Spreading of a surfactant monolayer on a thin liquid film: Onset and evolution of digitated structures

We describe the response of an insoluble surfactant monolayer spreading on the surface of a thin liquid film to small disturbances in the film thickness and surfactant concentration. The surface shear stress, which derives from variations in surfactant concentration at the air–liquid interface, rapidly drives liquid and surfactant from the source toward the distal region of higher surface tension. A previous linear stability analysis of a quasi-steady state solution describing the spreading of a finite strip of surfactant on a thin Newtonian film has predicted only stable modes. [Dynamics in Small Confining Systems III, Materials Research Society Symposium Proceedings, edited by J. M. Drake, J. Klafter, and E. R. Kopelman (Materials Research Society, Boston, 1996), Vol. 464, p. 237; Phys. Fluids A 9, 3645 (1997); O. K. Matar Ph.D. thesis, Princeton University, Princeton, NJ, 1998]. A perturbation analysis of the transient behavior, however, has revealed the possibility of significant amplification of disturbances in the film thickness within an order one shear time after the onset of flow [Phys. Fluids A 10, 1234 (1998); "Transient response of a surfactant monolayer spreading on a thin liquid film: Mechanism for amplification of disturbances," submitted to Phys. Fluids]. In this paper we describe the linearized transient behavior and interpret which physical parameters most strongly affect the disturbance amplification ratio. We show how the disturbances localize behind the moving front and how the inclusion of van der Waals forces further enhances their growth and lifetime. We also present numerical solutions to the fully nonlinear 2D governing equations. As time evolves, the nonlinear system sustains disturbances of longer and longer wavelength, consistent with the quasi-steady state and transient linearized descriptions. In addition, for the parameter set investigated, disturbances consisting of several harmonics of a fundamental wavenumber do not couple significantly. The system eventually singles out the smallest wavenumber disturbance in the chosen set. The summary of results to date seems to suggest that the fingering process may be a transient response which nonetheless has a dramatic influence on the spreading process since the digitated structures redirect the flux of liquid and surfactant to produce nonuniform surface coverage

Improving the Robustness and Accuracy of Crime Prediction with the Self-Exciting Point Process Through Isotropic Triggering

The self-exciting point process (SEPP) is a model of the spread of crime in space and time, incorporating background and triggering processes. It shows promising predictive performance and forms the basis of a popular commercial software package, however few detailed case studies describing the application of the SEPP to crime data exist in the scientific literature. Using open crime data from the City of Chicago, USA, we apply the SEPP to crime prediction of assaults and burglaries in nine distinct geographical regions of the city. The results indicate that the algorithm is not robust to certain features of the data, generating unrealistic triggering functions in various cases. A simulation study is used to demonstrate that this outcome is associated with a reduction in predictive accuracy. Analysing the second-order spatial properties of the data demonstrates that the failures in the algorithm are correlated with anisotropy. A modified version of the SEPP model is developed in which triggering is non-directional. We show that this provides improved robustness, both in terms of the triggering structure and the predictive accuracy

Aggregate models of climate change: development and applications

Impulse-response-function (lRF) models are designed for applications requiring a large number of climate simulations, such as multi-scenario climate change impact studies or cost-benefit integrated-assessment studies. The models apply linear response theory to reproduce the characteristics of the climate response tq external forcing computed with sophisticated state-of-the-art climate models like general circulation models of the physical ocean-atmosphere system and three-dimensional oceanic-plus-terrestrial carbon cycle models. Although highly computer efficient, IRF models are nonetheless capable of reproducing the full set of climate-change information generated by the complex models against which they are calibrated. While limited in principle to the linear response regime (less than about 3"C temperature change), the applicability of the IRn'model presented in this paper has been extended into the nonlinear domain through explicit treatment of the climate system's dominant nonlinearities: CO2 chemistry in ocean water, CO2 feúilization of land biota, and sublinear radiative forcing. The resultant Nonlinear Impulse-response model of the coupled Carbon cycle-Climate System (NICCS) computes the temporal evolution of spatial patterns of climate change in four climate variables of particular relevance for climate impact studies: near-surface temperature, cloud cover, precipitation, and sea level. The space-time response characteristics of the model are derived from an EoF analysis of a transient 850-year greenhouse warming simulation with the Hamburg atmosphere-ocean general circulation model ECHAM3-LSG and a similar response experiment with the Hamburg ocean carbon cycle model HAMOCC. Emission scenarios studied with the model cover time horizons ranging from 30 years (the Kiel-Volkswagen model) over projections for the 2L"t century (rras.L) to two idealized 1000-year scenarios which demonstrate that the use of all currently estimated fossil fuel resources would carry the Earth's climate far beyond the range of climate change for which reliable quantitative predictions are possible today, and that even a freezing of emissions to present-day levels would not be sufficient to prevent a major global warming in the long term. Further applications of the model include its combination with, and incorporation into, other models: integrated assessment studies, investigations of climate change feedbacks onto the terrestrial carbon cycle, and an educational tool developed for the EXPO2000 World Exhibition

A Survey on Reservoir Computing and its Interdisciplinary Applications Beyond Traditional Machine Learning

Reservoir computing (RC), first applied to temporal signal processing, is a recurrent neural network in which neurons are randomly connected. Once initialized, the connection strengths remain unchanged. Such a simple structure turns RC into a non-linear dynamical system that maps low-dimensional inputs into a high-dimensional space. The model's rich dynamics, linear separability, and memory capacity then enable a simple linear readout to generate adequate responses for various applications. RC spans areas far beyond machine learning, since it has been shown that the complex dynamics can be realized in various physical hardware implementations and biological devices. This yields greater flexibility and shorter computation time. Moreover, the neuronal responses triggered by the model's dynamics shed light on understanding brain mechanisms that also exploit similar dynamical processes. While the literature on RC is vast and fragmented, here we conduct a unified review of RC's recent developments from machine learning to physics, biology, and neuroscience. We first review the early RC models, and then survey the state-of-the-art models and their applications. We further introduce studies on modeling the brain's mechanisms by RC. Finally, we offer new perspectives on RC development, including reservoir design, coding frameworks unification, physical RC implementations, and interaction between RC, cognitive neuroscience and evolution.Comment: 51 pages, 19 figures, IEEE Acces

Generalized Exclusion Processes: Transport Coefficients

A class of generalized exclusion processes parametrized by the maximal occupancy, $k\geq 1$, is investigated. For these processes with symmetric nearest-neighbor hopping, we compute the diffusion coefficient and show that it is independent on the spatial dimension. In the extreme cases of $k=1$ (simple symmetric exclusion process) and $k=\infty$ (non-interacting symmetric random walks) the diffusion coefficient is constant; for $2\leq k<\infty$, the diffusion coefficient depends on the density and the maximal occupancy $k$. We also study the evolution of a tagged particle. It exhibits a diffusive behavior which is characterized by the coefficient of self-diffusion which we probe numerically.Comment: v1: 9 pages, 6 figures. v2: + 2 references. v3: 10 pages, 7 figures, published versio

Implementation of Adaptive Localization for Enhancing Ensemble-Based History Matching in Hydrocarbon Reservoir Management

In reservoir management, the ensemble-based history matching is applied to quantify and update uncertainty in reservoir characterization with the main objective to support high quality decisions. However, the ensemble-based history matching could suffer from statistical problems that make the ensemble unable to represent probability distributions and quantify uncertainty statistically-correctly. Localization can effectively solve the ensemble-based history matching problems. Localization weights the influence degree that observations have over model parameters in the analysis step of ensemble Kalman filter-based methods. In the non-adaptive localization scheme, the influence degree is fixed in time, and unimodal distributed for all types of observations and model parameters. Unlike the non-adaptive localization scheme, the adaptive localization scheme defines the influence degrees based on causality relationships among simulated observables and model parameters, so that the influence degrees can be time-variant, multimodal distributed, and dependent of reservoir dynamics and different types of model parameters and observations. The thesis lies in the research about the practical advantage of adaptive localization over non-adaptive localization schemes for ensembled-based history matching. The thesis is developed in five sections: i) generation of the initial ensemble; ii) development of an ensemble-based history matching without localization, the benchmark case, that applies ES-MDA; iii) selection of the best non-adaptive localization case, applying distance-based studies; iv) Selection of the best adaptive localization case, applying a denoising approach; and v) Comparative analysis among updated ensembles, defining selection criteria of the best ensemble-based history matching for the Reek field. The main conclusion from the thesis work is that the history matching with the adaptive localization scheme overperformed the history matching with the non-adaptive localization scheme and the benchmark case (i.e., no localization) for the Reek field. Therefore, adaptive localization scheme can improve uncertainty quantification and decision quality in ensemble-based reservoir management. The novelty of the thesis is that it has investigated the practical pros and cons of applying the adaptive localization scheme for ensemble-based history matching reservoir simulation models and proposed a general workflow to guide localization implementation and evaluation. The thesis work has brought state-of-the-art and innovative workflows to best practice in Equinor for implementing non-adaptive and adaptive localization schemes. Several guidelines of recommended practice of implementing the workflows have been proposed and developed. The effectiveness of the guidelines and workflows have been tested and evaluated, which contributes to further developing and improving the theories/workflows/guidelines and integrating them in Equinor’s existing workflows and software for quantitative and qualitative analysis of history matching results and for facilitating and enhancing the adaptive localization implementation in Equinor and the oil and gas industry