A QUADRATIC C degrees INTERIOR PENALTY METHOD FOR LINEAR FOURTH ORDER BOUNDARY VALUE PROBLEMS WITH BOUNDARY CONDITIONS OF THE CAHN-HILLIARD TYPE

We develop a quadratic C degrees interior penalty method for linear fourth order boundary value problems with essential and natural boundary conditions of the Cahn-Hilliard type. Both a priori and a posteriori error estimates are derived. The performance of the method is illustrated by numerical experiments.

Fidelity susceptibility of one-dimensional models with twisted boundary conditions

Recently it has been shown that the fidelity of the ground state of a quantum many-body system can be used todetect its quantum critical points (QCPs). If g denotes the parameter in the Hamiltonian with respect to which the fidelity is computed, we find that for one-dimensional models with large but finite size, the fidelity susceptibility chi(F) can detect a QCP provided that the correlation length exponent satisfies nu < 2. We then show that chi(F) can be used to locate a QCP even if nu >= 2 if we introduce boundary conditions labeled by a twist angle N theta, where N is the system size. If the QCP lies at g = 0, we find that if N is kept constant, chi(F) has a scaling form given by chi(F) similar to theta(-2/nu) f (g/theta(1/nu)) if theta << 2 pi/N. We illustrate this both in a tight-binding model of fermions with a spatially varying chemical potential with amplitude h and period 2q in which nu = q, and in a XY spin-1/2 chain in which nu = 2. Finally we show that when q is very large, the model has two additional QCPs at h = +/- 2 which cannot be detected by studying the energy spectrum but are clearly detected by chi(F). The peak value and width of chi(F) seem to scale as nontrivial powers of q at these QCPs. We argue that these QCPs mark a transition between extended and localized states at the Fermi energy. DOI: 10.1103/PhysRevB.86.245424

Analytical solutions for diffuse fluorescence spectroscopy/imaging in biological tissues. Part I: zero and extrapolated boundary conditions

The mathematical model for diffuse fluorescence spectroscopy/imaging is represented by coupled partial differential equations (PDEs), which describe the excitation and emission light propagation in soft biological tissues. The generic closed-form solutions for these coupled PDEs are derived in this work for the case of regular geometries using the Green's function approach using both zero and extrapolated boundary conditions. The specific solutions along with the typical data types, such as integrated intensity and the mean time of flight, for various regular geometries were also derived for both time-and frequency-domain cases. (C) 2013 Optical Society of America

Soft-spring wall based non-periodic boundary conditions for non-equilibrium molecular dynamics of dense fluids

Non-equilibrium molecular dynamics (MD) simulations require imposition of non-periodic boundary conditions (NPBCs) that seamlessly account for the effect of the truncated bulk region on the simulated MD region. Standard implementation of specular boundary conditions in such simulations results in spurious density and force fluctuations near the domain boundary and is therefore inappropriate for coupled atomistic-continuum calculations. In this work, we present a novel NPBC model that relies on boundary atoms attached to a simple cubic lattice with soft springs to account for interactions from particles which would have been present in an untruncated full domain treatment. We show that the proposed model suppresses the unphysical fluctuations in the density to less than 1% of the mean while simultaneously eliminating spurious oscillations in both mean and boundary forces. The model allows for an effective coupling of atomistic and continuum solvers as demonstrated through multiscale simulation of boundary driven singular flow in a cavity. The geometric flexibility of the model enables straightforward extension to nonplanar complex domains without any adverse effects on dynamic properties such as the diffusion coefficient. (c) 2015 AIP Publishing LLC.

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.

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.

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.

The influence of boundary conditions on tip leakage flow

Most of the current understanding of tip leakage flows has been derived from detailed cascade experiments. However, the cascade model is inherently approximate since it is difficult to simulate the boundary conditions present in a real machine, particularly the secondary flows convecting from the upstream stator row and the relative motion of the casing and blade. This problem is further complicated when considering the high pressure turbine rotors of aero engines, where the high Mach numbers must also be matched in order to correctly model the aerodynamics and heat transfer. More realistic tests can be performed on high-speed turbines, but the experimental fidelity and resolution achievable in such set-ups is limited. In order to examine the differences between cascade models and real-engine behavior, the influence of boundary conditions on the tip leakage flow in an unshrouded high pressure turbine rotor is investigated using RANS calculations. This study examines the influence of the rotor inlet condition and relative casing motion. A baseline calculation with a simplified inlet condition and no relative endwall motion exhibits similar behavior to cascade studies. Only minor changes to the leakage flow are induced by introducing either a more realistic inlet condition or relative casing motion. However when both of these conditions are applied simultaneously the pattern of leakage flow is very different, with ingestion of flow over much of the early suction surface. The paper explores the physical processes driving this change and the impact on leakage losses and modeling requirements. Copyright © 2013 by ASME.