Small polaron formation in many-particle states of the Hubbard-Holstein model: The one-dimensional case

We investigate polaron formation in a many-electron system in the presence of a local repulsion sufficiently strong to prevent local-bipolaron formation. Specifically, we consider a Hubbard-Holstein model of interacting electrons coupled to dispersionless phonons of frequency $\omega_0$. Numerically solving the model in a small one-dimensional cluster, we find that in the nearly adiabatic case $\omega_0 < t$, the necessary and sufficient condition for the polaronic regime to occur is that the energy gain in the atomic (i.e., extremely localized) regime ${\cal E}_{pol}$ overcomes the energy of the purely electronic system ${\cal E}_{el}$. In the antiadiabatic case, $\omega_0 > t$, polaron formation is instead driven by the condition of a large ionic displacement $g/\omega_0 >1$ ($g$ being the electron-phonon coupling). Dynamical properties of the model in the weak and moderately strong coupling regimes are also analyzed

Recent advances in modeling coastal tsunami hazard based on the geological record

In operational tsunami hazard assessment in a given area or oceanic basin, such as currently being performed in the US under the auspice of the National Tsunami Hazard Mitigation Program (NTHMP) (URI is in charge of developing inundation maps for the US East Coast, in collaboration with UoD), one has to model wave generation and coastal inundation resulting from all the relevant geological sources leading to Probable Maximum Tsunami (PMT) conditions. This typically includes co-seismic as well as landslide tsunami sources, the latter being comprised of Submarine Mass Failures (SMF) and subaerial slides, including volcanic flank collapse. Here, we review how the author and co-workers have used the geological record and related parameters to design and model relevant PMT scenarios for co-seismic and SMF tsunamis and subaerial slides. In particular, for SMFs along the US East Coast, a probabilistic Monte Carlo approach, based on slope stability analyses, was first used as a screening tool to estimate overall alongshore SMF tsunami hazard (Grilli et al., 2009). Consistent with the PMT approach, this was followed by siting extreme SMFs in areas deemed at higher risk where sediment availability and seafloor morphology indicated such SMFs were possible. The largest known historical SMF, the 165 km3 Currituck slide complex, was used as a proxy for the most extreme SMF and to maximize wave generation, it was modeled as a rigid slump (Grilli et al., 2015). Large slumps have been shown to have the potential for generating very large tsunamis in recent case studies (Tappin et al., 2008, 2014). The approach for modeling rigid SMF motion and the resulting wave generation is based on using a combination of simple analytical laws of motion verified in laboratory experiments (Enet and Grilli, 2007) and advanced non-hydrostatic models (Ma et al., 2012, 2013; Shi et al., 2012; Grilli et al., 2015; Tappin et al, 2014). Effects of SMF deformation/rheology on tsunami generation will also be discussed and illustrated using numerical modeling. Slides, both SMFs and subaerials, that are closer to debris flows, have also been modeled as heavy fluids. This will be illustrated, by the case of the possible flank collapse of the Cumbre Vieja Volcano (La Palma, Canary Islands), whose extreme 450 km3 scenario yields the dominant PMT in then North Atlantic Ocean basin (Abadie et al., 2012; Harris et al., 2012; Tehranirad et al., 2015)

A NUMERICAL MODEL FOR THE EFFICIENT SIMULATION OF MULTIPLE LANDSLIDE-TSUNAMI SCENARIOS

Submarine landslides can pose serious tsunami hazard to coastal communities, occurring frequently near the coast itself. The properties of the tsunami and the consequent inundation depend on many factors, such as the geometry, the rheology and the kinematic of the landslide and the local bathymetry. However, when evaluating the risk related to landslide tsunamis, it is very difficult to accurately predict all of the above mentioned parameters. It is therefore useful to carry out many simulations of tsunami generation and propagation, with reference to different landslide scenarios, in order to deal with such uncertainties (see for example the probabilistic approach by Grilli et al. 2009). Accurate computations of landslide tsunami generation, propagation, and inundation, however, is computationally expensive, thus limiting the possible maximum number of scenarios. To partially overcome this difficulty, in the present research, a numerical model is proposed that can efficiently compute a large number of tsunami simulations triggered by different landslides. The main goal is to provide a numerical tool that can be used in a Monte Carlo approach framework. Following the study by Ward (2001), we propose a methodology taking advantage of the linear superposition of elementary tsunami solutions

A simplified method to estimate tidal current effects on the ocean wave power resource

Although ocean wave power can be significantly modified by tidal currents, resource assessments at wave energy sites generally ignore this effect, mainly due to the difficulties and high computational cost of developing coupled wave-tide models. Furthermore, validating the prediction of wave-current interaction effects in a coupled model is a challenging task, due to the paucity of observational data. Here, as an alternative to fully coupled numerical models, we present a simplified analytical method, based on linear wave theory, to estimate the influence of tidal currents on the wave power resource. The method estimates the resulting increase (or decrease) in wave height and wavelength for opposing (or following) currents, as well as quantifying the change in wave power. The method is validated by applying it to two energetic locations around the UK shelf - Pentland Firth and Bristol Channel - where wave/current interactions are significant, and for which field data are available. Results demonstrate a good accuracy of the simplified analytical approach, which can thus be used as an efficient tool for making rapid estimates of tidal effects on the wave power resource. Additionally, the method can be used to help better interpret numerical model results, as well as observational data

The Electron-Phonon Interaction in the Presence of Strong Correlations

We investigate the effect of strong electron-electron repulsion on the electron-phonon interaction from a Fermi-liquid point of view: the strong interaction is responsible for vertex corrections, which are strongly dependent on the $v_Fq/\omega$ ratio. These corrections generically lead to a strong suppression of the effective coupling between quasiparticles mediated by a single phonon exchange in the $v_Fq/\omega \gg 1$ limit. However, such effect is not present when $v_Fq/\omega \ll 1$. Analyzing the Landau stability criterion, we show that a sizable electron-phonon interaction can push the system towards a phase-separation instability. A detailed analysis is then carried out using a slave-boson approach for the infinite-U three-band Hubbard model. In the presence of a coupling between the local hole density and a dispersionless optical phonon, we explicitly confirm the strong dependence of the hole-phonon coupling on the transferred momentum versus frequency ratio. We also find that the exchange of phonons leads to an unstable phase with negative compressibility already at small values of the bare hole-phonon coupling. Close to the unstable region, we detect Cooper instabilities both in s- and d-wave channels supporting a possible connection between phase separation and superconductivity in strongly correlated systems.Comment: LateX 3.14, 04.11.1994 Preprint no.101

Influence of electron-phonon interaction on superexchange

We investigate the influence of electron-phonon coupling on the superexchange interaction of magnetic insulators. Both the Holstein-Hubbard model where the phonons couple to the electron density, as well as an extended Su, Schrieffer, Heeger model where the coupling arises from modulation of the overlap integral are studied using exact diagonalization and perturbative methods. In all cases for both the adiabatic (but non-zero frequency) and anti-adiabatic parameter regions the electron-phonon coupling is found to enhance the superexchange.Comment: 14 pages+4 postscript figure

Numerical simulation and first-order hazard analysis of large co-seismic tsunamis generated in the Puerto Rico trench: near-field impact on the North shore of Puerto Rico and far-field impact on the US East Coast

We perform numerical simulations of the coastal impact of large co-seismic tsunamis, initiated in the Puerto Rican trench, both in far-field areas along the upper US East coast (and other Caribbean islands), and in more detail in the near-field, along the Puerto Rico North Shore (PRNS). We first model a magnitude 9.1 extreme co-seismic source and then a smaller 8.7 magnitude source, which approximately correspond to 600 and 200 year return periods, respectively. In both cases, tsunami generation and propagation (both near- and far-field) are first performed in a coarse 2′ basin scale grid, with ETOPO2 bathymetry, using a fully nonlinear and dispersive long wave tsunami model (FUNWAVE). Coastal runup and inundation are then simulated for two selected areas, using finer coastal nested grids. Thus, a 15″ (450 m) grid is used to calculate detailed far-field impact along the US East Coast, from New Jersey to Maine, and a 3″ (90 m) grid (for the finest resolution), encompassing the entire PRNS, is used to compute detailed near-field impact along the PRNS (runup and inundation). To perform coastal simulations in nested grids, accurate bathymetry/topography databases are constructed by combining ETOPO2 2′ data (in deep water) and USGS\u27 or NOAA\u27s 15″ or 3″ (in shallow water) data. In the far-field, runup caused by the extreme 9.1 source would be severe (over 10 m) for some nearby Caribbean islands, but would only reach up to 3 m along the selected section of the East coast. A sensitivity analysis to the bathymetric resolution (for a constant 3″ model grid) of runup along the PRNS, confirms the convergence of runup results for a topographic resolution 24″ or better, and thus stresses the importance of using sufficiently resolved bathymetric data, in order to accurately predict extreme runup values, particularly when bathymetric focusing is significant. Runup (10–22 m) and inundation are found to be very large at most locations for the extreme 9.1 source. Both simulated spatial inundation snapshots and time series indicate, the inundation would be particularly severe near and around the low-lying city of San Juan. For the 8.7 source, runup along the PRNS would be much less severe (3–6 m), but still significant, while inundation would only be significant near and around San Juan. This first-order tsunami hazard analysis stresses the importance of conducting more detailed and comprehensive studies, particularly of tsunami hazard along the PRNS, for a more complete and realistic selection of sources; such work is ongoing as part of a US funded (NTHMP) tsunami inundation mapping effort in Puerto Rico

Block-structured, equal-workload, multi-grid-nesting interface for the Boussinesq wave model FUNWAVE-TVD (Total Variation Diminishing)

We describe the development of a block-structured, equal-CPU-load (central processing unit), multi-grid-nesting interface for the Boussinesq wave model FUNWAVE-TVD (Fully Nonlinear Boussinesq Wave Model with Total Variation Diminishing Solver). The new model framework does not interfere with the core solver, and thus the core program, FUNWAVE-TVD, is still a standalone model used for a single grid. The nesting interface manages the time sequencing and two-way nesting processes between the parent grid and child grid with grid refinement in a hierarchical manner. Workload balance in the MPI-based (message passing interface) parallelization is handled by an equal-load scheme. A strategy of shared array allocation is applied for data management that allows for a large number of nested grids without creating additional memory allocations. Four model tests are conducted to verify the nesting algorithm with assessments of model accuracy and the robustness in the application in modeling transoceanic tsunamis and coastal effects

Hybrid Lattice-Boltzmann-Potential Flow Simulations of Turbulent Flow around Submerged Structures

We report on the development and validation of a 3D hybrid Lattice Boltzmann Model (LBM), with Large Eddy Simulation (LES), to simulate the interactions of incompressible turbulent flows with ocean structures. The LBM is based on a perturbation method, in which the velocity and pressure are expressed as the sum of an inviscid flow and a viscous perturbation. The far- to near-field flow is assumed to be inviscid and represented by potential flow theory, which can be efficiently modeled with a Boundary Element Method (BEM). The near-field perturbation flow around structures is modeled by the Navier–Stokes (NS) equations, based on a Lattice Boltzmann Method (LBM) with a Large Eddy Simulation (LES) of the turbulence. In the paper, we present the hybrid model formulation, in which a modified LBM collision operator is introduced to simulate the viscous perturbation flow, resulting in a novel perturbation LBM (pLBM) approach. The pLBM is then extended for the simulation of turbulence using the LES and a wall model to represent the viscous/turbulent sub-layer near solid boundaries. The hybrid model is first validated by simulating turbulent flows over a flat plate, for moderate to large Reynolds number values, Re ∈ [3.7×104;1.2×106]; the plate friction coefficient and near-field turbulence properties computed with the model are found to agree well with both experiments and direct NS simulations. We then simulate the flow past a NACA-0012 foil using a regular LBM-LES and the new hybrid pLBM-LES models with the wall model, for Re = 1.44 x 106. A good agreement is found for the computed lift and drag forces, and pressure distribution on the foil, with experiments and results of other numerical methods. Results obtained with the pLBM model are either nearly identical or slightly improved, relative to those of the standard LBM, but are obtained in a significantly smaller computational domain and hence at a much reduced computational cost, thus demonstrating the benefits of the new hybrid approach