Directed polymers and interfaces in random media : free-energy optimization via confinement in a wandering tube

We analyze, via Imry-Ma scaling arguments, the strong disorder phases that exist in low dimensions at all temperatures for directed polymers and interfaces in random media. For the uncorrelated Gaussian disorder, we obtain that the optimal strategy for the polymer in dimension $1+d$ with $0<d<2$ involves at the same time (i) a confinement in a favorable tube of radius $R_S \sim L^{\nu_S}$ with $\nu_S=1/(4-d)<1/2$ (ii) a superdiffusive behavior $R \sim L^{\nu}$ with $\nu=(3-d)/(4-d)>1/2$ for the wandering of the best favorable tube available. The corresponding free-energy then scales as $F \sim L^{\omega}$ with $\omega=2 \nu-1$ and the left tail of the probability distribution involves a stretched exponential of exponent $\eta= (4-d)/2$. These results generalize the well known exact exponents $\nu=2/3$, $\omega=1/3$ and $\eta=3/2$ in $d=1$, where the subleading transverse length $R_S \sim L^{1/3}$ is known as the typical distance between two replicas in the Bethe Ansatz wave function. We then extend our approach to correlated disorder in transverse directions with exponent $\alpha$ and/or to manifolds in dimension $D+d=d_{t}$ with $0<D<2$. The strategy of being both confined and superdiffusive is still optimal for decaying correlations ($\alpha<0$), whereas it is not for growing correlations ($\alpha>0$). In particular, for an interface of dimension $(d_t-1)$ in a space of total dimension $5/3<d_t<3$ with random-bond disorder, our approach yields the confinement exponent $\nu_S = (d_t-1)(3-d_t)/(5d_t-7)$. Finally, we study the exponents in the presence of an algebraic tail $1/V^{1+\mu}$ in the disorder distribution, and obtain various regimes in the $(\mu,d)$ plane.Comment: 19 page

Lagrangian predictability of high-resolution regional models: the special case of the Gulf of Mexico

The Lagrangian prediction skill (model ability to reproduce Lagrangian drifter trajectories) of the nowcast/forecast system developed for the Gulf of Mexico at the University of Colorado at Boulder is examined through comparison with real drifter observations. Model prediction error (MPE), singular values (SVs) and irreversible-skill time (IT) are used as quantitative measures of the examination. Divergent (poloidal) and nondivergent (toroidal) components of the circulation attractor at 50m depth are analyzed and compared with the Lagrangian drifter buoy data using the empirical orthogonal function (EOF) decomposition and the measures, respectively. Irregular (probably, chaotic) dynamics of the circulation attractor reproduced by the nowcast/forecast system is analyzed through Lyapunov dimension, global entropies, toroidal and poloidal kinetic energies. The results allow assuming exponential growth of prediction error on the attractor. On the other hand, the <it>q</it>-th moment of MPE grows by the power law with exponent of 3<it>q</it>/4. The probability density function (PDF) of MPE has a symmetrical but non-Gaussian shape for both the short and long prediction times and for spatial scales ranging from 20km to 300km. The phenomenological model of MPE based on a diffusion-like equation is developed. The PDF of IT is non-symmetric with a long tail stretched towards large ITs. The power decay of the tail was faster than 2 for long prediction times

Statistical signatures of critical behavior in small systems

The cluster distributions of different systems are examined to search for signatures of a continuous phase transition. In a system known to possess such a phase transition, both sensitive and insensitive signatures are present; while in systems known not to possess such a phase transition, only insensitive signatures are present. It is shown that nuclear multifragmentation results in cluster distributions belonging to the former category, suggesting that the fragments are the result of a continuous phase transition.Comment: 31 pages, two columns with 30 figure

Transcatheter mitral valve edge-to-edge repair in patients with severe mitral regurgitation: data from the MitraClip Russia Trial

Aim. To study the immediate and short-term outcomes of transcatheter mitral valve edge-to-edge repair with the MitraClip NT in patients with severe mitral regurgitation as part of the MitraClip Russia prospective single-center study.Material and methods. The study included 16 patients (men, 10; women, 6) with mean age of 70,1±2,1 years (mean Euroscore II, 6,90±5,56%; STS, 6,33±3,94%). Immediate technical success was defined as successful access, delivery, and removal of the device, and adequate placing the clip(s) to reduce the mitral regurgitation to grade 2 or below without the need for device- or procedure-related reintervention.Results. Immediate technical success was achieved in all patients. The average number of implanted clips per 1 patient was 1,7. In 1 patient (6,3%), a clip was attached to one mitral leaflet, which required an non-scheduled implantation of a second clip. In hospital mortality was 6,3%: a 92-year-old patient on the 3rd day after the operation had a sudden cardiac arrest followed by coma, hemispheric ischemic stroke and death on the 6th day. An autopsy revealed an iatrogenic atrial septal defect. Echocardiography performed on the 10th and 30th day after surgery showed a decrease in mitral regurgitation grade in 15 patients, while grade 3 residual mitral regurgitation did not reveal in any patient.Conclusion. Transcatheter mitral valve edge-to-edge repair with the MitraClip is a minimally invasive method for treating severe symptomatic mitral regurgitation (degenerative and functional). The results demonstrate high immediate efficacy and an acceptable safety profile in high surgical risk patients. Based on the analysis of death causes, the authors conclude that it is necessary to include initial pulmonary hypertension above 75 mm Hg as a relative contraindication to this procedure. The study limitations are the small sample size and short follow-up period

Atlantic Behavioral Response Study: Experimental Design, Analytical Methods, and Preliminary Results

Excerpted from ESOMM - 2018, 6th International Meeting on the Effects of Sound in the Ocean on Marine Mammals The Hague, The Netherlands

Failure mechanisms in alloy of polyamide 6,6/polyphenylene oxide under severe conditions

Toughening mechanisms of a polyamide 6,6/polyphenylene oxide alloy containing an elastomer tested under a slow rate, an impact rate, and a low temperature have been investigated using various microscopy techniques. It is found that the toughening mechanisms of the alloy may change from crazing/shear yielding, to crack bridging/crazing, and to transparticle failure, depending on the testing conditions. Except for the low temperature high strain rate testing condition and in the plane stress region of the crack, the crazing mechanism has been observed in all the conditions we studied. When the testing rate is high, the shear yielding mechanism is suppressed; multiple crazing and particle bridging mechanisms appear to dominate.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44700/1/10853_2004_Article_BF00557130.pd

Influence of particle size and particle size distribution on toughening mechanisms in rubber-modified epoxies

The principal toughening mechanism of a substantially toughened, rubber-modified epoxy has again been shown to involve internal cavitation of the rubber particles and the subsequent formation of shear bands. Additional evidence supporting this sequence of events which provides a significant amount of toughness enhancement, is presented. However, in addition to this well-known mechanism, more subtle toughening mechanisms have been found in this work. Evidence for such mechanisms as crack deflection and particle bridging is shown under certain circumstances in rubber-modified epoxies. The occurrence of these toughening mechanisms appears to have a particle size dependence. Relatively large particles provide only a modest increase in fracture toughness by a particle bridging/crack deflection mechanism. In contrast, smaller particles provide a significant increase in toughness by cavitation-induced shear banding. A critical, minimum diameter for particles which act as bridging particles exists and this critical diameter appears to scale with the properties of the neat epoxy. Bimodal mixtures of epoxies containing small and large particles are also examined and no synergistic effects are observed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44701/1/10853_2005_Article_BF01184979.pd

The toughness of epoxy-poly(butylene terephthalate) blends

Blends containing 5% poly(butylene terephthalate) (PBT) in an anhydride-cured epoxy with three different PBT morphologies were studied. The three morphologies were a dispersion of spherulites, a structureless gel and a gel with spherulites. The average fracture toughnesses, K Ic , and fracture energies, G Ic , for those morphologies were 0.83, 2.3 and 1.8 MPa m 1/2 and 240, 2000 and 1150 J m −2 , respectively. These values should be compared with the values of 0.72 MPa m 1/2 and 180 J m −2 , respectively, for the cured epoxy without PBT. The elastic moduli and yield strengths in compression for all three blend morphologies remained essentially unchanged from those of the cured epoxy without PBT, namely, 2.9 GPa for the modulus and 115 MPa for the yield strength. The fracture surfaces of the cured spherulitic dispersion blends indicate the absorption of fracture energy by crack bifurcation induced by the spherulites. The fracture surfaces of the cured structureless gel blends indicate that fracture energy was absorbed by matrix and PBT plastic deformation and by spontaneous crack bifurcation. But phase transformation of the PBT and anelastic strain of the matrix below the fracture surfaces may account for most of the large fracture energy of the cured structureless gel blends.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44733/1/10853_2004_Article_BF00366876.pd