Deterministic Realization Research Articles

Rate equation analysis for deterministic and unidirectional lasing in ring resonators with an S-shaped coupler

Ring resonators are traditionally popular optical devices that apply to various components in photonic ICs. They also play an important role in the on-chip generation of many novel optical states in topological systems and non-Hermitian systems. Unidirectional lasing of ring resonators is used in many such systems to create exotic states of light including optical vortexes and optical skyrmions, but the unidirectional behavior has not been fully understood. Previous research has constructed a simplified model to explain the steady state behaviors of unidirectional ring resonators, but the carrier dynamics and spontaneous emission were omitted. In this work, we give a numerical analysis of unidirectional ring resonators with an S-shaped coupler. We identified the importance of the gain saturation to robustness against backscattering and high unidirectionality by comparing to the model without saturation. We also discuss the effect of asymmetrical coupling on the deterministic realization of unidirectionality.

Deterministic realization of trace-preserving channels in linear-optical systems

Deterministic realization of trace-preserving channels in linear-optical systems

Uncertainty Quantification in Reservoir Simulation Using Modern Data Assimilation Algorithm

Production forecasting using numerical simulation has become a standard in the oil and gas industry. The model construction process requires an explicit definition of multiple uncertain parameters; thus, the outcome of the modelling is also uncertain. For the reservoirs with production data, the uncertainty can be reduced by history-matching. However, the manual matching procedure is time-consuming and usually generates one deterministic realization. Due to the ill-posed nature of the calibration process, the uncertainty cannot be captured sufficiently with only one simulation model. In this paper, the uncertainty quantification process carried out for a gas-condensate reservoir is described. The ensemble-based uncertainty approach was used with the ES-MDA algorithm, conditioning the models to the observed data. Along with the results, the author described the solutions proposed to improve the algorithm’s efficiency and to analyze the factors controlling modelling uncertainty. As a part of the calibration process, various geological hypotheses regarding the presence of an active aquifer were verified, leading to important observations about the drive mechanism of the analyzed reservoir.

The Value of Probabilistic Prediction for Lightning Ignited Fires

AbstractIn 2021, the availability of a physical model for lightning density prediction at ECMWF led to the development of data driven models to identify episodes conducive of fires. The machine‐learning classifiers worked remarkably well reaching an overall accuracy up to 78%. Still, errors in the lightning forecast substantially reduce the prediction skill. An ensemble of predictions is used to take into account the stochastic nature of the forecast errors. An assessment of the predictive skill in terms of probabilities is performed and is bench‐marked against the deterministic outcome provided by a single deterministic realization. The probabilistic prediction is more skillful than the deterministic one and there is an optimal probability threshold that allows to maximize the correlation between prediction and observed ignitions. Probabilistic forecast also brings the best value for money when a cost‐loss analysis is performed, and a potential economic value is attributed to the forecast.

The Application of Ensemble Wave Forcing to Quantify Uncertainty of Shoreline Change Predictions

AbstractReliable predictions and accompanying uncertainty estimates of coastal evolution on decadal to centennial time scales are increasingly sought. So far, most coastal change projections rely on a single, deterministic realization of the unknown future wave climate, often derived from a global climate model. Yet, deterministic projections do not account for the stochastic nature of future wave conditions across a variety of temporal scales (e.g., daily, weekly, seasonally, and interannually). Here, we present an ensemble Kalman filter shoreline change model to predict coastal erosion and uncertainty due to waves at a variety of time scales. We compare shoreline change projections, simulated with and without ensemble wave forcing conditions by applying ensemble wave time series produced by a computationally efficient statistical downscaling method. We demonstrate a sizable (site‐dependent) increase in model uncertainty compared with the unrealistic case of model projections based on a single, deterministic realization (e.g., a single time series) of the wave forcing. We support model‐derived uncertainty estimates with a novel mathematical analysis of ensembles of idealized process models. Here, the developed ensemble modeling approach is applied to a well‐monitored beach in Tairua, New Zealand. However, the model and uncertainty quantification techniques derived here are generally applicable to a variety of coastal settings around the world.

Deterministic realization of collective measurements via photonic quantum walks

Collective measurements on identically prepared quantum systems can extract more information than local measurements, thereby enhancing information-processing efficiency. Although this nonclassical phenomenon has been known for two decades, it has remained a challenging task to demonstrate the advantage of collective measurements in experiments. Here, we introduce a general recipe for performing deterministic collective measurements on two identically prepared qubits based on quantum walks. Using photonic quantum walks, we realize experimentally an optimized collective measurement with fidelity 0.9946 without post selection. As an application, we achieve the highest tomographic efficiency in qubit state tomography to date. Our work offers an effective recipe for beating the precision limit of local measurements in quantum state tomography and metrology. In addition, our study opens an avenue for harvesting the power of collective measurements in quantum information-processing and for exploring the intriguing physics behind this power.

Intrusive Galerkin Projection for Model Order Reduction of Uncertain Linear Dynamic Systems

This paper deals with model order reduction of random parameter-dependent (RPD) linear time invariant (LTI) systems by using the RPD-balanced realization (BR), recently developed by the same authors. A novel way to deal with this crucial issue is presented. It is based on the intrusive Galerkin projection of the RPD-BR. Indeed, it is shown, through numerical simulations, that the intrusive Galerkin projection of the RPD-BR into the generalized polynomial chaos (GPC) space enables to generate a deterministic realization preserving stability properties for the original RPD-model. Moreover, the new deterministic state variables, which are the stochastic modes of the RPD-balanced state variables, are ordered with respect to their sub-contributions to the RPD-input/output behaviour, measured by deterministic Hankel values. Hence, a deterministic reduced order model is derived by deleting the state variables with small Hankel values and the complete RPD-reduced order model is then obtained. The feasibility of the proposed method is analyzed while its accuracy is compared to the RPD-truncated balanced realization (RPD-TBR).

Analytical model for radiative transfer including the effects of a rough material interface

The reflected and transmitted radiance due to a source located above a water surface is computed based on models for radiative transfer in continuous optical media separated by a discontinuous air-water interface with random surface roughness. The air-water interface is described as the superposition of random, unresolved roughness on a deterministic realization of a stochastic wave surface at resolved scales. Under the geometric optics assumption, the bidirectional reflection and transmission functions for the air-water interface are approximated by applying regular perturbation methods to Snell's law and including the effects of a random surface roughness component. Formal analytical solutions to the radiative transfer problem under the small-angle scattering approximation account for the effects of scattering and absorption as light propagates through the atmosphere and water and also capture the diffusive effects due to the interaction of light with the rough material interface that separates the two optical media. Results of the analytical models are validated against Monte Carlo simulations, and the approximation to the bidirectional reflection function is also compared to another well-known analytical model.

Model-Free Predictive Anti-Slug Control of a Well-Pipeline-Riser

Simplied linearized discrete time dynamic state space models are developed for a 3-phase well-pipelineriser and tested together with a high delity dynamic model built in K-Spice and LedaFlow. In addition the Meglio pipeline-riser model is used as an example process. These models are developed from a subspace algorithm, i.e. Deterministic and Stochastic system identication and Realization (DSR), and implemented in a Model Predictive Controller (MPC) for stabilizing the slugging regime. The MPC, LQR and PI control strategies are tested.

Estimation of LPV-SS Models with Static Dependency using Correlation Analysis

Many global identification approaches described in the literature for estimating linear parameter-varying (LPV) discrete-time state-space (SS) models with affine dependence on the scheduling parameter suffer heavily from the curse of dimensionality making identification of moderate sized systems computationally intensive or infeasible. In this paper, we present a novel two-step approach to estimate LPV-SS models based on a single data set with varying scheduling signal by combining 1) LPV correlation analysis, and 2) a deterministic LPV realization scheme. Step 1 includes the estimation of the sub-Markov parameters of the system using correlation analysis of the involved signals. Subsequently, for Step 2, this paper presents a novel basis reduced exact Ho-Kalman like realization scheme, which uses only sub parts of the extended Hankel matrix. Therefore, the computational complexity is significantly reduced compared to the full scheme. To demonstrate that the basis reduction does not lead to a loss in performance, a simulation study is provided.

Model-free optimal anti-slug control of a well-pipeline-riser in the K-Spice/LedaFlow simulator

Simplified models are developed for a 3-phase well-pipeline-riser and tested together with a high fidelity dynamic model built in K-Spice and LedaFlow. These models are developed from a subspace algorithm, i.e. Deterministic and Stochastic system identification and Realization (DSR), and implemented in a Linear Quadratic optimal Regulator (LQR) for stabilizing the slugging regime. We are comparing LQR with PI controller using different performance measures.

Plasmonic nanoring fabrication tuned to pitch: Efficient, deterministic, and large scale realization of ultra-small gaps for next generation plasmonic devices

A double-patterning process for scalable, efficient, and deterministic nanoring array fabrication is presented. It enables gaps and features below a size of 20 nm. A writing time of 3 min/cm2 makes this process extremely appealing for scientific and industrial applications. Numerical simulations are in agreement with experimentally measured optical spectra. Therefore, a platform and a design tool for upcoming next generation plasmonic devices like hybrid plasmonic quantum systems are delivered.

Modelling Development of a Thermal Gas/Oil Gravity-Drainage Process in an Extraheavy-Oil Fractured Reservoir

Summary Thermal gas/oil gravity drainage (T-GOGD) is an attractive enhanced-oil-recovery method applicable to naturally fractured reservoirs (NFRs). The process is applied successfully in Qarn Alam, a heavy-oil field in Oman. This paper presents a case study featuring dynamic-modelling optimization and uncertainty-analysis workflow for T-GOGD in a bitumen-bearing fractured reservoir on the basis of realistic 3D fracture characterization. In T-GOGD, the fractures are displaced to steam to provide a (matrix) gravity-drainage potential while heating the reservoir at the same time. One of the recovery mechanisms associated with T-GOGD is thermal expansion, which can result in high initial rates, but may cause plugging of the fracture system in the case of extraheavy oil (bitumen) if the expanded oil cools down before it is being produced. This situation requires short-distance well configurations and/or steam-stimulation cycles to establish communication. In an NFR, steam vapour occupies the fracture system while oil drains through the matrix, increasing the area for heat transfer with respect to the steam-chamber case; the process therefore differs significantly from steam-assisted gravity drainage, and a different production function applies. Shell’s in-house reservoir simulator MoReS with advanced dual-permeability capability is used to model development of T-GOGD in a bitumen reservoir employing 3D element-of-symmetry (EOS) models. A realistic fracture-characterization and -modelling process is described. The geometrical well configuration and operating schedule and strategy are optimized on an economic function for a deterministic subsurface realization. Using an uncertainty-analysis work flow, cumulative distribution functions of recovery and steam/oil ratio (SOR) are generated. Finally, robust optimization is explored by use of an economic objective function. The study concludes that (1) relatively large well spacing is feasible while injector/producer horizontal well offset is necessary to avoid steam channeling to the producer well, (2) live steamproduction control is a robust operating strategy, (3) performance is most sensitive to matrix permeability and oil viscosity, and (4) vertical fracture connectivity plays an important role in the process performance. T-GOGD has significant potential to develop the bitumen resource in naturally fractured carbonates.

System Identification of a Non-Uniformly Sampled Multi-Rate System in Aluminium Electrolysis Cells

Standard system identication algorithms are usually designed to generate mathematical models with equidistant sampling instants, that are equal for both input variables and output variables. Unfortunately, real industrial data sets are often disrupted by missing samples, variations of sampling rates in the dierent variables (also known as multi-rate systems), and intermittent measurements. In industries with varying events based maintenance or manual operational measures, intermittent measurements are performed leading to uneven sampling rates. Such is the case with aluminium smelters, where in addition the materials fed into the cell create even more irregularity in sampling. Both measurements and feeding are mostly manually controlled. A simplied simulation of the metal level in an aluminium electrolysis cell is performed based on mass balance considerations. System identication methods based on Prediction Error Methods (PEM) such as Ordinary Least Squares (OLS), and the sub-space method combined Deterministic and Stochastic system identication and Realization (DSR), and its variants are applied to the model of a single electrolysis cell as found in the aluminium smelters. Aliasing phenomena due to large sampling intervals can be crucial in avoiding unsuitable models, but with knowledge about the system dynamics, it is easier to optimize the sampling performance, and hence achieve successful models. The results based on the simulation studies of molten aluminium height in the cells using the various algorithms give results which tally well with the synthetic data sets used. System identication on a smaller data set from a real plant is also implemented in this work. Finally, some concrete suggestions are made for using these models in the smelters.

Numerical strategy for unbiased homogenization of random materials

SUMMARYThis paper presents a numerical strategy that allows to lower the costs associated to the prediction of the value of homogenized tensors in elliptic problems. This is performed by solving a coupled problem, in which the complex microstructure is confined to a small region and surrounded by a tentative homogenized medium. The characteristics of this homogenized medium are updated using a self‐consistent approach and are shown to converge to the actual solution. The main feature of the coupling strategy is that it really couples the random microstructure with the deterministic homogenized model, and not one (deterministic) realization of the random medium with a homogenized model. The advantages of doing so are twofold: (a) the influence of the boundary conditions is significantly mitigated, and (b) the ergodicity of the random medium can be used in full through appropriate definition of the coupling operator. Both of these advantages imply that the resulting coupled problem is less expensive to solve, for a given bias, than the computation of homogenized tensor using classical approaches. Examples of 1‐D and 2‐D problems with continuous properties, as well as a 2‐D matrix‐inclusion problem, illustrate the effectiveness and potential of the method. Copyright © 2013 John Wiley & Sons, Ltd.

Single-photon logic gates using minimal resources

We present a simple architecture for deterministic quantum circuits operating on single-photon qubits. Few resources are necessary to implement two elementary gates and can be recycled for computing with large numbers of qubits. The deterministic realization of some key multiqubit gates, such as the Fredkin and Toffoli gate, is greatly simplified in this approach.

Prediction of Mass Flow Rate in Pneumatic Conveying Using a System Identification Modeling Approach

Accurate measurements of solids flow rate in pneumatic conveying systems have been a need for the different industries in which these systems are used. In this study, a system identification approach, which is called the Deterministic Stochastic Realization (DSR) method, is used to obtain a state-space model. The selection of inputs to the system identification model is based on conservation of energy related to the Bernoulli principle. Under this investigation, attempts were made to predict the mass flow rate of conveying solids in real time by using pressure data obtained from three different pressure sensors located on the conveying line, blow tank pressure, and total air volume flow rate. Tests were performed in two different pneumatic conveying rigs and with two different materials. The conveyed materials were baryte and dextrose. Dextrose and baryte were conveyed in dilute and dense phases, respectively. To evaluate the DSR model, the results were compared with one published method based on a scaling up technique of pneumatic conveying. The root mean squared error of prediction (RMSEP) of the cumulative mass of transported solids as a percentage of the total conveyed mass using the system identification model was between 1.4 and 5.6% for baryte and 3.2 and 7.8% for dextrose. The cumulative error was between 0.7 and 7.2% for baryte and 3.7 and 8.6% for dextrose.

A method for quantifying geological uncertainties in assessing remaining oil targets: a case study from the Glitne Field, North Sea

Abstract Evaluating the static volume potential of a field from a single geological reservoir model can be a risky business. Each piece of input data used to build the model carries an uncertainty that is not expressed in a single deterministic realization. In evaluating the technical and economic feasibility of drilling a new production well on the StatoilHydro operated Glitne Field, a quantified assessment of the range in expected volumes was undertaken. A geological uncertainty study was initiated to identify and quantify the input parameters of greatest impact on static volumetric uncertainty in the reservoir model and to identify potential upsides or downsides that would strongly affect the economics of the potential well target areas. For each geological input parameter, a high-case and low-case scenario was established to capture the end members (approximating to P90–P10) in that parameter uncertainty. IRAP RMS was used in combination with an in-house Microsoft Excel macro together with @Risk to produce a quantitative analysis of the uncertainty range in STOIIP and a ranking of the parameters most affecting the uncertainty in this range. This study has contributed to making a better-informed decision for drilling a new production well on the Glitne Field and thus increasing ultimate recovery and field life further. The workflow used has its limitations but this study shows that a geological uncertainty study can be performed relatively simply using only a limited number of software applications. This study also hopes to highlight the importance of having these studies undertaken by company asset teams as part of their reservoir characterization routines.

Modelling the effects of stratigraphical uncertainty on fault seal and trap-fill in faulted structures

A three-dimensional approach to migration modelling through faulted structures is described that allows the effects of stratigraphical uncertainty on potential hydrocarbon accumulations to be assessed. Deterministic, three-dimensional fault seal analysis typically produces results that are extremely sensitive to input parameters such as structural architecture and stratigraphical variation. These parameters can be amongst the most poorly defined of modelling inputs because subsurface structural detail and stratigraphical variation are often below the limit of seismic resolution and are not sampled by well data. The new technique is fully integrated with three-dimensional fault seal analysis and hydrocarbon flow pathway modelling to give a workflow that predicts the likelihood of fault-controlled hydrocarbon accumulations, given these uncertainties. Multiple deterministic realizations of the model are used to highlight specific uncertainties in stratigraphy to which predicted hydrocarbon accumulations are sensitive. The results of these realizations are incorporated into, and used to condition, a stochastic model to risk predicted accumulations based on their likelihood of occurrence and volume. This technique has many advantages over either purely deterministic or purely stochastic approaches. A single deterministic realization places over-optimistic faith in the accuracy of the geological model because of the high sensitivity of fault seal analysis to input parameters. Multiple realizations allow specific input parameter uncertainties to be investigated, and the resulting common traps can be considered low risk, but accumulations exclusive to individual realizations cannot be risked. Moreover, a purely stochastic simulation based on all uncertainties will, at best, reduce efficiency by modelling uncertainties to which the result is insensitive or, at worst, may bias results with geologically implausible, stochastically-generated trials.

Recycling Parrondo games

We consider a deterministic realization of Parrondo games, and use periodic orbit theory to analyse their asymptotic behaviour.