Correlated continuous-time random walks: combining scale-invariance with long-range memory for spatial and temporal dynamics

Standard continuous time random walk (CTRW) models are renewal processes in the sense that at each jump a new, independent pair of jump length and waiting time are chosen. Globally, anomalous diffusion emerges through action of the generalized central limit theorem leading to scale-free forms of the jump length or waiting time distributions. Here we present a modified version of recently proposed correlated CTRW processes, where we incorporate a power-law correlated noise on the level of both jump length and waiting time dynamics. We obtain a very general stochastic model, that encompasses key features of several paradigmatic models of anomalous diffusion: discontinuous, scale-free displacements as in Levy flights, scale-free waiting times as in subdiffusive CTRWs, and the long-range temporal correlations of fractional Brownian motion (FBM). We derive the exact solutions for the single-time probability density functions and extract the scaling behaviours. Interestingly, we find that different combinations of the model parameters lead to indistinguishable shapes of the emerging probability density functions and identical scaling laws. Our model will be useful to describe recent experimental single particle tracking data, that feature a combination of CTRW and FBM properties.Comment: 25 pages, IOP style, 5 figure

The Third Gravitational Lensing Accuracy Testing (GREAT3) Challenge Handbook

The GRavitational lEnsing Accuracy Testing 3 (GREAT3) challenge is the third in a series of image analysis challenges, with a goal of testing and facilitating the development of methods for analyzing astronomical images that will be used to measure weak gravitational lensing. This measurement requires extremely precise estimation of very small galaxy shape distortions, in the presence of far larger intrinsic galaxy shapes and distortions due to the blurring kernel caused by the atmosphere, telescope optics, and instrumental effects. The GREAT3 challenge is posed to the astronomy, machine learning, and statistics communities, and includes tests of three specific effects that are of immediate relevance to upcoming weak lensing surveys, two of which have never been tested in a community challenge before. These effects include realistically complex galaxy models based on high-resolution imaging from space; spatially varying, physically-motivated blurring kernel; and combination of multiple different exposures. To facilitate entry by people new to the field, and for use as a diagnostic tool, the simulation software for the challenge is publicly available, though the exact parameters used for the challenge are blinded. Sample scripts to analyze the challenge data using existing methods will also be provided. See http://great3challenge.info and http://great3.projects.phys.ucl.ac.uk/leaderboard/ for more information.Comment: 30 pages, 13 figures, submitted for publication, with minor edits (v2) to address comments from the anonymous referee. Simulated data are available for download and participants can find more information at http://great3.projects.phys.ucl.ac.uk/leaderboard

Upscaling nonreactive solute transport

This thesis focuses on solute transport upscaling. Upscaling of solute transport is usually required to obtain computationally efficient numerical models in many field applications such as, remediation of aquifers, environmental risk to groundwater resources or the design of underground repositories of nuclear waste. The non-Fickian behavior observed in the field, and manifested by peaked concentration profiles with pronounced tailing, has questioned the use of the classical advection-dispersion equation to simulate solute transport at field scale using numerical models with discretizations that cannot capture the field heterogeneity. In this context, we have investigated the use of the advection-dispersion equation with mass transfer as a tool for upscaling solute transport in a general numerical modeling framework. Solute transport by groundwater is very much affected by the presence of high and low water velocity zones, where the contaminant can be channelized or stagnant. These contrasting water velocity zones disappear in the upscaled model as soon as the scale of discretization is larger that the size of these zones. We propose, for the modeling solute transport at large scales, a phenomenological model based on the concept of memory functions, which are used to represent the unresolved processes taking place within each homogenized block in the numerical models. We propose a new method to estimate equivalent blocks, for which transport and mass transfer parameters have to be provided. The new upscaling technique consists in replacing each heterogeneous block by a homogeneous one in which the parameters associated to a memory functions are used to represent the unresolved mass exchange between highly mobile and less mobile zones occurring within the block. Flow upscaling is based on the Simple Laplacian with skin, whereas transport upscaling is based in the estimation of macrodispersion and mass transfer parameters as a result of the interpretation of the rLlerar Meza, G. (2009). Upscaling nonreactive solute transport [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/5848Palanci

Solute transport in bounded porous media characterized by Generalized Sub-Gaussian log-conductivity distributions

There are increasing evidences that probability distributions and associated statistical moments of a variety of hydrogeological and soil science variables and their spatial increments display distinctive scale-dependent features that are not captured by a typical Gaussian model. A Generalized Sub-Gaussian (GSG) model is able to capture key aspects of this pattern. We present the results of a suite of computational analyses set in a Monte Carlo framework and aimed at assessing the impact of a GSG structure of log hydraulic conductivity (Y) on transport of a conservative solute through a three-dimensional bounded porous medium under steady-state saturated Darcy flow. Our results indicate that the longitudinal spreading of a plume is on average significantly smaller for Sub-Gaussian than for Gaussian Y fields. Otherwise, the velocity field arising from a Sub-Gaussian Y field induces enhanced plume stretching with respect to what can be observed in a Gaussian Y setting, this aspect potentially influencing the strength of solute mixing within these two types of conductivity domains. We also find that, in some cases, it may be difficult to identify the nature of the underlying conductivity field relying solely on observations of solute concentrations migrating within the system. In this regard, we show that the action of local dispersion tends to mask the influence of Sub-Gaussianity on major transport metrics.The authors would like to thank the EU, MIUR, and MINECO for funding, in the frame of the collaborative international Consortium (WE-NEED) financed under the ERA-NET WaterWorks2014 Cofunded Call. This ERA-NET is an integral part of the 2015 Joint Activities developed by the Water Challenges for a Changing World Joint Programme Initiative (Water JPI). Part of the work was developed while Prof. A. Guadagnini was at the University of Strasbourg with funding from Région Grand-Est and Strasbourg-Eurométropole through the Chaire Gutenberg. The UPC authors acknowledge funding from AGAUR Research Groups, 2017 SGR 1485.Peer ReviewedPostprint (author's final draft

Modeling and simulating chemical weapon dispersal patterns in DIRSIG

Fieldable thermal infrared hyperspectral imaging spectrometers have made it possible to design and construct new instruments for better detection of battlefield hazards such as chemical weapon clouds. The availability of spectroscopic measurements of these clouds can be used not only for the detection and identification of specific chemical agents but also to potentially quantify the lethality of the cloud. The simulation of chemical weapon dispersal patterns in a synthetic imaging environment offers significant benefits to sensor designers. Such an environment allows designers to easily develop trade spaces to test detection and quantification algorithms without the need for expensive and dangerous field releases. This research focuses on the implementation of a generic gas dispersion model that has been integrated into the Digital Imaging and Remote Sensing Generation (DIRSIG) model. The gas cloud model utilizes a 3D Gaussian distribution based on theory to predict factory stack gas plumes. The model incorporates first order dynamics (drift and dispersion) to drive the macro-scale cloud development and movement. The model also attempts to account for turbulence by using fractal fractional Brownian motion techniques to reproduce the micro-scale variances within the cloud. The cloud pathlength concentrations are then processed by the DIRSIG radiometry sub-model to compute the emission and transmission of the cloud body on a per-pixel basis. Example hyperspectral image cubes containing common agents and release amounts are presented. Time lapse sequences are also provided to demonstrate the evolution of the cloud over time. Finally, recommendations and limitations of the model are listed for future improvements