On the applicability of the lognormal distribution in random dynamical systems

This paper is concerned with the probability density function of the energy of a random dynamical system subjected to harmonic excitation. It is shown that if the natural frequencies and mode shapes of the system conform to the Gaussian Orthogonal Ensemble, then under common types of loading the distribution of the energy of the response is approximately lognormal, providing the modal overlap factor is high (typically greater than two). In contrast, it is shown that the response of a system with Poisson natural frequencies is not approximately lognormal. Numerical simulations are conducted on a plate system to validate the theoretical findings and good agreement is obtained. Simulations are also conducted on a system made from two plates connected with rotational springs to demonstrate that the theoretical findings can be extended to a built-up system. The work provides a theoretical justification of the commonly used empirical practice of assuming that the energy response of a random system is lognormal.

Global analysis of dynamical decision-making models through local computation around the hidden saddle

Bistable dynamical switches are frequently encountered in mathematical modeling of biological systems because binary decisions are at the core of many cellular processes. Bistable switches present two stable steady-states, each of them corresponding to a distinct decision. In response to a transient signal, the system can flip back and forth between these two stable steady-states, switching between both decisions. Understanding which parameters and states affect this switch between stable states may shed light on the mechanisms underlying the decision-making process. Yet, answering such a question involves analyzing the global dynamical (i.e., transient) behavior of a nonlinear, possibly high dimensional model. In this paper, we show how a local analysis at a particular equilibrium point of bistable systems is highly relevant to understand the global properties of the switching system. The local analysis is performed at the saddle point, an often disregarded equilibrium point of bistable models but which is shown to be a key ruler of the decision-making process. Results are illustrated on three previously published models of biological switches: two models of apoptosis, the programmed cell death and one model of long-term potentiation, a phenomenon underlying synaptic plasticity. © 2012 Trotta et al.

Continuous dynamical systems that realize discrete optimization on the hypercube

We study the problem of finding a local minimum of a multilinear function E over the discrete set {0,1}n. The search is achieved by a gradient-like system in [0,1]n with cost function E. Under mild restrictions on the metric, the stable attractors of the gradient-like system are shown to produce solutions of the problem, even when they are not in the vicinity of the discrete set {0,1}n. Moreover, the gradient-like system connects with interior point methods for linear programming and with the analog neural network studied by Vidyasagar (IEEE Trans. Automat. Control 40 (8) (1995) 1359), in the same context. © 2004 Elsevier B.V. All rights reserved.

Experimental comparison of FBARs and SMRs responsitivities to mass loadings

The utilisation of thin film technology to develop film bulk acoustic resonators (FBARs) and solidly mounted resonators (SMRs), offers great potential to outperform the sensitivity and minimum detection limit of gravimetric sensors. Up to now, the choice between FBARs and SMRs depends primarily on the users' ability to design and fabricate Bragg reflectors and/or membranes, because neither of these two types of resonators has been demonstrated to be superior to the other. In the work reported here, it is shown that identically designed FBARs and SMRs resonating at the same frequency exhibit different responsitivities, Rm, to mass loadings, being the FBARs more responsive than the SMRs. For the specific device design and resonant frequency (∼2 GHz) of the resonators presented, FBARs' mass responsitivity is ∼20% greater than that of SMRs, and although this value should not be taken as universal for all possible device designs, it clearly indicates that FBAR devices should be favoured over SMRs in gravimetric sensing applications. © 2012 IEEE.

Low temperature growth of ultra-high mass density carbon nanotube forests on conductive supports

We grow ultra-high mass density carbon nanotube forests at 450°C on Ti-coated Cu supports using Co-Mo co-catalyst. X-ray photoelectron spectroscopy shows Mo strongly interacts with Ti and Co, suppressing both aggregation and lifting off of Co particles and, thus, promoting the root growth mechanism. The forests average a height of 0.38 μm and a mass density of 1.6 g cm -3. This mass density is the highest reported so far, even at higher temperatures or on insulators. The forests and Cu supports show ohmic conductivity (lowest resistance ∼22 kΩ), suggesting Co-Mo is useful for applications requiring forest growth on conductors. © 2013 AIP Publishing LLC.

On differentially dissipative dynamical systems

Dissipativity is an essential concept of systems theory. The paper provides an extension of dissipativity, named differential dissipativity, by lifting storage functions and supply rates to the tangent bundle. Differential dissipativity is connected to incremental stability in the same way as dissipativity is connected to stability. It leads to a natural formulation of differential passivity when restricting to quadratic supply rates. The paper also shows that the interconnection of differentially passive systems is differentially passive, and provides preliminary examples of differentially passive electrical systems. © IFAC.

A general mass law for broadband energy harvesting

It is well known that the power absorbed by a linear oscillator when excited by white noise base acceleration depends only on the mass of the oscillator and the spectral density of the base motion. This places an upper bound on the energy that can be harvested from a linear oscillator under broadband excitation, regardless of the stiffness of the system or the damping factor. It is shown here that the same result applies to any multi-degree-of-freedom nonlinear system that is subjected to white noise base acceleration: for a given spectral density of base motion the total power absorbed is proportional to the total mass of the system. The only restriction to this result is that the internal forces are assumed to be a function of the instantaneous value of the state vector. The result is derived analytically by several different approaches, and numerical results are presented for an example two-degree-of-freedom-system with various combinations of linear and nonlinear damping and stiffness. © 2013 The Author.

Determinations of MC-LR and [Dha(7)] MC-LR Concentrations and Physicochemical Properties by Liquid Chromatography-Tandem Mass Spectrometry

A liquid chromatography electrospray mass spectrometry (LC/ESI/MS) method working in multiple reactions monitoring mode for the determination of trace amounts of microcystin variants (MC-LR and [Dha(7)] MC-LR) in waters was developed. The limit of quantification was 0.05 mu g/L and the limit of detection was 0.015 mu g/L for MC-LR and [Dha(7)] MC-LR, respectively. Recoveries for MCs were in the range of 68%-81%. MC-LR and [Dha(7)] MC-LR were chemically stable with similar physiochemical behavior.

Carbon source/sink function of a subtropical, eutrophic lake determined from an overall mass balance and a gas exchange and carbon burial balance

Although studies on carbon burial in lake sediments have shown that lakes are disproportionately important carbon sinks, many studies on gaseous carbon exchange across the water-air interface have demonstrated that lakes are supersaturated with CO2 and CH4 causing a net release of CO2 and CH4 to the atmosphere. In order to more accurately estimate the net carbon source/sink function of lake ecosystems, a more comprehensive carbon budget is needed, especially for gaseous carbon exchange across the water-air interface. Using two methods, overall mass balance and gas exchange and carbon burial balance, we assessed the carbon source/sink function of Lake Donghu, a subtropical, eutrophic take, from April 2003 to March 2004. With the overall mass balance calculations, total carbon input was 14 905 t, total carbon output was 4950 1, and net carbon budget was +9955 t, suggesting that Lake Donghu was a great carbon sink. For the gas exchange and carbon burial balance, gaseous carbon (CO2 and CH4) emission across the water-air interface totaled 752 t while carbon burial in the lake sediment was 9477 t. The ratio of carbon emission into the atmosphere to carbon burial into the sediment was only 0.08. This low ratio indicates that Lake Donghu is a great carbon sink. Results showed good agreement between the two methods with both showing Lake Donghu to be a great carbon sink. This results from the high primary production of Lake Donghu, substantive allochthonous carbon inputs and intensive anthropogenic activity. Gaseous carbon emission accounted for about 15% of the total carbon output, indicating that the total output would be underestimated without including gaseous carbon exchange. (C) 2007 Elsevier Ltd. All rights reserved.

Simultaneous determination of microcystin-LR and its glutathione conjugate in fish tissues by liquid chromatography-tandem mass spectrometry

A sensitive and selective liquid chromatography-tandem mass spectrometry method was developed and validated for the simultaneous quantitative determination of microcystin-LR (MC-LR) and its glutathione conjugate (MC-LR-GSH) in fish tissues. The analytes were extracted from fish liver and kidney using 0.01 M EDTA-Na-2-5% acetic acid, followed by a solid-phase extraction (SPE) on Oasis HLB and silica cartridges. High-performance liquid chromatography (HPLC) with electrospray ionization mass spectrometry, operating in selected reaction monitoring (SRM) mode, was used to quantify MC-LR and its glutathione conjugate in fish liver and kidney. Recoveries of analytes were assessed at three concentrations (0.2, 1.0, and 5 mu g g(-1) dry weight [DW]) and ranged from 91 to 103% for MC-LR, and from 65.0 to 75.7% for MC-LR-GSH. The assay was linear within the range from 0.02 to 5.0 mu g g(-1) DW, with a limit of quantification (LOQ) of 0.02 mu g g(-1) DW. The limit of detection (LOD) of the method was 0.007 mu g g(-1) DW in both fish liver and kidney. The overall precision was determined on three different days. The values for within- and between-day precision in liver and kidney were within 15%. This method was applied to the identification and quantification of MC-LR and its glutathione conjugate in liver and kidney of fish with acute exposure of MC-LR. (c) 2007 Elsevier B.V. All rights reserved.