Representations and algorithms for finite-state bisimulations of linear discrete-time control systems

While a large amount of research over the past two decades has focused on discrete abstractions of infinite-state dynamical systems, many structural and algorithmic details of these abstractions remain unknown. To clarify the computational resources needed to perform discrete abstractions, this paper examines the algorithmic properties of an existing method for deriving finite-state systems that are bisimilar to linear discrete-time control systems. We explicitly find the structure of the finite-state system, show that it can be enormous compared to the original linear system, and give conditions to guarantee that the finite-state system is reasonably sized and efficiently computable. Though constructing the finite-state system is generally impractical, we see that special cases could be amenable to satisfiability based verification techniques. ©2009 IEEE.

Statistics of reaction progress variable and mixture fraction gradients from DNS of turbulent partially premixed flames

Statistically planar turbulent partially premixed flames for different initial intensities of decaying turbulence have been simulated for global equivalence ratios = 0.7 and 1.0 using three-dimensional, simplified chemistry-based direct numerical simulations (DNS). The simulation parameters are chosen such that the flames represent the thin reaction zones regime combustion. A random bimodal distribution of equivalence ratio is introduced in the unburned gas ahead of the flame to account for the mixture inhomogeneity. The results suggest that the probability density functions (PDFs) of the mixture fraction gradient magnitude |Δξ| (i.e., P(|Δξ|)) can be reasonably approximated using a log-normal distribution. However, this presumed PDF distribution captures only the qualitative nature of the PDF of the reaction progress variable gradient magnitude |Δc| (i.e., P(|Δc|)). It has been found that a bivariate log-normal distribution does not sufficiently capture the quantitative behavior of the joint PDF of |Δξ| and |Δc| (i.e., P(|Δξ|, |Δc|)), and the agreement with the DNS data has been found to be poor in certain regions of the flame brush, particularly toward the burned gas side of the flame brush. Moreover, the variables |Δξ| and |Δc| show appreciable correlation toward the burned gas side of the flame brush. These findings are corroborated further using a DNS data of a lifted jet flame to study the flame geometry dependence of these statistics. © 2013 Copyright Taylor and Francis Group, LLC.

Simulation and fabrication of thermo-optic variable optical attenuators based on multimode interference coupler

A type of thermo-optic variable optical attenuator based on multimode interference coupler is proposed. The optical field propagation properties of the devices are simulated using finite difference beam propagation method. The propagation loss of the fabricated device is 2-4.2 dB at the wavelength range 1510-1610 nm. The total power consumption is 370 mW and the maximum attenuation is more than 25 dB, which almost can meet the requirements of optical fiber communication systems.

The structure and function of neurons with variable nonlinear transfer function

One novel neuron with variable nonlinear transfer function is firstly proposed, It could also be called as subsection transfer function neuron. With different transfer function components, by virtue of multi-thresholded, the variable transfer function neuron switch on among different nonlinear excitated state. And the comparison of output's transfer characteristics between it and single-thresholded neuron will be illustrated, with some practical application experiments on Bi-level logic operation, at last the simple comparison with conventional BP, RBF, and even DBF NN is taken to expect the development foreground on the variable neuron.. The novel nonlinear transfer function neuron could implement the random nonlinear mapping relationship between input layer and output layer, which could make variable transfer function neuron have one much wider applications on lots of reseach realm such as function approximation pattern recognition data compress and so on.

Simulation and fabrication of thermo-optic variable optical attenuators based on multimode interference coupler

A type of thermo-optic variable optical attenuator based on multimode interference coupler is proposed. The optical field propagation properties of the devices are simulated using finite difference beam propagation method. The propagation loss of the fabricated device is 2-4.2 dB at the wavelength range 1510-1610 nm. The total power consumption is 370 mW and the maximum attenuation is more than 25 dB, which almost can meet the requirements of optical fiber communication systems.

Tip-induced dynamic characterization of multilayers and variable morphologies of cytochrome c molecules on highly oriented pyrolytic graphite revealed by in-situ scanning tunnelling microscopy

The dynamic states of cytochrome c multilayers on electrochemically pretreated highly oriented pyrolytic graphite (HOPG) have been studied by in-situ scanning tunnelling microscopy (STM) under potential control of both the tip and the substrate in cytochrome c and phosphate buffer solution. The dynamic characterization of cytochrome c multilayers and relatively stable adsorbed single cytochrome c molecules scattered on HOPG imply that physically adsorbed multilayers were more easily influenced by the STM tip than those of chemically adsorbed single molecules. In-situ STM images of chemically adsorbed cytochrome c molecules with discernible internal structures on HOPG revealed that morphologies of cytochrome c molecules also suffered tip influence; possible tip-sample-substrate interactions have been discussed.

On solvability of linear differential equations in ${\Bbb R}^{\Bbb N}$

We construct $x^0$ in ${\Bbb R}^{\Bbb N}$ and a row-finite matrix $T=\{T_{i,j}(t)\}_{i,j\in\N}$ of polynomials of one real variable $t$ such that the Cauchy problem $\dot x(t)=T_tx(t)$, $x(0)=x^0$ in the Fr\'echet space $\R^\N$ has no solutions. We also construct a row-finite matrix $A=\{A_{i,j}(t)\}_{i,j\in\N}$ of $C^\infty(\R)$ functions such that the Cauchy problem $\dot x(t)=A_tx(t)$, $x(0)=x^0$ in ${\Bbb R}^{\Bbb N}$ has no solutions for any $x^0\in{\Bbb R}^{\Bbb N}\setminus\{0\}$. We provide some sufficient condition of solvability and of unique solvability for linear ordinary differential equations $\dot x(t)=T_tx(t)$ with matrix elements $T_{i,j}(t)$ analytically dependent on $t$.