Some extremum theorems for the elastoplastic boundary value problem in the presence of large displacements

Summary The incremental boundary value problem for elastoplastic work-hardening continua, is discussed in the presence of large displacements but small strains, and allowing for distributed dislocations.Associated flow laws are assumed, as is the occurrence of interaction between yielding modes in singular points of the yield surface.Four extremum theorems are proved which reduce the problem to the optimization, under linear constraints, of convex quadratic forms (of a non linear form for the third theorem).Finally some results are specialized to small displacements and perfectly plastic (non hardening) cases.

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Sommario Si discute della soluzione incrementale del problema elastoplastico con incrudimento nel campo dei grandi spostamenti (ma con piccole deformazioni intrinseche), ed in presenza di distorsioni distribuite.Si assumono leggi costitutive del tipo associato, ammettendo la possibilità di interazione tra i modi plastici in corrispondenza dei punti singolari della superficie di snervamento.Si dimostrano quattro proprietà di minimo della soluzione; esse riconducono il problema alla ottimizzazione di funzionali convessi (quadratici tranne che nel caso del terzo teorema) vincolata da equazioni e diseguaglianze lineari.Si specializzano infine alcuni risultati al caso dei piccoli spostamenti e della elastoplasticità senza incrudimento.

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This study forms part of a research programme supported by the National (Italian) Research Council (C.N.R., Gruppo Plasticità).     

Separable geodesic action slicing in stationary spacetimes

A simple observation about the action for geodesics in a stationary spacetime with separable geodesic equations leads to a natural class of slicings of that spacetime whose orthogonal geodesic trajectories represent the world lines of freely falling fiducial observers. The time coordinate function can then be taken to be the observer proper time, leading to a unit lapse function, although the time coordinate lines still follow Killing trajectories to retain the explicitly stationary nature of the coordinate grid. This explains some of the properties of the original Painlevé-Gullstrand coordinates on the Schwarzschild spacetime and their generalization to the Kerr-Newman family of spacetimes, reproducible also locally for the Gödel spacetime. For the static spherically symmetric case the slicing can be chosen to be intrinsically flat with spherically symmetric geodesic observers, leaving all the gravitational field information in the shift vector field.     

Spin–rotation couplings: spinning test particles and Dirac field

The hypothesis of coupling between spin and rotation introduced long ago by Mashhoon is examined in the context of “1 + 3” and “3 + 1” space-time splitting techniques, either in special or in general relativity. Its content is discussed in terms of classical (Mathisson–Papapetrou–Dixon–Souriou model) as well as quantum physics (Foldy–Wouthuysen transformation for the Dirac field in an external field), reviewing and discussing all the relevant theoretical literature concerning the existence of such effect. Some original contributions are also included. Dedicated to Bahram Mashhoon for his 60th birthday.     

Biomagnetic measurements utilising a superparamagnetic marker: a feasibility study

Summary A preliminary study is here reported on a new potential marker for biomagnetic measurements. The marker consists of superparamagnetic polymer microspheres which were detected in the presence of external steady magnetic fields by means of an r.f.-SQUID magnetometer. The particles were prepared in samples differing in the concentration value and immersed in a homogeneous magnetic field of variable intensity. A simple model was taken into account for the distribution of the microspheres in the samples, so that the theoretical values were compared to the marker field values measured by the biomagnetic sensor. The overall sensitivity of the experimental apparatus and the minimum concentration value of the marker were then estimated.     

Equatorial Plane Circular Orbits in the Taub-NUT Spacetime

Accelerated circular orbits in the equatorial plane of the Taub-NUT spacetime are analyzed to investigate the effects of its gravitomagnetic monopole source. The effect of a small gravitomagnetic monopole on these orbits is compared to the corresponding orbits pushed slightly off the equatorial plane in the absence of the monopole.     

Electronic properties of b.c.c. transition metal solid solutions. a study of the Nr−Nb system

Summary Calculations of electron densities of states and of soft—X-ray absorption spectra in Zr−Nb alloys have been performed in the frame of the coherent potential approximation in its multiple-scattering version (KKR-CAP). It is shown that a lot of care is needed in applying the simple rigid-band model to these systems, in order to explain experimental data. Results are also diseussed in connection with existing experimental data and good agreement is found.

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Riassunto Sono stati eseguiti calcoli di densità di stati elettronici e di spettri di assorbimento di raggi X molli nella lega Zr−Nb a varie concentrazioni, nell'àmbito dell'approssimazione di potenziale coerente nella sua versione di scattering multiplo (KKR-CPA). Si mostra che è necessaria molta attenzione per poter interpretare dati sperimentali come semplice modello a bande rigide. I risultati sono inoltre, discussi in connessione con, i dati sperimentali esistenti con i quali si riscontra un buon accordo.

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Резюме в рамках приближения когерентного потенциала и его модификации для многократного рассеяния проводится вычисление плотностей электронных состояний и спектров поглощения мягких рентгеновских лучей в Zn−Nb сплавах. Показывается, что необходимо проявлять особое внимание при интерпретации экспериментальных данных с помощью простой модели недеформируемых зон. Полученные результаты обсуждаются в связи с имеющимися экспериментальными данными и овнаружено хорошее согласие.

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Work also sponsored by Assessorato Industria della Regione Siciliana.     

Molecular interactions in 1-pentanol +2-methyl-2-butanol mixtures: Static dielectric constant,viscosity and refractive index investigations at 5, 25 and 45°C

Static dielectric constants, refractive indices and viscosities of 1-pentanol +2-methyl-2-butanol mixtures were measured at 5, 25 and 45°C. The results show that the mixing of the two isomers modifies the polarizability and the resistence of viscous flow of the system depending on the composition and temperature. Short range intermolecular interactions producing hetero-alcohol open dimers are considered.     

Chromatin supraorganization, mitotic abnormalities and proliferation in cells with increased or down-regulated lox expression: Indirect evidence of a LOX-histone H1 interaction in vivo

Lysyl oxidases (LOXs) are enzymes that permit the covalent crosslinking of the component chains of collagen and elastin. These enzymes are present inside the nuclei of certain mammalian cells. Previous studies have proposed LOX binding to histone H1 in vitro, and histone H1 is known to control global chromatin compaction and mitotic chromosome architecture. Therefore, in the present study, we analyzed chromatin supraorganizational changes, mitotic abnormalities, mitotic indices and cell death ratios in COS-7 and NRK-49F cells with high and low lox expression levels, respectively. The objective was to support biochemical data of LOX-H1 interaction, by providing evidence of chromatin remodeling in vivo, under different lox expressions. Chromatin decondensation assessed by image analysis was observed in COS-7 cells with increased lox expression. This decondensation is suggested to be promoted by LOX actions on histone H1, which loosens the DNA-H1 complex. In NRK-49F cells transfected with antisense lox or subjected to treatment with beta-aminopropionitrile (BAPN), chromatin condensation and nuclear phenotypic variability were found, which may be due to reduced LOX-H1 interaction. When lox expression was increased in COS-7 cells, the frequency of irregular chromosome plates was not affected, but cell proliferation decreased and "cell death preceded by multinucleation" increased. In NRK-49F cells there was accelerated proliferation induced by transfection with the antisense lox, and confirmed when cells were treated with BAPN. Apoptosis increased in NRK-49F cells only with BAPN treatment whereas cell death preceded by multinucleation increased only after antisense lox transfection. The data presented herein regarding chromatin remodeling indirectly support the hypothesis that LOX binds to histone H1 in vivo. Cell proliferation in COS-7 and NRK-49F cells and cell death at least in COS-7 cells agree with predicted effects of LOX interference in these processes.     

A quasi-variational approach to a competitive economic equilibrium problem without strong monotonicity assumption

This paper is focused on the investigation of the Walrasian economic equilibrium problem involving utility functions. The equilibrium problem is here reformulated by means of a quasi-variational inequality problem. Our goal is to give an existence result without assuming strong monotonicity conditions. To this end, we make use of a perturbation procedure. In particular, we will consider suitable perturbed utility functions whose gradient satisfies a strong monotonicity condition and whose associated equilibrium problem admits a solution. Then, we will prove that the limit solution solves the unperturbed problem. We stress out that our result allows us to consider a wide class of utility functions in which the Walrasian equilibrium problem may be solved.