The turnpike property in finite-dimensional nonlinear optimal control

Turnpike properties have been established long time ago in finite-dimensional optimal control problems arising in econometry. They refer to the fact that, under quite general assumptions, the optimal solutions of a given optimal control problem settled in large time consist approximately of three pieces, the first and the last of which being transient short-time arcs, and the middle piece being a long-time arc staying exponentially close to the optimal steady-state solution of an associated static optimal control problem. We provide in this paper a general version of a turnpike theorem, valuable for nonlinear dynamics without any specific assumption, and for very general terminal conditions. Not only the optimal trajectory is shown to remain exponentially close to a steady-state, but also the corresponding adjoint vector of the Pontryagin maximum principle. The exponential closedness is quantified with the use of appropriate normal forms of Riccati equations. We show then how the property on the adjoint vector can be adequately used in order to initialize successfully a numerical direct method, or a shooting method. In particular, we provide an appropriate variant of the usual shooting method in which we initialize the adjoint vector, not at the initial time, but at the middle of the trajectory.     

Electron irradiation-enhanced core/shell organization of Al(Cr,Fe, Mn)Si dispersoids in Al–Mg–Si alloys

The age hardening 6061-T6 aluminium alloy has been chosen as structural material for the core vessel of the material testing Jules Horowitz nuclear reactor. The alloy contains incoherent Al(Cr, Fe, Mn)Si dispersoids whose characterization by energy-filtered transmission electron microscopy (EFTEM) analysis shows a core/shell organization tendency where the core is (Mn, Fe) rich, and the shell is Cr rich. The present work studies the stability of this organization under irradiation. TEM characterization on the same particles, before and after 1 MeV electron irradiation, reveals that the core/shell organization is enhanced after irradiation. It is proposed that the high level of point defects, created by irradiation, ensures a radiation-enhanced diffusion process favourable to the unmixing forces between (Fe, Mn) and Cr. Shell formation may result in the low-energy interface segregation of Cr atoms within the (Fe, Mn) system combined with the unmixing of Cr, Fe and Mn components.     

A Multifunctional Photoswitch: 6π Electrocyclization versus ESIPT and Metalation

A terthiazole‐based molecular switch associating 6π electrocyclization, excited state intramolecular proton transfer (ESIPT), and strong metal binding capability was prepared. The photochemical and photophysical properties of this molecule and of the corresponding nickel and copper complexes were thoroughly investigated by steady‐state and ultrafast absorption spectroscopy and rationalized by DFT/TDDFT calculations. The switch behaves as a biphotochrome with time‐dependent photochemical outcome and displays efficient ESIPT‐based fluorescence photoswitching. Both photochemical reactions are suppressed by nickel or copper metalation, and the main factors contributing to the quenching of the electrocyclization are discussed.     

Microwave-Assisted Desulfation of the Hemolytic Saponins Extracted from Holothuria scabra Viscera

Saponins are plant and marine animal specific metabolites that are commonly considered as molecular vectors for chemical defenses against unicellular and pluricellular organisms. Their toxicity is attributed to their membranolytic properties. Modifying the molecular structures of saponins by quantitative and selective chemical reactions is increasingly considered to tune the biological properties of these molecules (i) to prepare congeners with specific activities for biomedical applications and (ii) to afford experimental data related to their structure–activity relationship. In the present study, we focused on the sulfated saponins contained in the viscera of Holothuria scabra, a sea cucumber present in the Indian Ocean and abundantly consumed on the Asian food market. Using mass spectrometry, we first qualitatively and quantitatively assessed the saponin content within the viscera of H. scabra. We detected 26 sulfated saponins presenting 5 different elemental compositions. Microwave activation under alkaline conditions in aqueous solutions was developed and optimized to quantitatively and specifically induce the desulfation of the natural saponins, by a specific loss of H₂SO₄. By comparing the hemolytic activities of the natural and desulfated extracts, we clearly identified the sulfate function as highly responsible for the saponin toxicity.     

Influence of bit design on the stability of a rotary drilling system

Nonlinear Dynamics - This paper extends the RGD model originally proposed by Richard et al. (J Sound Vib 305(3):432–456, 2007, https://doi.org/10.1016/j.jsv.2007.04.015) to investigate...     

K-line X-ray fluorescence from highly charged iron ions under dense astrophysical plasma conditions

In the present work, we report an investigation of plasma environment effects on the atomic parameters associated with the K-vacancy states in highly charged iron ions within the astrophysical context of accretion disks around black holes. More particularly, the sensitivity of K-line X-ray fluorescence parameters (wavelengths, radiative transition probabilities, and Auger rates) in Fe XVII–Fe XXV ions has been estimated for plasma conditions characterized by an electron temperature ranging from 10⁵ to 10⁷ K and an electron density ranging from 10¹⁸ to 10²² cm⁻³. In order to do this, relativistic multiconfiguration Dirac-Fock atomic structure calculations have been carried out by considering a time averaged Debye-Hückel potential for both the electron–nucleus and electron–electron interactions.     

Reduced expression of <Emphasis Type="Italic">TAC1</Emphasis>, <Emphasis Type="Italic">PENK</Emphasis> and <Emphasis Type="Italic">SOCS2</Emphasis> in <Emphasis Type="Italic">Hcrtr-2</Emphasis> mutated narcoleptic dog brain

Background  

Narcolepsy causes dramatic behavioral alterations in both humans and dogs, with excessive sleepiness and cataplexy triggered by emotional stimuli. Deficiencies in the hypocretin system are well established as the origin of the condition; both from studies in humans who lack the hypocretin ligand (HCRT) and in dogs with a mutation in hypocretin receptor 2 (HCRTR2). However, little is known about molecular alterations downstream of the hypocretin signals.     

激光诱导Ti等离子体电子温度的实验研究

室温,常压下,利用Nd∶YAG脉冲激光器产生的波长为1 064 nm, 脉宽12 ns,能量分别180, 230和280 mJ的脉冲激光冲击Ti靶,使用中阶梯光栅光谱仪检测了三种激光能量下对应的光谱。调节延时器DG645的延迟时间,检测了延迟0～500 ns时间范围内Ti等离子体对应激光能量下的发射光谱,分析光谱,可以得到了九条不同的的TiⅠ 和TiⅡ等离子体谱线,证明在该实验条件下,Ti靶能够充分吸收能量电离且离子谱线具有不同的演化速率,利用Saha-Boltzmann法计算并分析Ti等离子体电子温度,实验结果表明：相同的延迟时间,激光能量越大,谱线相对强度越大,电子温度越高,谱线相对强度的变化量随激光能量的变化量增大而增大;在延时0～150 ns内,三种激光能量下的等离子体电子温度和谱线的相对强度都随延迟时间的增加而快速下降,其中280 mJ激光能量下的等离子体电子温度和谱线强度下降速率较快;在150～250 ns范围内,电子温度和谱线强度均随延迟时间的增加有一个缓慢的上升,180 mJ激光能量下的等离子体电子温度和谱线强度的上升速率较快。250～500 ns范围内,三种激光能量下的电子温度和谱线强度均随延迟时间的增加而缓慢下降。