On a stability condition for elastic plastic structures

Summary The paper considers discrete or discretized elastic-plastic structures subjected to conservative external forces and given imposed strains. Material flow laws are assumed to be associated; the plasticity condition and the hardening rule are piecewise linearized.For a given equilibrium configuration of such systems, a necessary and sufficient condition for the positivity of second order plastic work is proved. It is shown that this work is positive if and only if a certain matrix is positive definite. Connections with the kinematic stability of the configuration are discussed.The interest of the statement is two-fold. Firstly it provides a deeper understanding on the assumptions on which some techniques for elastic-plastic analysis are based. Secondly, it leads to operative procedures for stability analysis which may prove efficient in some cases, as it is illustrated with reference to the evaluation of the collapse load for elastic-perfectly plastic frames in the presence of second order geometrical effects.

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Sommario Si considerano strutture elasto-plastiche discrete e discretizzate, soggette a carichi esterni di tipo conservativo e a distorsioni assegnate. Si suppone che il legame costitutivo del materiale sia associato e la condizione di plasticità e le leggi di incrudimento vengano linearizzate a tratti.Per un'assegnata configurazione di equilibrio di un sistema di questo tipo, si dimostra una condizione necessaria e sufficiente per la positività del lavoro plastico del second'ordine; si mostra che esso è positivo se e solo se una certa matrice risulta positiva definita. Le implicazioni di questo evento con la stabilità della configurazione sono brevemente discusse.L'asserto dimostrato ha un duplice interesse. In primo luogo approfondisce il significato di alcune ipotesi alla base di certe tecniche numeriche per l'analisi elasto-plastica; in secondo luogo porta a procedimenti operativi per l'analisi della stabilità che possono rivelarsi utili in alcuni casi, come è illustrato con riferimento alla determinazione del carico di collasso di telai elasto-plastici in presenza di effetti del II ordine.

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Research sponsored by the C.N.R.     

Efficient plasmid DNA cleavage by copper(II) complexes of 1,4,7-triazacyclononane ligands featuring xylyl-linked guanidinium groups

Three new metal-coordinating ligands, L(1), L(2), and L(3), have been prepared by appending o-, m-, and p-xylylguanidine pendants, respectively, to one of the nitrogen atoms of 1,4,7-triazacyclononane (tacn). The copper(II) complexes of these ligands are able to accelerate cleavage of the P-O bonds within the model phosphodiesters bis(p-nitrophenyl)phosphate (BNPP) and [2-(hydroxypropyl)-p-nitrophenyl]phosphate (HPNPP), as well as supercoiled pBR 322 plasmid DNA. Their reactivity toward BNPP and HPNPP is not significantly different from that of the nonguanidinylated analogues, [Cu(tacn)(OH(2))(2)](2+) and [Cu(1-benzyl-tacn)(OH(2))(2)](2+), but they cleave plasmid DNA at considerably faster rates than either of these two complexes. The complex of L(1), [Cu(L(1)H(+))(OH(2))(2)](3+), is the most active of the series, cleaving the supercoiled plasmid DNA (form I) to the relaxed circular form (form II) with a k(obs) value of (2.7 ± 0.3) × 10(-4) s(-1), which corresponds to a rate enhancement of 22- and 12-fold compared to those of [Cu(tacn)(OH(2))(2)](2+) and [Cu(1-benzyl-tacn)(OH(2))(2)](2+), respectively. Because of the relatively fast rate of plasmid DNA cleavage, an observed rate constant of (1.2 ± 0.5) × 10(-5) s(-1) for cleavage of form II DNA to form III was also able to be determined. The X-ray crystal structures of the copper(II) complexes of L(1) and L(3) show that the distorted square-pyramidal copper(II) coordination sphere is occupied by three nitrogen atoms from the tacn ring and two chloride ions. In both complexes, the protonated guanidinium pendants extend away from the metal and form hydrogen bonds with solvent molecules and counterions present in the crystal lattice. In the complex of L(1), the distance between the guanidinium group and the copper(II) center is similar to that separating the adjacent phosphodiester groups in DNA (ca. 6 ?). The overall geometry of the complex is also such that if the guanidinium group were to form charge-assisted hydrogen-bonding interactions with a phosphodiester group, a metal-bound hydroxide would be well-positioned to affect the nucleophilic attack on the neighboring phosphodiester linkage. The enhanced reactivity of the complex of L(1) at neutral pH appears to also be, in part, due to the relatively low pK(a) of 6.4 for one of the coordinated water molecules.     

Photoelectron angular distributions from autoionizing 4s¹4p⁶6p¹ states in atomic krypton probed with femtosecond time resolution

Photoelectron angular distributions (PADs) are obtained for a pair of 4s(1)4p(6)6p(1) (a singlet and a triplet) autoionizing states in atomic krypton. A high-order harmonic pulse is used to excite the pair of states and a time-delayed 801 nm ionization pulse probes the PADs to the final 4s(1)4p(6) continuum with femtosecond time resolution. The ejected electrons are detected with velocity map imaging to retrieve the time-resolved photoelectron spectrum and PADs. The PAD for the triplet state is inherently separable by virtue of its longer autoionization lifetime. Measuring the total signal over time allows for the PADs to be extracted for both the singlet state and the triplet state. Anisotropy parameters for the triplet state are measured to be β(2)=0.55 ± 0.17 and β(4)=-0.01 ± 0.10, while the singlet state yields β(2)=2.19 ± 0.18 and β(4)=1.84 ± 0.14. For the singlet state, the ratio of radial transition dipole matrix elements, X, of outgoing S to D partial waves and total phase shift difference between these waves, Δ, are determined to be X=0.56 ± 0.08 and Δ=2.19 ± 0.11 rad. The continuum quantum defect difference between the S and D electron partial waves is determined to be -0.15 ± 0.03 for the singlet state. Based on previous analyses, the triplet state is expected to have anisotropy parameters independent of electron kinetic energy and equal to β(2)=5∕7 and β(4)=-12∕7. Deviations from the predicted values are thought to be a result of state mixing by spin-orbit and configuration interactions in the intermediate and final states; theoretical calculations are required to quantify these effects.     

Femtosecond photoelectron imaging of transient electronic states and Rydberg atom emission from electronically excited he droplets

Ultrafast relaxation of electronically excited pure He droplets is investigated by femtosecond time-resolved photoelectron imaging. Droplets are excited by extreme ultraviolet (EUV) pulses with photon energies below 24 eV. Excited states and relaxation products are probed by ionization with an infrared (IR) pulse with 1.6 eV photon energy. An initially excited droplet state decays on a time scale of 220 fs, leading predominantly to the emission of unaligned 1s3d Rydberg atoms. In a second relaxation channel, electronically aligned 1s4p Rydberg atoms are emitted from the droplet within less than 120 fs. The experimental results are described within a model that approximates electronically excited droplet states by localized, atomic Rydberg states perturbed by the local droplet environment in which the atom is embedded. The model suggests that, below 24 eV, EUV excitation preferentially leads to states that are localized in the surface region of the droplet. Electronically aligned 1s4p Rydberg atoms are expected to originate from excitations in the outermost surface regions, while nonaligned 1s3d Rydberg atoms emerge from a deeper surface region with higher local densities. The model is used to simulate the He droplet EUV absorption spectrum in good agreement with previously reported fluorescence excitation measurements.     

Detection of pentatetraene by reaction of the ethynyl radical (C2H) with allene (CH2=C=CH2) at room temperature

The reaction of ethynyl radical (C(2)H) with allene (C(3)H(4)) at room temperature is investigated using an improved synchrotron multiplexed photoionization mass spectrometer (MPIMS) coupled to tunable vacuum ultraviolet (VUV) synchrotron radiation from the Advanced Light Source at the Lawrence Berkeley National Laboratory (LBNL). The orthogonal-accelerated time-of-flight mass spectrometer (OA-TOF) compared to the magnetic sector mass spectrometer used in a previous investigation of the title reaction (Phys. Chem. Chem. Phys., 2007, 9, 4291) enables more sensitive and selective detection of low-yield isomeric products. The C(5)H(4) isomer with the lowest ionization energy, pentatetraene, is now identified as a product of the reaction. Pentatetraene is predicted to be formed based on recent ab initio/RRKM calculations (Phys. Chem. Chem. Phys., 2010, 12, 2606) on the C(5)H(5) potential energy surface. However, the computed branching fraction for pentatetraene is predicted to be five times higher than that for methyldiacetylene, whereas experimentally the branching fraction of pentatetraene is observed to be small compared to that of methyldiacetylene. Although H-atom assisted isomerization of the products can affect isomer distribution measurements, isomerization has a negligible effect in this case. The kinetic behavior of the several C(5)H(4) isomers is identical, as obtained by time-dependent photoionization spectra. Even for high allene concentrations (and hence higher H-atom concentrations) no decay of the pentatetraene fraction is observed, indicating that H-assisted isomerization of pentatetraene to methyldiacetylene does not account for the difference between the experimental data and the theoretical branching ratios.     

A Bus Driver Scheduling Problem: a?new mathematical model and a GRASP approximate solution

This paper addresses the problem of determining the best scheduling for Bus Drivers, a $\mathcal{NP}$ -hard problem consisting of finding the minimum number of drivers to cover a set of Pieces-Of-Work (POWs) subject to a variety of rules and regulations that must be enforced such as spreadover and working time. This problem is known in literature as Crew Scheduling Problem and, in particular in public transportation, it is designated as Bus Driver Scheduling Problem. We propose a new mathematical formulation of a Bus Driver Scheduling Problem under special constraints imposed by Italian transportation rules. Unfortunately, this model can only be usefully applied to small or medium size problem instances. For large instances, a Greedy Randomized Adaptive Search Procedure (GRASP) is proposed. Results are reported for a set of real-word problems and comparison is made with an exact method. Moreover, we report a comparison of the computational results obtained with our GRASP procedure with the results obtained by Huisman et al. (Transp. Sci. 39(4):491?C502, 2005).     

Some Novel Cobalt Diphenylphosphine Complexes: Synthesis,Characterization, and Behavior in the Polymerization of 1,3-Butadiene

Some novel cobalt diphenylphosphine complexes were synthesized by reacting cobalt(II) chloride with (2-methoxyethyl)diphenylphosphine, (2-methoxyphenyl)diphenylphosphine, and 2-(1,1-dimethylpropyl)-6-(diphenylphosphino)pyridine. Single crystals suitable for X-ray diffraction studies were obtained for the first two complexes, and their crystal structure was determined. The novel compounds were then used in association with methylaluminoxane (MAO) for the polymerization of 1,3-butadiene, and their behavior was compared with that exhibited in the polymerization of the same monomer by the systems CoCl₂(PⁿPrPh₂)₂/MAO and CoCl₂(PPh₃)₂/MAO. Some significant differences were observed depending on the MAO/Co ratio used, and a plausible interpretation for such a different behavior is proposed.     

Strong-field multiphoton ionization of hydrogen. TheS-matrix treatment of the elementary process

Summary A theoretical model is presented to treat the elementary act of strong-field multiphoton ionization of atoms when the electron continuum final-state distribution is important. It is based on theS-matrix formalism and treats the final-state electron-radiation interaction in an essentially nonperturbative way. Selected numerical calculations concern the ionization of hydrogen atoms and include differential and total cross-sections of several multiphoton channels as a function of the laser intensity. Good, qualitative agreement with the experimental observations is found for values of the field intensity which are not critical with respect to the simplifications adopted in constructing the theoretical model. It applies particularly to the use of an ideal model for the laser field. Significant departure from observations is instead found when the implications of the ideal laser model play a critical role, as occurs at channel inversion and suppression. It is concluded that the theoretical treatment to be completely satisfactory needs essentially to incorporate a more realistic laser model such as a multimode one.

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Riassunto Si presenta un modello teorico per il processo elementare della ionizzazione multifotonica di atomi da parte di un forte campo laser quando diventa importante la distribuzione degli stati finali del continuo dell'elettrone. Il modello si fonda sul formalismo della matriceS e tratta l'interazione elettrone-radiazione nello stato finale in modo non perturbativo. I calcoli numerici qui riportati si riferiscono alla ionizzazione di atomi d'idrogeno e includono sezioni d'urto totali e differenziali per diversi canali multifotonici in funzione dell'intensità del laser. Si trova un accordo qualitativo con i dati sperimentali per valori dell'intensità del campo che non sono critici rispetto alle semplificazioni adottate nella costruzione del modello teorico. Un significativo distacco dai dati sperimentali si ha quando le implicazioni del modello di laser ideale giocano un ruolo critico, come si ha per l'inversione e la scomparsa dei canali. Si conclude che il trattamento teorico per essere completamente soddisfacente necessita dell'introduzione di un modello di laser piú realistico, quale, ad esempio, quello a molti modi.

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Резюме Предлагается теоретическая модель для рассмотрения элементарного акта многофотонной ионизации атомов в сильном поле, когда распределение электронных непрерывных конечных состояний является существенным. Подход базируется на формализмеS-матрицы и взаимодействие электронов в конечном состоянии с полем излучения рассматривается непертурбационным образом. Численные вычисления касаются ионизации атомов водорода и включают дифференциальные и полные поперечные сечения для некоторых многофотонных каналов, как функции интенсивности лазерного излучения. Получено хорошее качественное согласие с экспериментальными результатами для значений интенсивности поля, которые не являются критическими по отношению к упрощениям, используемым при конструировании теоретической модели. Используется идеальная модель для лазерного поля. Обнаружено существенное отклонение от экспериментальных результатов в тех случаях, когда имеет место инверсия и подавление каналов. Делается вывод, что теоретический подход становится удовлетворительным, если используется более реалистическая модель лазера, как например, многомодовая модель.

     

Quantum mechanics for space applications

This paper is an introduction to the following articles in the scope of quantum mechanics for space study initiated by ESA and lead by ONERA. The context of quantum mechanics for space is summarised, and the fields under development are briefly introduced. Technological applications of quantum mechanics in space are explored and some tests of quantum mechanics are outlined. We also give a brief presentation of the opto-electronic section of the European Space Agency, and the technology development activities it carries out, with particular emphasis on those activities related to the topics of interest of the quantum mechanics in space workshop. As an example, a summary of two ESA studies on gravity gradiometry and their relevance to the field of atomic interferometry is given. In view of the scientific requirements, derived for both Earth observation and planetology for future space missions, atom interferometry shows promise and may provide an advantage over currently available accelerometer and inertial sensor systems. PACS 04.25.Nx; 04.80.Cc; 07.60.Ly; 95.30.Sf     

Copolymerization of Ethene and Carbon Monoxide with (Diphosphine)nickel Catalysts

This work presents the results of the ethene–CO copolymerization with in situ generated catalysts based on atropisomeric 1,4‐diphosphines and nickel(II). The influence of the reaction conditions and the NMR characterization of the copolymers are described.