Computation of Bounds for Exact Quantities of Interest in Elasticity Based on FEM and SFEM

2010 ◽  
pp. 491-496
Author(s):  
Zhaocheng Xuan ◽  
Yaohui Li ◽  
Hongjie Wang
Keyword(s):  
Quantities Of Interest

scholarly journals Figures of merit for stellarators near the magnetic axis

2021 ◽  
Vol 87 (1) ◽  
Author(s):  
Matt Landreman
Keyword(s):  
Magnetic Field ◽  
Field Strength ◽  
Magnetic Axis ◽  
Configuration Design ◽  
New Paradigm ◽  
First Order ◽  
Figures Of Merit ◽  
Minor Radius ◽  
Error Field ◽  
Quantities Of Interest

A new paradigm for rapid stellarator configuration design has been recently demonstrated, in which the shapes of quasisymmetric or omnigenous flux surfaces are computed directly using an expansion in small distance from the magnetic axis. To further develop this approach, here we derive several other quantities of interest that can be rapidly computed from this near-axis expansion. First, the $\boldsymbol {\nabla }\boldsymbol {B}$ and $\boldsymbol {\nabla }\boldsymbol {\nabla }\boldsymbol {B}$ tensors are computed, which can be used for direct derivative-based optimization of electromagnetic coil shapes to achieve the desired magnetic configuration. Moreover, if the norm of these tensors is large compared with the field strength for a given magnetic field, the field must have a short length scale, suggesting it may be hard to produce with coils that are suitably far away. Second, we evaluate the minor radius at which the flux surface shapes would become singular, providing a lower bound on the achievable aspect ratio. This bound is also shown to be related to an equilibrium beta limit. Finally, for configurations that are constructed to achieve a desired magnetic field strength to first order in the expansion, we compute the error field that arises due to second-order terms.

Unit Mobility Ratio Displacement Calculations for Pattern Floods in Homogeneous Medium

1966 ◽  
Vol 6 (03) ◽  
pp. 217-227 ◽  
Author(s):  
Hubert J. Morel-Seytoux
Keyword(s):  
Oil Recovery ◽  
Numerical Solutions ◽  
Mobility Ratio ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Numerical Techniques ◽  
Sweep Efficiency ◽  
Closed Form Solutions ◽  
Regular Patterns ◽  
Quantities Of Interest

Abstract The influence of pattern geometry on assisted oil recovery for a particular displacement mechanism is the object of investigation in this paper. The displacement is assumed to be of unit mobility ratio and piston-like. Fluids are assumed incompressible and gravity and capillary effects are neglected. With these assumptions it is possible to calculate by analytical methods the quantities of interest to the reservoir engineer for a great variety of patterns. Specifically, this paper presentsvery briefly, the methods and mathematical derivations required to obtain the results of engineering concern, andtypical results in the form of graphs or formulae that can be used readily without prior study of the methods. Results of this work provide checks for solutions obtained from programmed numerical techniques. They also reveal the effect of pattern geometry and, even though the assumptions of piston-like displacement and of unit mobility ratio are restrictive, they can nevertheless be used for rather crude but quick, cheap estimates. These estimates can be refined to account for non-unit mobility ratio and two-phase flow by correlating analytical results in the case M=1 and the numerical results for non-Piston, non-unit mobility ratio displacements. In an earlier paper1 it was also shown that from the knowledge of closed form solutions for unit mobility ratio, quantities called "scale factors" could be readily calculated, increasing considerably the flexibility of the numerical techniques. Many new closed form solutions are given in this paper. INTRODUCTION BACKGROUND Pattern geometry is a major factor in making water-flood recovery predictions. For this reason many numerical schemes have been devised to predict oil recovery in either regular patterns or arbitrary configurations. The numerical solutions, based on the method of finite difference approximation, are subject to errors often difficult to evaluate. An estimate of the error is possible by comparison with exact solutions. To provide a variety of checks on numerical solutions, a thorough study of the unit mobility ratio displacement process was undertaken. To calculate quantities of interest to the reservoir engineer (oil recovery, sweep efficiency, etc.), it is necessary to first know the pressure distribution in the pattern. Then analytical procedures are used to calculate, in order of increasing difficulty: injectivity, breakthrough areal sweep efficiency, normalized oil recovery and water-oil ratio as a function of normalized PV injected. BACKGROUND Pattern geometry is a major factor in making water-flood recovery predictions. For this reason many numerical schemes have been devised to predict oil recovery in either regular patterns or arbitrary configurations. The numerical solutions, based on the method of finite difference approximation, are subject to errors often difficult to evaluate. An estimate of the error is possible by comparison with exact solutions. To provide a variety of checks on numerical solutions, a thorough study of the unit mobility ratio displacement process was undertaken. To calculate quantities of interest to the reservoir engineer (oil recovery, sweep efficiency, etc.), it is necessary to first know the pressure distribution in the pattern. Then analytical procedures are used to calculate, in order of increasing difficulty: injectivity, breakthrough areal sweep efficiency, normalized oil recovery and water-oil ratio as a function of normalized PV injected.

scholarly journals Exploring the Sensitivity of Photosynthesis and Stomatal Resistance Parameters in a Land Surface Model

2017 ◽  
Vol 18 (3) ◽  
pp. 897-915 ◽  
Author(s):  
Jennifer L. Jefferson ◽  
Reed M. Maxwell ◽  
Paul G. Constantine
Keyword(s):  
Land Surface ◽  
Stomatal Resistance ◽  
Hydrologic Model ◽  
Surface Model ◽  
Land Surface Models ◽  
Common Land Model ◽  
Surface Models ◽  
Input Parameters ◽  
Rate Of Photosynthesis ◽  
Quantities Of Interest

Abstract Land surface models, like the Common Land Model component of the ParFlow integrated hydrologic model (PF-CLM), are used to estimate transpiration from vegetated surfaces. Transpiration rates quantify how much water moves from the subsurface through the plant and into the atmosphere. This rate is controlled by the stomatal resistance term in land surface models. The Ball–Berry stomatal resistance parameterization relies, in part, on the rate of photosynthesis, and together these equations require the specification of 20 input parameters. Here, the active subspace method is applied to 2100 year-long PF-CLM simulations, forced by atmospheric data from California, Colorado, and Oklahoma, to identify which input parameters are important and how they relate to three quantities of interest: transpiration, stomatal resistance from the sunlit portion of the canopy, and stomatal resistance from the shaded portion. The slope (mp) and intercept (bp) parameters associated with the Ball–Berry parameterization are consistently important for all locations, along with five parameters associated with ribulose bisphosphate carboxylase/oxygenase (RuBisCO)- and light-limited rates of photosynthesis [CO2 Michaelis–Menten constant at 25°C (kc25), maximum ratio of oxygenation to carboxylation (ocr), quantum efficiency at 25°C (qe25), maximum rate of carboxylation at 25°C (vcmx25), and multiplier in the denominator of the equation used to compute the light-limited rate of photosynthesis (wj1)]. The importance of these input parameters, quantified by the active variable weight, and the relationship between the input parameters and quantities of interest vary seasonally and diurnally. Input parameter values influence transpiration rates most during midday, summertime hours when fluxes are large. This research informs model users about which photosynthesis and stomatal resistance parameters should be more carefully selected. Quantifying sensitivities associated with the stomatal resistance term is necessary to better understand transpiration estimates from land surface models.

Differential Performance Signature Qualification for Additively Manufactured Parts

2018 ◽  
Author(s):  
John G. Michopoulos ◽  
John C. Steuben ◽  
Athanasios P. Iliopoulos
Keyword(s):  
Additive Manufacturing ◽  
Graphical Representation ◽  
Functional Performance ◽  
Complex Objects ◽  
Aircraft Landing ◽  
Differential Performance ◽  
Aircraft Landing Gear ◽  
Am Processes ◽  
Comparison Measures ◽  
Quantities Of Interest

Additive Manufacturing (AM) technologies and associated processes, enable successive accretion of material to a domain, and permit manufacturing of highly complex objects which would otherwise be unrealizable. However, the material micro- and meso-structures generated by AM processes can differ remarkably from those arising from conventional manufacturing (CM) methods. Often, a consequence of this fact is the sub-standard functional performance of the produced parts that can limit the use of AM in some applications. In the present work, we propose a rapid functional qualification methodology for AM-produced parts based on a concept defined as differential Performance Signature Qualification (dPSQ). The concept of Performance Signature (PerSig) is introduced both as a vector of featured quantities of interest (QoIs), and a graphical representation in the form of radar or spider graph, representing the QoIs associated with the performance of relevant parts. The PerSigs are defined for both the prequalified CM parts and the AM-produced ones. Comparison measures are defined and enable the construction of differential PerSigs (dPerSig) in a manner that captures the differential performance of the AM part vs. the prequalified CM one. The dPerSigs enable AM part qualification based on how their PerSigs are different from those of prequalified CM parts. After defining the steps of the proposed methodology, we describe its application on a part of an aircraft landing gear assembly and demonstrate its feasibility.

scholarly journals On a Class of Semi-Markov Risk Models Obtained as Classical Risk Models in a Markovian Environment

1984 ◽  
Vol 14 (1) ◽  
pp. 23-43 ◽  
Author(s):  
Jean-Marie Reinhard
Keyword(s):  
Risk Model ◽  
Risk Process ◽  
Ruin Probabilities ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Risk Models ◽  
Markovian Environment ◽  
Necessary And Sufficient ◽  
Natural Way ◽  
Quantities Of Interest

AbstractWe consider a risk model in which the claim inter-arrivals and amounts depend on a markovian environment process. Semi-Markov risk models are so introduced in a quite natural way. We derive some quantities of interest for the risk process and obtain a necessary and sufficient condition for the fairness of the risk (positive asymptotic non-ruin probabilities). These probabilities are explicitly calculated in a particular case (two possible states for the environment, exponential claim amounts distributions).

CREDIT MODELING UNDER JUMP DIFFUSIONS WITH EXPONENTIALLY DISTRIBUTED JUMPS — STABLE CALIBRATION, DYNAMICS AND GAP RISK

2013 ◽  
Vol 16 (04) ◽  
pp. 1350021 ◽  
Author(s):  
MARTIN HELLMICH ◽  
STEFAN KASSBERGER ◽  
WOLFGANG M. SCHMIDT
Keyword(s):  
Credit Default Swap ◽  
Jump Diffusion ◽  
Credit Spreads ◽  
Jump Diffusions ◽  
Time Dynamics ◽  
Credit Default ◽  
Gap Risk ◽  
Default Swap ◽  
Swap Spreads ◽  
Quantities Of Interest

This paper investigates a structural credit default model that is based on a hyper-exponential jump diffusion process for the value of the firm. For credit default swap prices and other quantities of interest, explicit expressions for the corresponding Laplace transforms are derived. The time-dynamics of the model are studied, particularly the jumps in credit spreads, the understanding of which is crucial e.g. for the pricing of gap risk. As an application of our findings, the model is calibrated to credit default swap spreads observed in the market.

DERIVING ROBUST BAYESIAN PREMIUMS UNDER BANDS OF PRIOR DISTRIBUTIONS WITH APPLICATIONS

2018 ◽  
Vol 49 (1) ◽  
pp. 147-168 ◽  
Author(s):  
M. Sánchez-Sánchez ◽  
M.A. Sordo ◽  
A. Suárez-Llorens ◽  
E. Gómez-Déniz
Keyword(s):  
Bayesian Analysis ◽  
Likelihood Ratio ◽  
Requirements Elicitation ◽  
Likelihood Ratio Order ◽  
Prior Distributions ◽  
Propagation Of Uncertainty ◽  
Distortion Functions ◽  
Wide Family ◽  
Class Of Priors ◽  
Quantities Of Interest

AbstractWe study the propagation of uncertainty from a class of priors introduced by Arias-Nicolás et al. [(2016) Bayesian Analysis, 11(4), 1107–1136] to the premiums (both the collective and the Bayesian), for a wide family of premium principles (specifically, those that preserve the likelihood ratio order). The class under study reflects the prior uncertainty using distortion functions and fulfills some desirable requirements: elicitation is easy, the prior uncertainty can be measured by different metrics, and the range of quantities of interest is easily obtained from the extremal members of the class. We illustrate the methodology with several examples based on different claim counts models.

An Evaluation of Material Weight and Contained Fluid Volume for Eccentric Intersecting Cylinders of Arbitrary Size

1989 ◽  
Vol 111 (3) ◽  
pp. 342-347
Author(s):  
Y. J. Chao ◽  
M. A. Sutton
Keyword(s):  
Vessel Diameter ◽  
Fluid Volume ◽  
Wide Range ◽  
Single Integral ◽  
Material Volume ◽  
Thin Walled ◽  
Special Case ◽  
Range Of Values ◽  
Engineering Personnel ◽  
Quantities Of Interest

Engineering personnel in industries which use pressurized containment vessels having attached nozzles are required not only to design portions of the lifting mechanism, but also to estimate the fluid volume which the vessel and nozzles will contain; most designers use simplified formulas for computing the quantities of interest. Typically, these formulas are valid approximations when the nozzle diameter is much smaller than the vessel diameter. The enclosed work develops three single-integral expressions which can be programmed and numerically integrated to obtain accurate estimates for both the material volume and also the containment volume present in a pair of eccentrically, or concentrically, intersecting thin-walled cylinders of arbitrary diameters. A table of such values is presented for a wide range of values of the standard nozzle pipe diameter and vessel diameter, for the special case of a concentric nozzle. In addition, an example is presented which compares the numerically integrated values for both the material volume and the containment volume to simplified upper and lower-bound estimates.

scholarly journals Improving the validation of turbulent jet breakup models

2019 ◽  
Author(s):  
Ben Trettel
Keyword(s):  
Fire Suppression ◽  
Experimental Studies ◽  
Droplet Size Distribution ◽  
Turbulent Jet ◽  
Liquid Jets ◽  
Experimental Database ◽  
Quality Guidelines ◽  
Water Jet Cutting ◽  
Jet Breakup ◽  
Quantities Of Interest

Understanding the physics of the breakup of turbulent liquid jets is important for a variety of applications including engine sprays, fire suppression systems, and water jet cutting. Models of turbulent jet breakup allow predictions of quantities of interest like the droplet size distribution and breakup length of the jet. These models are compared against experimental data in a process called validation. If the model predictions are within the experimental uncertainty, then the model is "validated" and believed to be accurate, and possibly can explain the physics. Uncertainty quantification is necessary for model validation. While unfortunately relatively few experimental studies quantify uncertainty, that is not the most pressing validation issue in turbulent jet breakup. I detail 3 additional problems that can make the apparent validation of a model actually an illusion, regardless of how well the model appears to match the data. These problems include: 1. important variables being omitted or guessed in experiments and models, 2. confounding between independent variables, that is, two variables changing simultaneously, making determining cause and effect impossible, and 3. testing only combinations of submodels and not each submodel in isolation. To avoid these problems and others, I developed validation guidelines that are detailed in this work. Following these guidelines, I compiled a large experimental database. Only 28 out of 47 experimental studies considered met my data quality guidelines. Only 18 studies had quantified uncertainty, and only 3 studies had substantial variation in the turbulence intensity.

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