Functional Concepts in Continuum Mechanics

This paper is an attempt to give a concise presentation of the main concepts of continuum mechanics and to show their articulation. Functional definitions have been favoured.The first section is devoted to a review of continuum mechanics.The second section deals with the mechanics of materials.Constitutive equations of the material are given first by equations of state and then by complementary equations written in order to fulfil the fundamental inequality concerning the production of entropy and the physical properties of the material (viscosity, plasticity, damage etc.).Section 3 gives the Lagrangian and the Hamiltonian formulations for a moving body. Section 4 is devoted to the motion of surfaces through which discontinuities appear, to show briefly two examples of application of the previous concepts. One can easily define the source of intrinsic inhomogeneity, of heat, of irreversible entropy on a surface of phase transition and also for a shockwave.SommarioIn questo lavoro si cerca di dare una presentazione concisa dei concetti fondamentali della meccanica dei continui e di mostrare le loro articolazioni,con particolare rilievo alle definizioni funzionali. La prima sezione è dedicata ad un esame generale introduttivo. La seconda alla meccanica dei materiali, le cui equazioni costitutive sono date come equazioni di stato e come equazioni complementari scritte al fine di soddisfare le diseguaglianze concernenti la produzionedi entropia e le proprietà fisiche dei materiali (qualiviscosità, plasticità, guasti...).La terza sezione dà le formulazioni Lagrangiana ed Hamiltoniana per il moto di un corpo.La quarta sezione è dedicata al moto di superfici di discontinuità per mostrare brevemente due esempi di applicazione dei concetti precedenti.Viene quindi definita la sorgente di disomogeneità intrinseca, di calore, di entropia irreversibile su di una superficie, di transizione di fase ed anche di un' onda d'urto.     

Syntheses of bis(imino)thietans

The reactions of sulfonyliminothiirans ($\text{1}$) with isonitriles and those of ketenimines with arylsulfonyl isothiocyanates yield the title compounds $\text{2}$. In contrast, benzoyl isothiocyanate undergoes a Diels-Alder reaction with ketenimines to give 1,3,5-oxadiazine-4-thiones ($\text{3}$).     

Chemical studies of marine invertebrates—XLIII: Novel sesquiterpenes from clavularia inflata and clavularia koellikeri (Coelenterata,Octocorallia,Stolonifera)

Two novel sesquiterpenes, 12-acetoxycyclosinularane (1) and 12-acetoxysinularene(2),have been isolated from Clavularia inftata. Their structures have been determined by X-ray diffraction analysis and chemical correlation respectively. Moreover, the new aromadendrane sesquiterpene(1R^*, 1aS^*, 4R^*, 7R^*, 7aS^*, 7bS^*, 5Z)-4,4a,7-trihydroxyaromadendr-5-en-8-oic acid methyl ester (19) has been isolated from the related species C. koellikeri. Its structure has been established by X-ray diffraction analysis. These compounds are the first sesquiterpenes isolated from Octocorallia of the order Stolonifera.     

Thermal and photolytic stabilities of perfluoroalkane sulfonic acids and their derivatives

The use of perfluoroalkanesulfonic acids and their derivatives in drastic conditions leads us to study their behaviour with respect to temperature and radiative factors.Such acids as CF₃SO₃H and C₂F₅SO₃H, used in a pure state as well as their related pure anhydride are stable until they reach a temperature of at least 180°C.On the other hand, the solutions of anhydride with its related acid, yield perfluorosulfonic esters and SO₂ at room temperature already:

This mechanism is discussed.These results involve a new and easy synthesis of symmetrical perfluorosulfonic esters R_FSO₃R_F with acids and P₂O₅.

Further more, it occurs no transformation of the anhydride under UV and visible irradiation. But under the same conditions, a small account of acids are deshydrated into anhydrides.A further experiment combining both effects of temperature and light leads to the esters.     

Mass spectra of some 3-substituted coumarins

The electron impact mass spectrometric fragmentation pathways for some 3-substituted derivatives of coumarin, benzo[f]coumarin, thieno[3,2-f]coumarin, thieno[2,3-h]coumarin and azacoumarin, viz nitriles, carboxamides, thiocarboxamides and esters were investigated. The initial cleavage of the pyrone ring is found to be largely dependent on the stability, under electron impact, of the attached functional group.     

Existence and Uniqueness of Solutions for a Quasilinear KdV Equation with Degenerate Dispersion

We consider a quasilinear KdV equation that admits compactly supported traveling wave solutions (compactons). This model is one of the most straightforward instances of degenerate dispersion, a phenomenon that appears in a variety of physical settings as diverse as sedimentation, magma dynamics and shallow water waves. We prove the existence and uniqueness of solutions with sufficiently smooth, spatially localized initial data. © 2019 Wiley Periodicals, Inc.     

On permanent nonlinear waves in a rotating fluid

The governing equation for long nonlinear gravity waves in a rotating fluid changes with the value of the Coriolis parameter f. (1) When f is large, i.e. in the strong rotation case, in an infinite ocean, there are only Sverdrup waves; in a semi-infinite ocean or in a channel, there are either solitary Kelvin waves, for which the governing equation is a KdV equation, or Poincaré waves, which can be obtained by superposition of two Sverdrup waves. (2) When f is small, i.e. in the weak rotation case, in an infinite ocean there are solitary or cnoidal waves governed by the Ostrovskiy equation, and we provide an explicit solution for both solitary and cnoidal Ostrovskiy progressive waves; and in a semi-infinite ocean or a channel, there are Sverdrup waves, which are governed either by Ostrovskiy equations or by the Grimshaw-Melville equation. (3) When f is very small, i.e. in the very weak rotation case, in an infinite ocean, or in a channel, there are solitary waves with a horizontal crest, but with a velocity component or a pressure gradient, which are governed by KdV equations as in the non-rotating case. Physically, that means that the most determining factor is the ratio of the Rossby radius of deformation over a characteristic length of the wave.     

Mesostructures of cobalt nanocrystals. 2. Mechanism

Mesoscopic patterns of cobalt nanocrystals produced by applying a magnetic field perpendicular to the substrate during the deposition process are presented. These mesoscopic patterns markedly differ with the size distribution of the cobalt nanocrystals. Well-defined columns are produced when the size distribution of cobalt nanocrystals is low; conversely, the coalescence of columns with formations of labyrinths occurs for a large size distribution. A formation mechanism of these structures is proposed.