Interval Computing Method for Analyzing Field-Scale Solute Transport

A major part of this book discusses the use of stochastic models for atmospheric convection, namely through the use of a stochastic model for CIN and a stochastic multicloud model which pertains to tracking the statistics of clouds of various types. These models rely on the theory of stochastic processes and Markov chains in particular. Here, we provide a brief introduction to this topic to help the reader better appreciate and comprehend the cloud models. The expert reader can skip this chapter. It is intended to readers with no or rather very little background in probability theory and stochastic processes. Nonetheless, we assume that the reader is familiar with the basic notions of probability distributions and random variables.

Many real-time systems must be fault-tolerant and must handle failures in a timely manner. An approach incorporating the redundancy-masking technique and the imprecise computation model is presented in this paper. The redundancy-masking technique is preferred for time-critical applications than the rollback-and-retry techniques because of the fast error detection and the potential for forward error recovery. The imprecise computation model provides flexible functionality by trading off the quality of the result produced by a task with the amount of processing time required to produce it. It therefore permits the performance of a real-time system to degrade gracefully. Several algorithms for scheduling replicated periodic tasks on a real-time multiprocessor system have been studied and evaluated by stochastic analysis and Monte Carlo simulations. The results show that the algorithms are resilient under hardware failures.

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This study implemented a large scale model for transient flow problems through the vadose zone derived using the stochastic approach to account for spatial variability of soil properties. The heterogeneity of natural soil formations were included in the effective hydraulic conductivity and specific moisture capacity. The set of stochastic differential equations was solved using a finite element formulation. A computer code was developed to implement the stochastic finite element formulation and a mesh generator was also developed to create the finite element mesh. Numerical simulations were performed for different scenarios using real data and the results for pressure head and volumetric water content distribution profiles at different times were compared to analytical and deterministic solutions, and experimental results. The stochastic perturbation approach showed to have the great advantage of being computationally much less expensive than the Monte Carlo method. The stochastic approach predicted significantly slower vertical movement and faster horizontal movement of the wetting front compared to the deterministic approach. The results agreed with field observations. The difference between stochastic and deterministic head pressure and volumetric moisture content profiles was significant and should not be discarded.

A criterion for the convergence of the stochastic Monte Carlo simulations is necessary to ensure the reliability of their results and to guarantee efficiency. Due to the finite scattering rate in Monte Carlo simulations all quantities are in general correlated in time. This makes the estimation of the stochastic error of the sampled statistics difficult. In this work the theoretical basis of a method found in literature is explored which allows to calculate the stochastic error of stationary Ensemble Monte Carlo simulations and which requires only a rough estimate of the magnitude of the largest correlation time of the sampled quantities. The feasibility of the method is demonstrated by application to substrate current calculations for nMOSFETs.

SUMMARY Stochastic approximation is a sequential technique which can be used for optimizing the mean of a random variable y(x) in terms of a parameter vector x, when the mean is unknown but y(x) can be observed for any value of x. This paper is intended to introduce and illustrate stochastic approximation to those statisticians unfamiliar with the technique. The Atlantic menhaden is a commercially important fish in the herring family (Clupeidae). Stochastic approximation is used in conjunction with a stochastic simulation model of the menhaden population to determine optimal values for the two parameters in a proposed class of menhaden harvesting policies. The objective is to maximize the expected utility of the random catch over a 25-year period. Optimization is a response-surface problem. Although some of the more familiar sequential response-surface methods might have been successfully applied, the nonsequential response-surface techniques would have been too expensive for estimation of a specific feature of the surface, such as the location of the maximum. The results of using stochastic approximation are encouraging. Atlantic menhaden are migratory fish caught from Florida to New England mainly by purse-seining. Menhaden are not palatable to humans, but they are processed into two important products, fish oil and fish meal. The oil is used in the manufacture of paints, lubricants, and cosmetics, and the meal is a high-protein ingredient in animal feed. Together, Atlantic and Gulf menhaden support the largest U.S. commercial fishery measured in pounds landed, and, excluding shellfish, menhaden catches rank next to those of tuna and salmon in monetary value. At present the Atlantic menhaden fishery is subjected to some intrastate regulation, but it is not managed on a fishery-wide basis. Catches of menhaden experienced a rapid decline after 1962 and have only partially recovered, but some biologists feel that proper management could increase future catches substantially. To explore the

In this paper, the two level stochastic optimisation approach has been suggested. In the lower level, the probability distribution functions (pdfs) for bus voltages and branch currents have been determined using the Monte Carlo simulation (MCS) to be employed in chance‐constrained probabilistic optimisation by taking into account solar radiation and power consumption uncertainties in the distribution networks (DNs). In the upper level, artificial hummingbird algorithm (AHA) handles the expected power loss minimisation subjected to chance constraints, which are related to bus voltages and branch currents, by optimising photovoltaic (PV) system capacities. This research examines the effect of uncertainties in PV system performing under diverse solar radiation and varying PV penetration level scenarios on expected power losses with stochastic DN limits. The stochastic optimisation approach has been compared with the deterministic method for observing the efficiency with optimal power usage. This research improves the knowledge base for optimal PV installation in DN by combining AHA with MCS and emphasising chance‐constrained methods. To indicate the efficacy of proposed strategy, the optimisation outcomes are tested utilising MCS under various uncertainty circumstances and DN parameters are assessed in terms of probabilities of exceeding limitations. The results are compared with the application of firefly algorithm (FA) using stochastic assessment and simulations. The simulation results show that the AHA technique outperforms the FA method in terms of effectively minimising power losses with less simulation time.

Summary Following identification of potential productivity gains from post-thinning fertilizer treatments (N+P) in NSW Pinus radiata plantations, financial analyses are undertaken for treatment of defined resource strata. Deterministic and stochastic approaches are employed in the estimation of key financial indicators. The latter technique enables risk (variation in cost and revenue parameters) to be explicitly addressed by definition of probability distributions describing the cost of fertilization, productivity gains due to fertilization, product mixes and prices and the difference between rates of inflation for costs and revenues. Monte Carlo simulation techniques are employed to generate probability distributions for Net Present Value (NPV), Benefit/Cost Ratio and Internal Rate of Return (IRR). Investments are compared on the basis of the expected values of NPV, B/C ratio and IRR and associated cumulative probability distributions. The methodology enables forest managers to routinely evaluate investment options on a site, plantation and market specific basis. Post-thinning fertilization of P. radiata plantations is demonstrated to be a potentially successful investment strategy (expected rates of return exceeding 8%) but the financial performance of fertilizer treatments within different resource strata varies considerably (mean NPV's between $62 ha −1 and $1169 ha1 from the stochastic model). This variation highlights the need for careful treatment selection and prioritization to maximise net benefits. Sensitivity analyses reveal that sawlog prices and volume gain (due to fertilization) are the main factors influencing investment performance. The “risk adverse” nature of many of the component distributions (volume gain and product mix) meant that expected values of the performance measures were lower under the stochastic simulation than calculated by the deterministic approach and rankings of investments were slightly modified when investment risk was considered. Under four of the five investment strategies there is at least a 90% probability that an IRR of 8% will be achieved.

In the realm of groundwater science, characterization of heterogeneous aquifers is pivotal for resolving diverse groundwater resource and engineering-related problems that require the detailed spatial distribution of hydraulic parameters. As research progresses, one hydraulic tomographical method, which is based on hydraulic travel time inversion, emerges as a promising and rapid method due to its robust and efficient calculation. In the field, the acquisition of hydraulic excitation and head observation data required for inversion is less time-consuming. Data collection from a single hydraulic test (such as a pumping test) typically takes only a few minutes or even a few tens of seconds. However, the field application of this method faces challenges. Hydraulic travel time is typically generated in the early stages of hydrogeological tests (e.g., early drawdown of a pumping test), yet accurate data may not be readily available because of the noise signals from test equipment, which can contaminate travel time signals, leading to inaccurate inversion results. A potential solution lies in utilizing the smooth head observation during the recovery period after the pump is turned off, which yields more accurate travel times for inversion calculations. In this paper, the mathematical development suggests that the travel time of the recovery phase aligns with that of the pumping phase when pumping reaches a steady or quasi-steady state. Subsequently, by employing Monte-Carlo simulations, 1200 realizations of two-dimensional heterogeneous confined aquifer models were generated for simulating pumping tests with different pumping durations. The calculated head data were then utilized to compute the travel time derived from drawdown data (t) and recovery data (t′), respectively. Comparisons showed that t is equal to t′ when drawdown reaches a steady or quasi-steady state. Conversely, when the pump is turned off before reaching a quasi-steady state, t differs from t′. However, results also indicate the fact that a decent hydraulic travel time diagnosis can be obtained, especially for the cases when travel times are smaller than 15 s. Given the statistical results of Monte-Carlo simulations, as well as experience during pumping tests in the field with different scenarios, using the recovery data from 60 s of pumping duration, or extended pumping durations of 100 s or 200 s as a more conservative alternative, can replace the aquifer characterization based on drawdown data. The new inversion strategy not only has less data uncertainty and equivalent inversion accuracy, but also can greatly enhance the repeatability of field tests and reduce the environmental impact of long-term pumping tests.

Part IV: Dynamic evolution of the particle size distribution in particulate processes. A comparative study between Monte Carlo and the generalized method of moments

The stochastic effective theory approach, often called stochastic inflation, is widely used in cosmology to describe scalar field dynamics during inflation. The existing formulations are, however, more qualitative than quantitative because the connection to the underlying quantum field theory (QFT) has not been properly established. A concrete sign of this is that the QFT parameters depend on the renormalization scale, and therefore the relation between the QFT and stochastic theory must have explicit scale dependence that cancels it. In this paper we achieve that by determining the parameters of the second-order stochastic effective theory of light scalar fields in de Sitter to linear order in the self-coupling constant λ. This is done by computing equal-time 2-point correlators to one-loop order both in QFT using dimensional regularization and the MS¯ renormalization scheme and the equal-time 4-point correlator to leading order in both theories, and demanding that the results obtained in the two theories agree. With these parameters, the effective theory is valid when m≲H and λ2≪m4/H4, and therefore it is applicable in cases where neither perturbation theory nor any previously proposed stochastic effective theories are. Published by the American Physical Society 2024

Risk assessment of the maintenance process for onshore oil and gas transmission pipelines under uncertainty

The objective of the present paper is to evaluate the application of a promising new mathematical technique called interval analysis for reentry flight clearance. Whereas a Monte Carlo approach clears the vehicle only for a finite number of sets of uncertainty parameters, the new approach clears the vehicle within prespecified uncertainty parameter intervals. The new approach is applied to the reentry trajectory of the Delft Aerospace Reentry Test Demonstrator, a hypothetical ballistic reentry vehicle equipped with an attitude-stabilizing flight control system. As the clearance requirement, the stability of the system is chosen, which is evaluated using two different mathematical criteria: worst-case linear eigenvalue analysis and nonlinear Lyapunov analysis. The new approach, based on interval analysis, is applied in an evaluation of both criteria. Subsequently, Monte Carlo analysis was performed to verify the validity of these results. I. Introduction R EENTRY flight is inseparable from the present and future spaceflight missions. During the reentry flight, a vehicle has to follow a predefined trajectory toward a designated landing area. Trajectory tracking, flight stability, and landing precision are important aspects in the reentry flight. The predefined trajectory has to be tracked with a sufficient margin of error. The stability margin has to be fulfilled against the variation and uncertainty in flight parameters such as aerothermodynamic parameters, mass, and inertia.Theaccuracyoflandingisimportantaswelltoensurethatthe vehicle and its contents reach the target ground intact. All of these aspects need to be analyzed and evaluated in a systematic way to ensure the stability and performance of the reentry vehicle. To certify a reentry vehicle as safe to fly, the reentry flight model has to be evaluated before actual flight. This is known as the reentry flight model clearance, or reentry flight clearance for short. One exampleofthe flightmodelclearanceistheevaluationofthestability and performance of the reentry vehicle model in its flight envelope. AsillustratedinFig.1,thereentry flightenvelopeisdefinedalongthe nominal flight trajectory. The flight safety is checked by evaluating the regions in the flight envelope using predefined stability or performance criteria. The region in which the criteria are fulfilled is then “cleared,” which means that, under the defined flight condition, the vehicle can fly safely in this region. The right-hand side of Fig. 1 shows a blown-up view of the envelope with flyable and nonflyable regionsasaresultoftheclearance.The flyableareasareshownbythe shaded rectangles in the flight envelope. Thechallengeforthereentry flightclearanceliesinthefactthatthe mathematical models of reentry vehicles and the environments are generally nonlinear. Moreover, the models may contain uncertainty due to the unknowns and variations in the dynamics or parameters. Therefore, to produce a reliable clearance result, mathematical analysis methods that account for the nonlinearity and uncertainty in the models are needed. To answer this question, this paper contributesasystematic approachtoperform reentry flightclearance using interval analysis. This method can meet the aforementioned challenge,for itcanbeapplied tolinearaswellasnonlinearsystems, and can account for the uncertainty in the system model. To give the reader an overview of the method, the algorithm is described in Sec. V. The strong point of the method is illustrated using an example of clearance for a nonlinear system. In the sequence, we perform clearance on a reentry vehicle model with a flight control system, with stability robustness in the presence of uncertainty as the clearance criteria (see Sec. VI). The mathematical modelofthesystemisnonlinearwithuncertainparameters.Toshow that the method canbe applied tolinear as well as nonlinear systems, both linearized and nonlinear models of the system are evaluated. The clearance is performed inside the vehicle’s reentry flight envelope. For the linearized system, the eigenvalue criteria is applied, whereas for the nonlinear system, the Lyapunov function isevaluated.TheresultsarevalidatedusingMonteCarloanalysis.As literature survey,Secs.IIandIIIprovidethereader withanoverview of the current clearance practice and of the available methods, which leads to the choice of the clearance method in this paper.

Supply chain and logistic optimization of industrial Spent Microbial Biomass distribution as a soil amendment for field crop production

Buckling of stochastically heterogeneous beams, using a functional perturbation method