Quantum Transport in Crystals: Effective Mass Theorem and K·P Hamiltonians

In this paper the effective mass approximation and the k·p multi-band models, describing quantum evolution of electrons in a crystal lattice, are discussed. Electrons are assumed to move in both a periodic potential and a macroscopic one. The typical period e{\epsilon} of the periodic potential is assumed to be very small, while the macroscopic potential acts on a much bigger length scale. Such homogenization asymptotic is investigated by using the envelope-function decomposition of the electron wave function. If the external potential is smooth enough, the k·p and effective mass models, well known in solid-state physics, are proved to be close (in the strong sense) to the exact dynamics. Moreover, the position density of the electrons is proved to converge weakly to its effective mass approximation.     

Pump−probe experiments at the TEMPO beamline using the low‐α operation mode of Synchrotron SOLEIL

The SOLEIL synchrotron radiation source is regularly operated in special filling modes dedicated to pump–probe experiments. Among others, the low‐α mode operation is characterized by shorter pulse duration and represents the natural bridge between 50 ps synchrotron pulses and femtosecond experiments. Here, the capabilities in low‐α mode of the experimental set‐ups developed at the TEMPO beamline to perform pump–probe experiments with soft X‐rays based on photoelectron or photon detection are presented. A 282 kHz repetition‐rate femtosecond laser is synchronized with the synchrotron radiation time structure to induce fast electronic and/or magnetic excitations. Detection is performed using a two‐dimensional space resolution plus time resolution detector based on microchannel plates equipped with a delay line. Results of time‐resolved photoelectron spectroscopy, circular dichroism and magnetic scattering experiments are reported, and their respective advantages and limitations in the framework of high‐time‐resolution pump–probe experiments compared and discussed.     

I λ-Groups and almost totally injective groups

Summary We introduce the class ofI _λ-groups, where λ is an ordinal, consisting of these abelianp-groupsG such thatG/p ^σ G is almost totally injective for every ordinal σ<λ. As an application of some results onI _λ-groups, we prove an extension property of almost totally injective groups.

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Riassunto Si introduce la classe degliI _λ-gruppi, dove λ è un ordinale, formata daip-gruppi abelianiG tali cheG/p ^σ G è quasi totalmente iniettivo per ogni ordinale σ<λ. Come applicazione di alcuni risultati sugliI _λ-gruppi, si prova una proprietà di estensione dei gruppi quasi totalmente iniettivi.

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Lavoro eseguito nell'ambito dei Gruppi di Ricerca Matematica del Consiglio Nazionale delle Ricerche.     

Completeness for flat modal fixpoint logics

This paper exhibits a general and uniform method to prove axiomatic completeness for certain modal fixpoint logics. Given a set Γ of modal formulas of the form γ(x,p₁,…,p_n), where x occurs only positively in γ, we obtain the flat modal fixpoint language L_?(Γ) by adding to the language of polymodal logic a connective ?_γ for each γ∈Γ. The term ?_γ(φ₁,…,φ_n) is meant to be interpreted as the least fixed point of the functional interpretation of the term γ(x,φ₁,…,φ_n). We consider the following problem: given Γ, construct an axiom system which is sound and complete with respect to the concrete interpretation of the language L_?(Γ) on Kripke structures. We prove two results that solve this problem.First, let be the logic obtained from the basic polymodal by adding a Kozen-Park style fixpoint axiom and a least fixpoint rule, for each fixpoint connective ?_γ. Provided that each indexing formula γ satisfies a certain syntactic criterion, we prove this axiom system to be complete.Second, addressing the general case, we prove the soundness and completeness of an extension of . This extension is obtained via an effective procedure that, given an indexing formula γ as input, returns a finite set of axioms and derivation rules for ?_γ, of size bounded by the length of γ. Thus the axiom system is finite whenever Γ is finite.     

Stochastic phase lockings in a relaxation oscillator forced by a periodic input with additive noise: A first-passage-time approach

Noise effects on phase lockings in a system consisting of a piecewise-linear van der Pol relaxation oscillator driven by a periodic input are studied. The problem of finding the period of the oscillator is reduced to the first-passage-time problem of the Ornstein-Uhlenbeck process with time-varying boundary. The probability density functions of the first-passage time are used to define the operator which governs a transition of an input phase density after one cycle of the oscillator. Phase lockings in a stochastic sense are investigated on the basis of the density evolution by the operator.     

An RQP algorithm using a differentiable exact penalty function for inequality constrained problems

In this paper we propose a recursive quadratic programming algorithm for nonlinear programming problems with inequality constraints that uses as merit function a differentiable exact penalty function. The algorithm incorporates an automatic adjustment rule for the selection of the penalty parameter and makes use of an Armijo-type line search procedure that avoids the need to evaluate second order derivatives of the problem functions. We prove that the algorithm possesses global and superlinear convergence properties. Numerical results are reported.     

Unprecedented Diastereoselective Arylogous Michael Addition of Unactivated Phthalides

The first highly enantioselective arylogous Michael reaction (AMR) of 3-unsubstituted phthalides has been described. This phase-transfer methodology, which uses catalytic amounts of KOH/18-crown-6 catalyst in mesitylene in the presence of N,O-bis(trimethylsilyl)acetamide (BSA), gives access to a broad range of 3-monosubstituted phthalides with high levels of syn diastereoselectivity and good yields, starting from 3-unsubstituted derivatives and diverse α,β-unsaturated carbonyl compounds. The reaction also applies to unactivated 3-alkyl phthalides to afford 3,3-dialkyl derivatives. A plausible mechanism has been suggested. DFT analysis of possible transition states gives a rationale of the high syn diastereoselectivity observed and its correlation with the solvent's dielectric constant.     

Acoustic waveguide filters made up of rigid stacked materials with elastic joints

Meccanica - The acoustic dispersion properties of monodimensional waveguide filters can be assessed by means of the simple prototypical mechanical system made of an infinite stack of periodic...     

Fracture behavior and mechanical,thermal, and rheological properties of biodegradable films extruded by flat die and calender

The development of biodegradable materials for tailored applications, particularly in the field of polymeric films and sheets, is a challenging technological goal as well as a contribution to help protect the environment. Poly(lactic) acid (PLA) is a promising substitute for several oil-based polymers; however, to overcome its thermal and mechanical drawbacks, researchers have developed solutions such as blending PLA with polybutylene adipate terephthalate (PBAT), which is capable of increasing the ductility of the final material. In this study, PLA/PBAT binary blends, with minimum possible content of nonrenewable materials, were examined from processing, thermal, morphological, and rheological perspective. An optimized PLA/PBAT ratio was chosen as the polymeric basis to obtain a biodegradable formulation by adding a biobased plasticizer and appropriate fillers to produce a micrometer film with tailored flexibility and tear resistance. The processing technology involved flat-die extrusion, followed by calendering. The tearing resistance of the produced film was investigated, and the results were compared with literature data. A study on the essential work of fracture was implemented to explore the mode III out-of-plane fracture resistance starting from a trouser tear test.