Supersymmetry: Boundary conditions and edge states

When spatial boundaries are inserted, supersymmetry (SUSY) can be broken. We have shown that in an N = 2 supersymmetric theory, all local boundary conditions allowed by self-adjointness of the Hamiltonian break N = 2 SUSY, while only a few of these boundary conditions preserve N = 1 SUSY. We have also shown that for a subset of the boundary conditions compatible with N = 1 SUSY, there exist fermionic ground states which are localized near the boundary. We also show that only very few nonlocal boundary conditions like periodic boundary conditions preserve full N = 2 supersymmetry, but none of them exhibits edge states.

Damage analysis of tetragonal perovskite structure ceramics implicated by asymptotic field solutions and boundary conditions

Cracking of ceramics with tetragonal perovskite grain structure is known to appear at different sites and scale level. The multiscale character of damage depends on the combined effects of electromechanical coupling, prevailing physical parameters and boundary conditions. These detail features are exhibited by application of the energy density criterion with judicious use of the mode I asymptotic and full field solution in the range of r/a = 10(-4) to 10(-2) where r and a are, respectively, the distance to the crack tip and half crack length. Very close to the stationary crack tip, bifurcation is predicted resembling the dislocation emission behavior invoked in the molecular dynamics model. At the macroscopic scale, crack growth is predicted to occur straight ahead with two yield zones to the sides. A multiscale feature of crack tip damage is provided for the first time. Numerical values of the relative distances and bifurcation angles are reported for the PZT-4 ceramic subjected to different electric field to applied stress ratio and boundary conditions that consist of the specification of electric field/mechanical stress, electric displacement/mechanical strain, and mixed conditions. To be emphasized is that the multiscale character of damage in piezoceramics does not appear in general. It occurs only for specific combinations of the external and internal field parameters, elastic/piezoelectric/dielectric constants and specified boundary conditions. (C) 2002 Published by Elsevier Science Ltd.

Assessment of natural resource conditions in and adjacent to Dry Tortugas National Park

This project characterized and assessed the condition of coastal water resources in the Dry Tortugas National Park (DRTO) located in the Florida Keys. The goal of the assessment was to: (1) identify the state of knowledge of natural resources that exist within the DRTO, (2) summarize the state of knowledge about natural and anthropogenic stressors and threats that affected these resources, and (3) describe strategies being implemented by DRTO managers to meet their resource management goals. The park, located in the Straits of Florida 113 km (70 miles) west of Key West, is relatively small (269 square kilometers) with seven small islands and extensive shallow water coral reefs. Significant natural resources within DRTO include coastal and oceanic waters, coral reefs, reef fisheries, seagrass beds, and sea turtle and bird nesting habitats. This report focuses on marine natural resources identified by DRTO resource managers and researchers as being vitally important to the Tortugas region and the wider South Florida ecosystem. Selected marine resources included physical resources (geology, oceanography, and water quality) and biological resources (coral reef and hardbottom benthic assemblages, seagrass and algal communities, reef fishes and macro invertebrates, and wildlife [sea turtles and sea-birds]). In the past few decades, some of these resources have deteriorated because of natural and anthropogenic factors that are local and global in scale. To meet mandated goals (Chapter 1), resource managers need information on: (1) the types and condition of natural and cultural resources that occur within the park and (2) the stressors and threats that can affect those resources. This report synthesizes and summarizes information on: (1) the status of marine natural resources occurring at DRTO; and (2) types of stressors and threats currently affecting those resources at the DRTO. Based on published information, the assessment suggests that marine resources at DRTO and its surrounding region are affected by several stressors, many of which act synergistically. Of the nine resource components assessed, one resource category – water quality – received an ecological condition ranking of "Good"; two components – the nonliving portion of coral reef and hardbottom and reef fishes – received a rating of "Caution"; and two components – the biotic components of coral reef and hardbottom substrates and sea turtles – received a rating of "Significant concern" (Table E-1). Seagrass and algal communities and seabirds were unrated for ecological condition because the available information was inadequate. The stressor category of tropical storms was the dominant and most prevalent stressor in the Tortugas region; it affected all of the resource components assessed in this report. Commercial and recreational fishing were also dominant stressors and affected 78% of the resource components assessed. The most stressed resource was the biotic component of coral reef and hardbottom resources, which was affected by 76% of the stressors. Water quality was the least affected; it was negatively affected by 12% of stressors. The systematic assessment of marine natural resources and stressors in the Tortugas region pointed to several gaps in the information. For example, of the nine marine resource components reviewed in this report, the living component of coral reefs and hardbottom resources had the best rated information with 25% of stressor categories rated "Good" for information richness. In contrast, the there was a paucity of information for seagrass and algal communities and sea birds resource components.

Comparisons of open boundary conditions in a barotropic model of the northern Arabian Sea

These simulations are focused on the sensitivity of the barotropic ocean non-linear model to the various open boundary conditions (OBCs). Different OBCs from gradient to radiation condition are examined to determine the best result and help to choose the most appropriate OBCs. Since the interior points are changing with time both implicit and explicit forms are applied. The simulations showed that the interior flow is sensitive to changes in the OBCs and the results are highly dependent on the bathymetry of the area. When a constant depth (100m) is used, the circulation pattern with all OBCs is same. The best boundary conditions are Orlanski Radiation and its modified form. These boundary conditions produce identical adjustment in velocity and are determined to be satisfactory for both constant depth and actual bathymetry.

Non-reflective boundary conditions for non-uniform mean velocity inlet and outlet flows

The numerical solution of problems in unbounded physical space requires a truncation of the computational domain to a reasonable size. As a result, the conditions on the artificial boundaries are generally unknown. Assumptions like constant pressure or velocities are only valid in the far field and lead to spurious reflections if applied on the boundaries of the truncated domain. A number of attempts have been made over the past decades to design conditions that prevent such reflections. One approach is based on characteristics. The standard analysis assumes a spatially uniform mean flow field but this is often impractical. In the present paper we show how to extend the formulation to the more general case of a non-uniform mean velocity field. A number of test cases are provided and our results compare favourably with other boundary conditions. In principle the present approach can be extended to include non-uniformities in all variables.

Off-wall boundary conditions for turbulent flows obtained from buffer-layer minimal flow units

There is strong evidence that the transport processes in the buffer region of wall-bounded turbulence are common across various flow configurations, even in the embryonic turbulence in transition (Park et al., Phys. Fl. 24). We use this premise to develop off-wall boundary conditions for turbulent simulations. Boundary conditions are constructed from DNS databases using periodic minimal flow units and reduced order modeling. The DNS data was taken from a channel at Reτ=400 and a zero-pressure gradient transitional boundary layer (Sayadi et al., submitted to J. Fluid Mech.). Both types of boundary conditions were first tested on a DNS of the core of the channel flow with the aim of extending their application to LES and to spatially evolving flows.

Direct numerical simulation of turbulent flows over superhydrophobic surfaces with gas pockets using linearized boundary conditions

Superhydrophobic surfaces are shown to be effective for surface drag reduction under laminar regime by both experiments and simulations (see for example, Ou and Rothstein, Phys. Fluids 17:103606, 2005). However, such drag reduction for fully developed turbulent flow maintaining the Cassie-Baxter state remains an open problem due to high shear rates and flow unsteadiness of turbulent boundary layer. Our work aims to develop an understanding of mechanisms leading to interface breaking and loss of gas pockets due to interactions with turbulent boundary layers. We take advantage of direct numerical simulation of turbulence with slip and no-slip patterned boundary conditions mimicking the superhydrophobic surface. In addition, we capture the dynamics of gas-water interface, by deriving a proper linearized boundary condition taking into account the surface tension of the interface and kinematic matching of interface deformation and normal velocity conditions on the wall. We will show results from our simulations predicting the dynamical behavior of gas pocket interfaces over a wide range of dimensionless surface tensions.

Boundary conditions in physical model tests-the influence of deck pinning on the response of piled bridge abutments in laterally spreading soils

Physical models are widely used in the study of geotechnical earthquake engineering phenomena, and the comparison of modelling results to observations from field reconnaissance provides a transparent means of evaluating the design of our physical models. This paper compares centrifuge tests of pile groups in laterally spreading slopes with the response of piled bridge abutments in the 2011 Christchurch earthquake. We show that the model foundation's fixity conditions strongly affect the success with which the mechanism of response of the real abutments is replicated in the tests. © 2012 American Society of Civil Engineers.