On the Asymptotic Behavior of Solutions of Differential Systems

There are many studies on the asymptotic behavior of solutions of differential equations. In the present paper, we consider another aspect of this problem, namely, the rate of the asymptotic convergence of solutions.Асимптотичній поведінці розв'язків диференціальних рівнянь присвячено чимало досліджень. У даній роботі проблему розглянуто з іншого боку, а саме, з точки зору швидкості асимптотичної збіжності розв'язків

Dissipation bounds asymmetry of finite-time cross-correlations

Recent studies have revealed an intimate connection between the asymmetry of cross-correlations and thermodynamic quantities in the short-time limit. In the finite-time regime, however, this relationship remains poorly understood. In this Letter, we comprehensively examine this issue and provide an affirmative resolution. Focusing on Markovian dynamics, we show that the asymmetry observed in finite-time cross-correlations is always upper bounded by dissipation. Precisely, we prove that, for systems in a steady state with arbitrary operational durations, the asymmetry exhibits, at most, linear growth over time, with the growth speed determined by the rates of entropy production and dynamical activity. In the long-time regime, the asymmetry exhibits exponential decay, with the decay rate dictated by the spectral gap of the transition matrix. Furthermore, we generalize the short-time bounds on correlation asymmetry, as reported by Shiraishi [arXiv:2304.12775] and Ohga et al.~[arXiv:2303.13116], to encompass finite-time scenarios. These findings offer novel insights into the thermodynamic aspects of correlation asymmetry.Comment: 6+6 pages, 1 figur

Physical properties of particles and their implications for the calculation of the human regional lung dose

This study aims to investigate the physical properties of particles and their implications for source apportionment and health human exposure studies. A wide range of particle number size distribution (PNSD) measurements was conducted in selected environments using state-of-the-art high time resolution instruments. It is found that PNSD varied in different environments, depending on emission sources and atmospheric processes. A mass balance model was used to predict the penetration, infiltration factors, deposition and loss rates of indoor particles. The loss rates of indoor particles, which are mainly subject to deposition, coagulation and evaporation, were found to be a function of particle size and time. Moreover, HTDMA measurements were performed to study the hygroscopic properties of particles in outdoor and indoor environments, and from five major indoor sources. The particles emitted from indoor sources were mostly hydrophobic. An enhanced lung deposition model based on the ICRP and MPPD models was developed to predict the deposition fraction of particles in the human respiratory tract, with consideration of their hygroscopicity. Furthermore, a combination of lung deposition models and the PMF technique was applied to identify which sources are mostly responsible for deposited particles in the different regions of lung

The structure of a minimal nn-chart with two crossings II: Neighbourhoods of Γ1∪Γn−1\Gamma_1\cup\Gamma_{n-1}

Given a 2-crossing minimal chart $\Gamma$, a minimal chart with two crossings, set $\alpha=\min\{~i~|~$there exists an edge of label $i$ containing a white vertex$\}$, and $\beta=\max\{~i~|~$there exists an edge of label $i$ containing a white vertex$\}$. In this paper we study the structure of a neighbourhood of $\Gamma_\alpha\cup\Gamma_\beta$, and propose a normal form for 2-crossing minimal $n$-charts, here $\Gamma_\alpha$ and $\Gamma_\beta$ mean the union of all the edges of label $\alpha$ and $\beta$ respectively.Comment: 57 pages, 36 figure

Prediction of shoreline changes in Almanarre beach using geospatial techniques

207-217In this study, the remote sensing and Geographic Information System (GIS) techniques coupled with the Digital Shoreline Analysis System (DSAS) is applied to detect the historical shoreline changes as well as to predict the future shoreline position along Almanarre beach which is being threatened by severe erosion. The results show that Almanarre beach suffered erosion with an average annual change rate of about -0.24 m/year over the period of 1973-2015. The most severe erosion was observed near Landmark B17 with the maximum erosion rate of -0.86 m/year. Moreover, the shoreline change in 2020 and 2050 are predicted at approximately -0.05 m/year and -0.22 m/year, respectively. The areas around Landmarks B06-08 and Landmarks B16-18 will be eroded with the maximum recession rates of -0.89 m/year and -0.94 m/year, respectively. This research proves that the combination of geospatial techniques and numerical model can be a reliable approach for investigating the shoreline change trend

An adaptive hierarchical sliding mode controller for autonomous underwater vehicles

The paper addresses a problem of efficiently controlling an autonomous underwater vehicle (AUV), where its typical underactuated model is considered. Due to critical uncertainties and nonlinearities in the system caused by unavoidable external disturbances such as ocean currents when it operates, it is paramount to robustly maintain motions of the vehicle over time as expected. Therefore, it is proposed to employ the hierarchical sliding mode control technique to design the closed-loop control scheme for the device. However, exactly determining parameters of the AUV control system is impractical since its nonlinearities and external disturbances can vary those parameters over time. Thus, it is proposed to exploit neural networks to develop an adaptive learning mechanism that allows the system to learn its parameters adaptively. More importantly, stability of the AUV system controlled by the proposed approach is theoretically proved to be guaranteed by the use of the Lyapunov theory. Effectiveness of the proposed control scheme was verified by the experiments implemented in a synthetic environment, where the obtained results are highly promising. © 2021 by the authors. Licensee MDPI, Basel, Switzerland. **Please note that there are multiple authors for this article therefore only the name of the first 5 including Federation University Australia affiliate “Linh Nguyen" is provided in this record*

Sources, Distribution and Toxicity of Polyaromatic Hydrocarbons (PAHs) in Particulate Matter

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