Hierarchical pinning models, quadratic maps and quenched disorder

We consider a hierarchical model of polymer pinning in presence of quenched disorder, introduced by B. Derrida, V. Hakim and J. Vannimenius in 1992, which can be re-interpreted as an infinite dimensional dynamical system with random initial condition (the disorder). It is defined through a recurrence relation for the law of a random variable {R_n}_{n=1,2,...}, which in absence of disorder (i.e., when the initial condition is degenerate) reduces to a particular case of the well-known Logistic Map. The large-n limit of the sequence of random variables 2^{-n} log R_n, a non-random quantity which is naturally interpreted as a free energy, plays a central role in our analysis. The model depends on a parameter alpha>0, related to the geometry of the hierarchical lattice, and has a phase transition in the sense that the free energy is positive if the expectation of R_0 is larger than a certain threshold value, and it is zero otherwise. It was conjectured by Derrida et al. (1992) that disorder is relevant (respectively, irrelevant or marginally relevant) if 1/2<alpha<1 (respectively, alpha<1/2 or alpha=1/2), in the sense that an arbitrarily small amount of randomness in the initial condition modifies the critical point with respect to that of the pure (i.e., non-disordered) model if alpha is larger or equal to 1/2, but not if alpha is smaller than 1/2. Our main result is a proof of these conjectures for the case alpha different from 1/2. We emphasize that for alpha>1/2 we find the correct scaling form (for weak disorder) of the critical point shift.Comment: 26 pages, 2 figures. v3: Theorem 1.6 improved. To appear on Probab. Theory Rel. Field

Fractional moment bounds and disorder relevance for pinning models

We study the critical point of directed pinning/wetting models with quenched disorder. The distribution K(.) of the location of the first contact of the (free) polymer with the defect line is assumed to be of the form K(n)=n^{-\alpha-1}L(n), with L(.) slowly varying. The model undergoes a (de)-localization phase transition: the free energy (per unit length) is zero in the delocalized phase and positive in the localized phase. For \alpha<1/2 it is known that disorder is irrelevant: quenched and annealed critical points coincide for small disorder, as well as quenched and annealed critical exponents. The same has been proven also for \alpha=1/2, but under the assumption that L(.) diverges sufficiently fast at infinity, an hypothesis that is not satisfied in the (1+1)-dimensional wetting model considered by Forgacs et al. (1986) and Derrida et al. (1992), where L(.) is asymptotically constant. Here we prove that, if 1/21, then quenched and annealed critical points differ whenever disorder is present, and we give the scaling form of their difference for small disorder. In agreement with the so-called Harris criterion, disorder is therefore relevant in this case. In the marginal case \alpha=1/2, under the assumption that L(.) vanishes sufficiently fast at infinity, we prove that the difference between quenched and annealed critical points, which is known to be smaller than any power of the disorder strength, is positive: disorder is marginally relevant. Again, the case considered by Forgacs et al. (1986) and Derrida et al. (1992) is out of our analysis and remains open.Comment: 20 pages, 1 figure; v2: few typos corrected, references revised. To appear on Commun. Math. Phy

UVB radiation induced effects on cells studied by FTIR spectroscopy

We have made a preliminary analysis of the results about the eVects on tumoral cell line (lymphoid T cell line Jurkat) induced by UVB radiation (dose of 310 mJ/cm^2) with and without a vegetable mixture. In the present study, we have used two techniques: Fourier transform infrared spectroscopy (FTIR) and flow cytometry. FTIR spectroscopy has the potential to provide the identiWcation of the vibrational modes of some of the major compounds (lipid, proteins and nucleic acids) without being invasive in the biomaterials. The second technique has allowed us to perform measurements of cytotoxicity and to assess the percentage of apoptosis. We already studied the induction of apoptotic process in the same cell line by UVB radiation; in particular, we looked for correspondences and correlations between FTIR spetroscopy and flow cytometry data finding three highly probable spectroscopic markers of apoptosis (Pozzi et al. in Radiat Res 168:698-705, 2007). In the present work, the results have shown significant changes in the absorbance and spectral pattern in the wavenumber protein and nucleic acids regions after the treatments

Remnant Fermi surface in the presence of an underlying instability in layered 1T-TaS_2

We report high resolution angle-scanned photoemission and Fermi surface (FS) mapping experiments on the layered transition-metal dichalcogenide 1T-TaS_2 in the quasi commensurate (QC) and the commensurate (C) charge-density-wave (CDW) phase. Instead of a nesting induced partially removed FS in the CDW phase we find a pseudogap over large portions of the FS. This remnant FS exhibits the symmetry of the one-particle normal state FS even when passing from the QC-phase to the C-phase. Possibly, this Mott localization induced transition represents the underlying instability responsible for the pseudogapped FS

Phase Segregation Dynamics in Particle Systems with Long Range Interactions I: Macroscopic Limits

We present and discuss the derivation of a nonlinear non-local integro-differential equation for the macroscopic time evolution of the conserved order parameter of a binary alloy undergoing phase segregation. Our model is a d-dimensional lattice gas evolving via Kawasaki exchange dynamics, i.e. a (Poisson) nearest-neighbor exchange process, reversible with respect to the Gibbs measure for a Hamiltonian which includes both short range (local) and long range (nonlocal) interactions. A rigorous derivation is presented in the case in which there is no local interaction. In a subsequent paper (part II), we discuss the phase segregation phenomena in the model. In particular we argue that the phase boundary evolutions, arising as sharp interface limits of the family of equations derived in this paper, are the same as the ones obtained from the corresponding limits for the Cahn-Hilliard equation.Comment: amstex with macros (included in the file), tex twice, 20 page

Probing the Gaseous Disk of T Tau N with CN 5-4 Lines

We present spectrally resolved observations of the young multiple system T Tau in atomic and molecular lines obtained with the Heterodyne Instrument for the Far Infrared on board Herschel. While CO, H2O, [C II], and SO lines trace the envelope and the outflowing gas up to velocities of 33 km s-1 with respect to systemic, the CN 5-4 hyperfine structure lines at 566.7, 566.9 GHz show a narrow double-peaked profile centered at systemic velocity, consistent with an origin in the outer region of the compact disk of T Tau N. Disk modeling of the T Tau N disk with the thermo-chemical code ProDiMo produces CN line fluxes and profiles consistent with the observed ones and constrain the size of the gaseous disk (R_out=110^{+10}_{-20} AU) and its inclination (i = 25°± 5°). The model indicates that the CN lines originate in a disk upper layer at 40-110 AU from the star, which is irradiated by the stellar UV field and heated up to temperatures of 50-700 K. With respect to previously observed CN 2-1 millimeter lines, the CN 5-4 lines appear to be less affected by envelope emission, due to their larger critical density and excitation temperature. Hence, high-J CN lines are a unique confusion-free tracer of embedded disks, such as the disk of T Tau N

Scanning Tunneling Microscopy in TTF-TCNQ :direct proof of phase and amplitude modulated charge density waves

Charge density waves (CDW) have been studied at the surface of a cleaved TTF-TCNQ single crystal using a low temperature scanning tunneling microscope (STM) under ultra high vacuum (UHV) conditions. All CDW phase transitions of TTF-TCNQ have been identified. The measurement of the modulation wave vector along the a direction provides the first evidence for the existence of domains comprising single plane wave modulated structures in the temperature regime where the transverse wave vector of the CDW is temperature dependent, as hinted by the theory more than 20 years ago.Comment: To appear in Phys.Rev.Rapid. Com