Nominal Design Values Research Articles

A survey of methane point source emissions from coal mines in Shanxi province of China using AHSI on board Gaofen-5B

Abstract. Satellite-based detection of methane (CH4) point sources is crucial in identifying and mitigating anthropogenic emissions of CH4, a potent greenhouse gas. Previous studies have indicated the presence of CH4 point source emissions from coal mines in Shanxi, China, which is an important source region with large CH4 emissions, but a comprehensive survey has remained elusive. This study aims to conduct a survey of CH4 point sources over Shanxi's coal mines based on observations of the Advanced Hyperspectral Imager (AHSI) on board the Gaofen-5B satellite (GF-5B/AHSI) between 2021 and 2023. The spectral shift in centre wavelength and change in full width at half-maximum (FWHM) from the nominal design values are estimated for all spectral channels, which are used as inputs for retrieving the enhancement of the column-averaged dry-air mole fraction of CH4 (ΔXCH4) using a matched-filter-based algorithm. Our results show that the spectral calibration on GF-5B/AHSI reduced estimation biases of the emission flux rate by up to 5.0 %. We applied the flood-fill algorithm to automatically extract emission plumes from ΔXCH4 maps. We adopted the integrated mass enhancement (IME) model to estimate the emission flux rate values from each CH4 point source. Consequently, we detected CH4 point sources in 32 coal mines with 93 plume events in Shanxi province. The estimated emission flux rate ranges from 761.78 ± 185.00 to 12 729.12 ± 4658.13 kg h−1. Our results show that wind speed is the dominant source of uncertainty contributing about 84.84 % to the total uncertainty in emission flux rate estimation. Interestingly, we found a number of false positive detections due to solar panels that are widely spread in Shanxi. This study also evaluates the accuracy of wind fields in ECMWF ERA5 reanalysis by comparing them with a ground-based meteorological station. We found a large discrepancy, especially in wind direction, suggesting that incorporating local meteorological measurements into the study CH4 point source are important to achieve high accuracy. The study demonstrates that GF-5B/AHSI possesses capabilities for monitoring large CH4 point sources over complex surface characteristics in Shanxi.

Use of DL Model to Capture Noise Variance of EV Motor by Eccentricity

In the era of mass-production of EVs, the expectations of performance and NVH performance required for power electric(PE) motors are gradually increasing. In order to satisfy the noise requirement and to prepare countermeasures, it is necessary not only to verify the nominal design value, but also to analyse the characteristics due to manufacturing variance. However, it was not easy to thoroughly examine the tilting and eccentricity issues that affect the noise characteristics of the axial type motor due to time and computational costs. To overcome this limitation, a machine learning model was developed to predict the electromagnetic(EM) excitation force of the motor eccentric condition. The training set of 2D EM FE results were generated with various eccentricity condition and RPMs. Using spatial-temporal frequency analysis and unbalanced magnetic pull analysis, the tendency of the excitation forces due to eccentricity was analysed. The distribution of electromagnetic force by time was predicted using random forest model. It showed R2 value of 0.999. The prediction model reduces the computational time within 5 minutes from 31 hours and enables the realistic analysis of tilting and eccentric condition. The 3D EM force distribution as Vibro-Acoustic FE model input could be predicted by putting the eccentricity value into the machine learning model.

Transient modelling of a multi-cell alkaline electrolyzer for gas crossover and safe system operation

Due to the intermittency of renewable energy sources, alkaline water electrolyzers are typically operated at partial load compared to the nominal design value. It is well-known that gas crossover is dominant at low current densities leading to higher anodic hydrogen content and higher cathodic oxygen content in the separator tanks. High anodic hydrogen content is tantamount to loss of product hydrogen which results in an explosive atmosphere in the gas phase if the volumetric hydrogen content in oxygen exceeds 4%. We have developed a transient model of a multi-cell stack which can describe the operation of the electrolyzer with mixed electrolyte flows (anolyte and catholyte), separated flows, or a combination thereof (dynamic switching). This is a major extension of the steady-state model developed by Haug et al. (International Journal of Hydrogen Energy, 2017, 42, 15,689–15707). In sharp contrast to the steady-state model by Haug et al., the transient model can calculate the gas crossover as the operating conditions (e.g. electrolyte flow cycles) dynamically change in time. Depending on the size of the stack and the separator tanks, the model estimates different rates for impurities to build up. The transient model is validated using independent experimental results by Haug et al. and Brauns et al. (Electrochimica Acta, 2022, 404, 139,715) The results show that the dynamic model can follow experimental results for fluctuating current densities for a period of several days. We found that the dynamic response and transition time to steady state depend significantly on the geometrical volume of the gas separators with respect to the single-cell stack. For a multi-cell stack, we find that the impurities build-up faster when increasing the number of cells in the stack. This model serves as a tool for sizing and process management of the electrolyzer system and the separator tanks especially with respect to explosion safety.

Parameter estimation of the shell transfer arm of a loading mechanism

The shell transfer arm is a key component of gun automatic loading mechanism, the coordination speed and positioning accuracy have an important impact on gun ammunition delivery effect. Establishing an accurate dynamic model is the foundation for better control and prediction, therefore, it is necessary to identify the dynamic parameters of the shell transfer arm. In this paper, the dynamic model is established based on the topology method. The parameter identification model of the shell transfer arm is constructed by applying the dynamic model and unscented Kalman filter theory. Dynamic parameters of the shell transfer arm such as the mass, inertia and centroid position are estimated under unscented Kalman filter scheme. By comparing the parameter estimation results with the nominal design values, the feasibility and effectiveness of applying the proposed method to identify the dynamic parameters of the shell transfer arm are verified.

High-precision luminosity instrumentation for the CMS detector at the HL-LHC

The high-luminosity upgrade of the LHC (HL-LHC) is foreseen to reach an instantaneous luminosity a factor of five to seven times the nominal LHC design value. This creates the need for new high-precision instrumentation at CMS, using radiation-hard detector technologies. This contribution introduces the instrumentation for bunch-by-bunch online luminosity and beam-induced background measurements in CMS. The Tracker Endcap Pixel Detector (TEPX) will be adapted for precision luminometry by implementing a dedicated trigger type and a real-time data processing system performing clustering on FPGA. The innermost ring of the last TEPX layer (D4R1) will be operated independently from the rest of TEPX, enabling beam monitoring during the LHC ramp and during unqualified beam conditions with a dedicated timing and trigger infrastructure. A new standalone luminometer, the Fast Beam Condition Monitor (FBCM), which will be fully independent from the central trigger and data acquisition services and will be able to operate during all times is also introduced. FBCM is foreseen to utilize silicon-pad sensors with sub-bunch-crossing time resolution enabling also the measurement of beam-induced background. The potential of the exploitation of other CMS subsystems such as the outer tracker, the barrel muon detectors and the 40 MHz L1 trigger scouting system using a common histogramming firmware is also discussed.

The method for calculating the probability of brittle destruction of NPP equipment in different operating modes with postulated defectiveness

The destruction of equipment metal by a brittle fracture mechanism is a probabilistic event at nuclear power plants (NPP). The calculation for resistance to brittle destruction is performed for NPP equipment exposed to neutron irradiation; for example, for a reactor plant such as a water-water energetic reactor (WWER), this is a reactor pressure vessel. The destruction of the reactor pressure vessel leads to a beyond design-basis accident, therefore, the determination of the probability of brittle destruction is an important task. The research method is probabilistic analysis of brittle destruction, which takes into account statistical data on residual defectiveness of equipment, experimental results of equipment fracture toughness and load for the main operating modes of NPP equipment. Residual defectiveness (a set of remaining defects in the equipment material that were not detected by non-destructive testing methods after manufacturing (operation), control and repair of the detected defects) is the most important characteristic of the equipment material that affects its strength and service life. A missed defect of a considerable size admitted into operation can reduce the bearing capacity and reduce the time of safe operation from the nominal design value down to zero; therefore, any forecast of the structure reliability without taking into account residual defectiveness will be incorrect. The application of the developed method is demonstrated on the example of an NPP reactor pressure vessel with a WWER-1000 reactor unit when using the maximum allowable operating loads, in the absence of load dispersion in different operating modes, and taking into account the actual values of the distributions of fracture toughness and residual defectiveness. The practical significance of the developed method lies in the possibility of obtaining values of the actual probability of destruction of NPP equipment in order to determine the reliability of equipment operation, as well as possible reliability margins for their subsequent optimization.

Statistical characterisation of expanded metal mesh strand, to propose a correlation between properties of parent material and finish product, EMM

The use of steel plate shear walls (SPSW) for the design of structures under low seismic intensity results in very thin infill SPSW panels. Construction of such structures is infeasible, mainly due to the difficulty in connecting the infill to the boundary members. Thus, a designer is compelled to use a thicker infill section which in turn leads to heavier boundary elements. In order to overcome this constraint of design, a new type of infill panel using Expanded Metal Mesh (EMM) is studied as an alternative in place of a solid infill SPSW panel. Available codes on expanded metal mesh specify requirements of workmanship, quality control, etc. but neither recommend the strength of expanded metal mesh as a whole nor the strength of its components. Thus, it is necessary to perform extensive tests to extract the strength of expanded metal mesh as a whole in terms of the strength of its components and to come out with a correlation between the strength of the parent material (material from which EMM is manufactured) and that of the finished product (EMM). This paper a) presents the statistical characterization of EMM strands, b) recommends nominal design values for basic mechanical properties and c) proposes the correlation between the strength of the parent material and that of EMM strand.

Reliability of elastomeric-isolated buildings under historical earthquakes with/without forward-directivity effects

Deviations from nominal design values of mechanical characteristics of seismic isolators are inevitable due to uncertainties and/or errors in material properties, element dimensions, construction methods, quality control, and/or installation steps, etc. In addition, due to uncertainties existing in active fault mechanisms affecting the site and local soil conditions, earthquake ground motions show record-to-record variability. Moreover, environmental conditions and/or time-dependent factors such as aging, temperature, and travel, etc. may also cause additional deviations in nominal values of characteristics of seismic isolators and thus in structural responses over the service life of structures. Therefore, in order to capture the dynamic behavior of base-isolated buildings realistically and design reliable base-isolated buildings, influence of such uncertainty should be taken into account. In this study, seismic reliability of realistic fully three-dimensional benchmark multi-story buildings equipped with nonlinear isolation systems is investigated under historical near-fault earthquakes. In order to take into account the uncertainties in the isolation system characteristics, pre-yield stiffness, post-yield stiffness, and yield displacement parameters are assumed as random variables, while the record-to-record variability nature of the ground motions is considered by using large sets of historical near-fault ground motions with or without forward-directivity effects. Two different levels of nominal isolation periods are taken into account while three different levels of uncertainty are considered for the random isolator characteristics. The reliability of the buildings is investigated in terms of structural integrity, isolation system safety, and the safety of the vibration-sensitive contents of the buildings using the peak bearing displacements and the peak floor accelerations obtained from the nonlinear time history analyses conducted in the framework of the Monte Carlo simulations. The plots including the average reliabilities for the displacement and the acceleration limit values provide a comprehensive picture in terms of the reliability level of the structural systems and of the vibration sensitive contents.

Longitudinal compression and transverse matching of electron bunch for external injection LPWA at ESCULAP

We present theoretical and numerical studies of longitudinal compression and transverse matching of electron bunch before injecting into the Laser–plasma Wake Field Accelerator (LWFA) foreseen at the ESCULAP project in ORSAY. Longitudinal compression is performed with a dogleg chicane, the chicane is designed based on theory of beam optics, beam dynamics in dogleg is studied with ImpactT (Martin Dohlus and Torsten Limberg, 2004) and cross checked with CSRtrack (Qiang and Steve Lidia, 2006), both 3D space charge (SC) and coherent synchrotron radiation (CSR) effects are included. Simulation results show that the energy chirp at the dogleg entrance should be smaller than the nominal optic design value, in order to compensate the negative energy chirp increase caused by longitudinal SC, while CSR can be ignored in our case. With an optimized configuration, the electron bunch (∼10 MeV, 10 pC) is compressed from 0.9 ps RMS to 70 fs RMS (53 fs FWHM), with a peak current of 152 A. Transverse matching is realized with a doublet and a triplet, they are matched with Madx and the electron bunch is tracked with ImpactT, simulation results show little difference with the nominal design values, that is due to the SC effect. Finally, by simply adjusting the quadrupole strength, a preliminary optimized configuration has been achieved, that matches the Courant–Snyder (C–S) parameters to αx=0.01,αy=−0.02,βx=0.014m,βy=0.012m at the plasma entrance.

On the probabilistic distribution of loads on a marine riser

Marine risers are subjected to various types of loads, such as axial tension and bending moments arising from the motions of an offshore platform in association with waves, winds, and currents. They are also exposed to internal and external pressure loads caused by internal flows and external water pressure respectively. The aim of this study is to quantify the probabilistic distribution of loads on a marine riser to aid in the determination of the nominal design values. Two methods are investigated here. The first one is to select a set of credible scenarios in association with site-specific metocean data, and then perform dynamic riser analysis to describe the probabilistic distribution of the loads. The second one is to develop a metamodel to predict the loads as a function of multiple input variables; a method that can also characterize the probabilistic load distribution by running a Monte Carlo simulation. A numerical example shows that the metamodel-based method is more appropriate to describe the loads at low exceedance probability. The characteristics of the loads on a marine riser are observed to be highly random and hence, the design loads must be determined based on the distribution of the influencing parameters.

Signal-to-noise ratio of temperature measurement with Cernox sensors at various supply currents

The Karlsruhe Institute of Technology (KIT) has developed a new thermal method for flow measurement, which is particularly suitable for the application in cryogenic systems. In this method, the stability and the resolution of temperature measurement is important, rather than precision. In other words, constant offsets in temperature measurements can be ignored, and the temperature sensors can be operated at supply currents beyond their nominal design value in order to gain resolution. For this application, the performance of two CernoxTM type CX-1050-SD-HT-1.4L sensors was measured in a temperature range between 300 K and 4 K. The experiments were carried out in the calibration cryostat at the Institute for Technical Physics. Sensors were connected to a Lake Shore Model 121 current source and a Keithley 2701/E digital multimeter for voltage measurements. At constant calibration temperatures, the supply currents were varied such that the resulting voltage drops lay in-between 10 mV and 100 mV. The influence on both the noise and the temperature offset are presented.

Assessment of damper performance in controlling cable vibrations using a reliability-based framework

Owing to their long flexible nature and low intrinsic damping, bridge stay cables are prone to various types of wind-induced vibrations, among which the rain-wind-induced vibration is most frequently observed on site. External dampers are widely used to control such unfavourable cable oscillations and their effectiveness in suppressing large-amplitude cable vibrations was addressed in many studies using deterministic approaches. However, the mechanical and/or physical properties of cables and the attached dampers could not only deviate from their respective nominal design values at a given design point, but also vary considerably during the lifetime of a cable-stayed bridge and thus affect damper efficiency. Hence, for a realistic damper performance assessment, these uncertainties should be taken into account. The objective of this paper is to present a time-variant reliability-based framework model to assess how uncertainties in the structural parameters of a cable-damper system would influence the time specific reliability performance of an external damper yielded from the current design practice.

Treatment of wastewater from service areas at motorways

Abstract This paper deals with wastewater treatment systems placed in motorway service areas (MSAs). In the years 2008-2009 eight of such facilities installed on the stretch of the A2 motorway between Poznań and Nowy Tomyśl were examined and analyzed. The system consists of a septic tank, a submerged aerated biofilter and an outflow filter. The volume of traffic on the highway was analyzed, the amount of water use was measured and peak factors were calculated. On this basis it was concluded that the inflows to the wastewater treatment systems in many cases exceeded the nominal design values. Based on the analysis of effluent quality it was found that the effects of plant operation in large part did not meet the requirements. It was found that the bioreactor aeration system and the design of the suspension separator (outflow filter) should be modified. One of the solutions was to use the soil-reed bed for wastewater treatment. The treatment of wastewater from the MSAs is a task that must take into account the unusual character of these facilities and the atypical quality of the effluent.

Adaptive tower damping control for offshore wind turbines

This paper deals with the problem of wind turbine tower damping control design and implementation in situations where the support structure parameters vary from their nominal design values. Such situations can, in practice, occur for onshore and especially offshore wind turbines and are attributed to aging, turbine installation, scour or marine sand dunes phenomena and biofouling. Practical experience of wind turbine manufacturing industry has shown that such effects are most easily quanti?ed in terms of the ?rst natural frequency of the turbine support structure. The paper brings forward a study regarding the amount to which nominal tower damping controller performance is affected by changes in the turbine natural frequency. Subsequently, an adaptive tower damping control loop is designed using linear parameter-varying control synthesis; the proposed tower damping controller depends on this varying parameter which is assumed throughout the study to be readily available. An investigation of the fatigue load reduction performance in comparison with the original tower damping control approach is given for a generic three-bladed horizontal-axis wind turbine. Copyright a#169; 2016 John Wiley aamp; Sons, Ltd.

Seismic isolation performance sensitivity to potential deviations from design values

Seismic isolation is often used in protecting mission-critical structures including hospitals, data centers, telecommunication buildings, etc. Such structures typically house vibration-sensitive equipment which has to provide continued service but may fail in case sustained accelerations during earthquakes exceed threshold limit values. Thus, peak floor acceleration is one of the two main parameters that control the design of such structures while the other one is peak base displacement since the overall safety of the structure depends on the safety of the isolation system. And in case peak base displacement exceeds the design base displacement during an earthquake, rupture and/or buckling of isolators as well as bumping against stops around the seismic gap may occur. Therefore, obtaining accurate peak floor accelerations and peak base displacement is vital. However, although nominal design values for isolation system and superstructure parameters are calculated in order to meet target peak design base displacement and peak floor accelerations, their actual values may potentially deviate from these nominal design values. In this study, the sensitivity of the seismic performance of structures equipped with linear and nonlinear seismic isolation systems to the aforementioned potential deviations is assessed in the context of a benchmark shear building under different earthquake records with near-fault and far-fault characteristics. The results put forth the degree of sensitivity of peak top floor acceleration and peak base displacement to superstructure parameters including mass, stiffness, and damping and isolation system parameters including stiffness, damping, yield strength, yield displacement, and post-yield to pre-yield stiffness ratio.

A broadband bi-stable flow energy harvester based on the wake-galloping phenomenon

Linear wake-galloping flow energy harvesters have a narrow frequency bandwidth restricted to the lock-in region, where the vortex shedding frequency is close to the natural frequency of the harvester. As a result, their performance is very sensitive to variations in the flow speed around the nominal design value. This letter demonstrates that the lock-in region of a wake-galloping flow energy harvester can be improved by exploiting a bi-stable restoring force. To demonstrate the enhanced performance, the response behavior of a bi-stable piezoelectric cantilever harvester is evaluated in a wind tunnel. A Von Kármán vortex street is generated by placing a rectangular rod in the windward direction of the harvester and the voltage response of the harvester is evaluated as a function of the wind speed. It is shown that, compared to the linear design, bi-stability can be used to improve the steady-state bandwidth considerably.

An eigenvector-based approach for improved parameter variation for multibody mechanical systems

ABSTRACTOptimal design of complex multibody mechanical systems involving numerous design parameters and constraints is a challenging problem. System parameters are typically determined through a recursive process which leads to a set of nominal values. While these nominal values satisfy design constraints they generally result in suboptimal performance. In practice, nominal design values can undergo a final adjustment step to improve performance while ensuring that design constraints are not violated. In this article, we present a framework for design parameter variation to optimize the performance of a multibody system. As an example, we apply the proposed method to an exploration rover and show that the proposed approach provides superior results compared to the standard sensitivity derivative approach.

Hazardous waste incinerators under waste uncertainty: Balancing and throughput maximization via heat recuperation

Hazardous waste incinerators (HWIs) differ substantially from thermal power facilities, since instead of maximizing energy production with the minimum amount of fuel, they aim at maximizing throughput. Variations in quantity or composition of received waste loads may significantly diminish HWI throughput (the decisive profit factor), from its nominal design value. A novel formulation of combustion balance is presented, based on linear operators, which isolates the wastefeed vector from the invariant combustion stoichiometry kernel. Explicit expressions for the throughput are obtained, in terms of incinerator temperature, fluegas heat recuperation ratio and design parameters, for an arbitrary number of wastes, based on fundamental principles (mass and enthalpy balances). The impact of waste variations, of recuperation ratio and of furnace temperature is explicitly determined. It is shown that in the presence of waste uncertainty, the throughput may be a decreasing or increasing function of incinerator temperature and recuperation ratio, depending on the sign of a dimensionless parameter related only to the uncertain wastes. The dimensionless parameter is proposed as a sharp a’ priori waste ‘fingerprint’, determining the necessary increase or decrease of manipulated variables (recuperation ratio, excess air, auxiliary fuel feed rate, auxiliary air flow) in order to balance the HWI and maximize throughput under uncertainty in received wastes. A 10-step procedure is proposed for direct application subject to process capacity constraints. The results may be useful for efficient HWI operation and for preparing hazardous waste blends.

Statistical Approach for Yield Optimization for Minimum Energy Operation in Subthreshold Circuits Considering Variability Issues

The supply voltage ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dd</sub> ) and threshold voltage ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sub> ) are two significant design variables that directly impact the performance and power consumption of circuits. The scaling of these voltages has become a popular option to satisfy performance and low power requirements. Subthreshold operation is a compelling approach for energy-constrained applications where processor speed is less important. However, subthreshold designs show dramatically increased sensitivity to process variations due to the exponential relationship of subthreshold drive current with <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sub> variation and drastically growing leakage power. If there is uncertainty in the value of the threshold or supply voltage, the power advantages of this very low-voltage operation diminishes. This paper presents a statistical methodology for choosing the optimum <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dd</sub> and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sub> under manufacturing uncertainties and different operating conditions to minimize energy for a given frequency in subthreshold operation while ensuring yield maximality. Unlike the traditional energy optimization, to find the optimal values for the voltages, we have considered the following factors to make the optimization technique more acceptable: the application-dependent design constraints, variations in the design variables due to manufacturing uncertainty, device sizing, activity factor of the circuit, and power reduction techniques. To maximize the yield, a two-level optimization is employed. First, the design metric is carefully chosen and deterministically optimized to the optimum point in the feasible region. At the second level, a tolerance box is moved over the design space to find the best location in order to maximize the yield. The feasible region, which is application dependent, is constrained by the minimum performance and the maximum ratio of leakage to total power in the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dd</sub> - <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sub> plane. The center of the tolerance box provides the nominal design values for <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dd</sub> and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sub> such that the design has a maximum immunity to the variations and maximizes the yield. The yield is estimated directly using the joint cumulative distribution function over the tolerance box requiring no numerical integration and saving considerable computational complexity for multidimensional problems. The optimal designs, verified by Monte Carlo and SPECTRE simulations, demonstrate significant increase in yield. By using this methodology, yield is found to be strongly dependent on the design metrics, circuit switching activity, transistor sizing, and the given constraints.

Measurement of flow in microfluidic networks with micrometer‐sized flow restrictors

AbstractThe fluid dynamics in micrometer‐sized flow restrictors was evaluated, to test the predictions of the Hagen–Poiseuille equation in small microchip devices. A photobleaching, time‐of‐flight linear flow rate measurement method was developed for the evaluation of flow in slot‐shaped channels with at least one dimension in the size range of 1–3 μm. For a linear flow rate range in the narrowest dimension of 0.3 to 16 mm/s (volumetric flow rates of 0.6 to 32 nL/s, maximum Reynolds number of 0.3), observed flow rates agreed with theoretical predictions within experimental error (2–3%). An empirical equation for the geometric form factor of a D‐shaped channel was developed, providing a useful working curve for use of the Hagen–Poiseuille equation in microfluidics design. The Hagen–Poiseuille solution can be used to design multiport devices with intersecting flow channel networks, achieving the intended flow rate ratios in channels with differing flow resistance with an accuracy of 1–2%. Despite the differences between achieved etched dimensions and the nominal design values a deviation of only 1–4% in the flow ratios was also achieved. This observation provides a useful guideline for predicting tolerance sensitivity in device manufacture. © 2005 American Institute of Chemical Engineers AIChE J, 2006