Texture investigation of the superelastic Ti-24Nb-4Zr-8Sn alloy

International audienceIn this work, the influence of crystallographic texture on mechanical properties was investigated by X-ray diffraction in the superelastic Ti-24Nb-4Zr-8Sn alloy. Different textures were obtained by changing the cold rolling reduction rate and the following thermal treatment (solution treatment or flash thermal treatment). The tensile tests performed show that Young's modulus, elongation at rupture and ultimate tensile strength are not influenced by texture. However, the superelastic property of the Ti-24Nb-4Zr-8Sn alloy after solution treatment clearly increases with the textural change into the γ-fiber texture with a (1 1 1)View the MathML source main component due to the increase of cold rolling rate. Contrarily, the texture change induced by the increase of cold rolling rate has no influence on superelasticity after flash thermal treatment. Flash thermal treatment gives also higher recovery strain than solution treatment due to a smaller grain size

Characterization of the nanophase precipitation in a metastable beta titanium-based alloy by electrical resistivity, dilatometry and neutron diffraction

The metastable beta Ti-6Mo-5Ta-4Fe (wt.%) alloys was synthesized by cold crucible levitation melting and then quenched in water from the beta phase field. In order to investigate the transformation sequence upon heating, thermal analysis methods such as electrical resistivity, dilatometry and neutron thermodiffraction were employed. By these methods, the different temperatures of transition were detected and solute partitioning was oberved to the beta matrix during the omega and alpha nanophase precipitatio

New invariants for entangled states

We propose new algebraic invariants that distinguish and classify entangled states. Considering qubits as well as higher spin systems, we obtained complete entanglement classifications for cases that were either unsolved or only conjectured in the literature.Comment: published versio

On the geometry of a class of N-qubit entanglement monotones

A family of N-qubit entanglement monotones invariant under stochastic local operations and classical communication (SLOCC) is defined. This class of entanglement monotones includes the well-known examples of the concurrence, the three-tangle, and some of the four, five and N-qubit SLOCC invariants introduced recently. The construction of these invariants is based on bipartite partitions of the Hilbert space in the form ${\bf C}^{2^N}\simeq{\bf C}^L\otimes{\bf C}^l$ with $L=2^{N-n}\geq l=2^n$. Such partitions can be given a nice geometrical interpretation in terms of Grassmannians Gr(L,l) of l-planes in ${\bf C}^L$ that can be realized as the zero locus of quadratic polinomials in the complex projective space of suitable dimension via the Plucker embedding. The invariants are neatly expressed in terms of the Plucker coordinates of the Grassmannian.Comment: 7 pages RevTex, Submitted to Physical Review

On the geometry of four qubit invariants

The geometry of four-qubit entanglement is investigated. We replace some of the polynomial invariants for four-qubits introduced recently by new ones of direct geometrical meaning. It is shown that these invariants describe four points, six lines and four planes in complex projective space ${\bf CP}^3$. For the generic entanglement class of stochastic local operations and classical communication they take a very simple form related to the elementary symmetric polynomials in four complex variables. Moreover, their magnitudes are entanglement monotones that fit nicely into the geometric set of $n$-qubit ones related to Grassmannians of $l$-planes found recently. We also show that in terms of these invariants the hyperdeterminant of order 24 in the four-qubit amplitudes takes a more instructive form than the previously published expressions available in the literature. Finally in order to understand two, three and four-qubit entanglement in geometric terms we propose a unified setting based on ${\bf CP}^3$ furnished with a fixed quadric.Comment: 19 page

Superelastic Behavior of Biomedical Metallic Alloys

In this this work, superelastic NiTi and Ni-free Ti-23Hf-3Mo-4Sn biomedical alloys were investigated by tensile tests in relationship with their microstructures. To follow the stress-induced martensitic transformations occurring in these alloys, in situ tensile tests under synchrotron beam were conducted. In NiTi, an intermediate trigonal R phase, which is first stress-induced before the B19 ' martensitic phase, was identified. However, the Ti-23Hf-3Mo-4Sn alloy does not present a transitional phase, and a direct beta into alpha '' reversible stress-induced martensitic transformation was observed. With NiTi, all the applied strain is recovered after unloading, and no residual plastic deformation occurs. However, the strain is not completely recovered with the Ti-23Hf-3Mo-4Sn alloy, and residual plastic strain was observed to prevent a complete recovery, thus explaining why the strain recovery is lower for Ti-23Hf-3Mo-4Sn compared with NiTi. We also showed that the maximum strain recovery depends on the texture in the Ti-23Hf-3Mo-4Sn alloy. The favorable texture leading to the highest strain recovery (4.6 pct) is the {111}< 110 and rang;(beta) texture, which can be obtained by a short-time solution treatment (0.3 ks) at 1073 K with this alloy

A Hopf laboratory for symmetric functions

An analysis of symmetric function theory is given from the perspective of the underlying Hopf and bi-algebraic structures. These are presented explicitly in terms of standard symmetric function operations. Particular attention is focussed on Laplace pairing, Sweedler cohomology for 1- and 2-cochains, and twisted products (Rota cliffordizations) induced by branching operators in the symmetric function context. The latter are shown to include the algebras of symmetric functions of orthogonal and symplectic type. A commentary on related issues in the combinatorial approach to quantum field theory is given.Comment: 29 pages, LaTeX, uses amsmat

Quadratic pseudosupersymmetry in two-level systems

Using the intertwining relation we construct a pseudosuperpartner for a (non-Hermitian) Dirac-like Hamiltonian describing a two-level system interacting in the rotating wave approximation with the electric component of an electromagnetic field. The two pseudosuperpartners and pseudosupersymmetry generators close a quadratic pseudosuperalgebra. A class of time dependent electric fields for which the equation of motion for a two level system placed in this field can be solved exactly is obtained. New interesting phenomenon is observed. There exists such a time-dependent detuning of the field frequency from the resonance value that the probability to populate the excited level ceases to oscillate and becomes a monotonically growing function of time tending to 3/4. It is shown that near this fixed excitation regime the probability exhibits two kinds of oscillations. The oscillations with a small amplitude and a frequency close to the Rabi frequency (fast oscillations) take place at the background of the ones with a big amplitude and a small frequency (slow oscillations). During the period of slow oscillations the minimal value of the probability to populate the excited level may exceed 1/2 suggesting for an ensemble of such two-level atoms the possibility to acquire the inverse population and exhibit lasing properties.Comment: 5 figure

Geometric descriptions of entangled states by auxiliaries varieties

The aim of the paper is to propose geometric descriptions of multipartite entangled states using algebraic geometry. In the context of this paper, geometric means each stratum of the Hilbert space, corresponding to an entangled state, is an open subset of an algebraic variety built by classical geometric constructions (tangent lines, secant lines) from the set of separable states. In this setting we describe well-known classifications of multipartite entanglement such as $2\times 2\times(n+1)$, for $n\geq 1$, quantum systems and a new example with the $2\times 3\times 3$ quantum system. Our description completes the approach of Miyake and makes stronger connections with recent work of algebraic geometers. Moreover for the quantum systems detailed in this paper we propose an algorithm, based on the classical theory of invariants, to decide to which subvariety of the Hilbert space a given state belongs.Comment: 32 pages, 15 Tables, 5 Figures. References and remarks adde

Supercharacters, symmetric functions in noncommuting variables (extended abstract)

International audienceWe identify two seemingly disparate structures: supercharacters, a useful way of doing Fourier analysis on the group of unipotent uppertriangular matrices with coefficients in a finite field, and the ring of symmetric functions in noncommuting variables. Each is a Hopf algebra and the two are isomorphic as such. This allows developments in each to be transferred. The identification suggests a rich class of examples for the emerging field of combinatorial Hopf algebras.Nous montrons que deux structures en apparence bien différentes peuvent être identifiées: les super-caractères, qui sont un outil commode pour faire de l'analyse de Fourier sur le groupe des matrices unipotentes triangulaires supérieures à coefficients dans un corps fini, et l'anneau des fonctions symétriques en variables non-commutatives. Ces deux structures sont des algèbres de Hopf isomorphes. Cette identification permet de traduire dans une structure les dévelopements conçus pour l'autre, et suggère de nombreux exemples dans le domaine nouveau des algèbres de Hopf combinatoires