingham Asphalt Tester (NAT). The mechanisms of HMA moisture sensitivity were reviewed and the test protocols using the NAT were developed. Different types of blends as moisture-sensitive groups and non-moisture-sensitive groups were used to evaluate the potential of the proposed test. The test results were analyzed with three parameters based on performance character: the retained flow number depending on critical permanent deformation failure (RFNP), the retained flow number depending on cohesion failure (RFNC), and energy ratio (ER). Analysis based on energy ratio of elastic strain (EREE ) at flow number of cohesion failure (FNC) has higher potential to evaluate the HMA moisture sensitivity than other parameters. If the measurement error in data-acquisition process is removed, analyses based on RFNP and RFNC would also have high potential to evaluate the HMA moisture sensitivity. The vacuum pressure saturation used in AASHTO T 283 and proposed test has a risk to damage specimen before the load applying.

Laser-induced forward transfer of liquids: Study of the droplet ejection process

Laser-induced forward transfer (LIFT) is a laser direct-write technique that offers the possibility of printing patterns with a high spatial resolution from a wide range of materials in a solid or liquid state, such as conductors, dielectrics, and biomolecules in solution. This versatility has made LIFT a very promising alternative to lithography-based processes for the rapid prototyping of biomolecule microarrays. Here, we study the transfer process through the LIFT of droplets of a solution suitable for microarray preparation. The laser pulse energy and beam size were systematically varied, and the effect on the transferred droplets was evaluated. Controlled transfers in which the deposited droplets displayed optimal features could be obtained by varying these parameters. In addition, the transferred droplet volume displayed a linear dependence on the laser pulse energy. This dependence allowed determining a threshold energy density value, independent of the laser focusing conditions, which acted as necessary conditions for the transfer to occur. The corresponding sufficient condition was given by a different total energy threshold for each laser beam dimension. The threshold energy density was found to be the dimensional parameter that determined the amount of the transferred liquid per laser pulse, and there was no substantial loss of material due to liquid vaporization during the transfer.

Accurate and efficient simulation of multiphase flow in a heterogeneous reservoir by using error estimate and control in the multiscale finite-volume framework

The multiscale finite-volume (MSFV) method is designed to reduce the computational cost of elliptic and parabolic problems with highly heterogeneous anisotropic coefficients. The reduction is achieved by splitting the original global problem into a set of local problems (with approximate local boundary conditions) coupled by a coarse global problem. It has been shown recently that the numerical errors in MSFV results can be reduced systematically with an iterative procedure that provides a conservative velocity field after any iteration step. The iterative MSFV (i-MSFV) method can be obtained with an improved (smoothed) multiscale solution to enhance the localization conditions, with a Krylov subspace method [e.g., the generalized-minimal-residual (GMRES) algorithm] preconditioned by the MSFV system, or with a combination of both. In a multiphase-flow system, a balance between accuracy and computational efficiency should be achieved by finding a minimum number of i-MSFV iterations (on pressure), which is necessary to achieve the desired accuracy in the saturation solution. In this work, we extend the i-MSFV method to sequential implicit simulation of time-dependent problems. To control the error of the coupled saturation/pressure system, we analyze the transport error caused by an approximate velocity field. We then propose an error-control strategy on the basis of the residual of the pressure equation. At the beginning of simulation, the pressure solution is iterated until a specified accuracy is achieved. To minimize the number of iterations in a multiphase-flow problem, the solution at the previous timestep is used to improve the localization assumption at the current timestep. Additional iterations are used only when the residual becomes larger than a specified threshold value. Numerical results show that only a few iterations on average are necessary to improve the MSFV results significantly, even for very challenging problems. Therefore, the proposed adaptive strategy yields efficient and accurate simulation of multiphase flow in heterogeneous porous media.

First-passage times for non-Markovian processes: Correlated impacts on a free process

We develop a method to obtain first-passage-time statistics for non-Markovian processes driven by dichotomous fluctuations. The fluctuations themselves need not be Markovian. We calculate analytic first-passage-time distributions and mean first-passage times for exponential, rectangular, and long-tail temporal distributions of the fluctuations.

Viral self-assembly as a thermodynamic process

The protein shells, or capsids, of nearly all spherelike viruses adopt icosahedral symmetry. In the present Letter, we propose a statistical thermodynamic model for viral self-assembly. We find that icosahedral symmetry is not expected for viral capsids constructed from structurally identical protein subunits and that this symmetry requires (at least) two internal switching configurations of the protein. Our results indicate that icosahedral symmetry is not a generic consequence of free energy minimization but requires optimization of internal structural parameters of the capsid proteins

Influence of hydrodynamic interactions on the adsoption process of large particles

We have studied the adsorption process of non-Brownian particles on a line. Our work differs from previously proposed models in that we have incorporated hydrodynamic interactions between the incoming particles and the preadsorbed particles as well as the surface. We then numerically analyze the effect of these interactions on quantities related to the adsorption process. Comparing our model to the ballistic deposition model (BM) shows a significant discrepancy in the pair correlation function. These results can explain some differences between recent experiments and BM predictions. Finally, the limitations of the applicability of BM are addressed.