Worst-case Limit Research Articles

Worst-case analysis of electronic circuits based on an analytic forward solver approach

PurposeThe purpose of this paper is to evaluate the worst-case behavior of a given electronic circuit by varying the values of the components in a meaningful way in order not to exceed pre-defined currents or voltages limits during a transient operation.Design/methodology/approachAn analytic formulation is used to identify the time-dependent solution of voltages or currents using proper state equations in closed form. Circuits with linear elements can be described by a system of differential equations, while circuits composing nonlinear elements are described by piecewise-linear models. A sequential quadratic program (SQP) is used to find the worst-case scenario.FindingsIt is found that the worst-case scenario can be obtained with as few solutions to the forward problem as possible by applying an SQP method.Originality/valueThe SQP method in combination with the analytic forward solver approach shows that the worst-case limit converges in a few steps even if the worst-case limit is not on the boundary of the parameters.

Optofluidic microsystems with integrated vertical one-dimensional photonic crystals for chemical analysis

In this work, we report all-silicon, integrated optofluidic microsystems (OFMs) fabricated by electrochemical micromachining (ECM) technology, in which high aspect-ratio (HAR) photonic crystal (PhC) devices (i.e. micromirrors, optical cavities) are integrated by one-etching-step, together with microfluidic reservoirs/channels, for the infiltration of liquids in the PhC air gaps, and with fiber grooves for alignment/positioning of readout optical fibers in front of the PhC, on the same silicon die. This has not previously been reported in the literature, and opens up new ground in, though not limited to, the optofluidics field, due to the low-cost and high-flexibility of the ECM technology that allows optofluidic microsystem fabrication to be performed in any lab. Optofluidic characterization of PhC-OFMs by both capillary-action and pressure-driven operations is carried out through the measurement of the reflectivity spectra of HAR-PhCs upon injection of liquids featuring different refractive index values in the HAR-PhC air gaps, by using readout optical fibers positioned in the on-chip fiber grooves. High sensitivity and good limit of detection of PhC-OFMs are obtained for both capillary-action and pressure-driven operations. A best sensitivity value of 670 nm/RIU and a worst-case limit of detection of the order of 10(-3) RIU are measured, the former being comparable to state-of-the-art integrated refractive index sensors and the latter being limited by constraints of the experimental setup. The proof of concept about the biosensing potential of PhC-OFMs is given by successfully carrying out a sandwich assay based on antigen-antibody interactions for the detection of the C-reactive protein (CRP) at a concentration value of 10 mg L(-1), which represents the boundary level between physiological and pathological conditions.

Deepwater Frac-Pack Maximum Treating Pressure Limits, An Examination Using BottomHole Pressure Gauges

Summary During frac-pack treatments, completion hardware is often subject to extreme differential pressures. This is especially true during early screenouts where the large hydrostatic differentials can suddenly be placed on the completion components, resulting in a high risk of collapse. Deep wells and completion-tool configuration can limit supporting pressures for these tools. To prevent damage to completion hardware such as crossover tools, fluid-loss devices, and blank pipe, the maximum surface treating pressure has been limited to a calculated Pmax (Jannise and Edwards 2007). Conventionally, the reservoir pressure was used as the internal supporting pressure in these calculations. Using the reservoir pressure to calculate the Pmax results in a worst-case pressure limit that prevents collapse in virtually any job. However, today many frac-pack treatments are being performed in low-pressure, subhydrostatic reservoirs. Many of these jobs could not be placed using just reservoir pressure for support, even when using high-strength, completion hardware materials. By analyzing a significant number of actual jobs, it was determined that the current standard equations are too conservative when compared to actual treating results. By using less conservative, modified equations, numerous additional wells have been completed with frac-pack technology. This paper studies a number of these successful frac-pack jobs that could not have been performed using the standard Pmax equation and safety factors. Postjob bottomhole-gauge data are examined to determine the true differential pressures and verify the accuracy of the assumptions that are used in the modified Pmax calculation, which provides valuable insight and recommendations for tool design, fluid properties, and maximum-pressure limitations for frac-pack completions.

Exact analysis of surface field reduction due to field-emitted vacuum space charge, in parallel-plane geometry, using simple dimensionless equations

This paper reports (a) a simple dimensionless equation relating to field-emitted vacuum space charge (FEVSC) in parallel-plane geometry, namely 9ζ2θ2−3θ−4ζ+3=0, where ζ is the FEVSC “strength” and θ is the reduction in emitter surface field (θ=field-with/field-without FEVSC), and (b) the formula j=9θ2ζ/4, where j is the ratio of emitted current density JP to that predicted by Child’s law. These equations apply to any charged particle, positive or negative, emitted with near-zero kinetic energy. They yield existing and additional basic formulas in planar FEVSC theory. The first equation also yields the well-known cubic equation describing the relationship between JP and applied voltage; a method of analytical solution is described. Illustrative FEVSC effects in a liquid metal ion source and in field electron emission are discussed. For Fowler–Nordheim plots, a “turn-over” effect is predicted in the high FEVSC limit. The higher the voltage-to-local-field conversion factor for the emitter concerned, then the higher is the field at which turn over occurs. Past experiments have not found complete turn over; possible reasons are noted. For real field emitters, planar theory is a worst-case limit; however, adjusting ζ on the basis of Monte Carlo calculations might yield formulae adequate for real situations.

Worst case plastic limit analysis of trusses under uncertain loads via mixed 0-1 programming

The paper presents a global optimization method to compute the minimum limit load factor of trusses subjected to unknown but bounded loads. We assume that the external forces consist of a part proportional to a load factor and a part that is uncertain around its nominal value. The worst-case limit load factor is introduced as the smallest limit load factor realized with some uncertain parameters. In order to detect the worst case, we have to find the global optimal solution of a nonconvex optimization problem, which is the major difficulty of the worst-case limit analysis. By reformulating the worstcase determination problem as a mixed 0-1 programming problem, we propose a global optimization algorithm as a combination of a branch-and-bound method based on the linear programming relaxations and a cutting plane method based on the disjunctive or lift-and-project cuts. The worst-case limit loads, as well as the corresponding critical loading patterns, are computed to demonstrate that our method converges to the global optimal solutions successfully.

122 混合整数計画を用いた不確定外力を受けるトラスの極限解析法

A global optimization method is presented for computing the minimum limit load factor of trusses subjected to unknown but bounded loads. We assume that the external forces consist of a part proportional to a load factor and a part that is uncertain around its nominal value. The worst-case limit load factor is introduced as the smallest limit load factor realized with some uncertain parameters. By reformulating the worst-case determination problem as a mixed 0-1 programming problem, we propose a global optimization algorithm by a combination of a branch-and-bound method based on the linear programming relaxations and a cutting plane method based on the disjunctive cuts.

Kinematic tolerance analysis

We present a general method for worst-case limit kinematic tolerance analysis: computing the range of variation in the kinematic function of a mechanism from its part tolerance specifications. The method covers fixed and multiple contact mechanisms with parametric or geometric part tolerances. We develop a new model of kinematic variation, called kinematic tolerance space, that generalizes the configuration space representation of nominal kinematic function. Kinematic tolerance space captures quantitative and qualitative variations in kinematic function due to variations in part shape and part configuration. We derive properties of kinematic tolerance space that express the relationship between the nominal kinematics of mechanisms and their kinematic variations. Using these properties, we develop a practical kinematic tolerance space computation algorithm for planar pairs with two degrees of freedom.

Evaluation of optical fiber lifetime models based on the power law

Twelve existing lifetime models for optical fibers, based on a power law to describe the stress-enhanced crack growth, are studied and compared. The number of models is reduced to only one basic model. This model takes into account the effects of a proof test. An alternative model, to be used when proof testing is performed on line, is given as a worst case limit. A choice of three testing methods to obtain information about the weak-flaw distribution is given: dynamic fatigue and variable screen testing of long lengths or the use of a failure number during the proof test. We show that the part of the crack growth that is controlled by transport of the reaction agent instead of by reaction speed (described by the power law) does not influence the model. It is also shown that weakening of the fiber during unloading has a minor effect on the presented model. The lifetime model cannot be used for fibers in water without further study.

A heat engine model of a reversible computation

Using the tools of information theory and thermodynamics, reversible computation at the binary level is modeled as a heat engine operating in a Carnot cycle. The model defines an information-theoretic temperature for a binary system and predicts that reversible computation can be accomplished without the dissipation of energy. However, in the worst-case limit, kT log 2 joules of stored energy operation per bit are required, where T is not the ambient temperature but the information-theoretic temperature, which for this case is infinite.