Abstract: The thermal conductivity of a fluid can be
significantly enhanced by dispersing nano-sized particles in it, and
the resultant fluid is termed as "nanofluid". A theoretical model for
estimating the thermal conductivity of a nanofluid has been proposed
here. It is based on the mechanism that evenly dispersed
nanoparticles within a nanofluid undergo Brownian motion in course
of which the nanoparticles repeatedly collide with the heat source.
During each collision a rapid heat transfer occurs owing to the solidsolid
contact. Molecular dynamics (MD) simulation of the collision
of nanoparticles with the heat source has shown that there is a pulselike
pick up of heat by the nanoparticles within 20-100 ps, the extent
of which depends not only on thermal conductivity of the
nanoparticles, but also on the elastic and other physical properties of
the nanoparticle. After the collision the nanoparticles undergo
Brownian motion in the base fluid and release the excess heat to the
surrounding base fluid within 2-10 ms. The Brownian motion and
associated temperature variation of the nanoparticles have been
modeled by stochastic analysis. Repeated occurrence of these events
by the suspended nanoparticles significantly contributes to the
characteristic thermal conductivity of the nanofluids, which has been
estimated by the present model for a ethylene glycol based nanofluid
containing Cu-nanoparticles of size ranging from 8 to 20 nm, with
Gaussian size distribution. The prediction of the present model has
shown a reasonable agreement with the experimental data available
in literature.
Abstract: This paper deals with the problem of passivity
analysis for stochastic neural networks with leakage, discrete and
distributed delays. By using delay partitioning technique, free
weighting matrix method and stochastic analysis technique, several
sufficient conditions for the passivity of the addressed neural
networks are established in terms of linear matrix inequalities
(LMIs), in which both the time-delay and its time derivative can be
fully considered. A numerical example is given to show the
usefulness and effectiveness of the obtained results.
Abstract: This paper studies the mean square exponential synchronization problem of a class of stochastic neutral type chaotic neural networks with mixed delay. On the Basis of Lyapunov stability theory, some sufficient conditions ensuring the mean square exponential synchronization of two identical chaotic neural networks are obtained by using stochastic analysis and inequality technique. These conditions are expressed in the form of linear matrix inequalities (LMIs), whose feasibility can be easily checked by using Matlab LMI Toolbox. The feedback controller used in this paper is more general than those used in previous literatures. One simulation example is presented to demonstrate the effectiveness of the derived results.
Abstract: In this paper, we investigate a class of fuzzy Cohen- Grossberg neural networks with time delays and impulsive effects. By virtue of stochastic analysis, Halanay inequality for stochastic differential equations, we find sufficient conditions for the global exponential square-mean synchronization of the FCGNNs under noise perturbation. In particular, the traditional assumption on the differentiability of the time-varying delays is no longer needed. Finally, a numerical example is given to show the effectiveness of the results in this paper.
Abstract: In the paper, based on stochastic analysis theory and Lyapunov functional method, we discuss the mean square stability of impulsive stochastic delay differential equations with markovian switching and poisson jumps, and the sufficient conditions of mean square stability have been obtained. One example illustrates the main results. Furthermore, some well-known results are improved and generalized in the remarks.
Abstract: The paper is devoted to stochastic analysis of finite
dimensional difference equation with dependent on ergodic Markov
chain increments, which are proportional to small parameter ". A
point-form solution of this difference equation may be represented
as vertexes of a time-dependent continuous broken line given on the
segment [0,1] with "-dependent scaling of intervals between vertexes.
Tending " to zero one may apply stochastic averaging and diffusion
approximation procedures and construct continuous approximation of
the initial stochastic iterations as an ordinary or stochastic Ito differential
equation. The paper proves that for sufficiently small " these
equations may be successfully applied not only to approximate finite
number of iterations but also for asymptotic analysis of iterations,
when number of iterations tends to infinity.
Abstract: In this paper, the problem of stability analysis for a class of impulsive stochastic fuzzy neural networks with timevarying delays and reaction-diffusion is considered. By utilizing suitable Lyapunov-Krasovskii funcational, the inequality technique and stochastic analysis technique, some sufficient conditions ensuring global exponential stability of equilibrium point for impulsive stochastic fuzzy cellular neural networks with time-varying delays and diffusion are obtained. In particular, the estimate of the exponential convergence rate is also provided, which depends on system parameters, diffusion effect and impulsive disturbed intention. It is believed that these results are significant and useful for the design and applications of fuzzy neural networks. An example is given to show the effectiveness of the obtained results.
Abstract: This paper is concerned with the delay-distributiondependent
stability criteria for bidirectional associative memory
(BAM) neural networks with time-varying delays. Based on the
Lyapunov-Krasovskii functional and stochastic analysis approach,
a delay-probability-distribution-dependent sufficient condition is derived
to achieve the globally asymptotically mean square stable of
the considered BAM neural networks. The criteria are formulated in
terms of a set of linear matrix inequalities (LMIs), which can be
checked efficiently by use of some standard numerical packages. Finally,
a numerical example and its simulation is given to demonstrate
the usefulness and effectiveness of the proposed results.
Abstract: In this paper, the issue of pth moment exponential stability of stochastic recurrent neural network with distributed time delays is investigated. By using the method of variation parameters, inequality techniques, and stochastic analysis, some sufficient conditions ensuring pth moment exponential stability are obtained. The method used in this paper does not resort to any Lyapunov function, and the results derived in this paper generalize some earlier criteria reported in the literature. One numerical example is given to illustrate the main results.
Abstract: In this work, we improve a previously developed
segmentation scheme aimed at extracting edge information from
speckled images using a maximum likelihood edge detector. The
scheme was based on finding a threshold for the probability density
function of a new kernel defined as the arithmetic mean-to-geometric
mean ratio field over a circular neighborhood set and, in a general
context, is founded on a likelihood random field model (LRFM). The
segmentation algorithm was applied to discriminated speckle areas
obtained using simple elliptic discriminant functions based on
measures of the signal-to-noise ratio with fractional order moments.
A rigorous stochastic analysis was used to derive an exact expression
for the cumulative density function of the probability density
function of the random field. Based on this, an accurate probability
of error was derived and the performance of the scheme was
analysed. The improved segmentation scheme performed well for
both simulated and real images and showed superior results to those
previously obtained using the original LRFM scheme and standard
edge detection methods. In particular, the false alarm probability was
markedly lower than that of the original LRFM method with
oversegmentation artifacts virtually eliminated. The importance of
this work lies in the development of a stochastic-based segmentation,
allowing an accurate quantification of the probability of false
detection. Non visual quantification and misclassification in medical
ultrasound speckled images is relatively new and is of interest to
clinicians.