Availability analysis of periodically inspected systems with random walk model

2001 ◽  
Vol 38 (4) ◽  
pp. 860-871 ◽  
Author(s):  
Lirong Cui ◽  
M. Xie
Keyword(s):  
Random Walk ◽  
Random Walk Model ◽  
Two Dimensional ◽  
Availability Analysis ◽  
Periodic Inspection ◽  
Dimensional Plane ◽  
Inspection And Maintenance ◽  
The Relationship

In this paper, the instantaneous availability of a system maintained under periodic inspection is investigated using random walk models. Two cases are considered. In the first model, the system is repaired or modified and it is assumed to be as good as new upon periodic inspection and maintenance. In the second model, the system is not modified after the inspection if the system is still working, and the condition of the system is assumed to be the same as that before the inspection. For both models the failures only can be found through the inspection. Perfect repair or replacement of a failed system is assumed to be carried out, but the time it takes can be constant or of a random length. The relationship between this problem and the random walk model in a two-dimensional plane is described. Several new results are also shown.

Availability analysis of periodically inspected systems with random walk model

2001 ◽  
Vol 38 (04) ◽  
pp. 860-871 ◽  
Author(s):  
Lirong Cui ◽  
M. Xie
Keyword(s):  
Random Walk ◽  
Random Walk Model ◽  
Two Dimensional ◽  
Availability Analysis ◽  
Periodic Inspection ◽  
Dimensional Plane ◽  
Inspection And Maintenance ◽  
The Relationship

In this paper, the instantaneous availability of a system maintained under periodic inspection is investigated using random walk models. Two cases are considered. In the first model, the system is repaired or modified and it is assumed to be as good as new upon periodic inspection and maintenance. In the second model, the system is not modified after the inspection if the system is still working, and the condition of the system is assumed to be the same as that before the inspection. For both models the failures only can be found through the inspection. Perfect repair or replacement of a failed system is assumed to be carried out, but the time it takes can be constant or of a random length. The relationship between this problem and the random walk model in a two-dimensional plane is described. Several new results are also shown.

The spatial distribution of gyrotactic swimming micro-organisms in laminar flow fields

2011 ◽  
Vol 680 ◽  
pp. 602-635 ◽  
Author(s):  
R. N. BEARON ◽  
A. L. HAZEL ◽  
G. J. THORN
Keyword(s):  
Random Walk ◽  
Diffusion Model ◽  
Diffusion Models ◽  
Random Walk Model ◽  
Two Dimensional ◽  
Local Flow ◽  
Spatial And Temporal Scales ◽  
Advection Diffusion ◽  
Micro Organisms ◽  
Good Agreement

We compare the results of two-dimensional, biased random walk models of individual swimming micro-organisms with advection–diffusion models for the whole population. In particular, we consider the influence of the local flow environment (gyrotaxis) on the resulting motion. In unidirectional flows, the results of the individual and population models are generally in good agreement, even in flows in which the cells can experience a range of shear environments, and both models successfully predict the phenomena of gravitactic focusing. Numerical results are also compared with asymptotic expressions for weak and strong shear. Discrepancies between the models arise in two cases: (i) when reflective boundary conditions change the orientation distribution in the random walk model from that predicted by the long-term asymptotics used to derive the advection–diffusion model; (ii) when the spatial and temporal scales are not large enough for the advection–diffusion model to apply. We also use a simple two-dimensional flow containing a variety of flow regimes to explore what happens when there are localized regions in which the generalized Taylor dispersion theory used in the derivation of the population model does not apply. For spherical cells, we find good agreement between the models outside the ‘break-down’ regions, but comparison of the results within these regions is complicated by the presence of nearby boundaries and their influence on the random walk model. In contrast, for rod-shaped cells which are reorientated by both vorticity and strain, we see qualitatively different spatial patterns between individual and advection–diffusion models even in the absence of gyrotaxis, because cells are advected between regions of differing rates of strain.

Deterministic Random Walks on the Two-Dimensional Grid

2009 ◽  
Vol 18 (1-2) ◽  
pp. 123-144 ◽  
Author(s):  
BENJAMIN DOERR ◽  
TOBIAS FRIEDRICH
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Random Walk Model ◽  
Two Dimensional ◽  
Expected Number ◽  
Fixed Order ◽  
The Difference ◽  
Propp Machine

Jim Propp's rotor–router model is a deterministic analogue of a random walk on a graph. Instead of distributing chips randomly, each vertex serves its neighbours in a fixed order. We analyse the difference between the Propp machine and random walk on the infinite two-dimensional grid. It is known that, apart from a technicality, independent of the starting configuration, at each time the number of chips on each vertex in the Propp model deviates from the expected number of chips in the random walk model by at most a constant. We show that this constant is approximately 7.8 if all vertices serve their neighbours in clockwise or order, and 7.3 otherwise. This result in particular shows that the order in which the neighbours are served makes a difference. Our analysis also reveals a number of further unexpected properties of the two-dimensional Propp machine.

scholarly journals Manipulation of particles in two dimensions using phase controllable ultrasonic standing waves

2011 ◽  
Vol 468 (2138) ◽  
pp. 337-360 ◽  
Author(s):  
C. R. P. Courtney ◽  
C.-K. Ong ◽  
B. W. Drinkwater ◽  
A. L. Bernassau ◽  
P. D. Wilcox ◽  
...  
Keyword(s):  
Acoustic Radiation ◽  
Sudden Change ◽  
Standing Waves ◽  
Radiation Force ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Dimensional Plane ◽  
System A ◽  
Propagating Waves ◽  
The Relationship

The ability to manipulate dense micrometre-scale objects in fluids is of interest to biosciences with a view to improving analysis techniques and enabling tissue engineering. A method of trapping micrometre-scale particles and manipulating them on a two-dimensional plane is proposed and demonstrated. Phase-controlled counter-propagating waves are used to generate ultrasonic standing waves with arbitrary nodal positions. The acoustic radiation force drives dense particles to pressure nodes. It is shown analytically that a series of point-like traps can be produced in a two-dimensional plane using two orthogonal pairs of counter-propagating waves. These traps can be manipulated by appropriate adjustment of the relative phases. Four 5 MHz transducers (designed to minimize reflection) are used as sources of counter-propagating waves in a water-filled cavity. Polystyrene beads of 10 μm diameter are trapped and manipulated. The relationship between trapped particle positions and the relative phases of the four transducers is measured and shown to agree with analytically derived expressions. The force available is measured by determining the response to a sudden change in field and found to be 30 pN, for a 30 V pp input, which is in agreement with the predictions of models of the system. A scalable fabrication approach to producing devices is demonstrated.

Random-Walk and Accumulator Models of Psychophysical Discrimination: A Critical Evaluation

Perception ◽  
1984 ◽  
Vol 13 (1) ◽  
pp. 57-65 ◽  
Author(s):  
Richard A Heath
Keyword(s):  
Computer Simulation ◽  
Random Walk ◽  
Critical Evaluation ◽  
Line Length ◽  
Random Walk Model ◽  
Mean Response Time ◽  
Accumulator Model ◽  
The Relationship ◽  
Parameter Estimation Techniques ◽  
Accumulator Models

The accumulator model proposed by Vickers and the modified random-walk model proposed by Link and Heath are compared in their ability to account for confidence judgments in line-length discrimination tasks. The random-walk model proves to be a viable alternative to the accumulator model, and is able to account for the relationship between mean response time and confidence. The parameter estimation techniques available for the random-walk model are considered advantageous when compared with the accumulator model, because the predictions from the latter have been obtained with the use of computer simulation.

A Two-Dimensional Random Walk Model for Polymers

1965 ◽  
Vol 20 (3) ◽  
pp. 423-427 ◽  
Author(s):  
V. D. Gupta ◽  
A. K. Gupta
Keyword(s):  
Random Walk ◽  
Random Walk Model ◽  
Two Dimensional

Agglomeration kinetics of monodisperse systems — computer simulation of agglomeration by a two-dimensional random walk model

1984 ◽  
Vol 38 (3) ◽  
pp. 211-216 ◽  
Author(s):  
H. Sunada ◽  
A. Otsuka ◽  
Y. Yamada ◽  
Y. Kawashima ◽  
H. Takernaka ◽  
...  
Keyword(s):  
Computer Simulation ◽  
Random Walk ◽  
Random Walk Model ◽  
Two Dimensional ◽  
Kinetics Of
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