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Exactly isochoric deformations of soft solids
Many materials of contemporary interest, such as gels, biological tissues and
elastomers, are easily deformed but essentially incompressible. Traditional
linear theory of elasticity implements incompressibility only to first order
and thus permits some volume changes, which become problematically large even
at very small strains. Using a mixed coordinate transformation originally due
to Gauss, we enforce the constraint of isochoric deformations exactly to
develop a linear theory with perfect volume conservation that remains valid
until strains become geometrically large. We demonstrate the utility of this
approach by calculating the response of an infinite soft isochoric solid to a
point force that leads to a nonlinear generalization of the Kelvin solution.
Our approach naturally generalizes to a range of problems involving
deformations of soft solids and interfaces in 2 dimensional and axisymmetric
geometries, which we exemplify by determining the solution to a distributed
load that mimics muscular contraction within the bulk of a soft solid
The Ultraviolet flash accompanying GRBs from neutron-rich internal shocks
In the neutron-rich internal shocks model for Gamma-ray Burts (GRBs), the
Lorentz factors (LFs) of ions shells are variable, so are the LFs of
accompanying neutron shells. For slow neutron shells with a typical LF tens,
the typical beta-decay radius reads R_{\beta,s} several 10^{14} cm, which is
much larger than the typical internal shocks radius 10^{13} cm, so their impact
on the internal shocks may be unimportant. However, as GRBs last long enough
(T_{90}>20(1+z) s), one earlier but slower ejected neutron shell will be swept
successively by later ejected ion shells in the range 10^{13}-10^{15} cm, where
slow neutrons have decayed significantly. We show in this work that ion shells
interacting with the beta-decay products of slow neutron shells can power a
ultraviolet (UV) flash bright to 12th magnitude during the prompt gamma-ray
emission phase or slightly delayed, which can be detected by the upcoming
Satellite SWIFT in the near future.Comment: 6 pages (2 eps figures), accepted for publication in ApJ
Modeling the IDV emissions of the BL Lac Objects with a Langevin type stochastic differential equation
In this paper, we introduce a simplified model for explaining the
observations of the optical intraday variability (IDV) of the BL Lac Objects.
We assume that the source of the IDV are the stochastic oscillations of an
accretion disk around a supermassive black hole. The Stochastic Fluctuations on
the vertical direction of the accretion disk are described by using a Langevin
type equation with a damping term and a random, white noise type force.
Furthermore, the preliminary numerical simulation results are presented, which
are based on the numerical analysis of the Langevin stochastic differential
equation.Comment: 4 pages, 4 figures, accepted for publication in J. Astrophys. Ast
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Filtering for nonlinear genetic regulatory networks with stochastic disturbances
In this paper, the filtering problem is investigated for nonlinear genetic regulatory networks with stochastic disturbances and time delays, where the nonlinear function describing the feedback regulation is assumed to satisfy the sector condition, the stochastic perturbation is in the form of a scalar Brownian motion, and the time delays exist in both the translation process and the feedback regulation process. The purpose of the addressed filtering problem is to estimate the true concentrations of the mRNA and protein. Specifically, we are interested in designing a linear filter such that, in the presence of time delays, stochastic disturbances as well as sector nonlinearities, the filtering dynamics of state estimation for the stochastic genetic regulatory network is exponentially mean square stable with a prescribed decay rate lower bound beta. By using the linear matrix inequality (LMI) technique, sufficient conditions are first derived for ensuring the desired filtering performance for the gene regulatory model, and the filter gain is then characterized in terms of the solution to an LMI, which can be easily solved by using standard software packages. A simulation example is exploited in order to illustrate the effectiveness of the proposed design procedures
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