Results 1  10
of
10
MODELING AND SIMULATION WITH OPERATOR SCALING
, 2009
"... Selfsimilar processes are useful in modeling diverse phenomena that exhibit scaling properties. Operator scaling allows a different scale factor in each coordinate. This paper develops practical methods for modeling and simulating stochastic processes with operator scaling. A simulation method for ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
Selfsimilar processes are useful in modeling diverse phenomena that exhibit scaling properties. Operator scaling allows a different scale factor in each coordinate. This paper develops practical methods for modeling and simulating stochastic processes with operator scaling. A simulation method for operator stable Lévy processes is developed, based on a series representation, along with a Gaussian approximation of the small jumps. Several examples are given to illustrate practical applications. A classification of operator stable Lévy processes in two dimensions is provided according to their exponents and symmetry groups. We conclude with some remarks and extensions to general operator selfsimilar processes.
HYDROLOGIC SYSTEMS BY
"... In this dissertation I discuss approaches to building hydrologic understanding in a changing world that go beyond the construction of models of evergreater complexity. These approaches aim to develop insight into the relationship between catchment properties and hydrologic dynamics using reducedco ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
In this dissertation I discuss approaches to building hydrologic understanding in a changing world that go beyond the construction of models of evergreater complexity. These approaches aim to develop insight into the relationship between catchment properties and hydrologic dynamics using reducedcomplexity models, andbylookingforpatternsthatrevealemergentrelationshipsbetweenhydrologicsystemsandthelandscapes they are embedded in. The dissertation proposes a framework for thinking about hydrologic systems in a changing world based on seeking a synthesis between the search for mechanistic descriptions of landscape processes, and the search for explanations for emergent landscape patterns. The dissertation is divided into two parts. The first describes a series of studies considering controls on the propagation of hydrologic variability through the landscape. One discusses the propagation of water and solutes through the vadose zone, another the lateral movement of water through a hillslope, and the third the accumulated effect of many hillslopes on the recession of flows at a watershed outlet. Each case builds on parsimonious representations of hydrologic processes to distill analytical results in terms of landscape and climate properties. These analytical results are used to define ‘regimes ’ of hydrologic behavior in which particular properties play decisive roles in the hydrologic system. The studies demonstrate that the regime framework yields insight into controls on the aggregate behavior of hydrologic system that can be used to
Contents lists available at ScienceDirect Computers and Mathematics with Applications
"... journal homepage: www.elsevier.com/locate/camwa On nonoscillation of mixed advanceddelay differential equations with ..."
Abstract
 Add to MetaCart
(Show Context)
journal homepage: www.elsevier.com/locate/camwa On nonoscillation of mixed advanceddelay differential equations with
1MODELING AND SIMULATION WITH OPERATOR SCALING: EXTENDED VERSION WITH ADDITIONAL EXAMPLES
"... Abstract. Selfsimilar processes are useful models for natural systems that exhibit scaling. Operator scaling allows a different scale factor in each coordinate. This paper develops practical methods for modeling and simulation. A simulation method is developed for operator scaling Lévy processes, ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. Selfsimilar processes are useful models for natural systems that exhibit scaling. Operator scaling allows a different scale factor in each coordinate. This paper develops practical methods for modeling and simulation. A simulation method is developed for operator scaling Lévy processes, based on a series representation, along with a Gaussian approximation of the small jumps. Several examples are given to illustrate the range of practical applications. A complete characterization of symmetries is given in two dimensions, for any exponent and spectral measure, to inform the choice of these model parameters. The paper concludes with some extensions to general operator selfsimilar processes. 1.
Journal of Multivariate Analysis 123 (2014) 172–183 Contents lists available at ScienceDirect Journal of Multivariate Analysis
"... journal homepage: www.elsevier.com/locate/jmva ..."
(Show Context)
Truncated MultiGaussian Fields and Effective Conductance of Binary Media
"... Truncated Gaussian fields provide a flexible model for defining binary media with dispersed (as opposed to layered) inclusions. General properties of excursion sets on these truncated fields are coupled with a distancebased upscaling algorithm and approximations of point process theory to develop ..."
Abstract
 Add to MetaCart
(Show Context)
Truncated Gaussian fields provide a flexible model for defining binary media with dispersed (as opposed to layered) inclusions. General properties of excursion sets on these truncated fields are coupled with a distancebased upscaling algorithm and approximations of point process theory to develop an estimation approach for effective conductivity in twodimensions. Estimation of effective conductivity is derived directly from knowledge of the kernel size used to create the multiGaussian field, defined as the fullwidth at half maximum (FWHM), the truncation threshold and conductance values of the two modes. Therefore, instantiation of the multiGaussian field is not necessary for estimation of the effective conductance. The critical component of the effective medium approximation developed here is the mean distance between high conductivity inclusions. This mean distance is characterized as a function of the FWHM, the truncation threshold and the ratio of the two modal conductivities. Sensitivity of the resulting effective conductivity to this mean distance is examined for two levels of contrast in the modal conductances and different FWHM sizes. Results demonstrate that the FWHM is a robust measure of mean travel distance in the background medium. The resulting effective conductivities are accurate when compared to numerical results and results obtained from effective media theory, distancebased upscaling and numerical simulation.
1 UPSCALING OF A DUALPERMEABILITY MONTE CARLO SIMULATION MODEL FOR CONTAMINANT TRANSPORT IN FRACTURED NETWORKS BY GENETIC ALGORITHM PARAMETER IDENTIFICATION
"... The transport of radionuclides in fractured media plays a fundamental role in determining the level of risk offered by a radioactive waste repository in terms of expected doses. Discrete Fracture Networks (DFN) methods can provide detailed solutions to the problem of modeling the contaminant transpo ..."
Abstract
 Add to MetaCart
(Show Context)
The transport of radionuclides in fractured media plays a fundamental role in determining the level of risk offered by a radioactive waste repository in terms of expected doses. Discrete Fracture Networks (DFN) methods can provide detailed solutions to the problem of modeling the contaminant transport in fractured media. However, within the framework of the performance assessment (PA) of radioactive waste repositories, the computational efforts required are not compatible with the repeated calculations that need to be performed for the probabilistic uncertainty and sensitivity analyses of PA. In this paper, we present a novel upscaling approach, which consists in computing the detailed numerical fractured flow and transport solutions on a small scale and use the results to derive the equivalent continuum parameters of a lean, onedimensional DualPermeability, Monte Carlo Simulation (DPMCS) model by means of a Genetic Algorithm search. The proposed upscaling procedure is illustrated with reference to a realistic case study of Pu239 migration taken from literature.
Influence of fracture statistics on advective transport and
"... implications for geologic repositories ..."
www.elsevier.com/locate/spa Modeling and simulation with operator scaling
, 2010
"... Selfsimilar processes are useful models for natural systems that exhibit scaling. Operator scaling allows a different scale factor in each coordinate. This paper develops practical methods for modeling and simulation. A simulation method is developed for operator scaling Lévy processes, based on a ..."
Abstract
 Add to MetaCart
(Show Context)
Selfsimilar processes are useful models for natural systems that exhibit scaling. Operator scaling allows a different scale factor in each coordinate. This paper develops practical methods for modeling and simulation. A simulation method is developed for operator scaling Lévy processes, based on a series representation, along with a Gaussian approximation of the small jumps. Several examples are given to illustrate the range of practical applications. A complete characterization of symmetries in two dimensions is given, for any exponent and spectral measure, to inform the choice of these model parameters. The paper concludes with some extensions to general operator selfsimilar processes.