Rigidity for C1C^1 actions on the interval arising from hyperbolicity I: solvable groups

We consider Abelian-by-cyclic groups for which the cyclic factor acts by hyperbolic automorphisms on the Abelian subgroup. We show that if such a group acts faithfully by $C^1$ diffeomorphisms of the closed interval with no global fixed point at the interior, then the action is topologically conjugated to that of an affine group. Moreover, in case of non-Abelian image, we show a rigidity result concerning the multipliers of the homotheties, despite the fact that the conjugacy is not necessarily smooth. Some consequences for non-solvable groups are proposed. In particular, we give new proofs/examples yielding the existence of finitely-generated, locally-indicable groups with no faithful action by $C^1$ diffeomorphisms of the interval.Comment: A more detailed proof of Proposition 4.15 adde

Electrical resistivity of the Ti4O7 Magneli phase under high pressure

We have measured resistivity as a function of temperature and pressure of Ti4O7 twinned crystals using different contact configurations. Pressures over 4kbar depress the localization of bipolarons and allow the study of the electrical conduction of the bipolaronic phase down to low temperatures. For pressures P > 40 kbar the bipolaron formation transition is suppressed and a nearly pressure independent behavior is obtained for the resistivity. We observed an anisotropic conduction. When current is injected parallel to the principal axis, a metallic conduction with interacting carrier effects is predominant. A superconducting state was not obtained down to 1.2 K, although evidences of the proximity of a quantum critical point were noticed. While when current is injected non-parallel to the crystal's principal axis, we obtained a logarithmic divergence of the resistivity at low temperatures. For this case, our results for the high pressure regime can be interpreted in the framework of interacting carriers (polarons or bipolarons) scattered by Two Level Systems.Comment: 9 Revtex pages, 12 EPS figures included, submitted to The European Physical Journal B. Contact author: C. Acha (e-mail address: [email protected]

Belousov-Zhabotinsky type reactions: the non-linear behavior of chemical systems

Chemical oscillators are open systems characterized by periodic variations of some reaction species concentration due to complex physico-chemical phenomena that may cause bistability, rise of limit cycle attractors, birth of spiral waves and Turing patterns and finally deterministic chaos. Specifically, the Belousov-Zhabotinsky reaction is a noteworthy example of non-linear behavior of chemical systems occurring in homogenous media. This reaction can take place in several variants and may offer an overview on chemical oscillators, owing to its simplicity of mathematical handling and several more complex deriving phenomena. This work provides an overview of Belousov-Zhabotinsky-type reactions, focusing on modeling under different operating conditions, from the most simple to the most widely applicable models presented during the years. In particular, the stability of simplified models as a function of bifurcation parameters is studied as causes of several complex behaviors. Rise of waves and fronts is mathematically explained as well as birth and evolution issues of the chaotic ODEs system describing the Györgyi-Field model of the Belousov-Zhabotinsky reaction. This review provides not only the general information about oscillatory reactions, but also provides the mathematical solutions in order to be used in future biochemical reactions and reactor designs

Calcium signalling links MYC to NUAK1

NUAK1 is a member of the AMPK-related family of kinases. Recent evidence suggests that NUAK1 is an important regulator of cell adhesion and migration, cellular and organismal metabolism, and regulation of TAU stability. As such, NUAK1 may play key roles in multiple diseases ranging from neurodegeneration to diabetes and metastatic cancer. Previous work revealed a crucial role for NUAK1 in supporting viability of tumour cells specifically when MYC is overexpressed. This role is surprising, given that NUAK1 is activated by the tumour suppressor LKB1. Here we show that, in tumour cells lacking LKB1, NUAK1 activity is maintained by an alternative pathway involving calcium-dependent activation of PKCα. Calcium/PKCα-dependent activation of NUAK1 supports engagement of the AMPK-TORC1 metabolic checkpoint, thereby protecting tumour cells from MYC-driven cell death, and indeed, MYC selects for this pathway in part via transcriptional regulation of PKCα and ITPR. Our data point to a novel role for calcium in supporting tumour cell viability and clarify the synthetic lethal interaction between NUAK1 and MYC

Phonon assisted dynamical Coulomb blockade in a thin suspended graphite sheet

The differential conductance in a suspended few layered graphene sample is fou nd to exhibit a series of quasi-periodic sharp dips as a function of bias at l ow temperature. We show that they can be understood within a simple model of dyn amical Coulomb blockade where energy exchanges take place between the charge carriers transmitted trough the sample and a dissipative electromagnetic envir onment with a resonant phonon mode strongly coupled to the electrons

High pressure transport studies of the LiFeAs analogues CuFeTe2 and Fe2As

We have synthesized two iron-pnictide/chalcogenide materials, CuFeTe2 and Fe2As, which share crystallographic features with known iron-based superconductors, and carried out high-pressure electrical resistivity measurements on these materials to pressures in excess of 30 GPa. Both compounds crystallize in the Cu2Sb-type crystal structure that is characteristic of LiFeAs (with CuFeTe2 exhibiting a disordered variant). At ambient pressure, CuFeTe2 is a semiconductor and has been suggested to exhibit a spin-density-wave transition, while Fe2As is a metallic antiferromagnet. The electrical resistivity of CuFeTe2, measured at 4 K, decreases by almost two orders of magnitude between ambient pressure and 2.4 GPa. At 34 GPa, the electrical resistivity decreases upon cooling the sample below 150 K, suggesting the proximity of the compound to a metal-insulator transition. Neither CuFeTe2 nor Fe2As superconduct above 1.1 K throughout the measured pressure range.Comment: 6 pages, 7 figure

Absence of a structural transition up to 40 Gpa in MgB2 and the relevance of magnesium non-stoichiometry

We report measurements on MgB2 up to ~40GPa. Increasing pressure yields a monotonous decrease of the lattice parameters and of the c/a ratio, but no structural transition down to parameters smaller than those of AlB2. The transition superconducting temperature also decreases with temperature in a sample dependent way. The results are explained by an increase of the filling of the 2D pxy bands with pressure, the Mg stoichiometry determining the starting position of the Fermi level. Our measurements indicate that these hole bands are the relevant ones for superconductivity.Comment: submitted March 9th 2001, PRB accepte