Structural instability of nonlinear plates modelling suspension bridges: mathematical answers to some long-standing questions

We model the roadway of a suspension bridge as a thin rectangular plate and we study in detail its oscillating modes. The plate is assumed to be hinged on its short edges and free on its long edges. Two different kinds of oscillating modes are found: longitudinal modes and torsional modes. Then we analyze a fourth order hyperbolic equation describing the dynamics of the bridge. In order to emphasize the structural behavior we consider an isolated equation with no forcing and damping. Due to the nonlinear behavior of the cables and hangers, a structural instability appears. With a finite dimensional approximation we prove that the system remains stable at low energies while numerical results show that for larger energies the system becomes unstable. We analyze the energy thresholds of instability and we show that the model allows to give answers to several questions left open by the Tacoma collapse in 1940.Comment: 33 page

Saddle Points Stability in the Replica Approach Off Equilibrium

We study the replica free energy surface for a spin glass model near the glassy temperature. In this model the simplicity of the equilibrium solution hides non trivial metastable saddle points. By means of the stability analysis performed for one and two real replicas constrained, an interpretation for some of them is achieved.Comment: 10 pages and 3 figures upon request, Univerista` di Roma I preprint 94/100

Partial symmetry and existence of least energy solutions to some nonlinear elliptic equations on Riemannian models

We consider least energy solutions to the nonlinear equation $-\Delta_g u=f(r,u)$ posed on a class of Riemannian models $(M,g)$ of dimension $n\ge 2$ which include the classical hyperbolic space $\mathbb H^n$ as well as manifolds with unbounded sectional geometry. Partial symmetry and existence of least energy solutions is proved for quite general nonlinearities $f(r,u)$, where $r$ denotes the geodesic distance from the pole of $M$

Uniqueness of the thermodynamic limit for driven disordered elastic interfaces

We study the finite size fluctuations at the depinning transition for a one-dimensional elastic interface of size $L$ displacing in a disordered medium of transverse size $M=k L^\zeta$ with periodic boundary conditions, where $\zeta$ is the depinning roughness exponent and $k$ is a finite aspect ratio parameter. We focus on the crossover from the infinitely narrow ($k\to 0$) to the infinitely wide ($k\to \infty$) medium. We find that at the thermodynamic limit both the value of the critical force and the precise behavior of the velocity-force characteristics are {\it unique} and $k$-independent. We also show that the finite size fluctuations of the critical force (bias and variance) as well as the global width of the interface cross over from a power-law to a logarithm as a function of $k$. Our results are relevant for understanding anisotropic size-effects in force-driven and velocity-driven interfaces.Comment: 10 pages, 12 figure

Orbital Polarization in Strained LaNiO3_{3}: Structural Distortions and Correlation Effects

Transition-metal heterostructures offer the fascinating possibility of controlling orbital degrees of freedom via strain. Here, we investigate theoretically the degree of orbital polarization that can be induced by epitaxial strain in LaNiO$_3$ films. Using combined electronic structure and dynamical mean-field theory methods we take into account both structural distortions and electron correlations and discuss their relative influence. We confirm that Hund's rule coupling tends to decrease the polarization and point out that this applies to both the $d^8\underline{L}$ and $d^7$ local configurations of the Ni ions. Our calculations are in good agreement with recent experiments, which revealed sizable orbital polarization under tensile strain. We discuss why full orbital polarization is hard to achieve in this specific system and emphasize the general limitations that must be overcome to achieve this goal.Comment: 13 pages, 13 figure

Non-steady relaxation and critical exponents at the depinning transition

We study the non-steady relaxation of a driven one-dimensional elastic interface at the depinning transition by extensive numerical simulations concurrently implemented on graphics processing units (GPUs). We compute the time-dependent velocity and roughness as the interface relaxes from a flat initial configuration at the thermodynamic random-manifold critical force. Above a first, non-universal microscopic time-regime, we find a non-trivial long crossover towards the non-steady macroscopic critical regime. This "mesoscopic" time-regime is robust under changes of the microscopic disorder including its random-bond or random-field character, and can be fairly described as power-law corrections to the asymptotic scaling forms yielding the true critical exponents. In order to avoid fitting effective exponents with a systematic bias we implement a practical criterion of consistency and perform large-scale (L~2^{25}) simulations for the non-steady dynamics of the continuum displacement quenched Edwards Wilkinson equation, getting accurate and consistent depinning exponents for this class: \beta = 0.245 \pm 0.006, z = 1.433 \pm 0.007, \zeta=1.250 \pm 0.005 and \nu=1.333 \pm 0.007. Our study may explain numerical discrepancies (as large as 30% for the velocity exponent \beta) found in the literature. It might also be relevant for the analysis of experimental protocols with driven interfaces keeping a long-term memory of the initial condition.Comment: Published version (including erratum). Codes and Supplemental Material available at https://bitbucket.org/ezeferrero/qe

Relaxation in yield stress systems through elastically interacting activated events

We study consequences of long-range elasticity in thermally assisted dynamics of yield stress materials. Within a two-dimensinal mesoscopic model we calculate the mean-square displacement and the dynamical structure factor for tracer particle trajectories. The ballistic regime at short time scales is associated with a compressed exponential decay in the dynamical structure factor, followed by a subdiffusive crossover prior to the onset of diffusion. We relate this crossover to spatiotemporal correlations and thus go beyond established mean field predictions.Comment: 5 pages, 2 figures, to appear in PR

Development of Beluga, Delphinapterus leucas, Capture and Satellite Tagging Protocol in Cook Inlet, Alaska

Attempts to capture and place satellite tags on belugas, Delphinapterus leucas, in Cook Inlet, Alaska were conducted during late spring and summer of 1995, 1997, and 1999. In 1995, capture attempts using a hoop net proved impractical in Cook Inlet. In 1997, capture efforts focused on driving belugas into nets. Although this method had been successful in the Canadian High Arctic, it failed in Cook Inlet due to the ability of the whales to detect and avoid nets in shallow and very turbid water. In 1999, belugas were successfully captured using a gillnet encirclement technique. A satellite tag was attached to a juvenile male, which subsequently provided the first documentation of this species’ movements within Cook Inlet during the summer months (31 May–17 September)