Approximate expressions for steady-state reliability indexes of Markov systems

1987 ◽  
Vol 27 (5) ◽  
pp. 939
Keyword(s):  
Steady State ◽  
Markov Systems ◽  
Approximate Expressions

BIFURCATIONS AND CLUSTERING IN GLOBALLY COUPLED ARRAYS OF PHASE-BISTABLE SYSTEMS

2002 ◽  
Vol 12 (02) ◽  
pp. 309-318 ◽  
Author(s):  
KEN McNEIL
Keyword(s):  
Steady State ◽  
Parametric Oscillators ◽  
Bistable Systems ◽  
Special Cases ◽  
Secondary Bifurcations ◽  
Approximate Expressions

This paper considers the behavior of a system of globally coupled identical parametric oscillators. The coupling is linear, with a phase chosen so that the system takes on steady, rather than oscillatory, states, and this work focuses on bifurcations from the zero steady state. Approximate expressions are given for the states which emerge at these bifurcations, and full expressions are given for special cases. Secondary bifurcations are also briefly discussed.

THEORIES OF DIFFUSION AT A MICRORING ELECTRODES: A REVIEW

2007 ◽  
Vol 06 (04) ◽  
pp. 699-713
Author(s):  
L. RAJENDRAN ◽  
G. RAHAMATHUNISSA ◽  
C. A. BASHA
Keyword(s):  
Steady State ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Area Ratio ◽  
Diffusion Control ◽  
Electrode Kinetics ◽  
Steady State Current ◽  
Approximate Expressions

Microring electrodes are useful for the investigation of electrode kinetics due to their large perimeter-to-area ratio and compact nature but have hitherto been limited in application due to the absence of the underpinning theory. In this review, the analytical solutions, approximate expressions, and numerical solutions of transient chronoamperometric current at a microring electrode under diffusion control are discussed. The steady and non-steady-state current for microring electrode for an EC' reaction are also discussed. Tabular compilations of dimensionless current are provided.

APPROXIMATE EXPRESSIONS FOR AVAILABILITY OF REPAIRABLE SERIES–PARALLEL STRUCTURES

1999 ◽  
Vol 06 (04) ◽  
pp. 319-333 ◽  
Author(s):  
U. DINESH KUMAR ◽  
A. BIROLINI
Keyword(s):  
Steady State ◽  
Numerical Evaluation ◽  
Complex Structures ◽  
Time To Failure ◽  
Maintenance Strategy ◽  
Reliability Engineering ◽  
Good Convergence ◽  
Parallel Structures ◽  
Mean Time ◽  
Approximate Expressions

The investigation of approximate expressions for availability of complex repairable structures is an important problem facing researchers in the field of reliability engineering. This is due to the fact that the availability evaluation of complex structures becomes time consuming even under the assumption that the failure and repair rates are constant and only the steady-state availability and mean time to failure (MTTF) are needed. The main reason for complexity is due to the large number of states required to describe the system. In such cases, approximate expressions can be useful. In this paper, approximate expressions for steady-state availability and MTTF of large series–parallel structures are derived under three different assumptions on maintenance strategy, namely, independent elements, macro-structures and independent macro-structures. An example is presented to illustrate the application of the method under the three assumptions. Numerical evaluation of the example problem shows a good convergence of the results.

Studies on Water in the Hydration Chamber of a Modified Electron Microscope

1970 ◽  
Vol 28 ◽  
pp. 544-545
Author(s):  
R. C. Moretz ◽  
G. G. Hausner ◽  
D. F. Parsons
Keyword(s):  
Thin Film ◽  
Thin Films ◽  
Electron Microscope ◽  
Steady State ◽  
Room Temperature ◽  
Small Mass ◽  
Equilibrium Pressure ◽  
Biological Objects ◽  
Mechanical Pump ◽  
Differential Pumping

Use of the electron microscope to examine wet objects is possible due to the small mass thickness of the equilibrium pressure of water vapor at room temperature. Previous attempts to examine hydrated biological objects and water itself used a chamber consisting of two small apertures sealed by two thin films. Extensive work in our laboratory showed that such films have an 80% failure rate when wet. Using the principle of differential pumping of the microscope column, we can use open apertures in place of thin film windows.Fig. 1 shows the modified Siemens la specimen chamber with the connections to the water supply and the auxiliary pumping station. A mechanical pump is connected to the vapor supply via a 100μ aperture to maintain steady-state conditions.

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