116 research outputs found
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
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