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Sample records for actual boundary conditions

  1. Numerical Boundary Condition Procedures

    NASA Technical Reports Server (NTRS)

    1981-01-01

    Topics include numerical procedures for treating inflow and outflow boundaries, steady and unsteady discontinuous surfaces, far field boundaries, and multiblock grids. In addition, the effects of numerical boundary approximations on stability, accuracy, and convergence rate of the numerical solution are discussed.

  2. Boundary Condition for Modeling Semiconductor Nanostructures

    NASA Technical Reports Server (NTRS)

    Lee, Seungwon; Oyafuso, Fabiano; von Allmen, Paul; Klimeck, Gerhard

    2006-01-01

    A recently proposed boundary condition for atomistic computational modeling of semiconductor nanostructures (particularly, quantum dots) is an improved alternative to two prior such boundary conditions. As explained, this boundary condition helps to reduce the amount of computation while maintaining accuracy.

  3. Tidal Boundary Conditions in SEAWAT

    USGS Publications Warehouse

    Mulligan, Ann E.; Langevin, Christian; Post, Vincent E.A.

    2011-01-01

    SEAWAT, a U.S. Geological Survey groundwater flow and transport code, is increasingly used to model the effects of tidal motion on coastal aquifers. Different options are available to simulate tidal boundaries but no guidelines exist nor have comparisons been made to identify the most effective approach. We test seven methods to simulate a sloping beach and a tidal flat. The ocean is represented in one of the three ways: directly using a high hydraulic conductivity (high-K) zone and indirect simulation via specified head boundaries using either the General Head Boundary (GHB) or the new Periodic Boundary Condition (PBC) package. All beach models simulate similar water fluxes across the upland boundary and across the sediment-water interface although the ratio of intertidal to subtidal flow is different at low tide. Simulating a seepage face results in larger intertidal fluxes and influences near-shore heads and salinity. Major differences in flow occur in the tidal flat simulations. Because SEAWAT does not simulate unsaturated flow the water table only rises via flow through the saturated zone. This results in delayed propagation of the rising tidal signal inland. Inundation of the tidal flat is delayed as is flow into the aquifer across the flat. This is severe in the high-K and PBC models but mild in the GHB models. Results indicate that any of the tidal boundary options are fine if the ocean-aquifer interface is steep. However, as the slope of that interface decreases, the high-K and PBC approaches perform poorly and the GHB boundary is preferable.

  4. Mean Flow Boundary Conditions for Computational Aeroacoustics

    NASA Technical Reports Server (NTRS)

    Hixon, R.; Nallasamy, M.; Sawyer, S.; Dyson, R.

    2003-01-01

    In this work, a new type of boundary condition for time-accurate Computational Aeroacoustics solvers is described. This boundary condition is designed to complement the existing nonreflective boundary conditions while ensuring that the correct mean flow conditions are maintained throughout the flow calculation. Results are shown for a loaded 2D cascade, started with various initial conditions.

  5. Absorbing boundary conditions for exterior problems

    NASA Technical Reports Server (NTRS)

    Hariharan, S. I.

    1985-01-01

    Elliptic and hyperbolic problems in unbounded regions are considered. These problems, when one wants to solve them numerically, have the difficulty of prescribing boundary conditions at infinity. Computationally, one needs a finite region in which to solve these problems. The corresponding conditions at infinity imposed on the finite distance boundaries should dictate the boundary condition at infinity and be accurate with respect to the interior numerical scheme. Such boundary conditions are commonly referred to as absorbing boundary conditions. A treatment is given of these boundary conditions for wave-like equations.

  6. Quantum "violation" of Dirichlet boundary condition

    NASA Astrophysics Data System (ADS)

    Park, I. Y.

    2017-02-01

    Dirichlet boundary conditions have been widely used in general relativity. They seem at odds with the holographic property of gravity simply because a boundary configuration can be varying and dynamic instead of dying out as required by the conditions. In this work we report what should be a tension between the Dirichlet boundary conditions and quantum gravitational effects, and show that a quantum-corrected black hole solution of the 1PI action no longer obeys, in the naive manner one may expect, the Dirichlet boundary conditions imposed at the classical level. We attribute the 'violation' of the Dirichlet boundary conditions to a certain mechanism of the information storage on the boundary.

  7. Probability of boundary conditions in quantum cosmology

    NASA Astrophysics Data System (ADS)

    Suenobu, Hiroshi; Nambu, Yasusada

    2017-02-01

    One of the main interest in quantum cosmology is to determine boundary conditions for the wave function of the universe which can predict observational data of our universe. For this purpose, we solve the Wheeler-DeWitt equation for a closed universe with a scalar field numerically and evaluate probabilities for boundary conditions of the wave function of the universe. To impose boundary conditions of the wave function, we use exact solutions of the Wheeler-DeWitt equation with a constant scalar field potential. These exact solutions include wave functions with well known boundary condition proposals, the no-boundary proposal and the tunneling proposal. We specify the exact solutions by introducing two real parameters to discriminate boundary conditions, and obtain the probability for these parameters under the requirement of sufficient e-foldings of the inflation. The probability distribution of boundary conditions prefers the tunneling boundary condition to the no-boundary boundary condition. Furthermore, for large values of a model parameter related to the inflaton mass and the cosmological constant, the probability of boundary conditions selects an unique boundary condition different from the tunneling type.

  8. Towards Arbitrary Accuracy Inviscid Surface Boundary Conditions

    NASA Technical Reports Server (NTRS)

    Dyson, Rodger W.; Hixon, Ray

    2002-01-01

    Inviscid nonlinear surface boundary conditions are currently limited to third order accuracy in time for non-moving surfaces and actually reduce to first order in time when the surfaces move. For steady-state calculations it may be possible to achieve higher accuracy in space, but high accuracy in time is required for efficient simulation of multiscale unsteady phenomena. A surprisingly simple technique is shown here that can be used to correct the normal pressure derivatives of the flow at a surface on a Cartesian grid so that arbitrarily high order time accuracy is achieved in idealized cases. This work demonstrates that nonlinear high order time accuracy at a solid surface is possible and desirable, but it also shows that the current practice of only correcting the pressure is inadequate.

  9. Boundary conditions of methamphetamine craving.

    PubMed

    Lopez, Richard B; Onyemekwu, Chukwudi; Hart, Carl L; Ochsner, Kevin N; Kober, Hedy

    2015-12-01

    Methamphetamine use has increased significantly and become a global health concern. Craving is known to predict methamphetamine use and relapse following abstinence. Some have suggested that cravings are automatic, generalized, and uncontrollable, but experimental work addressing these claims is lacking. In 2 exploratory studies, we tested the boundary conditions of methamphetamine craving by asking: (a) is craving specific to users' preferred route of administration?, and (b) can craving be regulated by cognitive strategies? Two groups of methamphetamine users were recruited. In Study 1, participants were grouped by their preferred route of administration (intranasal vs. smoking), and rated their craving in response to photographs and movies depicting methamphetamine use (via the intranasal vs. smoking route). In Study 2, methamphetamine smokers implemented cognitive regulation strategies while viewing photographs depicting methamphetamine smoking. Strategies involved either focusing on the positive aspects of smoking methamphetamine or the negative consequences of doing so-the latter strategy based on treatment protocols for addiction. In Study 1, we found a significant interaction between group and route of administration, such that participants who preferred to smoke methamphetamine reported significantly stronger craving for smoking stimuli, whereas those who preferred the intranasal route reported stronger craving for intranasal stimuli. In Study 2, participants reported significantly lower craving when focusing on the negative consequences associated with methamphetamine use. Taken together, these findings suggest that strength of craving for methamphetamine is moderated by users' route of administration and can be reduced by cognitive strategies. This has important theoretical, methodological, and clinical implications.

  10. Logarithmic minimal models with Robin boundary conditions

    NASA Astrophysics Data System (ADS)

    Bourgine, Jean-Emile; Pearce, Paul A.; Tartaglia, Elena

    2016-06-01

    We consider general logarithmic minimal models LM≤ft( p,{{p}\\prime}\\right) , with p,{{p}\\prime} coprime, on a strip of N columns with the (r, s) Robin boundary conditions introduced by Pearce, Rasmussen and Tipunin. On the lattice, these models are Yang-Baxter integrable loop models that are described algebraically by the one-boundary Temperley-Lieb algebra. The (r, s) Robin boundary conditions are a class of integrable boundary conditions satisfying the boundary Yang-Baxter equations which allow loop segments to either reflect or terminate on the boundary. The associated conformal boundary conditions are organized into infinitely extended Kac tables labelled by the Kac labels r\\in {Z} and s\\in {N} . The Robin vacuum boundary condition, labelled by ≤ft(r,s-\\frac{1}{2}\\right)=≤ft(0,\\frac{1}{2}\\right) , is given as a linear combination of Neumann and Dirichlet boundary conditions. The general (r, s) Robin boundary conditions are constructed, using fusion, by acting on the Robin vacuum boundary with an (r, s)-type seam consisting of an r-type seam of width w columns and an s-type seam of width d  =  s  -  1 columns. The r-type seam admits an arbitrary boundary field which we fix to the special value ξ =-\\fracλ{2} where λ =\\frac≤ft( {{p}\\prime}-p\\right)π{{{p}\\prime}} is the crossing parameter. The s-type boundary introduces d defects into the bulk. We consider the commuting double-row transfer matrices and their associated quantum Hamiltonians and calculate analytically the boundary free energies of the (r, s) Robin boundary conditions. Using finite-size corrections and sequence extrapolation out to system sizes N+w+d≤slant 26 , the conformal spectrum of boundary operators is accessible by numerical diagonalization of the Hamiltonians. Fixing the parity of N for r\

  11. Comparative study of boundary conditions with helix

    NASA Astrophysics Data System (ADS)

    Pillay, Shamini; Kumar, Deepak; Phua, Y. N.

    2016-11-01

    This paper presents a comparative study of dispersion characteristics of the circular waveguide with helical windings. Our waveguide is doubly unconventional in the choice of reverse boundary condition, in the choice of normal boundary condition and further with the presence of sheath helix between the core and cladding parameters. Two methods of winding the helix between the core and cladding are considered namely from right to left and left to right. Through mathematical analysis using field components and boundary conditions the modal characteristics are derived for both conditions. Normal boundary condition and reverse boundary conditions are used respectively to represent the helical windings. Here the characteristic equation is obtained in the form of Bessel and modified Bessel for both waveguides. Using the modal characteristic equation the dispersion curves are plotted for numerous angles and wavelengths. We find that the method of wrapping the helical material has significant effect on the dispersion properties with regards to the way the modes propagate.

  12. Boundary conditions for unsteady supersonic inlet analyses

    NASA Astrophysics Data System (ADS)

    Mayer, David W.; Paynter, Gerald C.

    1994-06-01

    New bleed and compressor face boundary conditions have been developed to improve the accuracy of unsteady supersonic inlet calculations. The new bleed boundary conditions relate changes in the bleed hole discharge coefficient to changes in the local flow conditions; the local bleed flow rate can more than double as a shock moves forward over a bleed band in response to inlet flow disturbances. The effects of inlet flow disturbances on the flow at the compressor face are represented more realistically with this new boundary condition than with traditional fixed static pressure or mass flow conditions.

  13. On boundary conditions in lattice Boltzmann methods

    SciTech Connect

    Chen, S.; Martinez, D. |; Mei, R.

    1996-09-01

    A lattice Boltzmann boundary condition for simulation of fluid flow using simple extrapolation is proposed. Numerical simulations, including two-dimensional Poiseuille flow, unsteady Couette flow, lid-driven square cavity flow, and flow over a column of cylinders for a range of Reynolds numbers, are carried out, showing that this scheme is of second order accuracy in space discretization. Applications of the method to other boundary conditions, including pressure condition and flux condition are discussed. {copyright} {ital 1996 American Institute of Physics.}

  14. Downstream boundary conditions for viscous flow problems

    NASA Technical Reports Server (NTRS)

    Fix, G.; Gunzburger, M.

    1977-01-01

    The problem of the specification of artificial outflow conditions in flow problems is studied. It is shown that for transport type equations incorrect outflow conditions will adversely affect the solution only in a small region near the outflow boundary, while for elliptic equations, e.g. those governing the streamfunction or pressure, a correct boundary specification is essential. In addition, integral outflow boundary conditions for fluid dynamical problems are considered. It is shown that such conditions are well posed, and their effect on the solutions of the Navier-Stokes equations is also considered.

  15. Boundary Conditions of the Heliosphere

    NASA Technical Reports Server (NTRS)

    Slavin, Jonathan D.; Frisch, Priscilla C .

    2001-01-01

    We present new calculations of the ionization of the Local Interstellar Cloud (LIC) by directly observed sources including nearby stellar extreme ultraviolet (EUV) sources and the diffuse emission of the Soft X-ray Background (SXRB). In addition, we model the important, unobserved EUV emission both from the hot gas responsible for the SXRB and from a possible evaporative boundary between the LIC and the hot gas. We show that these ionization sources can provide the necessary ionization and heating of the cloud to match observations. Including the radiation from the conductive boundary, while not required, does improve the agreement with observations of the temperature of the LIC. The ionization predicted in our models shows good agreement with pickup ion results, interstellar absorption line data towards epsilon CMa, and EUV opacity measurements of nearby white dwarf stars. The areas of disagreement point to a possible underabundance (relative to solar abundance) of neon in the LIC. The presence of dust in the cloud, or at least depleted abundances, is necessary to maintain the heating/cooling balance and reach the observed temperature.

  16. Experimental study on the regenerator under actual operating conditions

    NASA Astrophysics Data System (ADS)

    Nam, Kwanwoo; Jeong, Sangkwon

    2002-05-01

    An experimental apparatus was prepared to investigate thermal and hydrodynamic characteristics of the regenerator under its actual operating conditions. The apparatus included a compressor to pressurize and depressurize regenerator with various operating frequencies. Cold end of the regenerator was maintained around 100 K by means of liquid nitrogen container and heat exchanger. Instantaneous gas temperature and mass flow rate were measured at both ends of the regenerator during the whole pressure cycle. Pulsating pressure and pressure drop across the regenerator were also measured. The operating frequency of the pressure cycle was varied between 3 and 60 Hz, which are typical operating frequencies of Gifford-McMahon, pulse tube, and Stirling cryocoolers. First, friction factor for the wire screen mesh was directly determined from room temperature experiments. When the operating frequency was less than 9 Hz, the oscillating flow friction factor was nearly same as the steady flow friction factor for Reynolds number up to 100. For 60 Hz operations, the ratio of oscillating flow friction factor to steady flow one was increased as hydraulic Reynolds number became high. When the Reynolds number was 100, this ratio was about 1.6. Second, ineffectiveness of the regenerator was obtained when the cold-end was maintained around 100 K and the warm-end at 300 K to simulate the actual operating condition of the regenerator in cryocooler. Effect of the operating frequency on ineffectiveness of regenerator was discussed at low frequency range.

  17. NHWAVE: Consistent boundary conditions and turbulence modeling

    NASA Astrophysics Data System (ADS)

    Derakhti, Morteza; Kirby, James T.; Shi, Fengyan; Ma, Gangfeng

    2016-10-01

    Large-scale σ-coordinate ocean circulation models neglect the horizontal variation of σ in the calculation of stress terms and boundary conditions. Following this practice, the effects of surface and bottom slopes in the dynamic surface and bottom boundary conditions have been usually neglected in the available non-hydrostatic wave-resolving models using a terrain-following grid. In this paper, we derive consistent surface and bottom boundary conditions for the normal and tangential stress fields as well as a Neumann-type boundary condition for scalar fluxes. Further, we examine the role of surface slopes in the predicted near-surface velocity and turbulence fields in surface gravity waves. By comparing the predicted velocity field in a deep-water standing wave in a closed basin, we show that the consistent boundary conditions do not generate unphysical vorticity at the free surface, in contrast to commonly used, simplified stress boundary conditions developed by ignoring all contributions except vertical shear in the transformation of stress terms. In addition, it is shown that the consistent boundary conditions significantly improve predicted wave shape, velocity and turbulence fields in regular surf zone breaking waves, compared with the simplified case. A more extensive model-data comparison of various breaking wave properties in different types of surface breaking waves is presented in companion papers (Derakhti et al., 2016a,b).

  18. Probing temperature chaos through thermal boundary conditions

    NASA Astrophysics Data System (ADS)

    Wang, Wenlong; Machta, Jonathan; Katzgraber, Helmut

    2015-03-01

    Using population annealing Monte Carlo, we numerically study temperature chaos in the three-dimensional Edwards-Anderson Ising spin glass using thermal boundary conditions. In thermal boundary conditions all eight combinations of periodic vs antiperiodic boundary conditions in the three spatial directions appear in the ensemble with their respective Boltzmann weights, thus minimizing finite-size corrections due to domain walls. By studying salient features in the specific heat we show evidence of temperature chaos. Our results suggest that these bumps are mainly caused by system-size excitations where the free energy of two boundary conditions cross. Furthermore, we study the scaling of both entropy and energy at boundary condition crossings and find that the scaling of the energy is very different from the scaling obtained by a simple change of boundary conditions. We attribute this difference to the stronger finite-size effects induced via a simple change of boundary conditions. Finally, we show that temperature chaos occurs more frequently at higher temperatures within the spin-glass phase and for larger system sizes, while the normalized distribution function with respect to temperature is about the same for different system sizes. The work is supported from NSF (Grant No. DMR-1208046).

  19. Stable boundary conditions for Cartesian grid calculations

    NASA Technical Reports Server (NTRS)

    Berger, M. J.; Leveque, R. J.

    1990-01-01

    The inviscid Euler equations in complicated geometries are solved using a Cartesian grid. This requires solid wall boundary conditions in the irregular grid cells near the boundary. Since these cells may be orders of magnitude smaller than the regular grid cells, stability is a primary concern. An approach to this problem is presented and its use is illustrated.

  20. Experiments on initial and boundary conditions

    NASA Technical Reports Server (NTRS)

    Moretti, G.

    1980-01-01

    Effects of three different models for the treatment of subsonic boundary conditions, applied to the problem of flow in a channel with a bump, are discussed. A preliminary discussion of the numerical treatment of the corners is presented.

  1. An outflow boundary condition for aeroacoustic computations

    NASA Technical Reports Server (NTRS)

    Hayder, M. Ehtesham; Hagstrom, Thomas

    1995-01-01

    A formulation of boundary condition for flows with small disturbances is presented. The authors test their methodology in an axisymmetric jet flow calculation, using both the Navier-Stokes and Euler equations. Solutions in the far field are assumed to be oscillatory. If the oscillatory disturbances are small, the growth of the solution variables can be predicted by linear theory. Eigenfunctions of the linear theory are used explicitly in the formulation of the boundary conditions. This guarantees correct solutions at the boundary in the limit where the predictions of linear theory are valid.

  2. On High-Order Radiation Boundary Conditions

    NASA Technical Reports Server (NTRS)

    Hagstrom, Thomas

    1995-01-01

    In this paper we develop the theory of high-order radiation boundary conditions for wave propagation problems. In particular, we study the convergence of sequences of time-local approximate conditions to the exact boundary condition, and subsequently estimate the error in the solutions obtained using these approximations. We show that for finite times the Pade approximants proposed by Engquist and Majda lead to exponential convergence if the solution is smooth, but that good long-time error estimates cannot hold for spatially local conditions. Applications in fluid dynamics are also discussed.

  3. Boundary conditions for the gravitational field

    NASA Astrophysics Data System (ADS)

    Winicour, Jeffrey

    2012-06-01

    A review of the treatment of boundaries in general relativity is presented with the emphasis on application to the formulations of Einstein's equations used in numerical relativity. At present, it is known how to treat boundaries in the harmonic formulation of Einstein's equations and a tetrad formulation of the Einstein-Bianchi system. However, a universal approach valid for other formulations is not in hand. In particular, there is no satisfactory boundary theory for the 3+1 formulations which have been highly successful in binary black hole simulation. I discuss the underlying problems that make the initial-boundary-value problem much more complicated than the Cauchy problem. I review the progress that has been made and the important open questions that remain. Science is a differential equation. Religion is a boundary condition. (Alan Turing, quoted in J D Barrow, ‘Theories of Everything’)

  4. Spatial periodic boundary condition for MODFLOW.

    PubMed

    Laattoe, Tariq; Post, Vincent E A; Werner, Adrian D

    2014-01-01

    Small-scale hyporheic zone (HZ) models often use a spatial periodic boundary (SPB) pair to simulate an infinite repetition of bedforms. SPB's are common features of commercially available multiphysics modeling packages. MODFLOW's lack of this boundary type has precluded it from being effectively utilized in this area of HZ research. We present a method to implement the SPB in MODFLOW by development of the appropriate block-centered finite-difference expressions. The implementation is analogous to MODFLOW's general head boundary package. The difference is that the terms on the right hand side of the solution equations must be updated with each iteration. Consequently, models that implement the SPB converge best with solvers that perform both inner and outer iterations. The correct functioning of the SPB condition in MODFLOW is verified by two examples. This boundary condition allows users to build HZ-bedform models in MODFLOW, facilitating further research using related codes such as MT3DMS and PHT3D.

  5. Velocity boundary conditions at a tokamak resistive wall

    SciTech Connect

    Strauss, H. R.

    2014-03-15

    Velocity boundary conditions appropriate for magnetohydrodynamic simulations have been controversial recently. A comparison of numerical simulations of sideways wall force in disruptions is presented for Dirichlet, Neumann, Robin, and DEBS boundary conditions. It is shown that all the boundary conditions give qualitatively similar results. It is shown that Dirichlet boundary conditions are valid in the small Larmor radius limit of electromagnetic sheath boundary conditions.

  6. Boundary conditions for unsteady supersonic inlet analyses

    NASA Astrophysics Data System (ADS)

    Mayer, David W.; Paynter, Gerald C.

    1994-06-01

    New bleed and compresor face boundary conditions have been developed to improve the accuracy of unsteady supersonic inlet calculations. The new bleed boundary condition relates changes in the bleed hole discharge coefficient to change the local flow conditions; the local bleed flow rate can more than double as a shock moves forward over a bleed band in response to inlet flow disturbances. The stability margin of the inlet is strongly dependent on the throat bleed configuration since the locally rapid increase in bleed flow has a stong effect on the motion of the normal shock. The new compressor face boundary condition accounts for changes in the unsteady flow conditions at the compressor face by specifying the compressor face corrected mass flow or Mach number either as a constant or as a linear function of the stagnation conditions. The effects of inlet flow disturbances on the flow at the compressor face are represented more realistically with this new boundary condition than with traditional fixed static pressure or mass flow conditions. Euler calculations of the dynamic response of an inlet flow to a flow disturbance at the compressor face with 20- and 90-deg throat bleed hole angles are reported. These results indicate that an extra margin of stability for the inlet is obtained with 90-deg bleed holes because the increase in bleed flow rate as the shock moves forward over a bleed is much larger for 90-deg holes than for 20-deg holes.

  7. Establishing seasonal chronicles of actual evapotranspiration under sloping conditions

    NASA Astrophysics Data System (ADS)

    Zitouna Chebbi, R.; Prévot, L.; Jacob, F.; Voltz, M.

    2012-04-01

    Estimation of daily and seasonal actual evapotranspiration (ETa) is strongly needed for hydrological and agricultural purposes. Although the eddy covariance method is well suited for such estimation of land surface fluxes, this method suffers from limitations when establishing long time series. Missing data are often encountered, resulting from bad meteorological conditions, rejection by quality control tests, power failures… Numerous gap fill techniques have been proposed in the literature but there applicability in sloping conditions is not well known. In order to estimate ETa over long periods (agricultural cycle) on crops cultivated in sloping areas, a pluri-annual experiment was conducted in the Kamech catchment, located in North-eastern Tunisia. This Mediterranean site is characterized by a large heterogeneity in topography, soils and crops. Land surface fluxes were measured using eddy covariance systems. Measurements were collected on the two opposite sides of the Kamech V-shaped catchment, within small fields having slopes steeper than 5%. During three different years, four crops were studied: durum wheat, oat, fava bean and pasture. The topography of the catchment and the wind regime induced upslope and downslope flows over the study fields. In this study, we showed that gap filling of the turbulent fluxes (sensible and latent heat) can be obtained through linear regressions against net radiation. To account for the effect of the topography, linear regressions were calibrated by distinguishing upslope and downslope flows. This significantly improved the quality of the reconstructed data over 30 minute intervals. This gap filling technique also improved the energy balance closure at the daily time scale. As a result, seasonal chronicles of daily ETa throughout the growth cycle of the study crops in the Kamech watershed were established, thus providing useful information about the water use of annual crops in a semi-arid rainfed and hilly area.

  8. Scalar boundary conditions in Lifshitz spacetimes

    NASA Astrophysics Data System (ADS)

    Keeler, Cynthia

    2014-01-01

    We investigate the conditions imposable on a scalar field at the boundary of the so-called Lifshitz spacetime which has been proposed as the dual to Lifshitz field theories. For effective mass squared between -( d + z - 1)2 /4 and z 2 - ( d + z - 1)2 /4, we find a one-parameter choice of boundary condition type. The bottom end of this range corresponds to a Breitenlohner-Freedman bound; below it, the Klein-Gordon operator need not be positive, so we cannot make sense of the dynamics. Above the top end of the range, only one boundary condition type is available; here we expect compact initial data will remain compact in the future.

  9. Determining hydrodynamic boundary conditions from equilibrium fluctuations

    NASA Astrophysics Data System (ADS)

    Chen, Shuyu; Wang, Han; Qian, Tiezheng; Sheng, Ping

    2015-10-01

    The lack of a first-principles derivation has made the hydrodynamic boundary condition a classical issue for the past century. The fact that the fluid can have interfacial structures adds additional complications and ambiguities to the problem. Here we report the use of molecular dynamics to identify from equilibrium thermal fluctuations the hydrodynamic modes in a fluid confined by solid walls, thereby extending the application of the fluctuation-dissipation theorem to yield not only the accurate location of the hydrodynamic boundary at the molecular scale, but also the relevant parameter value(s) for the description of the macroscopic boundary condition. We present molecular dynamics results on two examples to illustrate the application of this approach—one on the hydrophilic case and one on the hydrophobic case. It is shown that the use of the orthogonality condition of the modes can uniquely locate the hydrodynamic boundary to be inside the fluid in both cases, separated from the molecular solid-liquid interface by a small distance Δ that is a few molecules in size. The eigenvalue equation of the hydrodynamic modes directly yields the slip length, which is about equal to Δ in the hydrophilic case but is larger than Δ in the hydrophobic case. From the decay time we also obtain the bulk viscosity which is in good agreement with the value obtained from dynamic simulations. To complete the picture, we derive the Green-Kubo relation for a finite fluid system and show that the boundary fluctuations decouple from the bulk only in the infinite-fluid-channel limit; and in that limit we recover the interfacial fluctuation-dissipation theorem first presented by Bocquet and Barrat. The coupling between the bulk and the boundary fluctuations provides both the justification and the reason for the effectiveness of the present approach, which promises broad utility for probing the hydrodynamic boundary conditions relevant to structured or elastic interfaces, as well as

  10. Boundary conditions in tunneling via quantum hydrodynamics

    NASA Technical Reports Server (NTRS)

    Nassar, Antonio B.

    1993-01-01

    Via the hydrodynamical formulation of quantum mechanics, an approach to the problem of tunneling through sharp-edged potential barriers is developed. Above all, it is shown how more general boundary conditions follow from the continuity of mass, momentum, and energy.

  11. Boundary Value Problems With Integral Conditions

    NASA Astrophysics Data System (ADS)

    Karandzhulov, L. I.; Sirakova, N. D.

    2011-12-01

    The weakly perturbed nonlinear boundary value problems (BVP) for almost linear systems of ordinary differential equations (ODE) are considered. We assume that the nonlinear part contain an additional function, which defines the perturbation as singular. Then the Poincare method is not applicable. The problem of existence, uniqueness and construction of a solution of the posed BVP with integral condition is studied.

  12. Boundary Conditions for Unsteady Compressible Flows

    NASA Technical Reports Server (NTRS)

    Hariharan, S. I.; Johnson, D. K.

    1994-01-01

    This paper explores solutions to the spherically symmetric Euler equations. Motivated by the work of Hagstrom and Hariharan and Geer and Pope, we modeled the effect of a pulsating sphere in a compressible medium. The literature available on this suggests that an accurate numerical solution requires artificial boundary conditions which simulate the propagation of nonlinear waves in open domains. Until recently, the boundary conditions available were in general linear and based on nonreflection. Exceptions to this are the nonlinear nonreflective conditions of Thompson, and the nonlinear reflective conditions of Hagstrom and Hariharan. The former are based on the rate of change of the incoming characteristics; the latter rely on asymptotic analysis and the method of characteristics and account for the coupling of incoming and outgoing characteristics. Furthermore, Hagstrom and Hariharan have shown that, in a test situation in which the flow would reach a steady state over a long time, Thompson's method could lead to an incorrect steady state. The current study considers periodic flows and includes all possible types and techniques of boundary conditions. The technique recommended by Hagstrom and Hariharan proved superior to all others considered and matched the results of asymptotic methods that are valid for low subsonic Mach numbers.

  13. Aspects of implementing constant traction boundary conditions in computational homogenization via semi-Dirichlet boundary conditions

    NASA Astrophysics Data System (ADS)

    Javili, A.; Saeb, S.; Steinmann, P.

    2017-01-01

    In the past decades computational homogenization has proven to be a powerful strategy to compute the overall response of continua. Central to computational homogenization is the Hill-Mandel condition. The Hill-Mandel condition is fulfilled via imposing displacement boundary conditions (DBC), periodic boundary conditions (PBC) or traction boundary conditions (TBC) collectively referred to as canonical boundary conditions. While DBC and PBC are widely implemented, TBC remains poorly understood, with a few exceptions. The main issue with TBC is the singularity of the stiffness matrix due to rigid body motions. The objective of this manuscript is to propose a generic strategy to implement TBC in the context of computational homogenization at finite strains. To eliminate rigid body motions, we introduce the concept of semi-Dirichlet boundary conditions. Semi-Dirichlet boundary conditions are non-homogeneous Dirichlet-type constraints that simultaneously satisfy the Neumann-type conditions. A key feature of the proposed methodology is its applicability for both strain-driven as well as stress-driven homogenization. The performance of the proposed scheme is demonstrated via a series of numerical examples.

  14. Symmetry boundary condition in dissipative particle dynamics

    NASA Astrophysics Data System (ADS)

    Pal, Souvik; Lan, Chuanjin; Li, Zhen; Hirleman, E. Daniel; Ma, Yanbao

    2015-07-01

    Dissipative particle dynamics (DPD) is a coarse-grained particle method for modeling mesoscopic hydrodynamics. Most of the DPD simulations are carried out in 3D requiring remarkable computation time. For symmetric systems, this time can be reduced significantly by simulating only one half or one quarter of the systems. However, such simulations are not yet possible due to a lack of schemes to treat symmetric boundaries in DPD. In this study, we propose a numerical scheme for the implementation of the symmetric boundary condition (SBC) in both dissipative particle dynamics (DPD) and multibody dissipative particle dynamics (MDPD) using a combined ghost particles and specular reflection (CGPSR) method. We validate our scheme in four different configurations. The results demonstrate that our scheme can accurately reproduce the system properties, such as velocity, density and meniscus shapes of a full system with numerical simulations of a subsystem. Using a symmetric boundary condition for one half of the system, we demonstrate about 50% computation time saving in both DPD and MDPD. This approach for symmetric boundary treatment can be also applied to other coarse-grained particle methods such as Brownian and Langevin Dynamics to significantly reduce computation time.

  15. Flux boundary conditions in particle simulations.

    PubMed

    Flekkøy, Eirik G; Delgado-Buscalioni, Rafael; Coveney, Peter V

    2005-08-01

    Flux boundary conditions are interesting in a number of contexts ranging from multiscale simulations to simulations of molecular hydrodynamics in nanoscale systems. Here we introduce, analyze, and test a general scheme to impose boundary conditions that simultaneously control the momentum and energy flux into open particle systems The scheme is shown to handle far from equilibrium simulations. It acquires its main characteristics from the requirement that it fulfills the second law of thermodynamics and thus minimizes the entropy production, when it is applied to reversible processes. It is shown both theoretically and through simulations that the scheme emulates the effect of an extended particle system as far as particle number fluctuations, temperature, and density profiles are concerned. The numerical scheme is further shown to be accurate and stable in both equilibrium and far from equilibrium contexts.

  16. Nonperiodic boundary conditions for solvated systems.

    PubMed

    Petraglio, Gabriele; Ceccarelli, Matteo; Parrinello, Michele

    2005-07-22

    The simulation of charged and/or strongly polar solutes represents a challenge for standard molecular-dynamics techniques. The use of periodic boundary conditions (PBCs) leads to artifacts due to the interaction between two replicas in the presence of the long-range Coulomb forces. A way to avoid these problems is the use of nonperiodic boundary conditions. A possible realization is to consider a finite system, a sphere, embedded in a reaction field described by the method of the images. In the present work the modified image approximation has been implemented in a molecular-dynamics code and optimized for the use of two standard solvents, water and acetonitrile. The methodology has then been applied to investigate the conformational changes in water-solvated alanine dipeptide. The free-energy surface calculated with this method is comparable to that obtained with PBC.

  17. Advances in Numerical Boundary Conditions for Computational Aeroacoustics

    NASA Technical Reports Server (NTRS)

    Tam, Christopher K. W.

    1997-01-01

    Advances in Computational Aeroacoustics (CAA) depend critically on the availability of accurate, nondispersive, least dissipative computation algorithm as well as high quality numerical boundary treatments. This paper focuses on the recent developments of numerical boundary conditions. In a typical CAA problem, one often encounters two types of boundaries. Because a finite computation domain is used, there are external boundaries. On the external boundaries, boundary conditions simulating the solution outside the computation domain are to be imposed. Inside the computation domain, there may be internal boundaries. On these internal boundaries, boundary conditions simulating the presence of an object or surface with specific acoustic characteristics are to be applied. Numerical boundary conditions, both external or internal, developed for simple model problems are reviewed and examined. Numerical boundary conditions for real aeroacoustic problems are also discussed through specific examples. The paper concludes with a description of some much needed research in numerical boundary conditions for CAA.

  18. Increasing Accuracy in Computed Inviscid Boundary Conditions

    NASA Technical Reports Server (NTRS)

    Dyson, Roger

    2004-01-01

    A technique has been devised to increase the accuracy of computational simulations of flows of inviscid fluids by increasing the accuracy with which surface boundary conditions are represented. This technique is expected to be especially beneficial for computational aeroacoustics, wherein it enables proper accounting, not only for acoustic waves, but also for vorticity and entropy waves, at surfaces. Heretofore, inviscid nonlinear surface boundary conditions have been limited to third-order accuracy in time for stationary surfaces and to first-order accuracy in time for moving surfaces. For steady-state calculations, it may be possible to achieve higher accuracy in space, but high accuracy in time is needed for efficient simulation of multiscale unsteady flow phenomena. The present technique is the first surface treatment that provides the needed high accuracy through proper accounting of higher-order time derivatives. The present technique is founded on a method known in art as the Hermitian modified solution approximation (MESA) scheme. This is because high time accuracy at a surface depends upon, among other things, correction of the spatial cross-derivatives of flow variables, and many of these cross-derivatives are included explicitly on the computational grid in the MESA scheme. (Alternatively, a related method other than the MESA scheme could be used, as long as the method involves consistent application of the effects of the cross-derivatives.) While the mathematical derivation of the present technique is too lengthy and complex to fit within the space available for this article, the technique itself can be characterized in relatively simple terms: The technique involves correction of surface-normal spatial pressure derivatives at a boundary surface to satisfy the governing equations and the boundary conditions and thereby achieve arbitrarily high orders of time accuracy in special cases. The boundary conditions can now include a potentially infinite number

  19. Some observations on boundary conditions for numerical conservation laws

    NASA Technical Reports Server (NTRS)

    Kamowitz, David

    1988-01-01

    Four choices of outflow boundary conditions are considered for numerical conservation laws. All four methods are stable for linear problems, for which examples are presented where either a boundary layer forms or the numerical scheme, together with the boundary condition, is unstable due to the formation of a reflected shock. A simple heuristic argument is presented for determining the suitability of the boundary condition.

  20. Open Boundary Conditions for Dissipative MHD

    SciTech Connect

    Meier, E T

    2011-11-10

    In modeling magnetic confinement, astrophysics, and plasma propulsion, representing the entire physical domain is often difficult or impossible, and artificial, or 'open' boundaries are appropriate. A novel open boundary condition (BC) for dissipative MHD, called Lacuna-based open BC (LOBC), is presented. LOBC, based on the idea of lacuna-based truncation originally presented by V.S. Ryaben'kii and S.V. Tsynkov, provide truncation with low numerical noise and minimal reflections. For hyperbolic systems, characteristic-based BC (CBC) exist for separating the solution into outgoing and incoming parts. In the hyperbolic-parabolic dissipative MHD system, such separation is not possible, and CBC are numerically unstable. LOBC are applied in dissipative MHD test problems including a translating FRC, and coaxial-electrode plasma acceleration. Solution quality is compared to solutions using CBC and zero-normal derivative BC. LOBC are a promising new open BC option for dissipative MHD.

  1. Boundary conditions and consistency of effective theories

    SciTech Connect

    Polonyi, Janos; Siwek, Alicja

    2010-04-15

    Effective theories are nonlocal at the scale of the eliminated heavy particles modes. The gradient expansion, which represents such nonlocality, must be truncated to have treatable models. This step leads to the proliferation of the degrees of freedom, which renders the identification of the states of the effective theory nontrivial. Furthermore, it generates nondefinite metric in the Fock space, which in turn endangers the unitarity of the effective theory. It is shown that imposing a generalized Kubo-Martin-Schwinger boundary conditions for the new degrees of freedom leads to reflection positivity for a wide class of Euclidean effective theories, thereby these lead to acceptable theories when extended to real-time.

  2. Thermal field theories and shifted boundary conditions

    NASA Astrophysics Data System (ADS)

    Giusti, L.; Meyer, H.

    The analytic continuation to an imaginary velocity of the canonical partition function of a thermal system expressed in a moving frame has a natural implementation in the Euclidean path-integral formulation in terms of shifted boundary conditions. The Poincare' invariance underlying a relativistic theory implies a dependence of the free-energy on the compact length L_0 and the shift xi only through the combination beta=L_0(1+xi^2)^(1/2). This in turn implies that the energy and the momentum distributions of the thermal theory are related, a fact which is encoded in a set of Ward identities among the correlators of the energy-momentum tensor. The latter have interesting applications in lattice field theory: they offer novel ways to compute thermodynamic potentials, and a set of identities to renormalize non-perturbatively the energy-momentum tensor. At fixed bare parameters the shifted boundary conditions also provide a simple method to vary the temperature in much smaller steps than with the standard procedure.

  3. Conformal counterterms and boundary conditions for open strings

    SciTech Connect

    de Beer, W.

    1988-03-15

    It is explained how Neumann boundary conditions still lead to the mixed boundary conditions required to calculate the functional determinants in the Polyakov model. Neumann boundary conditions on the conformal factor are obtained, thereby negating the need for a finite counterterm in the quantum bare action.

  4. Slip boundary conditions over curved surfaces

    NASA Astrophysics Data System (ADS)

    Guo, Lin; Chen, Shiyi; Robbins, Mark O.

    2016-01-01

    Molecular dynamics simulations are used to investigate the influence of surface curvature on the slip boundary condition for a simple fluid. The slip length is measured for flows in planar and cylindrical geometries with a range of wall-fluid interactions. As wall curvature increases, the slip length decreases dramatically for closely packed surfaces and increases for sparse ones. The magnitude of the changes depends on the crystallographic orientation and differs for flow along and perpendicular to the direction of curvature. These different patterns of behavior are related to the curvature-induced variation in the ratio of the spacing between fluid atoms to the spacing between minima in the potential from the solid surface. The results are consistent with a microscopic theory for the viscous friction between fluid and wall that expresses the slip length in terms of the lateral response of the fluid to the wall potential and the characteristic decay time of this response.

  5. Thermal momentum distribution from shifted boundary conditions

    NASA Astrophysics Data System (ADS)

    Giusti, L.

    At finite temperature the distribution of the total momentum is an observable characterizing the thermal state of a field theory, and its cumulants are related to thermodynamic potentials. In a relativistic system at zero chemical potential, for instance, the thermal variance of the total momentum is a direct measure of the entropy. We relate the generating function of the cumulants to the ratio of a path integral with properly shifted boundary conditions in the compact direction over the ordinary partition function. In this form it is well suited for Monte-Carlo evaluation, and the cumulants can be extracted straightforwardly. We test the method in the SU(3) Yang--Mills theory, and obtain the entropy density at three different temperatures.

  6. Characteristic boundary conditions for three-dimensional transonic unsteady aerodynamics

    NASA Technical Reports Server (NTRS)

    Whitlow, W., Jr.

    1984-01-01

    Characteristic far-field boundary conditions for the three-dimensional unsteady transonic small disturbance potential equation have been developed. The boundary conditions were implemented in the XTRAN3S finite difference code and tested for a flat plate rectangular wing with a pulse in angle of attack; the freestream Mach number was 0.85. The calculated force response shows that the characteristic boundary conditions reduce disturbances that are reflected from the computational boundaries.

  7. Time-Domain Impedance Boundary Conditions for Computational Aeroacoustics

    NASA Technical Reports Server (NTRS)

    Tam, Christopher K. W.; Auriault, Laurent

    1996-01-01

    It is an accepted practice in aeroacoustics to characterize the properties of an acoustically treated surface by a quantity known as impedance. Impedance is a complex quantity. As such, it is designed primarily for frequency-domain analysis. Time-domain boundary conditions that are the equivalent of the frequency-domain impedance boundary condition are proposed. Both single frequency and model broadband time-domain impedance boundary conditions are provided. It is shown that the proposed boundary conditions, together with the linearized Euler equations, form well-posed initial boundary value problems. Unlike ill-posed problems, they are free from spurious instabilities that would render time-marching computational solutions impossible.

  8. Dynamic behaviour of thin composite plates for different boundary conditions

    SciTech Connect

    Sprintu, Iuliana E-mail: rotaruconstantin@yahoo.com; Rotaru, Constantin E-mail: rotaruconstantin@yahoo.com

    2014-12-10

    In the context of composite materials technology, which is increasingly present in industry, this article covers a topic of great interest and theoretical and practical importance. Given the complex design of fiber-reinforced materials and their heterogeneous nature, mathematical modeling of the mechanical response under different external stresses is very difficult to address in the absence of simplifying assumptions. In most structural applications, composite structures can be idealized as beams, plates, or shells. The analysis is reduced from a three-dimensional elasticity problem to a oneor two-dimensional problem, based on certain simplifying assumptions that can be made because the structure is thin. This paper aims to validate a mathematical model illustrating how thin rectangular orthotropic plates respond to the actual load. Thus, from the theory of thin plates, new analytical solutions are proposed corresponding to orthotropic rectangular plates having different boundary conditions. The proposed analytical solutions are considered both for solving equation orthotropic rectangular plates and for modal analysis.

  9. Absorbing boundary conditions for second-order hyperbolic equations

    NASA Technical Reports Server (NTRS)

    Jiang, Hong; Wong, Yau Shu

    1989-01-01

    A uniform approach to construct absorbing artificial boundary conditions for second-order linear hyperbolic equations is proposed. The nonlocal boundary condition is given by a pseudodifferential operator that annihilates travelling waves. It is obtained through the dispersion relation of the differential equation by requiring that the initial-boundary value problem admits the wave solutions travelling in one direction only. Local approximation of this global boundary condition yields an nth-order differential operator. It is shown that the best approximations must be in the canonical forms which can be factorized into first-order operators. These boundary conditions are perfectly absorbing for wave packets propagating at certain group velocities. A hierarchy of absorbing boundary conditions is derived for transonic small perturbation equations of unsteady flows. These examples illustrate that the absorbing boundary conditions are easy to derive, and the effectiveness is demonstrated by the numerical experiments.

  10. Boundary Behavior of Viscous Fluids: Influence of Wall Roughness and Friction-driven Boundary Conditions

    NASA Astrophysics Data System (ADS)

    Bucur, Dorin; Feireisl, Eduard; Nečasová, Šárka

    2010-07-01

    We consider a family of solutions to the evolutionary Navier-Stokes system supplemented with the complete slip boundary conditions on domains with rough boundaries. We give a complete description of the asymptotic limit by means of Γ-convergence arguments, and identify a general class of boundary conditions.

  11. Measuring the entropy from shifted boundary conditions

    NASA Astrophysics Data System (ADS)

    Giusti, L.; Pepe, M.

    We explore a new computational strategy for determining the equation of state of the SU(3) Yang-Mills theory. By imposing shifted boundary conditions, the entropy density is computed from the vacuum expectation value of the off-diagonal components T_{0k} of the energy-momentum tensor. A step-scaling function is introduced to span a wide range in temperature values. We present preliminary numerical results for the entropy density and its step-scaling function obtained at eight temperature values in the range T_c - 15 T_c. At each temperature, discretization effects are removed by simulating the theory at several lattice spacings and by extrapolating the results to the continuum limit. Finite-size effects are always kept below the statistical errors. The absence of ultraviolet power divergences and the remarkably small discretization effects allow for a precise determination of the step-scaling function in the explored temperature range. These findings establish this strategy as a viable solution for an accurate determination of the equation of state in a wide range of temperature values.

  12. Analysis of Boundary Conditions for Crystal Defect Atomistic Simulations

    NASA Astrophysics Data System (ADS)

    Ehrlacher, V.; Ortner, C.; Shapeev, A. V.

    2016-12-01

    Numerical simulations of crystal defects are necessarily restricted to finite computational domains, supplying artificial boundary conditions that emulate the effect of embedding the defect in an effectively infinite crystalline environment. This work develops a rigorous framework within which the accuracy of different types of boundary conditions can be precisely assessed. We formulate the equilibration of crystal defects as variational problems in a discrete energy space and establish qualitatively sharp regularity estimates for minimisers. Using this foundation we then present rigorous error estimates for (i) a truncation method (Dirichlet boundary conditions), (ii) periodic boundary conditions, (iii) boundary conditions from linear elasticity, and (iv) boundary conditions from nonlinear elasticity. Numerical results confirm the sharpness of the analysis.

  13. Homogenized boundary conditions and resonance effects in Faraday cages

    PubMed Central

    Hewitt, I. J.

    2016-01-01

    We present a mathematical study of two-dimensional electrostatic and electromagnetic shielding by a cage of conducting wires (the so-called ‘Faraday cage effect’). Taking the limit as the number of wires in the cage tends to infinity, we use the asymptotic method of multiple scales to derive continuum models for the shielding, involving homogenized boundary conditions on an effective cage boundary. We show how the resulting models depend on key cage parameters such as the size and shape of the wires, and, in the electromagnetic case, on the frequency and polarization of the incident field. In the electromagnetic case, there are resonance effects, whereby at frequencies close to the natural frequencies of the equivalent solid shell, the presence of the cage actually amplifies the incident field, rather than shielding it. By appropriately modifying the continuum model, we calculate the modified resonant frequencies, and their associated peak amplitudes. We discuss applications to radiation containment in microwave ovens and acoustic scattering by perforated shells. PMID:27279775

  14. Homogenized boundary conditions and resonance effects in Faraday cages.

    PubMed

    Hewett, D P; Hewitt, I J

    2016-05-01

    We present a mathematical study of two-dimensional electrostatic and electromagnetic shielding by a cage of conducting wires (the so-called 'Faraday cage effect'). Taking the limit as the number of wires in the cage tends to infinity, we use the asymptotic method of multiple scales to derive continuum models for the shielding, involving homogenized boundary conditions on an effective cage boundary. We show how the resulting models depend on key cage parameters such as the size and shape of the wires, and, in the electromagnetic case, on the frequency and polarization of the incident field. In the electromagnetic case, there are resonance effects, whereby at frequencies close to the natural frequencies of the equivalent solid shell, the presence of the cage actually amplifies the incident field, rather than shielding it. By appropriately modifying the continuum model, we calculate the modified resonant frequencies, and their associated peak amplitudes. We discuss applications to radiation containment in microwave ovens and acoustic scattering by perforated shells.

  15. Homogenized boundary conditions and resonance effects in Faraday cages

    NASA Astrophysics Data System (ADS)

    Hewett, D. P.; Hewitt, I. J.

    2016-05-01

    We present a mathematical study of two-dimensional electrostatic and electromagnetic shielding by a cage of conducting wires (the so-called `Faraday cage effect'). Taking the limit as the number of wires in the cage tends to infinity, we use the asymptotic method of multiple scales to derive continuum models for the shielding, involving homogenized boundary conditions on an effective cage boundary. We show how the resulting models depend on key cage parameters such as the size and shape of the wires, and, in the electromagnetic case, on the frequency and polarization of the incident field. In the electromagnetic case, there are resonance effects, whereby at frequencies close to the natural frequencies of the equivalent solid shell, the presence of the cage actually amplifies the incident field, rather than shielding it. By appropriately modifying the continuum model, we calculate the modified resonant frequencies, and their associated peak amplitudes. We discuss applications to radiation containment in microwave ovens and acoustic scattering by perforated shells.

  16. Divergence Boundary Conditions for Vector Helmholtz Equations with Divergence Constraints

    NASA Technical Reports Server (NTRS)

    Kangro, Urve; Nicolaides, Roy

    1997-01-01

    The idea of replacing a divergence constraint by a divergence boundary condition is investigated. The connections between the formulations are considered in detail. It is shown that the most common methods of using divergence boundary conditions do not always work properly. Necessary and sufficient conditions for the equivalence of the formulations are given.

  17. Incorporation of a circular boundary condition into the program POISSON

    SciTech Connect

    Caspi, S.; Helm, M.; Laslett, L.J.

    1984-03-02

    Two-dimensional problems in electrostatics or magnetostatics frequently are solved numerically by means of relaxation techniques. In many such problems the ''sources'' (charges or currents, and regions of permeable material) lie exclusively within a finite closed boundary curve and the relaxation process in principle then could be confined to the region interior to such a boundary - provided a suitable boundary condition is imposed onto the solution at that boundary. The present notes discuss and illustrate the use of a boundary condition of such a nature as to imply the absence of external sources, in order thereby to avoid the inaccuracies and more extensive meshes present when alternatively a simple Dirichlet or Neumann boundary condition is specified on a somewhat more remote outer boundary.

  18. Boundary stability under nonequilibrium conditions. Final report

    SciTech Connect

    Hackney, S.A.; Lee, J.K.; Plichta, M.R.

    1999-08-01

    Summaries of research accomplished are given for the following areas: Morphological (Diffusional) Stability; A New Algorithm for Numerical Modeling of Non-equilibrium Materials Behavior; A Unified Treatment of Single and Microcrystalline Film Edge Instabilities; and Validation of the Structure Based Grain Boundary Diffusion/Migration Model.

  19. Implementation of nonreflecting boundary conditions for the nonlinear Euler equations

    NASA Astrophysics Data System (ADS)

    Atassi, Oliver V.; Galán, José M.

    2008-01-01

    Computationally efficient nonreflecting boundary conditions are derived for the Euler equations with acoustic, entropic and vortical inflow disturbances. The formulation linearizes the Euler equations near the inlet/outlet boundaries and expands the solution in terms of Fourier-Bessel modes. This leads to an 'exact' nonreflecting boundary condition, local in space but nonlocal in time, for each Fourier-Bessel mode of the perturbation pressure. The perturbation velocity and density are then calculated using acoustic, entropic and vortical mode splitting. Extension of the boundary conditions to nonuniform swirling flows is presented for the narrow annulus limit which is relevant to many aeroacoustic problems. The boundary conditions are implemented for the nonlinear Euler equations which are solved in space using the finite volume approximation and integrated in time using a MacCormack scheme. Two test problems are carried out: propagation of acoustic waves in an annular duct and the scattering of a vortical wave by a cascade. Comparison between the present exact conditions and commonly used approximate local boundary conditions is made. Results show that, unlike the local boundary conditions whose accuracy depends on the group velocity of the scattered waves, the present conditions give accurate solutions for a range of problems that have a wide array of group velocities. Results also show that this approach leads to a significant savings in computational time and memory by obviating the need to store the pressure field and calculate the nonlocal convolution integral at each point in the inlet and exit boundaries.

  20. Effects of initial and boundary conditions on thermal explosion development

    NASA Astrophysics Data System (ADS)

    Novozhilov, Vasily

    2017-01-01

    The paper investigates effects of non-uniform initial conditions, as well as oscillatory boundary conditions on critical conditions for thermal explosion. It is shown that natural convection plays significant role in case of initial non-uniformities in the temperature distribution. The role of convection is quantified considering critical Frank-Kamenetskii parameters at different Rayleigh numbers, relative to the same parameter at no-convection conditions. Preliminary results are presented for the effect of oscillatory boundary conditions. It is demonstrated that the system may develop thermal explosion if oscillations are imposed at the boundaries of otherwise thermally stable medium.

  1. Teachers' Perceptions of Their Working Conditions: How Predictive of Planned and Actual Teacher Movement?

    ERIC Educational Resources Information Center

    Ladd, Helen F.

    2011-01-01

    This quantitative study examines the relationship between teachers' perceptions of their working conditions and their intended and actual departures from schools. Based on rich administrative data for North Carolina combined with a 2006 statewide survey administered to all teachers in the state, the study documents that working conditions are…

  2. Chaos in spin glasses revealed through thermal boundary conditions

    NASA Astrophysics Data System (ADS)

    Wang, Wenlong; Machta, Jonathan; Katzgraber, Helmut G.

    2015-09-01

    We study the fragility of spin glasses to small temperature perturbations numerically using population annealing Monte Carlo. We apply thermal boundary conditions to a three-dimensional Edwards-Anderson Ising spin glass. In thermal boundary conditions all eight combinations of periodic versus antiperiodic boundary conditions in the three spatial directions are present, each appearing in the ensemble with its respective statistical weight determined by its free energy. We show that temperature chaos is revealed in the statistics of crossings in the free energy for different boundary conditions. By studying the energy difference between boundary conditions at free-energy crossings, we determine the domain-wall fractal dimension. Similarly, by studying the number of crossings, we determine the chaos exponent. Our results also show that computational hardness in spin glasses and the presence of chaos are closely related.

  3. Finite difference time domain implementation of surface impedance boundary conditions

    NASA Technical Reports Server (NTRS)

    Beggs, John H.; Luebbers, Raymond J.; Yee, Kane S.; Kunz, Karl S.

    1991-01-01

    Surface impedance boundary conditions are employed to reduce the solution volume during the analysis of scattering from lossy dielectric objects. In a finite difference solution, they also can be utilized to avoid using small cells, made necessary by shorter wavelengths in conducting media throughout the solution volume. The standard approach is to approximate the surface impedance over a very small bandwidth by its value at the center frequency, and then use that result in the boundary condition. Two implementations of the surface impedance boundary condition are presented. One implementation is a constant surface impedance boundary condition and the other is a dispersive surface impedance boundary condition that is applicable over a very large frequency bandwidth and over a large range of conductivities. Frequency domain results are presented in one dimension for two conductivity values and are compared with exact results. Scattering width results from an infinite square cylinder are presented as a 2-D demonstration. Extensions to 3-D should be straightforward.

  4. Finite difference time domain implementation of surface impedance boundary conditions

    NASA Technical Reports Server (NTRS)

    Beggs, John H.; Luebbers, Raymond J.; Yee, Kane S.; Kunz, Karl S.

    1991-01-01

    Surface impedance boundary conditions are employed to reduce the solution volume during the analysis of scattering from lossy dielectric objects. In the finite difference solution, they also can be utilized to avoid using small cells, made necessary by shorter wavelengths in conducting media throughout the solution volume. The standard approach is to approximate the surface impedance over a very small bandwidth by its value at the center frequency, and then use that result in the boundary condition. Here, two implementations of the surface impedance boundary condition are presented. One implementation is a constant surface impedance boundary condition and the other is a dispersive surface impedance boundary condition that is applicable over a very large frequency bandwidth and over a large range of conductivities. Frequency domain results are presented in one dimension for two conductivity values and are compared with exact results. Scattering width results from an infinite square cylinder are presented as a two dimensional demonstration. Extensions to three dimensions should be straightforward.

  5. Boundary conditions for direct simulations of compressible viscous flows

    NASA Technical Reports Server (NTRS)

    Poinsot, T. J.; Lele, S. K.

    1992-01-01

    The present consideration of procedures for the definition of boundary conditions for the Navier-Stokes equations emphasizes the derivation of boundary conditions that are compatible with nondissipative algorithms applicable to direct simulations of turbulent flows. A novel formulation for the Euler equations is derived on the basis of characteristic wave relations through boundaries; this formulation is generalized to the Navier-Stokes equations. The method, which applies to both sub- and supersonic flows, is used in reflecting and nonreflecting boundary-condition treatments. Attention is given to practical implementations involving inlet and outlet boundaries and slip and nonslip walls, as well as the test cases of a ducted shear layer, vortices propagating through boundaries, and Poiseuille flow.

  6. A non-local computational boundary condition for duct acoustics

    NASA Technical Reports Server (NTRS)

    Zorumski, William E.; Watson, Willie R.; Hodge, Steve L.

    1994-01-01

    A non-local boundary condition is formulated for acoustic waves in ducts without flow. The ducts are two dimensional with constant area, but with variable impedance wall lining. Extension of the formulation to three dimensional and variable area ducts is straightforward in principle, but requires significantly more computation. The boundary condition simulates a nonreflecting wave field in an infinite duct. It is implemented by a constant matrix operator which is applied at the boundary of the computational domain. An efficient computational solution scheme is developed which allows calculations for high frequencies and long duct lengths. This computational solution utilizes the boundary condition to limit the computational space while preserving the radiation boundary condition. The boundary condition is tested for several sources. It is demonstrated that the boundary condition can be applied close to the sound sources, rendering the computational domain small. Computational solutions with the new non-local boundary condition are shown to be consistent with the known solutions for nonreflecting wavefields in an infinite uniform duct.

  7. Boundary condition effects on maximum groundwater withdrawal in coastal aquifers.

    PubMed

    Lu, Chunhui; Chen, Yiming; Luo, Jian

    2012-01-01

    Prevention of sea water intrusion in coastal aquifers subject to groundwater withdrawal requires optimization of well pumping rates to maximize the water supply while avoiding sea water intrusion. Boundary conditions and the aquifer domain size have significant influences on simulating flow and concentration fields and estimating maximum pumping rates. In this study, an analytical solution is derived based on the potential-flow theory for evaluating maximum groundwater pumping rates in a domain with a constant hydraulic head landward boundary. An empirical correction factor, which was introduced by Pool and Carrera (2011) to account for mixing in the case with a constant recharge rate boundary condition, is found also applicable for the case with a constant hydraulic head boundary condition, and therefore greatly improves the usefulness of the sharp-interface analytical solution. Comparing with the solution for a constant recharge rate boundary, we find that a constant hydraulic head boundary often yields larger estimations of the maximum pumping rate and when the domain size is five times greater than the distance between the well and the coastline, the effect of setting different landward boundary conditions becomes insignificant with a relative difference between two solutions less than 2.5%. These findings can serve as a preliminary guidance for conducting numerical simulations and designing tank-scale laboratory experiments for studying groundwater withdrawal problems in coastal aquifers with minimized boundary condition effects.

  8. Hydrodynamic boundary conditions and dynamic forces between bubbles and surfaces.

    PubMed

    Manor, Ofer; Vakarelski, Ivan U; Tang, Xiaosong; O'Shea, Sean J; Stevens, Geoffrey W; Grieser, Franz; Dagastine, Raymond R; Chan, Derek Y C

    2008-07-11

    Dynamic forces between a 50 microm radius bubble driven towards and from a mica plate using an atomic force microscope in electrolyte and in surfactant exhibit different hydrodynamic boundary conditions at the bubble surface. In added surfactant, the forces are consistent with the no-slip boundary condition at the mica and bubble surfaces. With no surfactant, a new boundary condition that accounts for the transport of trace surface impurities explains variations of dynamic forces at different speeds and provides a direct connection between dynamic forces and surface transport effects at the air-water interface.

  9. Hydrodynamic Boundary Conditions and Dynamic Forces between Bubbles and Surfaces

    NASA Astrophysics Data System (ADS)

    Manor, Ofer; Vakarelski, Ivan U.; Tang, Xiaosong; O'Shea, Sean J.; Stevens, Geoffrey W.; Grieser, Franz; Dagastine, Raymond R.; Chan, Derek Y. C.

    2008-07-01

    Dynamic forces between a 50μm radius bubble driven towards and from a mica plate using an atomic force microscope in electrolyte and in surfactant exhibit different hydrodynamic boundary conditions at the bubble surface. In added surfactant, the forces are consistent with the no-slip boundary condition at the mica and bubble surfaces. With no surfactant, a new boundary condition that accounts for the transport of trace surface impurities explains variations of dynamic forces at different speeds and provides a direct connection between dynamic forces and surface transport effects at the air-water interface.

  10. Electrodynamic boundary conditions for planar arrays of thin magnetic elements

    SciTech Connect

    Lisenkov, Ivan; Tyberkevych, Vasyl; Slavin, Andrei; Nikitov, Sergei

    2015-08-24

    Approximate electrodynamic boundary conditions are derived for an array of dipolarly coupled magnetic elements. It is assumed that the elements' thickness is small compared to the wavelength of an electromagnetic wave in a free space. The boundary conditions relate electric and magnetic fields existing at the top and bottom sides of the array through the averaged uniform dynamic magnetization of the array. This dynamic magnetization is determined by the collective dynamic eigen-excitations (spin wave modes) of the array and is found using the external magnetic susceptibility tensor. The problem of oblique scattering of a plane electromagnetic wave on the array is considered to illustrate the use of the derived boundary conditions.

  11. What do we actually mean by 'sociotechnical'? On values, boundaries and the problems of language.

    PubMed

    Klein, Lisl

    2014-03-01

    The term 'sociotechnical' was first coined in the context of industrial democracy. In comparing two projects on shipping in Esso to help define the concept, the essential categories were found to be where systems boundaries were set, and what factors were considered to be relevant 'human' characteristics. This is often discussed in terms of values. During the nineteen-sixties and seventies sociotechnical theory related to the shop-floor work system, and contingency theory to the organisation as a whole, the two levels being distinct. With the coming of information technology, this distinction became blurred; the term 'socio-structural' is proposed to describe the whole system. IT sometimes is the operating technology, it sometimes supports the operating technology, or it may sometimes be mistaken for the operating technology. This is discussed with reference to recent air accidents.

  12. New statistical boundary conditions for argon-tungsten interactions.

    PubMed

    Ozhgibesov, M S; Leu, T S; Cheng, C H; Utkin, A V

    2012-09-01

    In this study, scattering processes of argon beam impinging on tungsten surface are investigated numerically by applying molecular dynamics (MD) simulations. Energy transfer, momentum change, and scattering processes of argon gas atoms from W(110) surface are discussed. A new model of argon-tungsten (Ar-W) interaction is proposed. Based on the new proposed model, one can simplify the boundary conditions of this problem. The new boundary conditions are proved to be in line with previous experimental and theoretical results. This paper demonstrates how to proceed normalization and further conversion of the MD simulation results into boundary conditions. Application of the new proposed boundary conditions for Ar-W interactions provides a significant speedup of computations.

  13. Two Baryons with Twisted Boundary Conditions

    SciTech Connect

    Briceno, Raul; Davoudi, Zohreh; Luu, Thomas; Savage, Martin

    2014-04-01

    The quantization condition for two particle systems with arbitrary number of two-body open coupled-channels, spin and masses in a finite cubic volume is presented. The condition presented is in agreement with all previous studies of two-body systems in a finite volume. The result is fully relativistic and holds for all momenta below inelastic thresholds and is exact up to exponential volume corrections that are governed by m{sub {pi}} L, where m{sub {pi}} is the pion mass and L is the spatial extent of my box. Its implication for the studies of coupled-channel baryon-baryon systems is discussed, and the necessary tools for implementing the formalism are review.

  14. Effect of boundary conditions on thermal plume growth

    NASA Astrophysics Data System (ADS)

    Kondrashov, A.; Sboev, I.; Rybkin, K.

    2016-07-01

    We have investigated the influence of boundary conditions on the growth rate of convective plumes. Temperature and rate fields were studied in a rectangular convective cell heated by a spot heater. The results of the full-scale test were compared with the numerical data calculated using the ANSYS CFX software package. The relationship between the heat plume growth rate and heat boundary conditions, the width and height of the cell, size of heater for different kinds of liquid was established.

  15. Boundary conditions for direct computation of aerodynamic sound generation

    NASA Technical Reports Server (NTRS)

    Colonius, Tim; Lele, Sanjiva K.; Moin, Parviz

    1992-01-01

    A numerical scheme suitable for the computation of both the near field acoustic sources and the far field sound produced by turbulent free shear flows utilizing the Navier-Stokes equations is presented. To produce stable numerical schemes in the presence of shear, damping terms must be added to the boundary conditions. The numerical technique and boundary conditions are found to give stable results for computations of spatially evolving mixing layers.

  16. Optimal control problem for impulsive systems with integral boundary conditions

    NASA Astrophysics Data System (ADS)

    Ashyralyev, Allaberen; Sharifov, Y. A.

    2012-08-01

    In the present work the optimal control problem is considered, when the state of the system is described by the impulsive differential equations with integral boundary conditions. Applying the Banach contraction principle the existence and uniqueness of solution is proved for the corresponding boundary problem by the fixed admissible control. The first and second variation of the functional is calculated. Various necessary conditions of optimality of the first and second order are obtained by the help of the variation of the controls.

  17. Coleman-Gurtin type equations with dynamic boundary conditions

    NASA Astrophysics Data System (ADS)

    Gal, Ciprian G.; Shomberg, Joseph L.

    2015-02-01

    We present a new formulation and generalization of the classical theory of heat conduction with or without fading memory. As a special case, we investigate the well-posedness of systems which consist of Coleman-Gurtin type equations subject to dynamic boundary conditions, also with memory. Nonlinear terms are defined on the interior of the domain and on the boundary and subject to either classical dissipation assumptions, or to a nonlinear balance condition in the sense of Gal (2012). Additionally, we do not assume that the interior and the boundary share the same memory kernel.

  18. Time-domain boundary conditions for outdoor ground surfaces

    NASA Astrophysics Data System (ADS)

    Collier, Sandra L.; Ostashev, Vladimir E.; Wilson, D. Keith; Marlin, David H.

    2003-10-01

    Finite-difference time-domain techniques are promising for detailed dynamic simulations of sound propagation in complex atmospheric environments. Success of such simulations requires the development of new techniques to accurately handle the reflective and absorptive properties of a porous ground. One method of treating the ground boundary condition in the time domain [Salomons et al., Acta Acust. 88, 483-492 (2002)] is to use modified fluid dynamic equations, where the ground is considered as a porous medium described by its physical properties. However, this approach significantly increases computation time, as the domain must be extended into the ground and a large number of grid points are needed. Standard impedance models for the ground boundary condition are frequency-domain models, which generally are non-causal [Y. H. Berthelot, J. Acoust. Soc. Am. 109, 1736-1739 (2001)]. The development of a time-domain boundary condition from these models requires removing the singularity from the impedance equation when transforming from the frequency domain to the time domain. Alternatively, as the impedance boundary condition is a flux equation, a time-domain boundary condition can be derived from first principles, using the physical properties of the ground. We report on our development of a time-domain ground boundary condition.

  19. A novel periodic boundary condition for computational hemodynamics studies.

    PubMed

    Bahramian, Fereshteh; Mohammadi, Hadi

    2014-07-01

    In computational fluid dynamics models for hemodynamics applications, boundary conditions remain one of the major issues in obtaining accurate fluid flow predictions. For major cardiovascular models, the realistic boundary conditions are not available. In order to address this issue, the whole computational domain needs to be modeled, which is practically impossible. For simulating fully developed turbulent flows using the large eddy simulation and dynamic numerical solution methods, which are very popular in hemodynamics studies, periodic boundary conditions are suitable. This is mainly because the computational domain can be reduced considerably. In this study, a novel periodic boundary condition is proposed, which is based on mass flow condition. The proposed boundary condition is applied on a square duct for the sake of validation. The mass-based condition was shown to obtain the solution in 15% less time. As such, the mass-based condition has two decisive advantages: first, the solution for a given Reynolds number can be obtained in a single simulation because of the direct specification of the mass flow, and second, simulations can be made more quickly.

  20. Scattering through a straight quantum waveguide with combined boundary conditions

    SciTech Connect

    Briet, Ph. Soccorsi, E.; Dittrich, J.

    2014-11-15

    Scattering through a straight two-dimensional quantum waveguide R×(0,d) with Dirichlet boundary conditions on (R{sub −}{sup *}×(y=0))∪(R{sub +}{sup *}×(y=d)) and Neumann boundary condition on (R{sub −}{sup *}×(y=d))∪(R{sub +}{sup *}×(y=0)) is considered using stationary scattering theory. The existence of a matching conditions solution at x = 0 is proved. The use of stationary scattering theory is justified showing its relation to the wave packets motion. As an illustration, the matching conditions are also solved numerically and the transition probabilities are shown.

  1. Boundary Condition Error for Parametric Updating of In-Operation SYSTEMS—APPLICATION to Piping Systems

    NASA Astrophysics Data System (ADS)

    FRIKHA, S.; GAUDIN, M.; COFFIGNAL, G.

    2001-03-01

    There is an increasing interest in experimental analysis of in-operation structures where a part of the boundary conditions is poorly known. This concerns particularly the case of coupled systems where some complex physical phenomena make the behaviour of both the system and its connectivity dependent on the functioning conditions. In this context, this paper presents a new frequency approach for parametric structural updating in the vibration and acoustic fields. This methodology is developed here in the case of piping systems. It follows the boundary conditions identification method previously developed by the authors. A boundary conditions error is presented and its efficiency to translate structural parameters error is shown. Thus, the proposed approach allows performing the identification of some unknown boundary conditions and, simultaneously, updating the model of the tested structure. The pertinence of a frequency choice criteria based on the smallest singular value of the solved system during the identification of the boundary conditions is shown. It specifically allows avoiding the bands of critical frequencies. The developed updating technique is tested with two actual cases: a laboratory test case and an industrial example.

  2. Asymptotic boundary conditions for dissipative waves: General theory

    NASA Technical Reports Server (NTRS)

    Hagstrom, Thomas

    1990-01-01

    An outstanding issue in the computational analysis of time dependent problems is the imposition of appropriate radiation boundary conditions at artificial boundaries. Accurate conditions are developed which are based on the asymptotic analysis of wave propagation over long ranges. Employing the method of steepest descents, dominant wave groups are identified and simple approximations to the dispersion relation are considered in order to derive local boundary operators. The existence of a small number of dominant wave groups may be expected for systems with dissipation. Estimates of the error as a function of domain size are derived under general hypotheses, leading to convergence results. Some practical aspects of the numerical construction of the asymptotic boundary operators are also discussed.

  3. Vibration of thermally stressed plates with various boundary conditions.

    NASA Technical Reports Server (NTRS)

    Bailey, C. D.

    1973-01-01

    By discarding Lurie's (1952) assumption of mode identity, it is shown that linear theory correctly predicts the frequency of all modes of a thermally stressed cantilever plate as well as the frequency and modes of plates with other boundary conditions. The thermal stress distribution is obtained for whatever temperature distribution and boundary conditions that may be specified. Experimental results are compared to calculated results for several different plates. Boundary conditions for the plates range from a plate with edges completely clamped to a plate with edges completely free with various other combinations of mixed and uniform edge conditions. Comparison of calculated data to experimental data shows that accurate, quantitative results can be obtained from linear theory for 'as cut' real plates for a significant range of heating when the assumption of mode identity is discarded.

  4. Exponential dichotomy for hyperbolic systems with periodic boundary conditions

    NASA Astrophysics Data System (ADS)

    Klyuchnyk, R.; Kmit, I.; Recke, L.

    2017-02-01

    We investigate evolution families generated by general linear first-order hyperbolic systems in one space dimension with periodic boundary conditions. We state explicit conditions on the coefficient functions that are sufficient for the existence of exponential dichotomies on R in the space of continuous periodic functions.

  5. Repulsive Casimir effect from extra dimensions and Robin boundary conditions: From branes to pistons

    SciTech Connect

    Elizalde, E.; Odintsov, S. D.; Saharian, A. A.

    2009-03-15

    We evaluate the Casimir energy and force for a massive scalar field with general curvature coupling parameter, subject to Robin boundary conditions on two codimension-one parallel plates, located on a (D+1)-dimensional background spacetime with an arbitrary internal space. The most general case of different Robin coefficients on the two separate plates is considered. With independence of the geometry of the internal space, the Casimir forces are seen to be attractive for special cases of Dirichlet or Neumann boundary conditions on both plates and repulsive for Dirichlet boundary conditions on one plate and Neumann boundary conditions on the other. For Robin boundary conditions, the Casimir forces can be either attractive or repulsive, depending on the Robin coefficients and the separation between the plates, what is actually remarkable and useful. Indeed, we demonstrate the existence of an equilibrium point for the interplate distance, which is stabilized due to the Casimir force, and show that stability is enhanced by the presence of the extra dimensions. Applications of these properties in braneworld models are discussed. Finally, the corresponding results are generalized to the geometry of a piston of arbitrary cross section.

  6. Boundary conditions for electropositive and electronegative radio-frequency sheaths

    NASA Astrophysics Data System (ADS)

    Sobolewski, Mark

    2016-09-01

    Plasma sheaths play a dominant role in determining ion bombardment energies. To optimize plasma processes, sheaths must be understood and carefully controlled, which requires predictive models. One very efficient approach is to only model the sheath, excluding the bulk plasma. This approach, however, requires boundary conditions at the plasma/sheath boundary. Models that use the step approximation for electron density require initial ion velocities. More exact models with Boltzmann electrons (and, for electronegative discharges, negative ions) require the electron temperature (and the temperature and relative density of negative ions). It is often assumed that these boundary conditions have negligible effects on ion energies, but, for certain conditions in radio-frequency sheaths, this is not true. Analytic models as well as numerical simulations show that, at low frequencies (<= 1 MHz) and high bias voltages, the amplitude of the low-energy peak in ion energy distributions (IEDs) at the electrode is very sensitive to the boundary conditions. By measuring IEDs and sheath voltage waveforms, we obtain the most appropriate values of the boundary conditions for electropositive (Ar) as well as electronegative (CF4) discharges and insight into their presheath dynamics.

  7. Kac boundary conditions of the logarithmic minimal models

    NASA Astrophysics Data System (ADS)

    Pearce, Paul A.; Tartaglia, Elena; Couvreur, Romain

    2015-01-01

    We develop further the implementation and analysis of Kac boundary conditions in the general logarithmic minimal models { {LM}}(p,p\\prime) with 1 ⩽ p < p‧ and p, p‧ coprime. Specifically, working in a strip geometry, we consider the (r, s) Kac boundary conditions. These boundary conditions are organized into infinitely extended Kac tables labeled by the Kac labels r, s = 1, 2, 3, …. They are conjugate to Virasoro Kac representations with conformal dimensions Δr, s given by the usual Kac formula. On a finite strip of width N, built from a square lattice, the associated integrable boundary conditions are constructed by acting on the vacuum (1, 1) boundary with an s-type seam of width s - 1 columns and an r-type seam of width ρ - 1 columns. The r-type seam contains an arbitrary boundary field ξ. While the usual fusion construction of the r-type seam relies on the existence of Wenzl-Jones projectors restricting its application to r ⩽ ρ < p‧, this limitation was recently removed by Pearce et al who further conjectured that the conformal boundary conditions labeled by r are realized, in particular, for ρ=ρ(r)=\\lfloor \\frac{rp\\prime}{p}\\rfloor . In this paper, we confirm this conjecture by performing extensive numerics on the commuting double row transfer matrices and their associated quantum Hamiltonian chains. Letting [x] denote the fractional part, we fix the boundary field to the specialized values ξ=\\fracπ{2} if [\\fracρ{p\\prime}]=0 and ξ=[\\fracρ p}{p\\prime}]\\frac{π{2} otherwise. For these boundary conditions, we obtain the Kac conformal weights Δr, s by numerically extrapolating the finite-size corrections to the lowest eigenvalue of the quantum Hamiltonians out to sizes N ⩽ 32 - ρ - s. Additionally, by solving local inversion relations, we obtain general analytic expressions for the boundary free energies allowing for more accurate estimates of the conformal data. This paper is dedicated to Jean-Bernard Zuber on the occassion

  8. Modeling sea-water intrusion with open boundary conditions

    SciTech Connect

    Padilla, F.; Cruz-Sanjulian, J.

    1997-07-01

    The present study concerns the application of a new numerical approach to describe the fresh-water/sea-water relationships in coastal aquifers. Essentially, a solution to the partial differential equation governing the regional motion of a phreatic surface and the resulting interface between fresh water and salt water is analyzed by a Galerkin finite-element formulation. A single-phase steady numerical model was applied to approximate, with simple triangular elements, the regional behavior of a coastal aquifer under appropriate sinks, sources, Neumann, outflow face, and open boundary conditions. On the one hand, outflow open boundaries at the coastline were not treated with other classical boundary conditions, but instead with a formal numerical approach for open boundaries inspired in this particular case by the Dupuit approximation of horizontal outflow at the boundary. The solution to this numerical model, together with the Ghyben-Herzberg principle, allows the correct simulation of fresh-water heads and the position of the salt-water interface for a steeply sloping coast. Although the solutions were precise and do not present classical numerical oscillations, this approach requires a previous solution with Dirichlet boundary conditions at the coastline in order to find a good convergence of the solution algorithm. On the other hand, the same precise results were obtained with a more restrictive open boundary condition, similar in a way to the outflow face approach, which required less computer time, did not need a prior numerical solution and could be extended to different coastline conditions. The steady-state problem was solved for different hypothetical coastal aquifers and fresh-water usage through three types of numerical tests.

  9. Transport synthetic acceleration with opposing reflecting boundary conditions

    SciTech Connect

    Zika, M.R.; Adams, M.L.

    2000-02-01

    The transport synthetic acceleration (TSA) scheme is extended to problems with opposing reflecting boundary conditions. This synthetic method employs a simplified transport operator as its low-order approximation. A procedure is developed that allows the use of the conjugate gradient (CG) method to solve the resulting low-order system of equations. Several well-known transport iteration algorithms are cast in a linear algebraic form to show their equivalence to standard iterative techniques. Source iteration in the presence of opposing reflecting boundary conditions is shown to be equivalent to a (poorly) preconditioned stationary Richardson iteration, with the preconditioner defined by the method of iterating on the incident fluxes on the reflecting boundaries. The TSA method (and any synthetic method) amounts to a further preconditioning of the Richardson iteration. The presence of opposing reflecting boundary conditions requires special consideration when developing a procedure to realize the CG method for the proposed system of equations. The CG iteration may be applied only to symmetric positive definite matrices; this condition requires the algebraic elimination of the boundary angular corrections from the low-order equations. As a consequence of this elimination, evaluating the action of the resulting matrix on an arbitrary vector involves two transport sweeps and a transmission iteration. Results of applying the acceleration scheme to a simple test problem are presented.

  10. Boundary conditions on internal three-body wave functions

    SciTech Connect

    Mitchell, Kevin A.; Littlejohn, Robert G.

    1999-10-01

    For a three-body system, a quantum wave function {Psi}{sub m}{sup {ell}} with definite {ell} and m quantum numbers may be expressed in terms of an internal wave function {chi}{sub k}{sup {ell}} which is a function of three internal coordinates. This article provides necessary and sufficient constraints on {chi}{sub k}{sup {ell}} to ensure that the external wave function {Psi}{sub k}{sup {ell}} is analytic. These constraints effectively amount to boundary conditions on {chi}{sub k}{sup {ell}} and its derivatives at the boundary of the internal space. Such conditions find similarities in the (planar) two-body problem where the wave function (to lowest order) has the form r{sup |m|} at the origin. We expect the boundary conditions to prove useful for constructing singularity free three-body basis sets for the case of nonvanishing angular momentum.

  11. Hydrodynamic and thermal slip flow boundary layers over a flat plate with constant heat flux boundary condition

    NASA Astrophysics Data System (ADS)

    Aziz, Abdul

    2010-03-01

    In this paper the boundary layer flow over a flat plat with slip flow and constant heat flux surface condition is studied. Because the plate surface temperature varies along the x direction, the momentum and energy equations are coupled due to the presence of the temperature gradient along the plate surface. This coupling, which is due to the presence of the thermal jump term in Maxwell slip condition, renders the momentum and energy equations non-similar. As a preliminary study, this paper ignores this coupling due to thermal jump condition so that the self-similar nature of the equations is preserved. Even this fundamental problem for the case of a constant heat flux boundary condition has remained unexplored in the literature. It was therefore chosen for study in this paper. For the hydrodynamic boundary layer, velocity and shear stress distributions are presented for a range of values of the parameter characterizing the slip flow. This slip parameter is a function of the local Reynolds number, the local Knudsen number, and the tangential momentum accommodation coefficient representing the fraction of the molecules reflected diffusively at the surface. As the slip parameter increases, the slip velocity increases and the wall shear stress decreases. These results confirm the conclusions reached in other recent studies. The energy equation is solved to determine the temperature distribution in the thermal boundary layer for a range of values for both the slip parameter as well as the fluid Prandtl number. The increase in Prandtl number and/or the slip parameter reduces the dimensionless surface temperature. The actual surface temperature at any location of x is a function of the local Knudsen number, the local Reynolds number, the momentum accommodation coefficient, Prandtl number, other flow properties, and the applied heat flux.

  12. Effect of kinetic boundary condition on the thermal transpiration coefficient

    NASA Astrophysics Data System (ADS)

    Sugimoto, Hiroshi; Amakawa, Kenjiro

    2014-12-01

    The effect of kinetic boundary condition on the free molecular thermal transpiration coefficient γ is analyzed numerically. The Maxwell model boundary condition is applied in its original form in the sense that its accommodation coefficient depends on the speed of incident molecules. The results show that the value of γ depends much on the velocity dependency of the accommodation coefficient. The experimental result, γ < 0.5, can be reproduced if the grazing molecules reflect diffusely. This makes a sharp contrast with the previous works that γ =0.5 for the velocity independent accommodation coefficient.

  13. Thermodynamically admissible boundary conditions for the regularized 13 moment equations

    SciTech Connect

    Rana, Anirudh Singh; Struchtrup, Henning

    2016-02-15

    A phenomenological approach to the boundary conditions for linearized R13 equations is derived using the second law of thermodynamics. The phenomenological coefficients appearing in the boundary conditions are calculated by comparing the slip, jump, and thermal creep coefficients with linearized Boltzmann solutions for Maxwell’s accommodation model for different values of the accommodation coefficient. For this, the linearized R13 equations are solved for viscous slip, thermal creep, and temperature jump problems and the results are compared to the solutions of the linearized Boltzmann equation. The influence of different collision models (hard-sphere, Bhatnagar–Gross–Krook, and Maxwell molecules) and accommodation coefficients on the phenomenological coefficients is studied.

  14. Boundary conditions in a meshless staggered particle code

    SciTech Connect

    Libersky, L.D.; Randles, P.W.

    1998-07-01

    A meshless method utilizing two sets of particles and generalized boundary conditions is introduced. Companion sets of particles, one carrying velocity and the other carrying stress, are employed to reduce the undesirable effects of colocation of all field variables and increase accuracy. Boundary conditions implemented within this staggered framework include contact, stress-free, stress, velocity, and symmetry constraints. Several test problems are used to evaluate the method. Of particular importance is the motion of stress particles relative to velocity particles in higher dimensions. Early results show promise, but difficulties remain that must be overcome if the staggered technique is to be successful.

  15. Poroelastic modeling of seismic boundary conditions across afracture

    SciTech Connect

    Schoenberg, M.A.; Nakagawa, S.

    2006-06-29

    A fracture within a porous background is modeled as a thin porous layer with increased compliance and finite permeability. For small layer thickness, a set of boundary conditions can be derived that relate particle velocity and stress across a fracture, induced by incident poroelastic waves. These boundary conditions are given via phenomenological parameters that can be used to examine and characterize the seismic response of a fracture. One of these parameters, here it is called membrane permeability, is shown through several examples to control the scattering amplitude of the slow P waves for very low-permeability fractures, which in turn controls the intrinsic attenuation of the waves.

  16. Maxwell boundary condition and velocity dependent accommodation coefficient

    SciTech Connect

    Struchtrup, Henning

    2013-11-15

    A modification of Maxwell's boundary condition for the Boltzmann equation is developed that allows to incorporate velocity dependent accommodation coefficients into the microscopic description. As a first example, it is suggested to consider the wall-particle interaction as a thermally activated process with three parameters. A simplified averaging procedure leads to jump and slip boundary conditions for hydrodynamics. Coefficients for velocity slip, temperature jump, and thermal transpiration flow are identified and compared with those resulting from the original Maxwell model and the Cercignani-Lampis model. An extension of the model leads to temperature dependent slip and jump coefficients.

  17. Effective boundary condition at a rough surface starting from a slip condition

    NASA Astrophysics Data System (ADS)

    Dalibard, Anne-Laure; Gérard-Varet, David

    We consider the homogenization of the Navier-Stokes equation, set in a channel with a rough boundary, of small amplitude and wavelength ɛ. It was shown recently that, for any non-degenerate roughness pattern, and for any reasonable condition imposed at the rough boundary, the homogenized boundary condition in the limit ɛ=0 is always no-slip. We give in this paper error estimates for this homogenized no-slip condition, and provide a more accurate effective boundary condition, of Navier type. Our result extends those obtained in Basson and Gérard-Varet (2008) [6] and Gerard-Varet and Masmoudi (2010) [13], in which the special case of a Dirichlet condition at the rough boundary was examined.

  18. Boundary condition optimal control problem in lava flow modelling

    NASA Astrophysics Data System (ADS)

    Ismail-Zadeh, Alik; Korotkii, Alexander; Tsepelev, Igor; Kovtunov, Dmitry; Melnik, Oleg

    2016-04-01

    We study a problem of steady-state fluid flow with known thermal conditions (e.g., measured temperature and the heat flux at the surface of lava flow) at one segment of the model boundary and unknown conditions at its another segment. This problem belongs to a class of boundary condition optimal control problems and can be solved by data assimilation from one boundary to another using direct and adjoint models. We derive analytically the adjoint model and test the cost function and its gradient, which minimize the misfit between the known thermal condition and its model counterpart. Using optimization algorithms, we iterate between the direct and adjoint problems and determine the missing boundary condition as well as thermal and dynamic characteristics of the fluid flow. The efficiency of optimization algorithms - Polak-Ribiere conjugate gradient and the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithms - have been tested with the aim to get a rapid convergence to the solution of this inverse ill-posed problem. Numerical results show that temperature and velocity can be determined with a high accuracy in the case of smooth input data. A noise imposed on the input data results in a less accurate solution, but still acceptable below some noise level.

  19. The Ablowitz-Ladik system with linearizable boundary conditions

    NASA Astrophysics Data System (ADS)

    Biondini, Gino; Bui, Anh

    2015-09-01

    The boundary value problem (BVP) for the Ablowitz-Ladik (AL) system on the natural numbers with linearizable boundary conditions is studied. In particular: (i) a discrete analogue is derived of the Bäcklund transformation that was used to solved similar BVPs for the nonlinear Schrödinger equation; (ii) an explicit proof is given that the Bäcklund-transformed solution of AL remains within the class of solutions that can be studied by the inverse scattering transform; (iii) an explicit linearizing transformation for the Bäcklund transformation is provided; (iv) explicit relations are obtained among the norming constants associated with symmetric eigenvalues; (v) conditions for the existence of self-symmetric eigenvalues are obtained. The results are illustrated by several exact soliton solutions, which describe the soliton reflection at the boundary with or without the presence of self-symmetric eigenvalues. This article is dedicated to Mark Ablowitz on the occasion of his seventieth birthday.

  20. Boundary conditions for the Boltzmann equation for rough walls

    NASA Astrophysics Data System (ADS)

    Brull, Stéphane; Charrier, Pierre

    2014-12-01

    In some applications, rarefied gases have to considered in a domain whose boundary presents some nanoscale roughness. That is why, we have considered (Brull,2014) a new derivation of boundary conditions for the Boltzmann equation, where the wall present some nanoscale roughness. In this paper, the interaction between the gas and the wall is represented by a kinetic equation defined in a surface layer at the scale of the nanometer close to the wall. The boundary conditions are obtained from a formal asymptotic expansion and are describded by a scattering kernel satisfying classical properties (non-negativeness, normalization, reciprocity). Finally, we present some numerical simulations of scattering diagrams showing the importance of the consideration of roughness for small scales in the model.

  1. A Robust Absorbing Boundary Condition for Compressible Flows

    NASA Technical Reports Server (NTRS)

    Loh, Ching Y.; orgenson, Philip C. E.

    2005-01-01

    An absorbing non-reflecting boundary condition (NRBC) for practical computations in fluid dynamics and aeroacoustics is presented with theoretical proof. This paper is a continuation and improvement of a previous paper by the author. The absorbing NRBC technique is based on a first principle of non reflecting, which contains the essential physics that a plane wave solution of the Euler equations remains intact across the boundary. The technique is theoretically shown to work for a large class of finite volume approaches. When combined with the hyperbolic conservation laws, the NRBC is simple, robust and truly multi-dimensional; no additional implementation is needed except the prescribed physical boundary conditions. Several numerical examples in multi-dimensional spaces using two different finite volume schemes are illustrated to demonstrate its robustness in practical computations. Limitations and remedies of the technique are also discussed.

  2. Multicomponent Gas Diffusion and an Appropriate Momentum Boundary Condition

    NASA Technical Reports Server (NTRS)

    Noever, David A.

    1994-01-01

    Multicomponent gas diffusion is reviewed with particular emphasis on gas flows near solid boundaries-the so-called Kramers-Kistemaker effect. The aim is to derive an appropriate momentum boundary condition which governs many gaseous species diffusing together. The many species' generalization of the traditional single gas condition, either as slip or stick (no-slip), is not obvious, particularly for technologically important cases of lower gas pressures and very dissimilar molecular weight gases. No convincing theoretical case exists for why two gases should interact with solid boundaries equally but in opposite flow directions, such that the total gas flow exactly vanishes. ln this way, the multicomponent no-slip boundary requires careful treatment The approaches discussed here generally adopt a microscopic model for gas-solid contact. The method has the advantage that the mathematics remain tractable and hence experimentally testable. Two new proposals are put forward, the first building in some molecular collision physics, the second drawing on a detailed view of surface diffusion which does not unphysically extrapolate bulk gas properties to govern the adsorbed molecules. The outcome is a better accounting of previously anomalous experiments. Models predict novel slip conditions appearing even for the case of equal molecular weight components. These approaches become particularly significant in view of a conceptual contradiction found to arise in previous derivations of the appropriate boundary conditions. The analogous case of three gases, one of which is uniformly distributed and hence non-diffusing, presents a further refinement which gives unexpected flow reversals near solid boundaries. This case is investigated alone and for aggregating gas species near their condensation point. In addition to predicting new physics, this investigation carries practical implications for controlling vapor diffusion in the growth of crystals used in medical diagnosis (e

  3. Yang - Mills - Higgs equations with nonhomogeneous boundary conditions

    NASA Astrophysics Data System (ADS)

    Tafel, Jacek

    1997-01-01

    The Yang - Mills - Higgs equations in a spatially bounded subset of the Minkowski space are studied under the assumption of a temporal gauge. It is shown that the Cauchy problem for these equations is uniquely solvable (locally in time) if nonhomogeneous boundary conditions of the metallic type are imposed.

  4. Investigation of Boundary Conditions for Flexible Multibody Spacecraft Dynamics

    NASA Technical Reports Server (NTRS)

    MacLean, John R.; Huynh, An; Quiocho, Leslie J.

    2007-01-01

    In support of both the Space Shuttle and International Space Station programs, a set of generic multibody dynamics algorithms integrated within the Trick simulation environment have addressed the variety of on-orbit manipulator simulation requirements for engineering analysis, procedures development and crew familiarization/training at the NASA Johnson Space Center (JSC). Enhancements to these dynamics algorithms are now being driven by a new set of Constellation program requirements for flexible multibody spacecraft simulation. One particular issue that has been discussed within the NASA community is the assumption of cantilever-type flexible body boundary conditions. This assumption has been commonly utilized within manipulator multibody dynamics formulations as it simplifies the computation of relative motion for articulated flexible topologies. Moreover, its use for modeling of space-based manipulators such as the Shuttle Remote Manipulator System (SRMS) and Space Station Remote Manipulator System (SSRMS) has been extensively validated against flight data. For more general flexible spacecraft applications, however, the assumption of cantilever-type boundary conditions may not be sufficient. This paper describes the boundary condition assumptions that were used in the original formulation, demonstrates that this formulation can be augmented to accommodate systems in which the assumption of cantilever boundary conditions no longer applies, and verifies the approach through comparison with an independent model previously validated against experimental hardware test data from a spacecraft flexible dynamics emulator.

  5. Calculation of Multistage Turbomachinery Using Steady Characteristic Boundary Conditions

    NASA Technical Reports Server (NTRS)

    Chima, Rodrick V.

    1998-01-01

    A multiblock Navier-Stokes analysis code for turbomachinery has been modified to allow analysis of multistage turbomachines. A steady averaging-plane approach was used to pass information between blade rows. Characteristic boundary conditions written in terms of perturbations about the mean flow from the neighboring blade row were used to allow close spacing between the blade rows without forcing the flow to be axisymmetric. In this report the multiblock code is described briefly and the characteristic boundary conditions and the averaging-plane implementation are described in detail. Two approaches for averaging the flow properties are also described. A two-dimensional turbine stator case was used to compare the characteristic boundary conditions with standard axisymmetric boundary conditions. Differences were apparent but small in this low-speed case. The two-stage fuel turbine used on the space shuttle main engines was then analyzed using a three-dimensional averaging-plane approach. Computed surface pressure distributions on the stator blades and endwalls and computed distributions of blade surface heat transfer coefficient on three blades showed very good agreement with experimental data from two tests.

  6. Unconstrained periodic boundary conditions for solid state elasticity

    NASA Astrophysics Data System (ADS)

    Linna, R. P.; Åström, J. A.; Timonen, J.

    2004-03-01

    We introduce a method to implement dynamics on an elastic lattice without imposing constraints via boundary or loading conditions. Using this method we are able to examine fracture processes in two-dimensional systems previously inaccessible for reliable computer simulations. We show the validity of the method by benchmarking and report a few preliminary results.

  7. Poroelastic modeling of seismic boundary conditions across a fracture.

    PubMed

    Nakagawa, Seiji; Schoenberg, Michael A

    2007-08-01

    Permeability of a fracture can affect how the fracture interacts with seismic waves. To examine this effect, a simple mathematical model that describes the poroelastic nature of wave-fracture interaction is useful. In this paper, a set of boundary conditions is presented which relate wave-induced particle velocity (or displacement) and stress including fluid pressure across a compliant, fluid-bearing fracture. These conditions are derived by modeling a fracture as a thin porous layer with increased compliance and finite permeability. Assuming a small layer thickness, the boundary conditions can be derived by integrating the governing equations of poroelastic wave propagation. A finite jump in the stress and velocity across a fracture is expressed as a function of the stress and velocity at the boundaries. Further simplification for a thin fracture yields a set of characteristic parameters that control the seismic response of single fractures with a wide range of mechanical and hydraulic properties. These boundary conditions have potential applications in simplifying numerical models such as finite-difference and finite-element methods to compute seismic wave scattering off nonplanar (e.g., curved and intersecting) fractures.

  8. On boundary conditions in the Lattice-Boltzmann method

    NASA Astrophysics Data System (ADS)

    Tessarotto, Massimo; Sarmah, Deep

    2004-11-01

    A critical issue in computational fluid dynamics is the treatment of boundary conditions adopted in particle-simulation methods based on discrete Lattice-Boltzmann (LB) kinetic descriptions. In fact, although progress has been in the past made regarding the mathematical treatment of boundary conditions in LB approaches [see for example 1,2 and references therein], the problem cannot be considered fully solved from the physical standpoint for several different reasons. In particular, the action of surface forces or local volume forces ( localized interactions), may be significant not only in the case of free boundaries, but also for fixed or moving boundaries characterized by prescribed velocity. Purpose of this work is to propose a novel LB approach which embodies not only the possible effect of localized interactions but also assures the correct fulfillment of fluid equations on fixed or moving boundaries. References 1 - R.Mei, W.Shyy, L.Luo, J.Comput.Phys.161(2), 680 (2000). 2 - X.Zhang, J.W.Crawford, A.G.Bengough, Y.M.Young, Ad. Wat. Res. 25, 601 (2002).

  9. Sheath Physics and Boundary Conditions for Edge Plasmas

    SciTech Connect

    Cohen, R H; Ryutov, D D

    2003-09-03

    The boundary conditions of mass, momentum, energy, and charge appropriate for fluid formulations of edge plasmas are surveyed. We re-visit the classic problem of 1-dimensional flow, and note that the ''Bohm sheath criterion'' is requirement of connectivity of the interior plasma with the external world, not the result of termination of the plasma by a wall. We show that the nature of the interior plasma solution is intrinsically different for ion sources that inject above and below the electron sound speed. We survey the appropriate conditions to apply, and resultant fluxes, for a magnetic field obliquely incident on a wall, including the presence of drifts and radial transport. We discuss the consequences of toroidal asymmetries in wall properties, as well as experimental tests of such effects. Finally, we discuss boundary-condition modifications in the case of rapidly varying plasma conditions.

  10. Smoothed Particle Hydrodynamics Continuous Boundary Force method for Navier-Stokes equations subject to Robin boundary condition

    SciTech Connect

    Pan, Wenxiao; Bao, Jie; Tartakovsky, Alexandre M.

    2014-02-15

    Robin boundary condition for the Navier-Stokes equations is used to model slip conditions at the fluid-solid boundaries. A novel Continuous Boundary Force (CBF) method is proposed for solving the Navier-Stokes equations subject to Robin boundary condition. In the CBF method, the Robin boundary condition at boundary is replaced by the homogeneous Neumann boundary condition at the boundary and a volumetric force term added to the momentum conservation equation. Smoothed Particle Hydrodynamics (SPH) method is used to solve the resulting Navier-Stokes equations. We present solutions for two-dimensional and three-dimensional flows in domains bounded by flat and curved boundaries subject to various forms of the Robin boundary condition. The numerical accuracy and convergence are examined through comparison of the SPH-CBF results with the solutions of finite difference or finite element method. Taken the no-slip boundary condition as a special case of slip boundary condition, we demonstrate that the SPH-CBF method describes accurately both no-slip and slip conditions.

  11. On the Huygens absorbing boundary conditions for electromagnetics

    SciTech Connect

    Berenger, Jean-Pierre

    2007-09-10

    A new absorbing boundary condition (ABC) is presented for the solution of Maxwell equations in unbounded spaces. Called the Huygens ABC, this condition is a generalization of two previously published ABCs, namely the multiple absorbing surfaces (MAS) and the re-radiating boundary condition (rRBC). The properties of the Huygens ABC are derived theoretically in continuous spaces and in the finite-difference (FDTD) discretized space. A solution is proposed to render the Huygens ABC effective for the absorption of evanescent waves. Numerical experiments with the FDTD method show that the effectiveness of the Huygens ABC is close to that of the PML ABC in some realistic problems of numerical electromagnetics. It is also shown in the paper that a combination of the Huygens ABC with the PML ABC is very well suited to the solution of some particular problems.

  12. Time-domain implementation of an impedance boundary condition with boundary layer correction

    NASA Astrophysics Data System (ADS)

    Brambley, E. J.; Gabard, G.

    2016-09-01

    A time-domain boundary condition is derived that accounts for the acoustic impedance of a thin boundary layer over an impedance boundary, based on the asymptotic frequency-domain boundary condition of Brambley (2011) [25]. A finite-difference reference implementation of this condition is presented and carefully validated against both an analytic solution and a discrete dispersion analysis for a simple test case. The discrete dispersion analysis enables the distinction between real physical instabilities and artificial numerical instabilities. The cause of the latter is suggested to be a combination of the real physical instabilities present and the aliasing and artificial zero group velocity of finite-difference schemes. It is suggested that these are general properties of any numerical discretization of an unstable system. Existing numerical filters are found to be inadequate to remove these artificial instabilities as they have a too wide pass band. The properties of numerical filters required to address this issue are discussed and a number of selective filters are presented that may prove useful in general. These filters are capable of removing only the artificial numerical instabilities, allowing the reference implementation to correctly reproduce the stability properties of the analytic solution.

  13. Matched interface and boundary (MIB) for the implementation of boundary conditions in high-order central finite differences

    PubMed Central

    Zhao, Shan; Wei, G. W.

    2010-01-01

    SUMMARY High-order central finite difference schemes encounter great difficulties in implementing complex boundary conditions. This paper introduces the matched interface and boundary (MIB) method as a novel boundary scheme to treat various general boundary conditions in arbitrarily high-order central finite difference schemes. To attain arbitrarily high order, the MIB method accurately extends the solution beyond the boundary by repeatedly enforcing only the original set of boundary conditions. The proposed approach is extensively validated via boundary value problems, initial-boundary value problems, eigenvalue problems, and high-order differential equations. Successful implementations are given to not only Dirichlet, Neumann, and Robin boundary conditions, but also more general ones, such as multiple boundary conditions in high-order differential equations and time-dependent boundary conditions in evolution equations. Detailed stability analysis of the MIB method is carried out. The MIB method is shown to be able to deliver high-order accuracy, while maintaining the same or similar stability conditions of the standard high-order central difference approximations. The application of the proposed MIB method to the boundary treatment of other non-standard high-order methods is also considered. PMID:20485574

  14. Bond chaos in spin glasses revealed through thermal boundary conditions

    NASA Astrophysics Data System (ADS)

    Wang, Wenlong; Machta, Jonathan; Katzgraber, Helmut G.

    2016-06-01

    Spin glasses have competing interactions that lead to a rough energy landscape which is highly susceptible to small perturbations. These chaotic effects strongly affect numerical simulations and, as such, gaining a deeper understanding of chaos in spin glasses is of much importance. The use of thermal boundary conditions is an effective approach to study chaotic phenomena. Here we generalize population annealing Monte Carlo, combined with thermal boundary conditions, to study bond chaos due to small perturbations in the spin-spin couplings of the three-dimensional Edwards-Anderson Ising spin glass. We show that bond and temperature-induced chaos share the same scaling exponents and that bond chaos is stronger than temperature chaos.

  15. Revisiting Johnson and Jackson boundary conditions for granular flows

    SciTech Connect

    Li, Tingwen; Benyahia, Sofiane

    2012-07-01

    In this article, we revisit Johnson and Jackson boundary conditions for granular flows. The oblique collision between a particle and a flat wall is analyzed by adopting the classic rigid-body theory and a more realistic semianalytical model. Based on the kinetic granular theory, the input parameter for the partial-slip boundary conditions, specularity coefficient, which is not measurable in experiments, is then interpreted as a function of the particle-wall restitution coefficient, the frictional coefficient, and the normalized slip velocity at the wall. An analytical expression for the specularity coefficient is suggested for a flat, frictional surface with a low frictional coefficient. The procedure for determining the specularity coefficient for a more general problem is outlined, and a working approximation is provided.

  16. Benchmarking sheath subgrid boundary conditions for macroscopic-scale simulations

    NASA Astrophysics Data System (ADS)

    Jenkins, T. G.; Smithe, D. N.

    2015-02-01

    The formation of sheaths near metallic or dielectric-coated wall materials in contact with a plasma is ubiquitous, often giving rise to physical phenomena (sputtering, secondary electron emission, etc) which influence plasma properties and dynamics both near and far from the material interface. In this paper, we use first-principles PIC simulations of such interfaces to formulate a subgrid sheath boundary condition which encapsulates fundamental aspects of the sheath behavior at the interface. Such a boundary condition, based on the capacitive behavior of the sheath, is shown to be useful in fluid simulations wherein sheath scale lengths are substantially smaller than scale lengths for other relevant physical processes (e.g. radiofrequency wavelengths), in that it enables kinetic processes associated with the presence of the sheath to be numerically modeled without explicit resolution of spatial and temporal sheath scales such as electron Debye length or plasma frequency.

  17. A Boundary Condition for Simulation of Flow Over Porous Surfaces

    NASA Technical Reports Server (NTRS)

    Frink, Neal T.; Bonhaus, Daryl L.; Vatsa, Veer N.; Bauer, Steven X. S.; Tinetti, Ana F.

    2001-01-01

    A new boundary condition is presented.for simulating the flow over passively porous surfaces. The model builds on the prior work of R.H. Bush to eliminate the need for constructing grid within an underlying plenum, thereby simplifying the numerical modeling of passively porous flow control systems and reducing computation cost. Code experts.for two structured-grid.flow solvers, TLNS3D and CFL3D. and one unstructured solver, USM3Dns, collaborated with an experimental porosity expert to develop the model and implement it into their respective codes. Results presented,for the three codes on a slender forebody with circumferential porosity and a wing with leading-edge porosity demonstrate a good agreement with experimental data and a remarkable ability to predict the aggregate aerodynamic effects of surface porosity with a simple boundary condition.

  18. Boundary conditions for simulating large SAW devices using ANSYS.

    PubMed

    Peng, Dasong; Yu, Fengqi; Hu, Jian; Li, Peng

    2010-08-01

    In this report, we propose improved substrate left and right boundary conditions for simulating SAW devices using ANSYS. Compared with the previous methods, the proposed method can greatly reduce computation time. Furthermore, the longer the distance from the first reflector to the last one, the more computation time can be reduced. To verify the proposed method, a design example is presented with device center frequency 971.14 MHz.

  19. Hydrodynamic boundary condition of water on hydrophobic surfaces.

    PubMed

    Schaeffel, David; Yordanov, Stoyan; Schmelzeisen, Marcus; Yamamoto, Tetsuya; Kappl, Michael; Schmitz, Roman; Dünweg, Burkhard; Butt, Hans-Jürgen; Koynov, Kaloian

    2013-05-01

    By combining total internal reflection fluorescence cross-correlation spectroscopy with Brownian dynamics simulations, we were able to measure the hydrodynamic boundary condition of water flowing over a smooth solid surface with exceptional accuracy. We analyzed the flow of aqueous electrolytes over glass coated with a layer of poly(dimethylsiloxane) (advancing contact angle Θ = 108°) or perfluorosilane (Θ = 113°). Within an error of better than 10 nm the slip length was indistinguishable from zero on all surfaces.

  20. Stability analysis of intermediate boundary conditions in approximate factorization schemes

    NASA Technical Reports Server (NTRS)

    South, J. C., Jr.; Hafez, M. M.; Gottlieb, D.

    1986-01-01

    The paper discusses the role of the intermediate boundary condition in the AF2 scheme used by Holst for simulation of the transonic full potential equation. It is shown that the treatment suggested by Holst led to a restriction on the time step and ways to overcome this restriction are suggested. The discussion is based on the theory developed by Gustafsson, Kreiss, and Sundstrom and also on the von Neumann method.

  1. Energy Based Multiscale Modeling with Non-Periodic Boundary Conditions

    DTIC Science & Technology

    2013-05-13

    was implemented numerically utilizing Python scripting to invoke the nested FE solution within the commercial FE software ABAQUS. To reduce initial...between Python and the ABAQUS solver. The left-hand side of Figure 8 highlights the localization process which involves passing of the macroscopic...deformation gradient from the UMAT to the custom Python script which then modifies the boundary conditions to a unit-cell, or RVE, ABAQUS input file

  2. Arterial wall tethering as a distant boundary condition

    NASA Astrophysics Data System (ADS)

    Hodis, S.; Zamir, M.

    2009-11-01

    A standing difficulty in the problem of blood vessel tethering has been that only one of the two required boundary conditions can be fully specified, namely, that at the inner (endothelial) wall surface. The other, at the outer layer of the vessel wall, is not known except in the limiting case where the wall is fully tethered such that its outer layer is prevented from any displacement. In all other cases, where the wall is either free or partially tethered, a direct boundary condition is not available. We present a method of determining this missing boundary condition by considering the limiting case of a semi-infinite wall. The result makes it possible to define the degree of tethering imposed by surrounding tissue more accurately in terms of the displacement of the outer layer of the vessel wall, rather than in terms of equivalent added mass which has been done in the past. This new approach makes it possible for the first time to describe the effect of partial tethering in its full range, from zero to full tethering. The results indicate that high tethering leads to high stresses and low displacements within the vessel wall, while low tethering leads to low stresses and high displacements. Since both extremes would be damaging to wall tissue, particularly elastin, this suggest that moderate tethering would be optimum in the physiological setting.

  3. High Energy Boundary Conditions for a Cartesian Mesh Euler Solver

    NASA Technical Reports Server (NTRS)

    Pandya, Shishir A.; Murman, Scott M.; Aftosmis, Michael J.

    2004-01-01

    Inlets and exhaust nozzles are often omitted or fared over in aerodynamic simulations of aircraft due to the complexities involving in the modeling of engine details such as complex geometry and flow physics. However, the assumption is often improper as inlet or plume flows have a substantial effect on vehicle aerodynamics. A tool for specifying inlet and exhaust plume conditions through the use of high-energy boundary conditions in an established inviscid flow solver is presented. The effects of the plume on the flow fields near the inlet and plume are discussed.

  4. Inflow/Outflow Boundary Conditions with Application to FUN3D

    NASA Technical Reports Server (NTRS)

    Carlson, Jan-Renee

    2011-01-01

    Several boundary conditions that allow subsonic and supersonic flow into and out of the computational domain are discussed. These boundary conditions are demonstrated in the FUN3D computational fluid dynamics (CFD) code which solves the three-dimensional Navier-Stokes equations on unstructured computational meshes. The boundary conditions are enforced through determination of the flux contribution at the boundary to the solution residual. The boundary conditions are implemented in an implicit form where the Jacobian contribution of the boundary condition is included and is exact. All of the flows are governed by the calorically perfect gas thermodynamic equations. Three problems are used to assess these boundary conditions. Solution residual convergence to machine zero precision occurred for all cases. The converged solution boundary state is compared with the requested boundary state for several levels of mesh densities. The boundary values converged to the requested boundary condition with approximately second-order accuracy for all of the cases.

  5. Flow modeling of actual human nasal cavity for various breathing conditions

    NASA Astrophysics Data System (ADS)

    Mokhtar, Nur Hazwani; Yaakob, Muhammad Syauki; Osman, Kahar; Kadir, Mohammed Rafiq Abdul; Abdullah, Wan Kamil Wan; Haron, Juhara

    2012-06-01

    Flow in the human nasal cavity varies when the body is under various physical activities. However, in order to visualize the flow pattern, traditional in-vivo technique may disturb the flow patterns. In this study, computational method was used to model the flow in the nasal cavity under various breathing conditions. Image from CT-Scan was used to mimic the actual cavity geometry. The image was computationally constructed and EFD. Lab was used to predict the flow behavior. Steady incompressible flow was considered for all case studies. The result shows that, for all breathing conditions, vortices were observed in the turbinate region which confirms the turbinate functions as a filter before the flow reaches the olfactory area. Larger vortices were detected when the flow rates were higher. In the olfactory region, the flow velocities were shown to be dramatically dropped to the ideal odorant uptake velocity range for all cases studied. This study had successfully produced visual description of air flow pattern in the nasal cavity.

  6. Nonstationary Stokes System in Cylindrical Domains Under Boundary Slip Conditions

    NASA Astrophysics Data System (ADS)

    Zaja¸czkowski, Wojciech M.

    2017-03-01

    Existence and uniqueness of solutions to the nonstationary Stokes system in a cylindrical domain {Ωsubset{R}^3} and under boundary slip conditions are proved in anisotropic Sobolev spaces. Assuming that the external force belong to {L_r(Ω×(0,T))} and initial velocity to {W_r^{2-2/r}(Ω)} there exists a solution such that velocity belongs to {W_r^{2,1}(Ω×(0,T))} and gradient of pressure to {L_r(Ω×(0,T))}, {rin(1,∞)}, {T > 0}. Thanks to the slip boundary conditions and a partition of unity the Stokes system is transformed to the Poisson equation for pressure and the heat equation for velocity. The existence of solutions to these equations is proved by applying local considerations. In this case we have to consider neighborhoods near the edges which by local mapping can be transformed to dihedral angle {π/2}. Hence solvability of the problem bases on construction local Green functions (near an interior point, near a point of a smooth part of the boundary, near a point of the edge) and their appropriate estimates. The technique presented in this paper can also work in other functional spaces: Sobolev-Slobodetskii, Besov, Nikolskii, Hölder and so on.

  7. Study on plate silencer with general boundary conditions

    NASA Astrophysics Data System (ADS)

    Liu, Gongmin; Zhao, Xiaochen; Zhang, Wenping; Li, Shuaijun

    2014-09-01

    A plate silencer consists of an expansion chamber with two side-branch rigid cavities covered by plates. Previous studies showed that, in a duct, the introduction of simply supported or clamped plates into an air conveying system could achieve broadband quieting from low to medium frequencies. In this study, analytical formulation is extended to the plate silencer with general boundary conditions. A set of static beam functions, which are a combination of sine series and third-order polynomial, is employed as the trial functions of the plate vibration velocity. Greens function and Kirchhoff-Helmholtz integral are used to solve the sound radiation in the duct and the cavity, and then the vibration velocity of the plate is obtained. Having obtained the vibration velocity, the pressure perturbations induced by the plate oscillation and the transmission loss are found. Optimization is carried out in order to obtain the widest stopband. The transmission loss calculated by the analytical method agrees closely with the result of the finite element method simulation. Further studies with regard to the plate under several different classical boundary conditions based on the validated model show that a clamped-free plate silencer has the worst stopband. Attempts to release the boundary restriction of the plate are also made to study its effect on sound reflection. Results show that a softer end for a clamped-clamped plate silencer helps increase the optimal bandwidth, while the same treatment for simply supported plate silencer will result in performance degradation.

  8. A Poisson-Boltzmann dynamics method with nonperiodic boundary condition

    NASA Astrophysics Data System (ADS)

    Lu, Qiang; Luo, Ray

    2003-12-01

    We have developed a well-behaved and efficient finite difference Poisson-Boltzmann dynamics method with a nonperiodic boundary condition. This is made possible, in part, by a rather fine grid spacing used for the finite difference treatment of the reaction field interaction. The stability is also made possible by a new dielectric model that is smooth both over time and over space, an important issue in the application of implicit solvents. In addition, the electrostatic focusing technique facilitates the use of an accurate yet efficient nonperiodic boundary condition: boundary grid potentials computed by the sum of potentials from individual grid charges. Finally, the particle-particle particle-mesh technique is adopted in the computation of the Coulombic interaction to balance accuracy and efficiency in simulations of large biomolecules. Preliminary testing shows that the nonperiodic Poisson-Boltzmann dynamics method is numerically stable in trajectories at least 4 ns long. The new model is also fairly efficient: it is comparable to that of the pairwise generalized Born solvent model, making it a strong candidate for dynamics simulations of biomolecules in dilute aqueous solutions. Note that the current treatment of total electrostatic interactions is with no cutoff, which is important for simulations of biomolecules. Rigorous treatment of the Debye-Hückel screening is also possible within the Poisson-Boltzmann framework: its importance is demonstrated by a simulation of a highly charged protein.

  9. Transport across nanogaps using self-consistent boundary conditions

    NASA Astrophysics Data System (ADS)

    Biswas, D.; Kumar, R.

    2012-06-01

    Charge particle transport across nanogaps is studied theoretically within the Schrodinger-Poisson mean field framework. The determination of self-consistent boundary conditions across the gap forms the central theme in order to allow for realistic interface potentials (such as metal-vacuum) which are smooth at the boundary and do not abruptly assume a constant value at the interface. It is shown that a semiclassical expansion of the transmitted wavefunction leads to approximate but self consistent boundary conditions without assuming any specific form of the potential beyond the gap. Neglecting the exchange and correlation potentials, the quantum Child-Langmuir law is investigated. It is shown that at zero injection energy, the quantum limiting current density (Jc) is found to obey the local scaling law Jc ~ Vgα/D5-2α with the gap separation D and voltage Vg. The exponent α > 1.1 with α → 3/2 in the classical regime of small de Broglie wavelengths.

  10. Electrostatics of solvated systems in periodic boundary conditions

    NASA Astrophysics Data System (ADS)

    Andreussi, Oliviero; Marzari, Nicola

    2014-12-01

    Continuum solvation methods can provide an accurate and inexpensive embedding of quantum simulations in liquid or complex dielectric environments. Notwithstanding a long history and manifold applications to isolated systems in open boundary conditions, their extension to materials simulations, typically entailing periodic boundary conditions, is very recent, and special care is needed to address correctly the electrostatic terms. We discuss here how periodic boundary corrections developed for systems in vacuum should be modified to take into account solvent effects, using as a general framework the self-consistent continuum solvation model developed within plane-wave density-functional theory [O. Andreussi et al., J. Chem. Phys. 136, 064102 (2012), 10.1063/1.3676407]. A comprehensive discussion of real- and reciprocal-space corrective approaches is presented, together with an assessment of their ability to remove electrostatic interactions between periodic replicas. Numerical results for zero- and two-dimensional charged systems highlight the effectiveness of the different suggestions, and underline the importance of a proper treatment of electrostatic interactions in first-principles studies of charged systems in solution.

  11. Negative bending mode curvature via Robin boundary conditions

    NASA Astrophysics Data System (ADS)

    Adams, Samuel D. M.; Craster, Richard V.; Guenneau, Sébastien

    2009-06-01

    We examine the band spectrum, and associated Floquet-Bloch eigensolutions, arising in straight walled acoustic waveguides that have periodic structure along the guide. Homogeneous impedance (Robin) conditions are imposed along the guide walls and we find that in certain circumstances, negative curvature of the lowest (bending) mode can be achieved. This is unexpected, and has not been observed in a variety of physical situations examined by other authors. Further unexpected properties include the existence of the bending mode only on a subset of the Brillouin zone, as well as permitting otherwise unobtainable velocities of energy transmission. We conclude with a discussion of how such boundary conditions might be physically reproduced using effective conditions and homogenization theory, although the methodology to achieve these effective conditions is an open problem. To cite this article: S.D.M. Adams et al., C. R. Physique 10 (2009).

  12. Boundary conditions towards realistic simulation of jet engine noise

    NASA Astrophysics Data System (ADS)

    Dhamankar, Nitin S.

    Strict noise regulations at major airports and increasing environmental concerns have made prediction and attenuation of jet noise an active research topic. Large eddy simulation coupled with computational aeroacoustics has the potential to be a significant research tool for this problem. With the emergence of petascale computer clusters, it is now computationally feasible to include the nozzle geometry in jet noise simulations. In high Reynolds number experiments on jet noise, the turbulent boundary layer on the inner surface of the nozzle separates into a turbulent free shear layer. Inclusion of a nozzle with turbulent inlet conditions is necessary to simulate this phenomenon realistically. This will allow a reasonable comparison of numerically computed noise levels with the experimental results. Two viscous wall boundary conditions are implemented for modeling the nozzle walls. A characteristic-based approach is compared with a computationally cheaper, extrapolation-based formulation. In viscous flow over a circular cylinder under two different regimes, excellent agreement is observed between the results of the two approaches. The results agree reasonably well with reference experimental and numerical results. Both the boundary conditions are thus found to be appropriate, the extrapolation-based formulation having an edge with its low cost. This is followed with the crucial step of generation of a turbulent boundary layer inside the nozzle. A digital filter-based turbulent inflow condition, extended in a new way to non-uniform curvilinear grids is implemented to achieve this. A zero pressure gradient flat plate turbulent boundary layer is simulated at a high Reynolds number to show that the method is capable of producing sustained turbulence. The length of the adjustment region necessary for synthetic inlet turbulence to recover from modeling errors is estimated. A low Reynolds number jet simulation including a round nozzle geometry is performed and the method

  13. Spectral asymptotics of Euclidean quantum gravity with diff-invariant boundary conditions

    NASA Astrophysics Data System (ADS)

    Esposito, Giampiero; Fucci, Guglielmo; Kamenshchik, Alexander Yu; Kirsten, Klaus

    2005-03-01

    A general method is known to exist for studying Abelian and non-Abelian gauge theories, as well as Euclidean quantum gravity, at 1-loop level on manifolds with boundary. In the latter case, boundary conditions on metric perturbations h can be chosen to be completely invariant under infinitesimal diffeomorphisms, to preserve the invariance group of the theory and BRST symmetry. In the de Donder gauge, however, the resulting boundary-value problem for the Laplace-type operator acting on h is known to be self-adjoint but not strongly elliptic. The latter is a technical condition ensuring that a unique smooth solution of the boundary-value problem exists, which implies, in turn, that the global heat-kernel asymptotics yielding 1-loop divergences and 1-loop effective action actually exists. The present paper shows that, on the Euclidean 4-ball, only the scalar part of perturbative modes for quantum gravity is affected by the lack of strong ellipticity. Further evidence for lack of strong ellipticity, from an analytic point of view, is therefore obtained. Interestingly, three sectors of the scalar-perturbation problem remain elliptic, while lack of strong ellipticity is 'confined' to the remaining fourth sector. The integral representation of the resulting ζ-function asymptotics on the Euclidean 4-ball is also obtained; this remains regular at the origin by virtue of a spectral identity here obtained for the first time.

  14. Convolution quadrature for the wave equation with impedance boundary conditions

    NASA Astrophysics Data System (ADS)

    Sauter, S. A.; Schanz, M.

    2017-04-01

    We consider the numerical solution of the wave equation with impedance boundary conditions and start from a boundary integral formulation for its discretization. We develop the generalized convolution quadrature (gCQ) to solve the arising acoustic retarded potential integral equation for this impedance problem. For the special case of scattering from a spherical object, we derive representations of analytic solutions which allow to investigate the effect of the impedance coefficient on the acoustic pressure analytically. We have performed systematic numerical experiments to study the convergence rates as well as the sensitivity of the acoustic pressure from the impedance coefficients. Finally, we apply this method to simulate the acoustic pressure in a building with a fairly complicated geometry and to study the influence of the impedance coefficient also in this situation.

  15. Applying twisted boundary conditions for few-body nuclear systems

    NASA Astrophysics Data System (ADS)

    Körber, Christopher; Luu, Thomas

    2016-05-01

    We describe and implement twisted boundary conditions for the deuteron and triton systems within finite volumes using the nuclear lattice EFT formalism. We investigate the finite-volume dependence of these systems with different twist angles. We demonstrate how various finite-volume information can be used to improve calculations of binding energies in such a framework. Our results suggests that with appropriate twisting of boundaries, infinite-volume binding energies can be reliably extracted from calculations using modest volume sizes with cubic length L ≈8 -14 fm. Of particular importance is our derivation and numerical verification of three-body analogs of "i-periodic" twist angles that eliminate the leading-order finite-volume effects to the three-body binding energy.

  16. Boundary Condition Effects on Taylor States in SSX

    NASA Astrophysics Data System (ADS)

    Han, Jeremy; Shrock, Jaron; Kaur, Manjit; Brown, Michael; Schaffner, David

    2016-10-01

    Three different boundary conditions are applied to the SSX 0.15 m diameter plasma wind tunnel and the resultant Taylor states are characterized. The glass walls of the wind tunnel act as an insulating boundary condition. For the second condition, a flux conserver is wrapped around the tunnel to trap magnetic field lines inside the SSX. For the last condition, the flux conserver is segmented to add theta pinch coils, which will accelerate the plasma. We used resistive stainless steel and copper mesh for the flux conservers, which have soak times of 3 μs and 250 μs , respectively. The goal is to increase the speed, temperature, and density of the plasma plume by adding magnetic energy into the system using the coils and compressing the plasma into small volumes by stagnation. The time of flight is measured by using a linear array of magnetic pick-up loops, which track the plasma plume's location as a function of time. The density is measured by precision quadrature He-Ne laser interferometry, and the temperature is measured by ion Doppler spectroscopy. Speed and density without the coils are 30km /s and 1015cm-3 . We will reach a speed of 100km /s and density of 1016cm-3 by adding the coil. Work supported by DOE OFES and ARPA-E ALPHA program.

  17. Three dimensional dynamics of rotating structures under mixed boundary conditions

    NASA Astrophysics Data System (ADS)

    Bediz, Bekir; Romero, L. A.; Ozdoganlar, O. Burak

    2015-12-01

    This paper presents the spectral-Tchebychev (ST) technique for solution of three dimensional (3D) dynamics of rotating structures. In particular, structures that exhibit coupled dynamic response require a 3D modeling approach to capture their dynamic behavior. Rotational motions further complicate this behavior, inducing coriolis, centrifugal softening, and (nonlinear) stress-stiffening effects. Therefore, a 3D solution approach is needed to accurately capture the rotational dynamics. The presented 3D-ST technique provides a fast-converging and precise solution approach for rotational dynamics of structures with complex geometries and mixed boundary conditions. Specifically, unlike finite elements techniques, the presented technique uses a series expansion approach considering distributed-parameter system equations: The integral boundary value problem for rotating structures is discretized using the spectral-Tchebychev approach. To simplify the domain of the structures, cross-sectional and rotational transformations are applied to problems with curved cross-section and pretwisted geometry. The nonlinear terms included in the integral boundary value problem are linearized around an equilibrium solution using the quasi-static method. As a result, mass, damping, and stiffness matrices, as well as a forcing vector, are obtained for a given rotating structure. Several case studies are then performed to demonstrate the application and effectiveness of the 3D-ST solution. For each problem, the natural frequencies and modes shapes from the 3D-ST solution are compared to those from the literature (when available) and to those from a commercial finite elements software. The case studies include rotating/spinning parallelepipeds under free and mixed boundary conditions, and a cantilevered pretwisted beam (i.e., rotating blade) with an airfoil geometry rotating on a hub. It is seen that the natural frequencies and mode shapes from the 3D-ST technique differ from those from the

  18. Cesium adsorption/desorption behavior of clay minerals considering actual contamination conditions in Fukushima

    PubMed Central

    Mukai, Hiroki; Hirose, Atsushi; Motai, Satoko; Kikuchi, Ryosuke; Tanoi, Keitaro; Nakanishi, Tomoko M.; Yaita, Tsuyoshi; Kogure, Toshihiro

    2016-01-01

    Cesium adsorption/desorption experiments for various clay minerals, considering actual contamination conditions in Fukushima, were conducted using the 137Cs radioisotope and an autoradiography using imaging plates (IPs). A 50 μl solution containing 0.185 ~ 1.85 Bq of 137Cs (10−11 ~ 10−9 molL−1 of 137Cs) was dropped onto a substrate where various mineral particles were arranged. It was found that partially-vermiculitized biotite, which is termed “weathered biotite” (WB) in this study, from Fukushima sorbed 137Cs far more than the other clay minerals (fresh biotite, illite, smectite, kaolinite, halloysite, allophane, imogolite) on the same substrate. When WB was absent on the substrate, the amount of 137Cs sorbed to the other clay minerals was considerably increased, implying that selective sorption to WB caused depletion of radiocesium in the solution and less sorption to the coexisting minerals. Cs-sorption to WB continued for about one day, whereas that to ferruginous smectite was completed within one hour. The sorbed 137Cs in WB was hardly leached with hydrochloric acid at pH 1, particularly in samples with a longer sorption time. The presence/absence of WB sorbing radiocesium is a key factor affecting the dynamics and fate of radiocesium in Fukushima. PMID:26868138

  19. Cesium adsorption/desorption behavior of clay minerals considering actual contamination conditions in Fukushima

    NASA Astrophysics Data System (ADS)

    Mukai, Hiroki; Hirose, Atsushi; Motai, Satoko; Kikuchi, Ryosuke; Tanoi, Keitaro; Nakanishi, Tomoko M.; Yaita, Tsuyoshi; Kogure, Toshihiro

    2016-02-01

    Cesium adsorption/desorption experiments for various clay minerals, considering actual contamination conditions in Fukushima, were conducted using the 137Cs radioisotope and an autoradiography using imaging plates (IPs). A 50 μl solution containing 0.185 ~ 1.85 Bq of 137Cs (10-11 ~ 10-9 molL-1 of 137Cs) was dropped onto a substrate where various mineral particles were arranged. It was found that partially-vermiculitized biotite, which is termed “weathered biotite” (WB) in this study, from Fukushima sorbed 137Cs far more than the other clay minerals (fresh biotite, illite, smectite, kaolinite, halloysite, allophane, imogolite) on the same substrate. When WB was absent on the substrate, the amount of 137Cs sorbed to the other clay minerals was considerably increased, implying that selective sorption to WB caused depletion of radiocesium in the solution and less sorption to the coexisting minerals. Cs-sorption to WB continued for about one day, whereas that to ferruginous smectite was completed within one hour. The sorbed 137Cs in WB was hardly leached with hydrochloric acid at pH 1, particularly in samples with a longer sorption time. The presence/absence of WB sorbing radiocesium is a key factor affecting the dynamics and fate of radiocesium in Fukushima.

  20. Do we know the actual magnetopause position for typical solar wind conditions?

    NASA Astrophysics Data System (ADS)

    Samsonov, A. A.; Gordeev, E.; Tsyganenko, N. A.; Å afránková, J.; Němeček, Z.; Å imůnek, J.; Sibeck, D. G.; Tóth, G.; Merkin, V. G.; Raeder, J.

    2016-07-01

    We compare predicted magnetopause positions at the subsolar point and four reference points in the terminator plane obtained from several empirical and numerical MHD models. Empirical models using various sets of magnetopause crossings and making different assumptions about the magnetopause shape predict significantly different magnetopause positions (with a scatter >1 RE) even at the subsolar point. Axisymmetric magnetopause models cannot reproduce the cusp indentations or the changes related to the dipole tilt effect, and most of them predict the magnetopause closer to the Earth than nonaxisymmetric models for typical solar wind conditions and zero tilt angle. Predictions of two global nonaxisymmetric models do not match each other, and the models need additional verification. MHD models often predict the magnetopause closer to the Earth than the nonaxisymmetric empirical models, but the predictions of MHD simulations may need corrections for the ring current effect and decreases of the solar wind pressure that occur in the foreshock. Comparing MHD models in which the ring current magnetic field is taken into account with the empirical Lin et al. model, we find that the differences in the reference point positions predicted by these models are relatively small for Bz=0. Therefore, we assume that these predictions indicate the actual magnetopause position, but future investigations are still needed.

  1. On the nonlinear Schrodinger equation with nonzero boundary conditions

    NASA Astrophysics Data System (ADS)

    Fagerstrom, Emily

    integral, provided the initial condition satisfies further conditions. Modulational instability (focusing NLS with symmetric nonzero boundary conditions at infinity.) The focusing NLS equation is considered with potentials that are "box-like" piecewise constant functions. Several results are obtained. In particular, it is shown that there are conditions on the parameters of the potential for which there are no discrete eigenvalues. Thus there is a class of potentials for which the corresponding solutions of the NLS equation have no solitons. Hence, solitons cannot be the medium for the modulational instability. This contradicts a recent conjecture by Zakharov. On the other hand, it is shown for a different class of potentials the scattering problem always has a discrete eigenvalue along the imaginary axis. Thus, there exist arbitrarily small perturbations of the constant potential for which solitons exist, so no area theorem is possible. The existence, number and location of discrete eigenvalues in other situations are studied numerically. Finally, the small-deviation limit of the IST is computed and compared with the direct linearization of the NLS equation around a constant background. From this it is shown that there is an interval of the continuous spectrum on which the eigenvalue is imaginary and the scattering parameter is imaginary. The Jost eigenfunctions corresponding to this interval are the nonlinear analogue of the unstable Fourier modes. Defocusing NLS equation with asymmetric boundary conditions at infinity. The defocusing NLS equation with asymmetric boundary conditions is considered. To do so, first the case of symmetric boundary conditions is revisited. While the IST for this case has been formulated in the literature, it is usually done through the use of a uniformization variable. This was done because the eigenvalues of the scattering problem have branching; the uniformization variable allows one to move from a 2-sheeted Riemann surface to the complex

  2. The effects of external conditions in turbulent boundary layers

    NASA Astrophysics Data System (ADS)

    Brzek, Brian G.

    The effects of multiple external conditions on turbulent boundary layers were studied in detail. These external conditions include: surface roughness, upstream turbulence intensity, and pressure gradient. Furthermore, the combined effects of these conditions show the complicated nature of many realistic flow conditions. It was found that the effects of surface roughness are difficult to generalize, given the importance of so many parameters. These parameters include: roughness geometry, roughness regime, roughness height to boundary layer thickness, (k/delta), roughness parameter, ( k+), Reynolds number, and roughness function (Delta B+). A further complication, is the difficulty in computing the wall shear stress, tauw/rho. For the sand grain type roughness, the mean velocity and Reynolds stresses were studied in inner and outer variables, as well as, boundary layer parameters, anisotropy tensor, production term, and viscous stress and form drag contributions. To explore the effects of roughness and Reynolds number dependence in the boundary layer, a new experiment was carefully designed to properly capture the x-dependence of the single-point statistics. It was found that roughness destroys the viscous layer near the wall, thus, reducing the contribution of the viscous stress in the wall region. As a result, the contribution in the skin friction due to form drag increases, while the viscous stress decreases. This yields Reynolds number invariance in the skin friction, near-wall roughness parameters, and inner velocity profiles as k + increases into the fully rough regime. However, in the transitionally rough regime, (i.e., 5 < k+ < 70), it was found that these parameters are functions of both Reynolds number and roughness. For the sand grain type roughnesses, only the Zagarola and Smits scaling, Uinfinitydelta*/delta, is able to remove the effects of roughness and Reynolds number from the velocity profiles in outer variables, provided there is no freestream

  3. Breaking generalized covariance, classical renormalization, and boundary conditions from superpotentials

    SciTech Connect

    Livshits, Gideon I.

    2014-02-15

    Superpotentials offer a direct means of calculating conserved charges associated with the asymptotic symmetries of space-time. Yet superpotentials have been plagued with inconsistencies, resulting in nonphysical or incongruent values for the mass, angular momentum, and energy loss due to radiation. The approach of Regge and Teitelboim, aimed at a clear Hamiltonian formulation with a boundary, and its extension to the Lagrangian formulation by Julia and Silva have resolved these issues, and have resulted in a consistent, well-defined and unique variational equation for the superpotential, thereby placing it on a firm footing. A hallmark solution of this equation is the KBL superpotential obtained from the first-order Lovelock Lagrangian. Nevertheless, here we show that these formulations are still insufficient for Lovelock Lagrangians of higher orders. We present a paradox, whereby the choice of fields affects the superpotential for equivalent on-shell dynamics. We offer two solutions to this paradox: either the original Lagrangian must be effectively renormalized, or that boundary conditions must be imposed, so that space-time be asymptotically maximally symmetric. Non-metricity is central to this paradox, and we show how quadratic non-metricity in the bulk of space-time contributes to the conserved charges on the boundary, where it vanishes identically. This is a realization of the gravitational Higgs mechanism, proposed by Percacci, where the non-metricity is the analogue of the Goldstone boson.

  4. Compressible turbulent channel flow with impedance boundary conditions

    NASA Astrophysics Data System (ADS)

    Scalo, Carlo; Bodart, Julien; Lele, Sanjiva

    2014-11-01

    We have performed large-eddy simulations of compressible turbulent channel flow at one bulk Reynolds number, Reb = 6900, for bulk Mach numbers Mb = 0.05, 0.2, 0.5, with linear acoustic impedance boundary conditions (IBCs). The IBCs are formulated in the time domain following Fung and Ju (2004) and coupled with a Navier-Stokes solver. The impedance model adopted is a three-parameter Helmholtz oscillator with resonant frequency tuned to the outer layer eddies. The IBC's resistance, R, has been varied in the range, R = 0.01, 0.10, 1.00. Tuned IBCs result in a noticeable drag increase for sufficiently high Mb and/or low R, exceeding 300% for Mb = 0.5 and R = 0.01, and thus represents a promising passive control technique for delaying boundary layer separation and/or enhancing wall heat transfer. Alterations to the turbulent flow structure are confined to the first 15% of the boundary layer thickness where the classical buffer-layer coherent vortical structures are replaced by an array of Kelvin-Helmholtz-like rollers. The non-zero asymptotic value of the Reynolds shear stress gradient at the wall results in the disappearance of the viscous sublayer and very early departure of the mean velocity profiles from the law of the wall.

  5. Artificial Boundary Conditions Based on the Difference Potentials Method

    NASA Technical Reports Server (NTRS)

    Tsynkov, Semyon V.

    1996-01-01

    While numerically solving a problem initially formulated on an unbounded domain, one typically truncates this domain, which necessitates setting the artificial boundary conditions (ABC's) at the newly formed external boundary. The issue of setting the ABC's appears to be most significant in many areas of scientific computing, for example, in problems originating from acoustics, electrodynamics, solid mechanics, and fluid dynamics. In particular, in computational fluid dynamics (where external problems present a wide class of practically important formulations) the proper treatment of external boundaries may have a profound impact on the overall quality and performance of numerical algorithms. Most of the currently used techniques for setting the ABC's can basically be classified into two groups. The methods from the first group (global ABC's) usually provide high accuracy and robustness of the numerical procedure but often appear to be fairly cumbersome and (computationally) expensive. The methods from the second group (local ABC's) are, as a rule, algorithmically simple, numerically cheap, and geometrically universal; however, they usually lack accuracy of computations. In this paper we first present a survey and provide a comparative assessment of different existing methods for constructing the ABC's. Then, we describe a relatively new ABC's technique of ours and review the corresponding results. This new technique, in our opinion, is currently one of the most promising in the field. It enables one to construct such ABC's that combine the advantages relevant to the two aforementioned classes of existing methods. Our approach is based on application of the difference potentials method attributable to V. S. Ryaben'kii. This approach allows us to obtain highly accurate ABC's in the form of certain (nonlocal) boundary operator equations. The operators involved are analogous to the pseudodifferential boundary projections first introduced by A. P. Calderon and then

  6. Simulation Study of the Flow Boundary Condition for Rough Surfaces

    NASA Astrophysics Data System (ADS)

    He, Gang; Robbins, Mark O.

    2001-03-01

    In order to solve a flow problem with the continuum Navier-Stokes equation, a boundary condition must be assumed. In most cases, a no-slip condition is used, i.e. the velocity of the fluid is set equal to that of a bounding solid at their interface. Deviations from this condition can be quantified by a slip length S that represents the additional width of fluid that would be needed to accomodate any velocity difference at the interface. Previous simulations with atomically flat surfaces show that S can be very large in certain limits. (P. A. Thompson and M. O. Robbins, Phys. Rev. A, 41), 6830(1990). ( J.-L. Barrat and L. Bocquet, Phys. Rev. Lett., 82), 4671(1999). A dramatic divergence with S as shear rate increases has also been seen.( P. A. Thompson and S. M. Troian, Nature, 389), 360(1997) We have extended these simulations to surfaces with random roughness, steps, and angled facets typical of twin boundaries. In all cases, S decreases rapidly as the roughness increases. When peak-to-peak roughness is only two atomic diameters, values of S have dropped from more than 20 diameters to only one or two. In addition, the non-linear regime where S diverges with shear rate is supressed by surface roughness. These results suggest that the experimental behavior of atomically flat surfaces such as mica may be very different than that of more typical rough surfaces.

  7. Hawking radiation, covariant boundary conditions, and vacuum states

    SciTech Connect

    Banerjee, Rabin; Kulkarni, Shailesh

    2009-04-15

    The basic characteristics of the covariant chiral current and the covariant chiral energy-momentum tensor are obtained from a chiral effective action. These results are used to justify the covariant boundary condition used in recent approaches of computing the Hawking flux from chiral gauge and gravitational anomalies. We also discuss a connection of our results with the conventional calculation of nonchiral currents and stress tensors in different (Unruh, Hartle-Hawking and Boulware) states.

  8. Proceedings for the ICASE Workshop on Heterogeneous Boundary Conditions

    NASA Technical Reports Server (NTRS)

    Perkins, A. Louise; Scroggs, Jeffrey S.

    1991-01-01

    Domain Decomposition is a complex problem with many interesting aspects. The choice of decomposition can be made based on many different criteria, and the choice of interface of internal boundary conditions are numerous. The various regions under study may have different dynamical balances, indicating that different physical processes are dominating the flow in these regions. This conference was called in recognition of the need to more clearly define the nature of these complex problems. This proceedings is a collection of the presentations and the discussion groups.

  9. Analytical solutions with Generalized Impedance Boundary Conditions (GIBC)

    NASA Technical Reports Server (NTRS)

    Syed, H. H.; Volakis, John L.

    1991-01-01

    Rigorous uniform geometrical theory of diffraction (UTD) diffraction coefficients are presented for a coated convex cylinder simulated with generalized impedance boundary conditions. In particular, ray solutions are obtained which remain valid in the transition region and reduce uniformly to those in the deep lit and shadow regions. These involve new transition functions in place of the usual Fock-type integrals, characteristics to the impedance cylinder. A uniform asymptotic solution is also presented for observations in the close vicinity of the cylinder. The diffraction coefficients for the convex cylinder are obtained via a generalization of the corresponding ones for the circular cylinder.

  10. Periodic boundary conditions for dislocation dynamics simulations in three dimensions

    SciTech Connect

    Bulatov, V V; Rhee, M; Cai, W

    2000-11-20

    This article presents an implementation of periodic boundary conditions (PBC) for Dislocation Dynamics (DD) simulations in three dimensions (3D). We discuss fundamental aspects of PBC development, including preservation of translational invariance and line connectivity, the choice of initial configurations compatible with PBC and a consistent treatment of image stress. On the practical side, our approach reduces to manageable proportions the computational burden of updating the long-range elastic interactions among dislocation segments. The timing data confirms feasibility and practicality of PBC for large-scale DD simulations in 3D.

  11. Boundary conditions and generalized functions in a transition radiation problem

    NASA Astrophysics Data System (ADS)

    Villavicencio, M.; Jiménez, J. L.

    2017-03-01

    The aim of this work is to show how all the components of the electromagnetic field involved in the transition radiation problem can be obtained using distribution functions. The handling of the products and derivatives of distributions appearing in the differential equations governing transition radiation, allows to obtain the necessary boundary conditions, additional to those implied by Maxwell's equations, in order to exactly determine the longitudinal components of the electromagnetic field. It is shown that this method is not only useful but it is really convenient to achieve a full analysis of the problem.

  12. Boundary conditions for soft glassy flows: slippage and surface fluidization.

    PubMed

    Mansard, Vincent; Bocquet, Lydéric; Colin, Annie

    2014-09-28

    We explore the question of surface boundary conditions for the flow of a dense emulsion. We make use of microlithographic tools to create surfaces with well controlled roughness patterns and measure using dynamic confocal microscopy both the slip velocity and the shear rate close to the wall, which we relate to the notion of surface fluidization. Both slippage and wall fluidization depend non-monotonously on the roughness. We interpret this behavior within a simple model in terms of the building of a stratified layer and the activation of plastic events by the surface roughness.

  13. Reconnection properties in collisionless plasma with open boundary conditions

    SciTech Connect

    Sun, H. E.; Ma, Z. W.; Huang, J.

    2014-07-15

    Collisionless magnetic reconnection in a Harris current sheet with different initial thicknesses is investigated using a 21/2 -D Darwin particle-in-cell simulation with the magnetosonic open boundary condition. It is found that the thicknesses of the ion dissipation region and the reconnection current sheet, when the reconnection rate E{sub r} reaches its first peak, are independent of the initial thickness of the current sheet; while the peak reconnection rate depends on it. The peak reconnection rate increases with decrease of the current sheet thickness as E{sub r}∼a{sup −1/2}, where a is the initial current sheet half-thickness.

  14. Magnetospheric conditions near the equatorial footpoints of proton isotropy boundaries

    NASA Astrophysics Data System (ADS)

    Sergeev, V. A.; Chernyaev, I. A.; Angelopoulos, V.; Ganushkina, N. Y.

    2015-12-01

    Data from a cluster of three THEMIS (Time History of Events and Macroscale Interactions during Substorms) spacecraft during February-March 2009 frequently provide an opportunity to construct local data-adaptive magnetospheric models, which are suitable for the accurate mapping along the magnetic field lines at distances of 6-9 Re in the nightside magnetosphere. This allows us to map the isotropy boundaries (IBs) of 30 and 80 keV protons observed by low-altitude NOAA POES (Polar Orbiting Environmental Satellites) to the equatorial magnetosphere (to find the projected isotropy boundary, PIB) and study the magnetospheric conditions, particularly to evaluate the ratio KIB (Rc/rc; the magnetic field curvature radius to the particle gyroradius) in the neutral sheet at that point. Special care is taken to control the factors which influence the accuracy of the adaptive models and mapping. Data indicate that better accuracy of an adaptive model is achieved when the PIB distance from the closest spacecraft is as small as 1-2 Re. For this group of most accurate predictions, the spread of KIB values is still large (from 4 to 32), with the median value KIB ~13 being larger than the critical value Kcr ~ 8 expected at the inner boundary of nonadiabatic angular scattering in the current sheet. It appears that two different mechanisms may contribute to form the isotropy boundary. The group with K ~ [4,12] is most likely formed by current sheet scattering, whereas the group having KIB ~ [12,32] could be formed by the resonant scattering of low-energy protons by the electromagnetic ion-cyclotron (EMIC) waves. The energy dependence of the upper K limit and close proximity of the latter event to the plasmapause locations support this conclusion. We also discuss other reasons why the K ~ 8 criterion for isotropization may fail to work, as well as a possible relationship between the two scattering mechanisms.

  15. Solvability of a fourth-order boundary value problem with periodic boundary conditions II

    DOE PAGES

    Gupta, Chaitan P.

    1991-01-01

    Lemore » t f : [ 0 , 1 ] × R 4 → R be a function satisfying Caratheodory's conditions and e ( x ) ∈ L 1 [ 0 , 1 ] . This paper is concerned with the solvability of the fourth-order fully quasilinear boundary value problem d 4 u d x 4 + f ( x , u ( x ) , u ′ ( x ) , u ″ ( x ) , u ‴ ( x ) ) = e ( x ) ,    0 < x < 1 , with u ( 0 ) − u ( 1 ) = u ′ ( 0 ) − u ′ ( 1 ) = u ″ ( 0 ) - u ″ ( 1 ) = u ‴ ( 0 ) - u ‴ ( 1 ) = 0 . This problem was studied earlier by the author in the special case when f was of the form f ( x , u ( x ) ) , i.e., independent of u ′ ( x ) , u ″ ( x ) , u ‴ ( x ) . It turns out that the earlier methods do not apply in this general case. The conditions need to be related to both of the linear eigenvalue problems d 4 u d x 4 = λ 4 u and d 4 u d x 4 = − λ 2 d 2 u d x 2 with periodic boundary conditions.« less

  16. Effective slip boundary conditions for sinusoidally corrugated surfaces

    NASA Astrophysics Data System (ADS)

    Guo, Lin; Chen, Shiyi; Robbins, Mark O.

    2016-11-01

    Molecular dynamics simulations are used to investigate the effective slip boundary condition for a simple fluid flowing over surfaces with one-dimensional sinusoidal roughness in the Wenzel state. The effective slip length is calculated as a function of the corrugation amplitude for flows along two principal orientations: transverse and longitudinal to the corrugation. Different atomic configurations, bent and stepped, are examined for strong and weak wall-fluid interactions and high and low wall densities. Molecular dynamics results for sparse bent surfaces quantitatively agree with continuum hydrodynamic predictions with a constant local slip length. Increasing the roughness amplitude reduces the effective slip length and the reduction is larger for transverse flow than longitudinal flow. Atomic effects become important for dense surfaces, because the local slip length varies with the local curvature and atomic spacing along the wall. These effects can be captured by applying a spatially varying boundary condition to the Navier-Stokes equations. Results for stepped surfaces are qualitatively different than continuum predictions, with the effect of corrugation rising linearly with corrugation amplitude rather than quadratically. There is an increased drag for transverse flow that is proportional to the density of step edges and lowers the slip length. Edges tend to increase the slip length for longitudinal flow because of order induced along the edges.

  17. Mixed singular-regular boundary conditions in multislab radiation transport

    NASA Astrophysics Data System (ADS)

    de Abreu, Marcos Pimenta

    2004-06-01

    This article reports a computational method for approximately solving radiation transport problems with anisotropic scattering defined on multislab domains irradiated from one side with a beam of monoenergetic neutral particles. We assume here that the incident beam may have a monodirectional component and a continuously distributed component in angle. We begin by defining the target problem representing the class of radiation transport problems that we are focused on. We then Chandrasekhar decompose the target problem into an uncollided transport problem with left singular boundary conditions and a diffusive transport problem with regular boundary conditions. We perform an analysis of these problems to derive the exact solution of the uncollided transport problem and a discrete ordinates solution in open form to the diffusive transport problem. These solutions are the basis for the definition of a computational method for approximately solving the target problem. We illustrate the numerical accuracy of our method with three basic problems in radiative transfer and neutron transport, and we conclude this article with a discussion and directions for future work.

  18. Complex Wall Boundary Conditions for Modeling Combustion in Catalytic Channels

    NASA Astrophysics Data System (ADS)

    Zhu, Huayang; Jackson, Gregory

    2000-11-01

    Monolith catalytic reactors for exothermic oxidation are being used in automobile exhaust clean-up and ultra-low emissions combustion systems. The reactors present a unique coupling between mass, heat, and momentum transport in a channel flow configuration. The use of porous catalytic coatings along the channel wall presents a complex boundary condition when modeled with the two-dimensional channel flow. This current work presents a 2-D transient model for predicting the performance of catalytic combustion systems for methane oxidation on Pd catalysts. The model solves the 2-D compressible transport equations for momentum, species, and energy, which are solved with a porous washcoat model for the wall boundary conditions. A time-splitting algorithm is used to separate the stiff chemical reactions from the convective/diffusive equations for the channel flow. A detailed surface chemistry mechanism is incorporated for the catalytic wall model and is used to predict transient ignition and steady-state conversion of CH4-air flows in the catalytic reactor.

  19. Spatial heterogeneity of ocean surface boundary conditions under sea ice

    NASA Astrophysics Data System (ADS)

    Barthélemy, Antoine; Fichefet, Thierry; Goosse, Hugues

    2016-06-01

    The high heterogeneity of sea ice properties implies that its effects on the ocean are spatially variable at horizontal scales as small as a few meters. Previous studies have shown that taking this variability into account in models could be required to simulate adequately mixed layer processes and the upper ocean temperature and salinity structures. Although many advanced sea ice models include a subgrid-scale ice thickness distribution, potentially providing heterogeneous surface boundary conditions, the information is lost in the coupling with a unique ocean grid cell underneath. The present paper provides a thorough examination of boundary conditions at the ocean surface in the NEMO-LIM model, which can be used as a guideline for studies implementing subgrid-scale ocean vertical mixing schemes. Freshwater, salt, solar heat and non-solar heat fluxes are examined, as well as the norm of the surface stress. All of the thermohaline fluxes vary considerably between the open water and ice fractions of grid cells. To a lesser extent, this is also the case for the surface stress. Moreover, the salt fluxes in both hemispheres and the solar heat fluxes in the Arctic show a dependence on the ice thickness category, with more intense fluxes for thinner ice, which promotes further subgrid-scale heterogeneity. Our analysis also points out biases in the simulated open water fraction and in the ice thickness distribution, which should be investigated in more details in order to ensure that the latter is used to the best advantage.

  20. On free convection heat transfer with well defined boundary conditions

    SciTech Connect

    Davies, M.R.D.; Newport, D.T.; Dalton, T.M.

    1999-07-01

    The scaling of free convection heat transfer is investigated. The non-dimensional groups for Boussinesq and fully compressible variable property free convection, driven by isothermal surfaces, are derived using a previously published novel method of dimensional analysis. Both flows are described by a different set of groups. The applicability of each flow description is experimentally investigated for the case of the isothermal horizontal cylinder in an air-filled isothermal enclosure. The approach taken to the boundary conditions differs from that of previous investigations. Here, it is argued that the best definition of the boundary conditions is achieved for heat exchange between the cylinder and the enclosure rather than the cylinder and an arbitrarily chosen fluid region. The enclosure temperature is shown both analytically and experimentally to affect the Nusselt number. The previously published view that the Boussinesq approximation has only a limited range of application is confirmed, and the groups derived for variable property compressible free convection are demonstrated to be correct experimentally. A new correlation for horizontal cylinder Nusselt number prediction is presented.

  1. Boundary conditions on the vapor liquid interface at strong condensation

    NASA Astrophysics Data System (ADS)

    Kryukov, A. P.; Levashov, V. Yu.

    2016-07-01

    The problem of the formulation of boundary conditions on the vapor-liquid interface is considered. The different approaches to this problem and their difficulties are discussed. Usually, a quasi-equilibrium scheme is used. At sufficiently large deviations from thermodynamic equilibrium, a molecular kinetics approach should be used for the description of the vapor flow at condensation. The formulation of the boundary conditions at the vapor liquid interface to solve the Boltzmann kinetic equation for the distribution of molecules by velocity is a sophisticated problem. It appears that molecular dynamics simulation (MDS) can be used to provide this solution at the interface. The specific problems occur in the realization of MDS on large time and space scales. Some of these problems, and a hierarchy of continuum, kinetic and molecular dynamic time scales, are discussed in the paper. A description of strong condensation at the kinetic level is presented for the steady one-dimensional problem. A formula is provided for the calculation of the limiting condensation coefficient. It is shown that as the condensation coefficient approaches the limiting value, the vapor pressure rises significantly. The results of the corresponding calculations for the Mach number and temperature at different vapor flows are demonstrated. As a result of the application of the molecular kinetics method and molecular dynamics simulation to the problem of the determination of argon condensation coefficients in the range of temperatures of vapor and liquid ratio 1.0-4.0, it is concluded that the condensation coefficient is close to unity.

  2. A Comparison of Transparent Boundary Conditions for the Fresnel Equation

    NASA Astrophysics Data System (ADS)

    Yevick, David; Friese, Tilmann; Schmidt, Frank

    2001-04-01

    We consider two numerical transparent boundary conditions that have been previously introduced in the literature. The first condition (BPP) was proposed by Baskakov and Popov (1991, Wave Motion14, 121-128) and Papadakis et al. (1992, J. Acoust. Soc. Am.92, 2030-2038) while the second (SDY) is that of Schmidt and Deuflhard (1995, Comput. Math. Appl.29, 53-76) and Schmidt and Yevick (1997, J. Comput. Phys.134, 96-107). The latter procedure is explicitly tailored to the form of the underlying numerical propagation scheme and is therefore unconditionally stable and highly precise. Here we present a new derivation of the SDY approach. As a result of this analysis, we obtain a simple modification of the BPP method that guarantees accuracy and stability for long propagation step lengths.

  3. Experimental verification of boundary conditions for numerical simulation of airflow in a benchmark ventilation channel

    NASA Astrophysics Data System (ADS)

    Lizal, Frantisek; Niedoba, Pavel; Seda, Libor; Jedelsky, Jan; Jicha, Miroslav

    2016-03-01

    Correct definition of boundary conditions is crucial for the appropriate simulation of a flow. It is a common practice that simulation of sufficiently long upstream entrance section is performed instead of experimental investigation of the actual conditions at the boundary of the examined area, in the case that the measurement is either impossible or extremely demanding. We focused on the case of a benchmark channel with ventilation outlet, which models a regular automotive ventilation system. At first, measurements of air velocity and turbulence intensity were performed at the boundary of the examined area, i.e. in the rectangular channel 272.5 mm upstream the ventilation outlet. Then, the experimentally acquired results were compared with results obtained by numerical simulation of further upstream entrance section defined according to generally approved theoretical suggestions. The comparison showed that despite the simple geometry and general agreement of average axial velocity, certain difference was found in the shape of the velocity profile. The difference was attributed to the simplifications of the numerical model and the isotropic turbulence assumption of the used turbulence model. The appropriate recommendations were stated for the future work.

  4. Influence of Spanwise Boundary Conditions on Slat Noise Simulations

    NASA Technical Reports Server (NTRS)

    Lockard, David P.; Choudhari, Meelan M.; Buning, Pieter G.

    2015-01-01

    The slat noise from the 30P/30N high-lift system is being investigated through computational fluid dynamics simulations with the OVERFLOW code in conjunction with a Ffowcs Williams-Hawkings acoustics solver. In the present study, two different spanwise grids are being used to investigate the effect of the spanwise extent and periodicity on the near-field unsteady structures and radiated noise. The baseline grid with periodic boundary conditions has a short span equal to 1/9th of the stowed chord, whereas the other, longer span grid adds stretched grids on both sides of the core, baseline grid to allow inviscid surface boundary conditions at both ends. The results indicate that the near-field mean statistics obtained using the two grids are similar to each other, as are the directivity and spectral shapes of the radiated noise. However, periodicity forces all acoustic waves with less than one wavelength across the span to be two-dimensional, without any variation in the span. The spanwise coherence of the acoustic waves is what is needed to make estimates of the noise that would be radiated from realistic span lengths. Simulations with periodic conditions need spans of at least six slat chords to allow spanwise variation in the low-frequencies associated with the peak of broadband slat noise. Even then, the full influence of the periodicity is unclear, so employing grids with a fine, central region and highly stretched meshes that go to slip walls may be a more efficient means of capturing the spanwise decorrelation of low-frequency acoustic phenomena.

  5. Nonlinear acoustic wave propagation in atmosphere. Absorbing boundary conditions for exterior problems

    NASA Technical Reports Server (NTRS)

    Hariharan, S. I.

    1985-01-01

    Elliptic and hyperbolic problems in unbounded regions are considered. These problems, when one wants to solve them numerically, have the difficulty of prescribing boundary conditions at infinity. Computationally, one needs a finite region in which to solve these problems. The corresponding conditions at infinity imposed on the finite distance boundaries should dictate the boundary conditions at infinity and be accurate with respect to the interior numerical scheme. The treatment of these boundary conditions for wave-like equations is discussed.

  6. Atom-partitioned multipole expansions for electrostatic potential boundary conditions

    NASA Astrophysics Data System (ADS)

    Lee, M.; Leiter, K.; Eisner, C.; Knap, J.

    2017-01-01

    Applications such as grid-based real-space density functional theory (DFT) use the Poisson equation to compute electrostatics. However, the expected long tail of the electrostatic potential requires either the use of a large and costly outer domain or Dirichlet boundary conditions estimated via multipole expansion. We find that the oft-used single-center spherical multipole expansion is only appropriate for isotropic mesh domains such as spheres and cubes. In this work, we introduce a method suitable for high aspect ratio meshes whereby the charge density is partitioned into atomic domains and multipoles are computed for each domain. While this approach is moderately more expensive than a single-center expansion, it is numerically stable and still a small fraction of the overall cost of a DFT calculation. The net result is that when high aspect ratio systems are being studied, form-fitted meshes can now be used in lieu of cubic meshes to gain computational speedup.

  7. Fluid flow in nanopores: Accurate boundary conditions for carbon nanotubes

    NASA Astrophysics Data System (ADS)

    Sokhan, Vladimir P.; Nicholson, David; Quirke, Nicholas

    2002-11-01

    Steady-state Poiseuille flow of a simple fluid in carbon nanopores under a gravitylike force is simulated using a realistic empirical many-body potential model for carbon. Building on our previous study of slit carbon nanopores we show that fluid flow in a nanotube is also characterized by a large slip length. By analyzing temporal profiles of the velocity components of particles colliding with the wall we obtain values of the Maxwell coefficient defining the fraction of molecules thermalized by the wall and, for the first time, propose slip boundary conditions for smooth continuum surfaces such that they are equivalent in adsorption, diffusion, and fluid flow properties to fully dynamic atomistic models.

  8. Modeling solar wind with boundary conditions from interplanetary scintillations

    DOE PAGES

    Manoharan, P.; Kim, T.; Pogorelov, N. V.; ...

    2015-09-30

    Interplanetary scintillations make it possible to create three-dimensional, time- dependent distributions of the solar wind velocity. Combined with the magnetic field observations in the solar photosphere, they help perform solar wind simulations in a genuinely time-dependent way. Interplanetary scintillation measurements from the Ooty Radio Astronomical Observatory in India provide directions to multiple stars and may assure better resolution of transient processes in the solar wind. In this paper, we present velocity distributions derived from Ooty observations and compare them with those obtained with the Wang-Sheeley-Arge (WSA) model. We also present our simulations of the solar wind flow from 0.1 AUmore » to 1 AU with the boundary conditions based on both Ooty and WSA data.« less

  9. Modeling solar wind with boundary conditions from interplanetary scintillations

    SciTech Connect

    Manoharan, P.; Kim, T.; Pogorelov, N. V.; Arge, C. N.

    2015-09-30

    Interplanetary scintillations make it possible to create three-dimensional, time- dependent distributions of the solar wind velocity. Combined with the magnetic field observations in the solar photosphere, they help perform solar wind simulations in a genuinely time-dependent way. Interplanetary scintillation measurements from the Ooty Radio Astronomical Observatory in India provide directions to multiple stars and may assure better resolution of transient processes in the solar wind. In this paper, we present velocity distributions derived from Ooty observations and compare them with those obtained with the Wang-Sheeley-Arge (WSA) model. We also present our simulations of the solar wind flow from 0.1 AU to 1 AU with the boundary conditions based on both Ooty and WSA data.

  10. Simulating flight boundary conditions for orbiter payload modal survey

    NASA Technical Reports Server (NTRS)

    Chung, Y. T.; Sernaker, M. L.; Peebles, J. H.

    1993-01-01

    An approach to simulate the characteristics of the payload/orbiter interfaces for the payload modal survey was developed. The flexure designed for this approach is required to provide adequate stiffness separation in the free and constrained interface degrees of freedom to closely resemble the flight boundary condition. Payloads will behave linearly and demonstrate similar modal effective mass distribution and load path as the flight if the flexure fixture is used for the payload modal survey. The potential non-linearities caused by the trunnion slippage during the conventional fixed base modal survey may be eliminated. Consequently, the effort to correlate the test and analysis models can be significantly reduced. An example is given to illustrate the selection and the sensitivity of the flexure stiffness. The advantages of using flexure fixtures for the modal survey and for the analytical model verification are also demonstrated.

  11. Thermal Momentum Distribution from Path Integrals with Shifted Boundary Conditions

    NASA Astrophysics Data System (ADS)

    Giusti, Leonardo; Meyer, Harvey B.

    2011-04-01

    For a thermal field theory formulated in the grand canonical ensemble, the distribution of the total momentum is an observable characterizing the thermal state. We show that its cumulants are related to thermodynamic potentials. In a relativistic system, for instance, the thermal variance of the total momentum is a direct measure of the enthalpy. We relate the generating function of the cumulants to the ratio of (a) a partition function expressed as a Matsubara path integral with shifted boundary conditions in the compact direction and (b) the ordinary partition function. In this form the generating function is well suited for Monte Carlo evaluation, and the cumulants can be extracted straightforwardly. We test the method in the SU(3) Yang-Mills theory and obtain the entropy density at three different temperatures.

  12. Micromagnetic simulations with periodic boundary conditions: Hard-soft nanocomposites

    SciTech Connect

    Wysocki, Aleksander L.; Antropov, Vladimir P.

    2016-12-01

    Here, we developed a micromagnetic method for modeling magnetic systems with periodic boundary conditions along an arbitrary number of dimensions. The main feature is an adaptation of the Ewald summation technique for evaluation of long-range dipolar interactions. The method was applied to investigate the hysteresis process in hard-soft magnetic nanocomposites with various geometries. The dependence of the results on different micromagnetic parameters was studied. We found that for layered structures with an out-of-plane hard phase easy axis the hysteretic properties are very sensitive to the strength of the interlayer exchange coupling, as long as the spontaneous magnetization for the hard phase is significantly smaller than for the soft phase. The origin of this behavior was discussed. Additionally, we investigated the soft phase size optimizing the energy product of hard-soft nanocomposites.

  13. Micromagnetic simulations with periodic boundary conditions: Hard-soft nanocomposites

    NASA Astrophysics Data System (ADS)

    Wysocki, Aleksander L.; Antropov, Vladimir P.

    2017-04-01

    We developed a micromagnetic method for modeling magnetic systems with periodic boundary conditions along an arbitrary number of dimensions. The main feature is an adaptation of the Ewald summation technique for evaluation of long-range dipolar interactions. The method was applied to investigate the hysteresis process in hard-soft magnetic nanocomposites with various geometries. The dependence of the results on different micromagnetic parameters was studied. We found that for layered structures with an out-of-plane hard phase easy axis the hysteretic properties are very sensitive to the strength of the interlayer exchange coupling, as long as the spontaneous magnetization for the hard phase is significantly smaller than for the soft phase. The origin of this behavior was discussed. Additionally, we investigated the soft phase size optimizing the energy product of hard-soft nanocomposites.

  14. Micromagnetic simulations with periodic boundary conditions: Hard-soft nanocomposites

    DOE PAGES

    Wysocki, Aleksander L.; Antropov, Vladimir P.

    2016-12-01

    Here, we developed a micromagnetic method for modeling magnetic systems with periodic boundary conditions along an arbitrary number of dimensions. The main feature is an adaptation of the Ewald summation technique for evaluation of long-range dipolar interactions. The method was applied to investigate the hysteresis process in hard-soft magnetic nanocomposites with various geometries. The dependence of the results on different micromagnetic parameters was studied. We found that for layered structures with an out-of-plane hard phase easy axis the hysteretic properties are very sensitive to the strength of the interlayer exchange coupling, as long as the spontaneous magnetization for the hardmore » phase is significantly smaller than for the soft phase. The origin of this behavior was discussed. Additionally, we investigated the soft phase size optimizing the energy product of hard-soft nanocomposites.« less

  15. Unsteady Squeezing Flow of Carbon Nanotubes with Convective Boundary Conditions.

    PubMed

    Hayat, Tasawar; Muhammad, Khursheed; Farooq, Muhammad; Alsaedi, Ahmad

    2016-01-01

    Unsteady flow of nanofluids squeezed between two parallel plates is discussed in the presence of viscous dissipation. Heat transfer phenomenon is disclosed via convective boundary conditions. Carbon nanotubes (single-wall and multi-wall) are used as nanoparticles which are homogeneously distributed in the base fluid (water). A system of non-linear differential equations for the flow is obtained by utilizing similarity transformations through the conservation laws. Influence of various emerging parameters on the velocity and temperature profiles are sketched graphically and discussed comprehensively. Analyses of skin fraction coefficient and Nusselt number are also elaborated numerically. It is found out that velocity is smaller for squeezing parameter in the case of multi-wall carbon nanotubes when compared with single-wall carbon nanotubes.

  16. On boundary condition in heat-exchange processes

    NASA Astrophysics Data System (ADS)

    Stolyarov, E. P.

    2016-10-01

    This paper describes the numerical study of heat-exchange of solid body with high-temperature external flow. As follows from the Newton's boundary condition, connecting a heat-flux density with temperature difference between the flow and a body, the heat-exchange coefficient is physically equivalent to the body-surface-normal component of the entropy flux from external flow at equilibrium flow regime. The method of determination of the heat-exchange characteristics using the time-history temperature measurements by a thin-film thermocouple sensor is described. As it is shown from the numerical analysis, the asymptotic value of the heat-exchange coefficient that corresponded to equilibrium regime of external flow exists. Implementation time of this value, i.e. relaxation time, may be of some characteristic time scales of the sensor measuring layer.

  17. Estimating Thermal Inertia with a Maximum Entropy Boundary Condition

    NASA Astrophysics Data System (ADS)

    Nearing, G.; Moran, M. S.; Scott, R.; Ponce-Campos, G.

    2012-04-01

    Thermal inertia, P [Jm-2s-1/2K-1], is a physical property the land surface which determines resistance to temperature change under seasonal or diurnal heating. It is a function of volumetric heat capacity, c [Jm-3K-1], and thermal conductivity, k [Wm-1K-1] of the soil near the surface: P=√ck. Thermal inertia of soil varies with moisture content due the difference between thermal properties of water and air, and a number of studies have demonstrated that it is feasible to estimate soil moisture given thermal inertia (e.g. Lu et al, 2009, Murray and Verhoef, 2007). We take the common approach to estimating thermal inertia using measurements of surface temperature by modeling the Earth's surface as a 1-dimensional homogeneous diffusive half-space. In this case, surface temperature is a function of the ground heat flux (G) boundary condition and thermal inertia and a daily value of P was estimated by matching measured and modeled diurnal surface temperature fluctuations. The difficulty is in measuring G; we demonstrate that the new maximum entropy production (MEP) method for partitioning net radiation into surface energy fluxes (Wang and Bras, 2011) provides a suitable boundary condition for estimating P. Adding the diffusion representation of heat transfer in the soil reduces the number of free parameters in the MEP model from two to one, and we provided a sensitivity analysis which suggests that, for the purpose of estimating P, it is preferable to parameterize the coupled MEP-diffusion model by the ratio of thermal inertia of the soil to the effective thermal inertia of convective heat transfer to the atmosphere. We used this technique to estimate thermal inertia at two semiarid, non-vegetated locations in the Walnut Gulch Experimental Watershed in southeast AZ, USA and compared these estimates to estimates of P made using the Xue and Cracknell (1995) solution for a linearized ground heat flux boundary condition, and we found that the MEP-diffusion model produced

  18. Equilibrium boundary conditions, dynamic vacuum energy, and the big bang

    SciTech Connect

    Klinkhamer, F. R.

    2008-10-15

    The near-zero value of the cosmological constant {lambda} in an equilibrium context may be due to the existence of a self-tuning relativistic vacuum variable q. Here, a cosmological nonequilibrium context is considered with a corresponding time-dependent cosmological parameter {lambda}(t) or vacuum energy density {rho}{sub V}(t). A specific model of a closed Friedmann-Robertson-Walker universe is presented, which is determined by equilibrium boundary conditions at one instant of time (t=t{sub eq}) and a particular form of vacuum-energy dynamics (d{rho}{sub V}/dt{proportional_to}{rho}{sub M}). This homogeneous and isotropic model has a standard big bang phase at early times (t<

  19. Gas cushion model and hydrodynamic boundary conditions for superhydrophobic textures

    NASA Astrophysics Data System (ADS)

    Nizkaya, Tatiana V.; Asmolov, Evgeny S.; Vinogradova, Olga I.

    2014-10-01

    Superhydrophobic Cassie textures with trapped gas bubbles reduce drag, by generating large effective slip, which is important for a variety of applications that involve a manipulation of liquids at the small scale. Here we discuss how the dissipation in the gas phase of textures modifies their friction properties. We propose an operator method, which allows us to map the flow in the gas subphase to a local slip boundary condition at the liquid-gas interface. The determined uniquely local slip length depends on the viscosity contrast and underlying topography, and can be immediately used to evaluate an effective slip of the texture. Besides superlubricating Cassie surfaces, our approach is valid for rough surfaces impregnated by a low-viscosity "lubricant," and even for Wenzel textures, where a liquid follows the surface relief. These results provide a framework for the rational design of textured surfaces for numerous applications.

  20. Sensitivity and uncertainty analysis of the recharge boundary condition

    NASA Astrophysics Data System (ADS)

    Jyrkama, M. I.; Sykes, J. F.

    2006-01-01

    The reliability analysis method is integrated with MODFLOW to study the impact of recharge on the groundwater flow system at a study area in New Jersey. The performance function is formulated in terms of head or flow rate at a pumping well, while the recharge sensitivity vector is computed efficiently by implementing the adjoint method in MODFLOW. The developed methodology not only quantifies the reliability of head at the well in terms of uncertainties in the recharge boundary condition, but it also delineates areas of recharge that have the highest impact on the head and flow rate at the well. The results clearly identify the most important land use areas that should be protected in order to maintain the head and hence production at the pumping well. These areas extend far beyond the steady state well capture zone used for land use planning and management within traditional wellhead protection programs.

  1. Introduction of periodic boundary conditions into UNRES force field.

    PubMed

    Sieradzan, Adam K

    2015-05-05

    In this article, implementation of periodic boundary conditions (PBC) into physics-based coarse-grained UNited RESidue (UNRES) force field is presented, which replaces droplet-like restraints previously used. Droplet-like restraints are necessary to keep multichain systems together and prevent them from dissolving to infinitely low concentration. As an alternative for droplet-like restrains cuboid PBCs with imaging of the molecules were introduced. Owing to this modification, artificial forces which arose from restraints keeping a droplet together were eliminated what leads to more realistic trajectories. Due to computational reasons cutoff and smoothing functions were introduced on the long range interactions. The UNRES force field with PBC was tested by performing microcanonical simulations. Moreover, to asses the behavior of the thermostat in PBCs Langevin and Berendsen thermostats were studied. The influence of PBCs on association pattern was compared with droplet-like restraints on the ββα hetero tetramer 1 protein system.

  2. Unsteady Squeezing Flow of Carbon Nanotubes with Convective Boundary Conditions

    PubMed Central

    Hayat, Tasawar; Muhammad, Khursheed; Farooq, Muhammad; Alsaedi, Ahmad

    2016-01-01

    Unsteady flow of nanofluids squeezed between two parallel plates is discussed in the presence of viscous dissipation. Heat transfer phenomenon is disclosed via convective boundary conditions. Carbon nanotubes (single-wall and multi-wall) are used as nanoparticles which are homogeneously distributed in the base fluid (water). A system of non-linear differential equations for the flow is obtained by utilizing similarity transformations through the conservation laws. Influence of various emerging parameters on the velocity and temperature profiles are sketched graphically and discussed comprehensively. Analyses of skin fraction coefficient and Nusselt number are also elaborated numerically. It is found out that velocity is smaller for squeezing parameter in the case of multi-wall carbon nanotubes when compared with single-wall carbon nanotubes. PMID:27149208

  3. Divergence of actual and reference evapotranspiration observations for irrigated sugarcane with windy tropical conditions

    Technology Transfer Automated Retrieval System (TEKTRAN)

    Standardized reference evapotranspiration (ET) and ecosystem-specific vegetation coefficients are frequently used to estimate actual ET. However, equations for calculating reference ET have not been well validated in more humid environments. We measured ET (ETEC) using Eddy Covariance (EC) towers a...

  4. Behavior of the Reversed Field Pinch with Nonideal Boundary Conditions.

    NASA Astrophysics Data System (ADS)

    Ho, Yung-Lung

    The linear and nonlinear magnetohydrodynamic stability of current-driven modes is studied for a reversed field pinch with nonideal boundary conditions. The plasma is bounded by a thin resistive shell surrounded by a vacuum region out to a radius at which a perfectly conducting wall is situated. The distant wall and the thin shell problems are studied by removing either the resistive shell or the conducting wall. Linearly, growth rates of tearing modes and kink modes are calculated by analytical solutions based on the modified Bessel function model for the equilibrium. The effects of variation of the shell resistivity and wall proximity on the growth rates are investigated. The modes that may be important in different parameter regimes and with different boundary conditions are identified. These results then help to guide the nonlinear study, and also help to interpret the quasilinear aspect of the nonlinear results. The nonlinear behaviors are studied with a three -dimensional magnetohydrodynamics code. The fluctuations generally rise with increasing distance between the conducting wall and the plasma. The enhanced fluctuation induced v times b electric field primarily oppose toroidal current; hence, loop voltage must increase to sustain the constant. If the loop voltage is held constant, the current decreases and the plasma evolves toward a nonreversed tokamak-like state. Quasilinear interaction between modes typically associated with the dynamo action is identified as the most probable nonlinear destabilization mechanism. The helicity and energy balance properties of the simulation results are discussed. The interruption of current density along field lines intersecting the resistive shell is shown to lead to surface helicity leakage. This effect is intimately tied to stability, as fluctuation induced v times b electric field is necessary to transport the helicity to the surface. In this manner, all aspects of helicity balance, i.e., injection, transport, and

  5. Behavior of the reversed field pinch with nonideal boundary conditions

    NASA Astrophysics Data System (ADS)

    Ho, Yung-Lung

    1988-11-01

    The linear and nonlinear magnetohydrodynamic stability of current-driven modes are studied for a reversed field pinch with nonideal boundary conditions. The plasma is bounded by a thin resistive shell surrounded by a vacuum region out to a radius at which a perfectly conducting wall is situated. The distant wall and the thin shell problems are studied by removing either the resistive shell or the conducting wall. Linearly, growth rates of tearing modes and kink modes are calculated by analytical solutions based on the modified Bessel function model for the equilibrium. The effects of variation of the shell resistivity and wall proximity on the growth rates are investigated. The modes that may be important in different parameter regimes and with different boundary conditions are identified. The nonlinear behaviors are studied with a three-dimensional magnetohydrodynamics code. The fluctuations generally rise with increasing distance between the conducting wall and the plasma. The enhanced fluctuation induced v x b electric field primarily oppose toroidal current; hence, loop voltage must increase to sustain the constant. Quasilinear interaction between modes typically associated with the dynamo action is identified as the most probable nonlinear destabilization mechanism. The helicity and energy balance properties of the simulation results are discussed. The interruption of current density along field lines intersecting the resistive shell is shown to lead to surface helicity leakage. This effect is intimately tied to stability, as fluctuation induced v x b electric field is necessary to transport the helicity to the surface. In this manner, all aspects of helicity balance, i.e., injection, transport, and dissipation, are considered self-consistently. The importance of the helicity and energy dissipation by the mean components of the magnetic field and current density is discussed.

  6. Solution of the Boundary Value Problems with Boundary Conditions in the Form of Gravitational Curvatures

    NASA Astrophysics Data System (ADS)

    Sprlak, M.; Novak, P.; Pitonak, M.; Hamackova, E.

    2015-12-01

    Values of scalar, vectorial and second-order tensorial parameters of the Earth's gravitational field have been collected by various sensors in geodesy and geophysics. Such observables have been widely exploited in different parametrization methods for the gravitational field modelling. Moreover, theoretical aspects of these quantities have extensively been studied and are well understood. On the other hand, new sensors for observing gravitational curvatures, i.e., components of the third-order gravitational tensor, are currently under development. This fact may be documented by the terrestrial experiments Dulkyn and Magia, as well as by the proposal of the gravity-dedicated satellite mission called OPTIMA. As the gravitational curvatures represent new types of observables, their exploitation for modelling of the Earth's gravitational field is a subject of this study. Firstly, we derive integral transforms between the gravitational potential and gravitational curvatures, i.e., we find analytical solutions of the boundary value problems with gravitational curvatures as boundary conditions. Secondly, properties of the corresponding Green kernel functions are studied in the spatial and spectral domains. Thirdly, the correctness of the new analytical solutions is tested in a simulation study. The presented mathematical apparatus reveal important properties of the gravitational curvatures. It also extends the Meissl scheme, i.e., an important theoretical paradigm that relates various parameters of the Earth's gravitational field.

  7. Numerical Studies of Urban Planetary Boundary-Layer Structure under Realistic Synoptic Conditions.

    NASA Astrophysics Data System (ADS)

    Seaman, Nelson L.; Ludwig, Francis L.; Donall, Evelyn G.; Warner, Thomas T.; Bhumralkar, Chandrakant M.

    1989-08-01

    The Pennsylvania State University (PSU)/National Center for Atmospheric Research (NCAR) mesoscale model was modified and used to simulate the evolution of meteorological conditions in the vicinity of St. Louis, Missouri, from near sunrise to noon on 25 July 1975. Observations obtained during the METROMEX (Metropolitan Meteorological Experiment) and RAPS (Regional Air Pollution Study) field programs were available for comparison with modeled conditions. The PSU/NCAR model used a nested grid with two-way interaction between the coarse mesh (7.5 km) and the fine mesh (2.5 km), where the fine domain covered the city and its immediate suburban and rural surroundings. Realistic three-dimensionally variable initial and lateral boundary conditions were obtained from the observations so that the numerical experiments could be used for quantitative evaluation of certain urban effects. After simulation of the actual conditions (control experiment), the importance of a number of processes on the urban planetary boundary layer (PBL) structure were investigated. The PBL effects were isolated by using realistic surface parameters as well as those based on the preurban conditions and an expanded urban environment. Sensitivities to surface evaporative fluxes, radiative processes, and different surface roughness associated with urbanization were examined. The control simulations of the temperature, boundary layer depth, specific humidity and wind fields exhibited essentially the same behavior as observed in the urban PBL throughout the morning forecast period. Unlike many other documented cases that displayed strong urban-induced low-level convergence, the confluence on this morning was relatively weak, with the center of the heat island displaced (in both the simulation and the observations) downwind (south) of the city. A relative minimum in windspeed was associated with the center of the displaced heat island. The sensitivity experiments clearly demonstrated and maintenance of

  8. Compressible turbulent channel flow with impedance boundary conditions

    NASA Astrophysics Data System (ADS)

    Scalo, Carlo; Bodart, Julien; Lele, Sanjiva K.

    2015-03-01

    We have performed large-eddy simulations of isothermal-wall compressible turbulent channel flow with linear acoustic impedance boundary conditions (IBCs) for the wall-normal velocity component and no-slip conditions for the tangential velocity components. Three bulk Mach numbers, Mb = 0.05, 0.2, 0.5, with a fixed bulk Reynolds number, Reb = 6900, have been investigated. For each Mb, nine different combinations of IBC settings were tested, in addition to a reference case with impermeable walls, resulting in a total of 30 simulations. The adopted numerical coupling strategy allows for a spatially and temporally consistent imposition of physically realizable IBCs in a fully explicit compressible Navier-Stokes solver. The IBCs are formulated in the time domain according to Fung and Ju ["Time-domain impedance boundary conditions for computational acoustics and aeroacoustics," Int. J. Comput. Fluid Dyn. 18(6), 503-511 (2004)]. The impedance adopted is a three-parameter damped Helmholtz oscillator with resonant angular frequency, ωr, tuned to the characteristic time scale of the large energy-containing eddies. The tuning condition, which reads ωr = 2πMb (normalized with the speed of sound and channel half-width), reduces the IBCs' free parameters to two: the damping ratio, ζ, and the resistance, R, which have been varied independently with values, ζ = 0.5, 0.7, 0.9, and R = 0.01, 0.10, 1.00, for each Mb. The application of the tuned IBCs results in a drag increase up to 300% for Mb = 0.5 and R = 0.01. It is shown that for tuned IBCs, the resistance, R, acts as the inverse of the wall-permeability and that varying the damping ratio, ζ, has a secondary effect on the flow response. Typical buffer-layer turbulent structures are completely suppressed by the application of tuned IBCs. A new resonance buffer layer is established characterized by large spanwise-coherent Kelvin-Helmholtz rollers, with a well-defined streamwise wavelength λx, traveling downstream with

  9. Combining characteristic forms of boundary conditions and conservation equations at boundaries of cell-centered Euler-flow calculations

    NASA Astrophysics Data System (ADS)

    Boerstoel, J. W.

    1987-04-01

    A numerical method to obtain the additional equations in Euler-flow calculations based on cell-centered schemes when the number of equations required to determine the flow-state evaluation at grid points half a mesh outside the flow domain exceeds the number of boundary-condition equations provided by characteristic theory, is presented. A layer of auxiliary cells on flow boundaries is introduced, and semidiscrete conservation equations for these cells are defined. The time variations of the state in these auxiliary cells at the boundary are transformed into characteristic form, and time variations of characteristic variables corresponding to incoming information from the boundary into the flow are replaced by boundary conditions for these time variations. The boundary equations so obtained are mapped back into a form with primitive variables, and numerically integrated in time. The characteristic boundary conditions are first-order differential equations for time variations at boundary points of characteristic variables. These equations may be chosen to express that given functions of the flow state on the boundary should asymptotically tend with time to prescribed steady-state values.

  10. Effects of boundary conditions and partial drainage on cyclic simple shear test results - a numerical study

    NASA Astrophysics Data System (ADS)

    Wang, Bin; Popescu, Radu; Prevost, Jean H.

    2004-08-01

    Owing to imperfect boundary conditions in laboratory soil tests and the possibility of water diffusion inside the soil specimen in undrained tests, the assumption of uniform stress/strain over the sample is not valid. This study presents a qualitative assessment of the effects of non-uniformities in stresses and strains, as well as effects of water diffusion within the soil sample on the global results of undrained cyclic simple shear tests. The possible implications of those phenomena on the results of liquefaction strength assessment are also discussed. A state-of-the-art finite element code for transient analysis of multi-phase systems is used to compare results of the so-called element tests (numerical constitutive experiments assuming uniform stress/strain/pore pressure distribution throughout the sample) with results of actual simulations of undrained cyclic simple shear tests using a finite element mesh and realistic boundary conditions. The finite element simulations are performed under various conditions, covering the entire range of practical situations: (1) perfectly drained soil specimen with constant volume, (2) perfectly undrained specimen, and (3) undrained test with possibility of water diffusion within the sample. The results presented here are restricted to strain-driven tests performed for a loose uniform fine sand with relative density Dr=40%. Effects of system compliance in undrained laboratory simple shear tests are not investigated here. Copyright

  11. Towards Direct Simulations of Counterflow Flames with Consistent Differential-Algebraic Boundary Conditions

    DTIC Science & Technology

    2015-01-05

    discretization of the steady- state Navier-Stokes equations at the inflow boundaries, numerically algebraic equations are imposed as boundary conditions...conditions for the counterflow configuration is presented. Upon discretization of the steady- state Navier-Stokes equations at the inflow boundaries...boundary conditions for the counterflow configu- ration is presented. Upon discretization of the steady- state Navier-Stokes equations at the inflow

  12. On dualities for SSEP and ASEP with open boundary conditions

    NASA Astrophysics Data System (ADS)

    Ohkubo, J.

    2017-03-01

    Duality relations for simple exclusion processes with general open boundaries are discussed. It is shown that a combination of spin operators and bosonic operators enables us to have a unified discussion about duality relations with open boundaries. As for the symmetric simple exclusion process (SSEP), more general results than those from previous studies are obtained. It is clarified that not only the absorbing sites, but also additional sites—called copying sites— are needed for the boundaries in the dual process for the SSEP. The role of the copying sites is to conserve information about the particle states on the boundary sites. Similar discussions are applied to the asymmetric simple exclusion process (ASEP), in which the q-analogues are employed, and it is clarified that the ASEP with open boundaries has a complicated dual process on the boundaries.

  13. Reconstructing geographical boundary conditions for palaeoclimate modelling during the Cenozoic

    NASA Astrophysics Data System (ADS)

    Baatsen, Michiel; van Hinsbergen, Douwe J. J.; von der Heydt, Anna S.; Dijkstra, Henk A.; Sluijs, Appy; Abels, Hemmo A.; Bijl, Peter K.

    2016-08-01

    Studies on the palaeoclimate and palaeoceanography using numerical model simulations may be considerably dependent on the implemented geographical reconstruction. Because building the palaeogeographic datasets for these models is often a time-consuming and elaborate exercise, palaeoclimate models frequently use reconstructions in which the latest state-of-the-art plate tectonic reconstructions, palaeotopography and -bathymetry, or vegetation have not yet been incorporated. In this paper, we therefore provide a new method to efficiently generate a global geographical reconstruction for the middle-late Eocene. The generalised procedure is also reusable to create reconstructions for other time slices within the Cenozoic, suitable for palaeoclimate modelling. We use a plate-tectonic model to make global masks containing the distribution of land, continental shelves, shallow basins and deep ocean. The use of depth-age relationships for oceanic crust together with adjusted present-day topography gives a first estimate of the global geography at a chosen time frame. This estimate subsequently needs manual editing of areas where existing geological data indicate that the altimetry has changed significantly over time. Certain generic changes (e.g. lowering mountain ranges) can be made relatively easily by defining a set of masks while other features may require a more specific treatment. Since the discussion regarding many of these regions is still ongoing, it is crucial to make it easy for changes to be incorporated without having to redo the entire procedure. In this manner, a complete reconstruction can be made that suffices as a boundary condition for numerical models with a limited effort. This facilitates the interaction between experts in geology and palaeoclimate modelling, keeping reconstructions up to date and improving the consistency between different studies. Moreover, it facilitates model inter-comparison studies and sensitivity tests regarding certain

  14. A new method of imposing boundary conditions in pseudospectral approximations of hyperbolic equations

    NASA Technical Reports Server (NTRS)

    Funaro, D.; Gottlieb, D.

    1988-01-01

    A new method to impose boundary conditions for pseudospectral approximations to hyperbolic equations is suggested. This method involves the collocation of the equation at the boundary nodes as well as satisfying boundary conditions. Stability and convergence results are proven for the Chebyshev approximation of linear scalar hyperbolic equations. The eigenvalues of this method applied to parabolic equations are shown to be real and negative.

  15. Eigenmode Analysis of Boundary Conditions for One-Dimensional Preconditioned Euler Equations

    NASA Technical Reports Server (NTRS)

    Darmofal, David L.

    1998-01-01

    An analysis of the effect of local preconditioning on boundary conditions for the subsonic, one-dimensional Euler equations is presented. Decay rates for the eigenmodes of the initial boundary value problem are determined for different boundary conditions. Riemann invariant boundary conditions based on the unpreconditioned Euler equations are shown to be reflective with preconditioning, and, at low Mach numbers, disturbances do not decay. Other boundary conditions are investigated which are non-reflective with preconditioning and numerical results are presented confirming the analysis.

  16. Heat and moisture diffusion in slab products due to convective boundary condition

    NASA Astrophysics Data System (ADS)

    Yilbas, B. S.; Hussain, M. M.; Dincer, I.

    2002-08-01

    In the present study, a closed form solution for the temperature distributions inside the solid substrate due to convective boundary condition at the surface is presented, particularly for drying applications. The analytical solution for the diffusion equation is introduced with constant concentration at the surface case. Temperature and moisture distributions inside apple slab are computed in this regard. It is found that temperature rises rapidly in the surface region of the substrate material during the early heating period and as the heating period progresses, temperature gradient attains almost steady value with advancing time. Moisture content variation in the surface region is considerably high in the early period and as time progresses, the rate of change of concentration in the substrate reduces. The present model is verified with actual data for heat conduction and moisture diffusion and a considerably high agreement is found.

  17. Comparative analysis of operational forecasts versus actual weather conditions in airline flight planning, volume 2

    NASA Technical Reports Server (NTRS)

    Keitz, J. F.

    1982-01-01

    The impact of more timely and accurate weather data on airline flight planning with the emphasis on fuel savings is studied. This volume of the report discusses the results of Task 2 of the four major tasks included in the study. Task 2 compares various catagories of flight plans and flight tracking data produced by a simulation system developed for the Federal Aviation Administrations by SRI International. (Flight tracking data simulate actual flight tracks of all aircraft operating at a given time and provide for rerouting of flights as necessary to resolve traffic conflicts.) The comparisons of flight plans on the forecast to flight plans on the verifying analysis confirm Task 1 findings that wind speeds are generally underestimated. Comparisons involving flight tracking data indicate that actual fuel burn is always higher than planned, in either direction, and even when the same weather data set is used. Since the flight tracking model output results in more diversions than is known to be the case, it was concluded that there is an error in the flight tracking algorithm.

  18. Space-fractional advection-diffusion and reflective boundary condition.

    PubMed

    Krepysheva, Natalia; Di Pietro, Liliana; Néel, Marie-Christine

    2006-02-01

    Anomalous diffusive transport arises in a large diversity of disordered media. Stochastic formulations in terms of continuous time random walks (CTRWs) with transition probability densities showing space- and/or time-diverging moments were developed to account for anomalous behaviors. A broad class of CTRWs was shown to correspond, on the macroscopic scale, to advection-diffusion equations involving derivatives of noninteger order. In particular, CTRWs with Lévy distribution of jumps and finite mean waiting time lead to a space-fractional equation that accounts for superdiffusion and involves a nonlocal integral-differential operator. Within this framework, we analyze the evolution of particles performing symmetric Lévy flights with respect to a fluid moving at uniform speed . The particles are restricted to a semi-infinite domain limited by a reflective barrier. We show that the introduction of the boundary condition induces a modification in the kernel of the nonlocal operator. Thus, the macroscopic space-fractional advection-diffusion equation obtained is different from that in an infinite medium.

  19. Heating the Solar Corona: Observations for Model Boundary Conditions

    NASA Astrophysics Data System (ADS)

    Nestlerode, C. M.; Poland, A. I.

    2005-12-01

    A prominent question in solar physics concerns the sources of coronal heating. This problem can be addressed through observations of closed magnetic loops which have high enough density to provide adequate temporal, spatial, and spectral resolution. Measurements of temperature, density, and velocity throughout the loop can be used for boundary conditions and compared with quantities for model calculations. In this paper, we present Solar Ultraviolet Measurements from Emitted Radiation (SUMER) data from the Solar and Heliospheric Observatory's (SOHO's) JOP 161 program. The SUMER instrument has high spatial and spectral resolution over several different spectral lines and therefore the data cover a large temperature range. The analyzed lines include Mg VIII, Mg IX, N III, N IV, Ne VIII, O IV, O V, S IV, S V, and S X with temperatures ranging from 60,000 K (S IV) to 0.9 MK (Mg IX). The velocity profiles are created using Gaussian fitting with wavelength calibration determined using average quiet Sun velocities from known Doppler velocity shifts. The velocity profiles show important changes in solar foot point plasma speed both spatially and temporally. This analysis builds on previous analysis of solar spectral lines observed with the SOHO Coronal Diagnostic Spectrometer (CDS); the advantage of the SUMER instrument is better resolution, both spectrally and spatially. This work was funded by NASA, Living with a Star Program.

  20. Brain-skull boundary conditions in a computational deformation model

    NASA Astrophysics Data System (ADS)

    Ji, Songbai; Liu, Fenghong; Roberts, David; Hartov, Alex; Paulsen, Keith

    2007-03-01

    Brain shift poses a significant challenge to accurate image-guided neurosurgery. To this end, finite element (FE) brain models have been developed to estimate brain motion during these procedures. The significance of the brain-skull boundary conditions (BCs) for accurate predictions in these models has been explored in dynamic impact and inertial rotation injury computational simulations where the results have shown that the brain mechanical response is sensitive to the type of BCs applied. We extend the study of brain-skull BCs to quasi-static brain motion simulations which prevail in neurosurgery. Specifically, a frictionless brain-skull BC using a contact penalty method master-slave paradigm is incorporated into our existing deformation forward model (forced displacement method). The initial brain-skull gap (CSF thickness) is assumed to be 2mm for demonstration purposes. The brain surface nodes are assigned as either fixed (at bottom along the gravity direction), free (at brainstem), with prescribed displacement (at craniotomy) or as slave nodes potentially in contact with the skull (all the remaining). Each slave node is assigned a penalty parameter (β=5) such that when the node penetrates the rigid body skull inner-surface (master surface), a contact force is introduced proportionally to the penetration. Effectively, brain surface nodes are allowed to move towards or away from the cranium wall, but are ultimately restricted from penetrating the skull. We show that this scheme improves the model's ability to represent the brain-skull interface.

  1. Positive solutions of quasilinear parabolic systems with nonlinear boundary conditions

    NASA Astrophysics Data System (ADS)

    Pao, C. V.; Ruan, W. H.

    2007-09-01

    The aim of this paper is to investigate the existence, uniqueness, and asymptotic behavior of solutions for a coupled system of quasilinear parabolic equations under nonlinear boundary conditions, including a system of quasilinear parabolic and ordinary differential equations. Also investigated is the existence of positive maximal and minimal solutions of the corresponding quasilinear elliptic system as well as the uniqueness of a positive steady-state solution. The elliptic operators in both systems are allowed to be degenerate in the sense that the density-dependent diffusion coefficients Di(ui) may have the property Di(0)=0 for some or all i. Our approach to the problem is by the method of upper and lower solutions and its associated monotone iterations. It is shown that the time-dependent solution converges to the maximal solution for one class of initial functions and it converges to the minimal solution for another class of initial functions; and if the maximal and minimal solutions coincide then the steady-state solution is unique and the time-dependent solution converges to the unique solution. Applications of these results are given to three model problems, including a porous medium type of problem, a heat-transfer problem, and a two-component competition model in ecology. These applications illustrate some very interesting distinctive behavior of the time-dependent solutions between density-independent and density-dependent diffusions.

  2. Positive solutions of quasilinear parabolic systems with Dirichlet boundary condition

    NASA Astrophysics Data System (ADS)

    Pao, C. V.; Ruan, W. H.

    Coupled systems for a class of quasilinear parabolic equations and the corresponding elliptic systems, including systems of parabolic and ordinary differential equations are investigated. The aim of this paper is to show the existence, uniqueness, and asymptotic behavior of time-dependent solutions. Also investigated is the existence of positive maximal and minimal solutions of the corresponding quasilinear elliptic system. The elliptic operators in both systems are allowed to be degenerate in the sense that the density-dependent diffusion coefficients D(u) may have the property D(0)=0 for some or all i=1,…,N, and the boundary condition is u=0. Using the method of upper and lower solutions, we show that a unique global classical time-dependent solution exists and converges to the maximal solution for one class of initial functions and it converges to the minimal solution for another class of initial functions; and if the maximal and minimal solutions coincide then the steady-state solution is unique and the time-dependent solution converges to the unique solution. Applications of these results are given to three model problems, including a scalar polynomial growth problem, a coupled system of polynomial growth problem, and a two component competition model in ecology.

  3. High Energy Boundary Conditions for a Cartesian Mesh Euler Solver

    NASA Technical Reports Server (NTRS)

    Pandya, Shishir; Murman, Scott; Aftosmis, Michael

    2003-01-01

    Inlets and exhaust nozzles are common place in the world of flight. Yet, many aerodynamic simulation packages do not provide a method of modelling such high energy boundaries in the flow field. For the purposes of aerodynamic simulation, inlets and exhausts are often fared over and it is assumed that the flow differences resulting from this assumption are minimal. While this is an adequate assumption for the prediction of lift, the lack of a plume behind the aircraft creates an evacuated base region thus effecting both drag and pitching moment values. In addition, the flow in the base region is often mis-predicted resulting in incorrect base drag. In order to accurately predict these quantities, a method for specifying inlet and exhaust conditions needs to be available in aerodynamic simulation packages. A method for a first approximation of a plume without accounting for chemical reactions is added to the Cartesian mesh based aerodynamic simulation package CART3D. The method consists of 3 steps. In the first step, a components approach where each triangle is assigned a component number is used. Here, a method for marking the inlet or exhaust plane triangles as separate components is discussed. In step two, the flow solver is modified to accept a reference state for the components marked inlet or exhaust. In the third step, the flow solver uses these separated components and the reference state to compute the correct flow condition at that triangle. The present method is implemented in the CART3D package which consists of a set of tools for generating a Cartesian volume mesh from a set of component triangulations. The Euler equations are solved on the resulting unstructured Cartesian mesh. The present methods is implemented in this package and its usefulness is demonstrated with two validation cases. A generic missile body is also presented to show the usefulness of the method on a real world geometry.

  4. Rheological investigation of body cream and body lotion in actual application conditions

    NASA Astrophysics Data System (ADS)

    Kwak, Min-Sun; Ahn, Hye-Jin; Song, Ki-Won

    2015-08-01

    The objective of the present study is to systematically evaluate and compare the rheological behaviors of body cream and body lotion in actual usage situations. Using a strain-controlled rheometer, the steady shear flow properties of commercially available body cream and body lotion were measured over a wide range of shear rates, and the linear viscoelastic properties of these two materials in small amplitude oscillatory shear flow fields were measured over a broad range of angular frequencies. The temperature dependency of the linear viscoelastic behaviors was additionally investigated over a temperature range most relevant to usual human life. The main findings obtained from this study are summarized as follows: (1) Body cream and body lotion exhibit a finite magnitude of yield stress. This feature is directly related to the primary (initial) skin feel that consumers usually experience during actual usage. (2) Body cream and body lotion exhibit a pronounced shear-thinning behavior. This feature is closely connected with the spreadability when cosmetics are applied onto the human skin. (3) The linear viscoelastic behaviors of body cream and body lotion are dominated by an elastic nature. These solid-like properties become a criterion to assess the selfstorage stability of cosmetic products. (4) A modified form of the Cox-Merz rule provides a good ability to predict the relationship between steady shear flow and dynamic viscoelastic properties for body cream and body lotion. (5) The storage modulus and loss modulus of body cream show a qualitatively similar tendency to gradually decrease with an increase in temperature. In the case of body lotion, with an increase in temperature, the storage modulus is progressively decreased while the loss modulus is slightly increased and then decreased. This information gives us a criterion to judge how the characteristics of cosmetic products are changed by the usual human environments.

  5. Zero-derivative boundary condition for pulsed distributed systems. [column chromatography example

    NASA Technical Reports Server (NTRS)

    Lashmet, P. K.; Woodrow, P. T.

    1975-01-01

    To permit use of experimentally determined Peclet numbers in numerical simulations of pulsed distributed flow systems such as chromatograph columns, substitution of the zero-derivative boundary condition for the infinite boundary condition used in treating data is examined. Moment analysis shows that application of the zero-derivative condition external to the column will yield equivalent numerical results for the two boundary conditions. Criteria for locating this position are provided as a function of the Peclet number.

  6. A Discrete Analysis of Non-reflecting Boundary Conditions for Discontinuous Galerkin Method

    NASA Technical Reports Server (NTRS)

    Hu, Fang Q.; Atkins, Harold L.

    2003-01-01

    We present a discrete analysis of non-reflecting boundary conditions for the discontinuous Galerkin method. The boundary conditions considered in this paper include the recently proposed Perfectly Matched Layer absorbing boundary condition for the linearized Euler equation and two non-reflecting boundary conditions based on the characteristic decomposition of the flux on the boundary. The analyses for the three boundary conditions are carried out in a unifled way. In each case, eigensolutions of the discrete system are obtained and applied to compute the numerical reflection coefficients of a specified out-going wave. The dependencies of the reflections at the boundary on the out-going wave angle and frequency as well as the mesh sizes arc? studied. Comparisons with direct numerical simulation results are also presented.

  7. Asymptotic boundary conditions with immersed finite elements for interface magnetostatic/electrostatic field problems with open boundary

    NASA Astrophysics Data System (ADS)

    Chu, Yuchuan; Cao, Yong; He, Xiaoming; Luo, Min

    2011-11-01

    Many of the magnetostatic/electrostatic field problems encountered in aerospace engineering, such as plasma sheath simulation and ion neutralization process in space, are not confined to finite domain and non-interface problems, but characterized as open boundary and interface problems. Asymptotic boundary conditions (ABC) and immersed finite elements (IFE) are relatively new tools to handle open boundaries and interface problems respectively. Compared with the traditional truncation approach, asymptotic boundary conditions need a much smaller domain to achieve the same accuracy. When regular finite element methods are applied to an interface problem, it is necessary to use a body-fitting mesh in order to obtain the optimal convergence rate. However, immersed finite elements possess the same optimal convergence rate on a Cartesian mesh, which is critical to many applications. This paper applies immersed finite element methods and asymptotic boundary conditions to solve an interface problem arising from electric field simulation in composite materials with open boundary. Numerical examples are provided to demonstrate the high global accuracy of the IFE method with ABC based on Cartesian meshes, especially around both interface and boundary. This algorithm uses a much smaller domain than the truncation approach in order to achieve the same accuracy.

  8. Development and validation of characteristic boundary conditions for cell-centered Euler flow calculations

    NASA Astrophysics Data System (ADS)

    van den Berg, J. I.; Boerstoel, J. W.

    An overview of the development, analysis, and numerical validation of a solid-wall boundary condition for cell-centered Euler-flow calculations is presented. This solid-wall boundary condition is provided by the theory of characteristics, and is based on a central-difference scheme. The boundary condition was developed to investigate the effect of various boundary-condition algorithms on the accuracy of calculation results for three-dimensional Euler flows around delta wings. A mathematical analysis of the boundary condition was performed. The numerical validation consists of a comparison of calculation results with various boundary conditions. Also discretization and convergence errors were investigated. As a test case, the NLR 7301 profile under supercritical, shock-free flow conditions of M = 0.721, alpha = -0.194 deg, were chosen.

  9. Improvement of boundary conditions for non-planar boundaries represented by polygons with an initial particle arrangement technique

    NASA Astrophysics Data System (ADS)

    Zhang, Tiangang; Koshizuka, Seiichi; Murotani, Kohei; Shibata, Kazuya; Ishii, Eiji; Ishikawa, Masanori

    2016-02-01

    The boundary conditions represented by polygons in moving particle semi-implicit (MPS) method (Koshizuka and Oka, Nuclear Science and Engineering, 1996) have been widely used in the industry simulations since it can simply simulate complex geometry with high efficiency. However, the inaccurate particle number density near non-planar wall boundaries dramatically affects the accuracy of simulations. In this paper, we propose an initial boundary particle arrangement technique coupled with the wall weight function method (Zhang et al. Transaction of JSCES, 2015) to improve the particle number density near slopes and curved surfaces with boundary conditions represented by polygons in three dimensions. Two uniform grids are utilized in the proposed technique. The grid points in the first uniform grid are used to construct boundary particles, and the second uniform grid stores the same information as in the work by Zhang et al. The wall weight functions of the grid points in the second uniform grid are calculated by newly constructed boundary particles. The wall weight functions of the fluid particles are interpolated from the values stored on the grid points in the second uniform grid. Because boundary particles are located on the polygons, complex geometries can be accurately represented. The proposed method can dramatically improve the particle number density and maintain the high efficiency. The performance of the previously proposed wall weight function (Zhang et al.) with the boundary particle arrangement technique is verified in comparison with the wall weight function without boundary particle arrangement by investigating two example geometries. The simulations of a water tank with a wedge and a complex geometry show the general applicability of the boundary particle arrangement technique to complex geometries and demonstrate its improvement of the wall weight function near the slopes and curved surfaces.

  10. Comparative analysis of operational forecasts versus actual weather conditions in airline flight planning: Summary report

    NASA Technical Reports Server (NTRS)

    Keitz, J. F.

    1982-01-01

    The impact of more timely and accurate weather data on airline flight planning with the emphasis on fuel savings is studied. This summary report discusses the results of each of the four major tasks of the study. Task 1 compared airline flight plans based on operational forecasts to plans based on the verifying analyses and found that average fuel savings of 1.2 to 2.5 percent are possible with improved forecasts. Task 2 consisted of similar comparisons but used a model developed for the FAA by SRI International that simulated the impact of ATc diversions on the flight plans. While parts of Task 2 confirm the Task I findings, inconsistency with other data and the known impact of ATC suggests that other Task 2 findings are the result of errors in the model. Task 3 compares segment weather data from operational flight plans with the weather actually observed by the aircraft and finds the average error could result in fuel burn penalties (or savings) of up to 3.6 percent for the average 8747 flight. In Task 4 an in-depth analysis of the weather forecast for the 33 days included in the study finds that significant errors exist on 15 days. Wind speeds in the area of maximum winds are underestimated by 20 to 50 kts., a finding confirmed in the other three tasks.

  11. Comparative analysis of operational forecasts versus actual weather conditions in airline flight planning, volume 3

    NASA Technical Reports Server (NTRS)

    Keitz, J. F.

    1982-01-01

    The impact of more timely and accurate weather data on airline flight planning with the emphasis on fuel savings is studied. This volume of the report discusses the results of Task 3 of the four major tasks included in the study. Task 3 compares flight plans developed on the Suitland forecast with actual data observed by the aircraft (and averaged over 10 degree segments). The results show that the average difference between the forecast and observed wind speed is 9 kts. without considering direction, and the average difference in the component of the forecast wind parallel to the direction of the observed wind is 13 kts. - both indicating that the Suitland forecast underestimates the wind speeds. The Root Mean Square (RMS) vector error is 30.1 kts. The average absolute difference in direction between the forecast and observed wind is 26 degrees and the temperature difference is 3 degree Centigrade. These results indicate that the forecast model as well as the verifying analysis used to develop comparison flight plans in Tasks 1 and 2 is a limiting factor and that the average potential fuel savings or penalty are up to 3.6 percent depending on the direction of flight.

  12. Many-body-localization transition: sensitivity to twisted boundary conditions

    NASA Astrophysics Data System (ADS)

    Monthus, Cécile

    2017-03-01

    For disordered interacting quantum systems, the sensitivity of the spectrum to twisted boundary conditions depending on an infinitesimal angle ϕ can be used to analyze the many-body-localization transition. The sensitivity of the energy levels {{E}n}(φ ) is measured by the level curvature {{K}n}=En\\prime \\prime(0) , or more precisely by the Thouless dimensionless curvature {{k}n}={{K}n}/{{ Δ }n} , where {{ Δ }n} is the level spacing that decays exponentially with the size L of the system. For instance {{ Δ }n}\\propto {{2}-L} in the middle of the spectrum of quantum spin chains of L spins, while the Drude weight {{D}n}=L{{K}n} studied recently by Filippone et al (arxiv:1606.07291v1) involves a different rescaling. The sensitivity of the eigenstates |{{\\psi}n}(φ )> is characterized by the susceptibility {χn}=-Fn\\prime \\prime(0) of the fidelity {{F}n}= |<{{\\psi}n}(0)|{{\\psi}n}(φ )>| . Both observables are distributed with probability distributions displaying power-law tails {{P}β}(k)≃ {{A}β}|k{{|}-(2+β )} and Q(χ )≃ {{B}β}{χ-\\frac{3+β{2}}} , where β is the level repulsion index taking the values {β\\text{GOE}}=1 in the ergodic phase and {β\\text{loc}}=0 in the localized phase. The amplitudes {{A}β} and {{B}β} of these two heavy tails are given by some moments of the off-diagonal matrix element of the local current operator between two nearby energy levels, whose probability distribution has been proposed as a criterion for the many-body-localization transition by Serbyn et al (2015 Phys. Rev. X 5 041047).

  13. Error transport equation boundary conditions for the Euler and Navier-Stokes equations

    NASA Astrophysics Data System (ADS)

    Phillips, Tyrone S.; Derlaga, Joseph M.; Roy, Christopher J.; Borggaard, Jeff

    2017-02-01

    Discretization error is usually the largest and most difficult numerical error source to estimate for computational fluid dynamics, and boundary conditions often contribute a significant source of error. Boundary conditions are described with a governing equation to prescribe particular behavior at the boundary of a computational domain. Boundary condition implementations are considered sufficient when discretized with the same order of accuracy as the primary governing equations; however, careless implementations of boundary conditions can result in significantly larger numerical error. Investigations into different numerical implementations of Dirichlet and Neumann boundary conditions for Burgers' equation show a significant impact on the accuracy of Richardson extrapolation and error transport equation discretization error estimates. The development of boundary conditions for Burgers' equation shows significant improvements in discretization error estimates in general and a significant improvement in truncation error estimation. The latter of which is key to accurate residual-based discretization error estimation. This research investigates scheme consistent and scheme inconsistent implementations of inflow and outflow boundary conditions up to fourth order accurate and a formulation for a slip wall boundary condition for truncation error estimation are developed for the Navier-Stokes and Euler equations. The scheme consistent implementation resulted in much smoother truncation error near the boundaries and more accurate discretization error estimates.

  14. Impact of age and cognitive demand on lane choice and changing under actual highway conditions.

    PubMed

    Reimer, Bryan; Donmez, Birsen; Lavallière, Martin; Mehler, Bruce; Coughlin, Joseph F; Teasdale, Normand

    2013-03-01

    Previous research suggests that drivers change lanes less frequently during periods of heightened cognitive load. However, lane changing behavior of different age groups under varying levels of cognitive demand is not well understood. The majority of studies which have evaluated lane changing behavior under cognitive workload have been conducted in driving simulators. Consequently, it is unclear if the patterns observed in these simulation studies carry over to actual driving. This paper evaluates data from an on-road study to determine the effects of age and cognitive demand on lane choice and lane changing behavior. Three age groups (20-29, 40-49, and 60-69) were monitored in an instrumented vehicle. The 40's age group had 147% higher odds of exhibiting a lane change than the 60's group. In addition, drivers in their 60's were less likely to drive on the leftmost lane compared to drivers in their 20's and 40's. These results could be interpreted as evidence that older adults adopt a more conservative driving style as reflected in being less likely to choose the leftmost lane than the younger groups and less likely to change lanes than drivers in their 40's. Regardless of demand level, cognitive workload reduced the frequency of lane changes for all age groups. This suggests that in general drivers of all ages attempt to regulate their behavior in a risk reducing direction when under added cognitive demand. The extent to which such self-regulation fully compensates for the impact of added cognitive demand remains an open question.

  15. Constructing non-reflecting boundary conditions using summation-by-parts in time

    NASA Astrophysics Data System (ADS)

    Frenander, Hannes; Nordström, Jan

    2017-02-01

    In this paper we provide a new approach for constructing non-reflecting boundary conditions. The boundary conditions are based on summation-by-parts operators and derived without Laplace transformation in time. We prove that the new non-reflecting boundary conditions yield a well-posed problem and that the corresponding numerical approximation is unconditionally stable. The analysis is demonstrated on a hyperbolic system in two space dimensions, and the theoretical results are confirmed by numerical experiments.

  16. Simplified transfer matrix approach in the two-dimensional Ising model with various boundary conditions

    NASA Astrophysics Data System (ADS)

    Kastening, Boris

    2002-11-01

    A recent simplified transfer matrix solution of the two-dimensional Ising model on a square lattice with periodic boundary conditions is generalized to periodic-antiperiodic, antiperiodic-periodic, and antiperiodic-antiperiodic boundary conditions. It is suggested to employ linear combinations of the resulting partition functions to investigate finite-size scaling. An exact relation of such a combination to the partition function corresponding to Brascamp-Kunz boundary conditions is found.

  17. Revisit boundary conditions for the self-adjoint angular flux formulation

    SciTech Connect

    Wang, Yaqi; Gleicher, Frederick N.

    2015-03-01

    We revisit the boundary conditions for SAAF. We derived the equivalent parity variational form ready for coding up. The more rigorous approach of evaluating odd parity should be solving the odd parity equation coupled with the even parity. We proposed a symmetric reflecting boundary condition although neither positive definiteness nor even-odd decoupling is achieved. A simple numerical test verifies the validity of these boundary conditions.

  18. Boundary Conditions for Scalar Conservation Laws from a Kinetic Point of View

    NASA Astrophysics Data System (ADS)

    Nouri, A.; Omrane, A.; Vila, J. P.

    1999-03-01

    Boundary conditions for multidimensional scalar conservation laws are obtained in the context of hydrodynamic limits from a kinetic point of view. The initial boundary value kinetic problem is well posed since inward and outward characteristics of the domain can be distinguished. The convergence of the first momentum of the distribution function to an entropy solution of the conservation law is established. Boundary conditions are obtained. The equivalence with the Bardos, Leroux, and Nedelec conditions is studied.

  19. Periodic Time-Domain Nonlocal Nonreflecting Boundary Conditions for Duct Acoustics

    NASA Technical Reports Server (NTRS)

    Watson, Willie R.; Zorumski, William E.

    1996-01-01

    Periodic time-domain boundary conditions are formulated for direct numerical simulation of acoustic waves in ducts without flow. Well-developed frequency-domain boundary conditions are transformed into the time domain. The formulation is presented here in one space dimension and time; however, this formulation has an advantage in that its extension to variable-area, higher dimensional, and acoustically treated ducts is rigorous and straightforward. The boundary condition simulates a nonreflecting wave field in an infinite uniform duct and is implemented by impulse-response operators that are applied at the boundary of the computational domain. These operators are generated by convolution integrals of the corresponding frequency-domain operators. The acoustic solution is obtained by advancing the Euler equations to a periodic state with the MacCormack scheme. The MacCormack scheme utilizes the boundary condition to limit the computational space and preserve the radiation boundary condition. The success of the boundary condition is attributed to the fact that it is nonreflecting to periodic acoustic waves. In addition, transient waves can pass rapidly out of the solution domain. The boundary condition is tested for a pure tone and a multitone source in a linear setting. The effects of various initial conditions are assessed. Computational solutions with the boundary condition are consistent with the known solutions for nonreflecting wave fields in an infinite uniform duct.

  20. An Explicit Time-Domain Hybrid Formulation Based on the Unified Boundary Condition

    SciTech Connect

    Madsen, N; Fasenfest, B J; White, D; Stowell, M; Jandhyala, V; Pingenot, J; Champagne, N J; Rockway, J D

    2007-02-28

    An approach to stabilize the two-surface, time domain FEM/BI hybrid by means of a unified boundary condition is presented. The first-order symplectic finite element formulation [1] is used along with a version of the unified boundary condition of Jin [2] reformulated for Maxwell's first-order equations in time to provide both stability and accuracy over the first-order ABC. Several results are presented to validate the numerical solutions. In particular the dipole in a free-space box is analyzed and compared to the Dirchlet boundary condition of Ziolkowski and Madsen [3] and to a Neuman boundary condition approach.

  1. Almost exact boundary condition for one-dimensional Schrödinger equations.

    PubMed

    Pang, Gang; Bian, Lei; Tang, Shaoqiang

    2012-12-01

    An explicit local boundary condition is proposed for finite-domain simulations of the linear Schrödinger equation on an unbounded domain. Based on an exact boundary condition in terms of the Bessel functions, it takes a simple form with 16 neighboring grid points, and it involves no empirical parameter. While the computing load is rather low, the proposed boundary condition is effective in reflection suppression, comparable to the exact convolution treatments. An extension to nonlinear Schrödinger equations is also proposed. Numerical comparisons clearly demonstrate the effectiveness of this ALmost EXact (ALEX) boundary condition for both the linear and the cubic nonlinear Schrödinger equations.

  2. Conditions at the downstream boundary for simulations of viscous incompressible flow

    NASA Technical Reports Server (NTRS)

    Hagstrom, Thomas

    1990-01-01

    The proper specification of boundary conditions at artificial boundaries for the simulation of time-dependent fluid flows has long been a matter of controversy. A general theory of asymptotic boundary conditions for dissipative waves is applied to the design of simple, accurate conditions at downstream boundary for incompressible flows. For Reynolds numbers far enough below the critical value for linear stability, a scaling is introduced which greatly simplifies the construction of the asymptotic conditions. Numerical experiments with the nonlinear dynamics of vortical disturbances to plane Poiseuille flow are presented which illustrate the accuracy of our approach. The consequences of directly applying the scalings to the equations are also considered.

  3. Experimental investigation of panel radiator heat output enhancement for efficient thermal use under actual operating conditions

    NASA Astrophysics Data System (ADS)

    Calisir, Tamer; Baskaya, Senol; Onur Yazar, Hakan; Yucedag, Sinan

    2015-05-01

    In this study the heat output of a panel-convector-convector-panel radiator (PCCP) under controlled laboratory conditions under Turkish household and especially Ankara conditions was investigated experimentally. In this sense, investigations were performed for different heating water mass flow rates, water inlet temperatures and radiator inlet and outlet connection positions, which are most commonly used in Turkey. An experimental setup was built for this purpose in a test room where temperature was controlled and held constant during the experiments. Inlet and outlet water temperatures and mass flow rates were measured and heat output of the radiator was calculated. Infrared thermal camera visualizations of the steel panel radiator front surface were also performed.

  4. Boundary conditions for conformally coupled scalar in AdS4

    NASA Astrophysics Data System (ADS)

    Oh, Jae-Hyuk

    2015-06-01

    We consider conformally coupled scalar with ɸ4 coupling in AdS4 and study its various boundary conditions on AdS boundary. We have obtained perturbative solutions of equation of motion of the conformally coupled scalar with power expansion order by order in ɸ4 coupling λ up to λ2 order. In its dual CFT, we get 2, 4 and 6 point functions by using this solution with Dirichlet and Neumann boundary conditions via AdS/CFT dictionary. We also consider marginal deformation on AdS boundary and get its on-shell and boundary effective actions.

  5. A Novel Method for Modeling Neumann and Robin Boundary Conditions in Smoothed Particle Hydrodynamics

    SciTech Connect

    Ryan, Emily M.; Tartakovsky, Alexandre M.; Amon, Cristina

    2010-08-26

    In this paper we present an improved method for handling Neumann or Robin boundary conditions in smoothed particle hydrodynamics. The Neumann and Robin boundary conditions are common to many physical problems (such as heat/mass transfer), and can prove challenging to model in volumetric modeling techniques such as smoothed particle hydrodynamics (SPH). A new SPH method for diffusion type equations subject to Neumann or Robin boundary conditions is proposed. The new method is based on the continuum surface force model [1] and allows an efficient implementation of the Neumann and Robin boundary conditions in the SPH method for geometrically complex boundaries. The paper discusses the details of the method and the criteria needed to apply the model. The model is used to simulate diffusion and surface reactions and its accuracy is demonstrated through test cases for boundary conditions describing different surface reactions.

  6. Melting curve of the deep mantle applied to properties of early magma ocean and actual core-mantle boundary

    NASA Astrophysics Data System (ADS)

    Andrault, Denis; Lo Nigro, Giacomo; Bolfan-Casanova, Nathalie; Bouhifd, Mohamed A.; Garbarino, Gaston; Mezouar, Mohamed

    2010-05-01

    Our planet experienced partial melting early in its history as a consequence of energy release due to accretion. Partial mantle melting could still happen today in the lowermost mantle. Occurrence of melting is primordial for the chemical segregation between the different Earth's reservoirs and for the dynamics of the whole planet. Melting of iron-alloys is relatively easy to achieve, but the silicated mantle happens to be more refractory. We investigated experimentally melting properties of two starting material, forsterite and chondritic-mantle, at pressures ranging from 25 to 140 GPa, using laser-heated diamond anvil cell coupled with synchrotron radiation. We show that partial melting in the lowermost mantle, as suggested by seismology on the basis of the ultra-low velocity zones (ULVZ), requires temperatures above 4200 K at the core-mantle boundary. At low pressures, our curve plots significantly lower than previous reports. Compared to recent estimates of mantle geotherm, while this temperature remains possible if the Earth's core is very hot, it is more likely that ULVZs correspond to high concentration of incompatible elements driven down to the D"-layer by subducting slabs or extracted out from the outer core. When our chondritic melting curve is coupled with recent isentropic temperature profiles for a magma ocean, we obtain a correlation between magma ocean depth and the potential temperature (Tp) at its surface; an ocean depth of 1000 km (equivalent to ~40 GPa) corresponds to Tp=2000 K, which happens to be significantly hotter than the estimated surface temperature of a sustained magma ocean. It emphasizes the importance of a lid at the magma ocean surface at an epoch as early as that of core-mantle segregation.

  7. Actual measurement, hygrothermal response experiment and growth prediction analysis of microbial contamination of central air conditioning system in Dalian, China

    PubMed Central

    Lv, Yang; Hu, Guangyao; Wang, Chunyang; Yuan, Wenjie; Wei, Shanshan; Gao, Jiaoqi; Wang, Boyuan; Song, Fangchao

    2017-01-01

    The microbial contamination of central air conditioning system is one of the important factors that affect the indoor air quality. Actual measurement and analysis were carried out on microbial contamination in central air conditioning system at a venue in Dalian, China. Illumina miseq method was used and three fungal samples of two units were analysed by high throughput sequencing. Results showed that the predominant fungus in air conditioning unit A and B were Candida spp. and Cladosporium spp., and two fungus were further used in the hygrothermal response experiment. Based on the data of Cladosporium in hygrothermal response experiment, this paper used the logistic equation and the Gompertz equation to fit the growth predictive model of Cladosporium genera in different temperature and relative humidity conditions, and the square root model was fitted based on the two environmental factors. In addition, the models were carried on the analysis to verify the accuracy and feasibility of the established model equation. PMID:28367963

  8. The effect of actual and imaginary handgrip on postural stability during different balance conditions.

    PubMed

    VanderHill, M S; Wolf, E E; Langenderfer, J E; Ustinova, K I

    2014-09-01

    The stabilizing effect of holding an object on upright posture has been demonstrated in a variety of settings. The mechanism of this effect is unknown but could be attributed to either additional sensorimotor activity triggered by a hand contact or cognitive efforts related to performance of a supra-postural task. A potential mechanism was investigated by comparing postural stability in young healthy individuals while gripping a custom instrumented wooden stick with a 5N force and while imagining holding the same stick in the hand. Twenty subjects were tested during three standing balance conditions: on a stationary surface, on a freely moving rockerboard, and with an unexpected perturbation of 10° forward rockerboard tipping. Postural stability was evaluated as velocity of the center of mass (COM) and center of pressure (COP) compared across all experimental conditions. COM and COP velocities were equally reduced when subjects gripped the stick and imagined gripping while standing stationary and on the rockerboard. When perturbed, subjects failed to show any postural stability improvements regardless of handgrip task. Results indicate a stabilizing effect of focusing attention on motor task performance. This cognitive strategy does not appear to contribute any additional stabilization when subjects are perturbed. This study adds to the current understanding of postural stabilization strategies.

  9. Haar based numerical solution of Fredholm-Volterra fractional integro-differential equation with nonlocal boundary conditions

    NASA Astrophysics Data System (ADS)

    Setia, Amit; Prakash, Bijil; Vatsala, Aghalaya S.

    2017-01-01

    In this paper, a numerical method is proposed to solve the Fredholm-Volterra fractional integro-differential equation with nonlocal boundary conditions by using Haar wavelets. A collocation based Galerkin's method is applied by using Haar wavelets as basis functions over the interval [0, 1). It converts the Fredholm-Volterra fractional integro-differential equation into a system of m linear equations. On incorporating q nonlocal boundary conditions, it leads to further q equations. All together it will give a system of (m + q) linear equations in (m + q) variables which can be solved. A variety of test examples are considered to illustrate the proposed method. The actual error is also measured with respect to a norm and the results are validated through error bounds.

  10. Entropy Stable Wall Boundary Conditions for the Compressible Navier-Stokes Equations

    NASA Technical Reports Server (NTRS)

    Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.

    2014-01-01

    Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite volume, finite difference, discontinuous Galerkin, and flux reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.

  11. Entropy Stable Wall Boundary Conditions for the Three-Dimensional Compressible Navier-Stokes Equations

    NASA Technical Reports Server (NTRS)

    Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.

    2015-01-01

    Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the three-dimensional compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators on unstructured grids are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite difference, finite volume, discontinuous Galerkin, and flux reconstruction/correction procedure via reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.

  12. Neumann and Robin boundary conditions for heat conduction modeling using smoothed particle hydrodynamics

    NASA Astrophysics Data System (ADS)

    Esmaili Sikarudi, M. A.; Nikseresht, A. H.

    2016-01-01

    Smoothed particle hydrodynamics is a robust Lagrangian particle method which is widely used in various applications, from astrophysics to hydrodynamics and heat conduction. It has intrinsic capabilities for simulating large deformation, composites, multiphysics events, and multiphase fluid flows. It is vital to use reliable boundary conditions when boundary value problems like heat conduction or Poisson equation for incompressible flows are solved. Since smoothed particle hydrodynamics is not a boundary fitted grids method, implementation of boundary conditions can be problematic. Many methods have been proposed for enhancing the accuracy of implementation of boundary conditions. In the present study a new approach for facilitating the implementation of Robin and Neumann boundary conditions is proposed and proven to give accurate results. Also there is no need to use complicated preprocessing as in virtual particle method. The new method is compared to an equivalent one dimensional moving least square scheme and it is shown that the present method is less sensitive to particle disorder.

  13. Green's function of a heat problem with a periodic boundary condition

    NASA Astrophysics Data System (ADS)

    Erzhanov, Nurzhan E.

    2016-08-01

    In the paper, a nonlocal initial-boundary value problem for a non-homogeneous one-dimensional heat equation is considered. The domain under consideration is a rectangle. The classical initial condition with respect to t is put. A nonlocal periodic boundary condition by a spatial variable x is put. It is well-known that a solution of problem can be constructed in the form of convergent orthonormal series according to eigenfunctions of a spectral problem for an operator of multiple differentiation with periodic boundary conditions. Therefore Green's function can be also written in the form of an infinite series with respect to trigonometric functions (Fourier series). For classical first and second initial-boundary value problems there also exists a second representation of the Green's function by Jacobi function. In this paper we find the representation of the Green's function of the nonlocal initial-boundary value problem with periodic boundary conditions in the form of series according to exponents.

  14. Absorption and impedance boundary conditions for phased geometrical-acoustics methods.

    PubMed

    Jeong, Cheol-Ho

    2012-10-01

    Defining accurate acoustical boundary conditions is of crucial importance for room acoustic simulations. In predicting sound fields using phased geometrical acoustics methods, both absorption coefficients and surface impedances of the boundary surfaces can be used, but no guideline has been developed on which boundary condition produces accurate results. In this study, various boundary conditions in terms of normal, random, and field incidence absorption coefficients and normal incidence surface impedance are used in a phased beam tracing model, and the simulated results are validated with boundary element solutions. Two rectangular rooms with uniform and non-uniform absorption distributions are tested. Effects of the neglect of reflection phase shift are also investigated. It is concluded that the impedance, random incidence, and field incidence absorption boundary conditions produce reasonable results with some exceptions at low frequencies for acoustically soft materials.

  15. QCT/FEA predictions of femoral stiffness are strongly affected by boundary condition modeling

    PubMed Central

    Rossman, Timothy; Kushvaha, Vinod; Dragomir-Daescu, Dan

    2015-01-01

    Quantitative computed tomography-based finite element models of proximal femora must be validated with cadaveric experiments before using them to assess fracture risk in osteoporotic patients. During validation it is essential to carefully assess whether the boundary condition modeling matches the experimental conditions. This study evaluated proximal femur stiffness results predicted by six different boundary condition methods on a sample of 30 cadaveric femora and compared the predictions with experimental data. The average stiffness varied by 280% among the six boundary conditions. Compared with experimental data the predictions ranged from overestimating the average stiffness by 65% to underestimating it by 41%. In addition we found that the boundary condition that distributed the load to the contact surfaces similar to the expected contact mechanics predictions had the best agreement with experimental stiffness. We concluded that boundary conditions modeling introduced large variations in proximal femora stiffness predictions. PMID:25804260

  16. An outflow boundary condition and algorithm for incompressible two-phase flows with phase field approach

    NASA Astrophysics Data System (ADS)

    Dong, S.

    2014-06-01

    We present an effective outflow boundary condition, and an associated numerical algorithm, within the phase-field framework for dealing with two-phase outflows or open boundaries. The set of two-phase outflow boundary conditions for the phase-field and flow variables are designed to prevent the un-controlled growth in the total energy of the two-phase system, even in situations where strong backflows or vortices may be present at the outflow boundaries. We also present an additional boundary condition for the phase field function, which together with the usual Dirichlet condition can work effectively as the phase-field inflow conditions. The numerical algorithm for dealing with these boundary conditions is developed on top of a strategy for de-coupling the computations of all flow variables and for overcoming the performance bottleneck caused by variable coefficient matrices associated with variable density/viscosity. The algorithm contains special constructions, for treating the variable dynamic viscosity in the outflow boundary condition, and for preventing a numerical locking at the outflow boundaries for time-dependent problems. Extensive numerical tests with incompressible two-phase flows involving inflow and outflow boundaries demonstrate that, the two-phase outflow boundary conditions and the numerical algorithm developed herein allow for the fluid interface and the two-phase flow to pass through the outflow or open boundaries in a smooth and seamless fashion, and that our method produces stable simulations when large density ratios and large viscosity ratios are involved and when strong backflows are present at the outflow boundaries.

  17. A semi analytical method for electro-thermo-mechanical nonlinear vibration analysis of nanobeam resting on the Winkler-Pasternak foundations with general elastic boundary conditions

    NASA Astrophysics Data System (ADS)

    Zarepour, Misagh; Amirhosein Hosseini, Seyed

    2016-08-01

    This study presents an examination of nonlinear free vibration of a nanobeam under electro-thermo-mechanical loading with elastic medium and various boundary conditions, especially the elastic boundary condition. The nanobeam is modeled as an Euler-Bernoulli beam. The von Kármán strain-displacement relationship together with Hamilton’s principle and Eringen’s theory are employed to derive equations of motion. The nonlinear free vibration frequency is obtained for simply supported (S-S) and elastic supported (E-E) boundary conditions. E-E boundary condition is a general and actual form of boundary conditions and it is chosen because of more realistic behavior. By applying the differential transform method (DTM), the nanobeam’s natural frequencies can be easily obtained for the two different boundary conditions mentioned above. Performing a precise study led to investigation of the influences of nonlocal parameter, temperature change, spring constants (either for elastic medium or boundary condition) and imposed electric potential on the nonlinear free vibration characteristics of nanobeam. The results for S-S and E-E nanobeams are compared with each other. In order to validate the results, some comparisons are presented between DTM results and open literature to show the accuracy of this new approach. It has been discovered that DTM solves the equations with minimum calculation cost.

  18. General Considerations of the Electrostatic Boundary Conditions in Oxide Heterostructures

    SciTech Connect

    Higuchi, Takuya

    2011-08-19

    When the size of materials is comparable to the characteristic length scale of their physical properties, novel functionalities can emerge. For semiconductors, this is exemplified by the 'superlattice' concept of Esaki and Tsu, where the width of the repeated stacking of different semiconductors is comparable to the 'size' of the electrons, resulting in novel confined states now routinely used in opto-electronics. For metals, a good example is magnetic/non-magnetic multilayer films that are thinner than the spin-scattering length, from which giant magnetoresistance (GMR) emerged, used in the read heads of hard disk drives. For transition metal oxides, a similar research program is currently underway, broadly motivated by the vast array of physical properties that they host. This long-standing notion has been recently invigorated by the development of atomic-scale growth and probe techniques, which enables the study of complex oxide heterostructures approaching the precision idealized in Fig. 1(a). Taking the subset of oxides derived from the perovskite crystal structure, the close lattice match across many transition metal oxides presents the opportunity, in principle, to develop a 'universal' heteroepitaxial materials system. Hand-in-hand with the continual improvements in materials control, an increasingly relevant challenge is to understand the consequences of the electrostatic boundary conditions which arise in these structures. The essence of this issue can be seen in Fig. 1(b), where the charge sequence of the sublayer 'stacks' for various representative perovskites is shown in the ionic limit, in the (001) direction. To truly 'universally' incorporate different properties using different materials components, be it magnetism, ferroelectricity, superconductivity, etc., it is necessary to access and join different charge sequences, labelled here in analogy to the designations 'group IV, III-V, II-VI' for semiconductors. As we will review, interfaces between

  19. Inflow/outflow with Dirichlet boundary conditions for pressure in ISPH

    NASA Astrophysics Data System (ADS)

    Kunz, P.; Hirschler, M.; Huber, M.; Nieken, U.

    2016-12-01

    In the present work we propose a new algorithm for open boundary treatment in ISPH. In the literature a few models for open boundary conditions are available, but most of them are applied to weakly compressible SPH (WCSPH) only. In our method the inflow/outflow is driven by true Dirichlet boundary conditions of the projected pressure field. We ensure the Dirichlet boundary condition by a particle mirroring technique at the open boundary to compute the pressure field. This procedure enables us to handle variable inlet velocities across the open boundary. The Dirichlet boundary conditions are introduced for the projected pressure matrix. We apply an error analysis for a Hagen-Poiseuille flow driven by a pressure gradient and demonstrate the robustness and accuracy with a flow around a cylinder and an oscillating flow, where inlet and outlet conditions periodically change. Additionally, a volume flux controller is presented in combination with variable pressure boundary conditions. Finally, the new open boundary treatment is applied to a bubble formation process during gas injection and validated with experimental results.

  20. Hydromagnetic conditions near the core-mantle boundary

    NASA Technical Reports Server (NTRS)

    Backus, George E.

    1995-01-01

    The main results of the grant were (1) finishing the manuscript of a proof of completeness of the Poincare modes in an incompressible nonviscous fluid corotating with a rigid ellipsoidal boundary, (2) partial completion of a manuscript describing a definition of helicity that resolved questions in the literature about calculating the helicities of vector fields with complicated topologies, and (3) the beginning of a reexamination of the inverse problem of inferring properties of the geomagnetic field B just outside the core-mantle boundary (CMB) from measurements of elements of B at and above the earth's surface. This last work has led to a simple general formalism for linear and nonlinear inverse problems that appears to include all the inversion schemes so far considered for the uniqueness problem in geomagnetic inversion. The technique suggests some new methods for error estimation that form part of this report.

  1. Conditions affecting boundary response to messages out of awareness.

    PubMed

    Fisher, S

    1976-05-01

    Multiple studies evaluated the role of the following parameters in mediating the effects of auditory subliminal inputs upon the body boundary: being made aware that exposure to subliminal stimuli is occurring, nature of the priming preliminary to the input, length of exposure, competing sensory input, use of specialized content messages, tolerance for unrealistic experience, and masculinity-feminity. A test-retest design was typically employed that involved measuring the baseline Barrier score with the Holtzman bolts and then ascertaining the Barrier change when responding to a second series of Holtzman blots at the same time that subliminal input was occurring. Complex results emerged that defined in considerably new detail what facilitates and blocks the boundary-disrupting effects of subliminal messages in men and to a lesser degree in women.

  2. The effect of external boundary conditions on condensation heat transfer in rotating heat pipes

    NASA Technical Reports Server (NTRS)

    Daniels, T. C.; Williams, R. J.

    1979-01-01

    Experimental evidence shows the importance of external boundary conditions on the overall performance of a rotating heat pipe condenser. Data are presented for the boundary conditions of constant heat flux and constant wall temperature for rotating heat pipes containing either pure vapor or a mixture of vapor and noncondensable gas as working fluid.

  3. Impacts of Lateral Boundary Conditions on U.S. Ozone Modeling Analyses

    EPA Science Inventory

    Chemical boundary conditions are a key input to regional-scale photochemical models. In this study, we perform annual simulations over North America with chemical boundary conditions prepared from two global models (GEOS-CHEM and Hemispheric CMAQ). Results indicate that the impac...

  4. On the Effective Construction of Compactly Supported Wavelets Satisfying Homogenous Boundary Conditions on the Interval

    NASA Technical Reports Server (NTRS)

    Chiavassa, G.; Liandrat, J.

    1996-01-01

    We construct compactly supported wavelet bases satisfying homogeneous boundary conditions on the interval (0,1). The maximum features of multiresolution analysis on the line are retained, including polynomial approximation and tree algorithms. The case of H(sub 0)(sup 1)(0, 1)is detailed, and numerical values, required for the implementation, are provided for the Neumann and Dirichlet boundary conditions.

  5. Open boundary conditions for ISPH and their application to micro-flow

    NASA Astrophysics Data System (ADS)

    Hirschler, Manuel; Kunz, Philip; Huber, Manuel; Hahn, Friedemann; Nieken, Ulrich

    2016-02-01

    Open boundary conditions for incompressible Smoothed Particle Hydrodynamics (ISPH) are rare. For stable simulations with open boundary conditions, one needs to specify all boundary conditions correctly in the pressure force as well as in the linear equation system for pressure calculation. Especially for homogeneous or non-homogeneous Dirichlet boundary conditions for pressure there exist several possibilities but only a few lead to stable results. However, this isn't trivial for open boundary conditions. We introduce a new approach for open boundary conditions for ISPH to enable stable simulations. In contrast to existing models for weakly-compressible SPH, we can specify open pressure boundary conditions because in ISPH, pressure can be calculated independently of the density. The presented approach is based on the mirror particle approach already introduced for solid wall boundary conditions. Here we divide the mirror axis in several segments with time-dependent positions. We validate the presented approach for the example of Poiseuille flow and flow around a cylinder at different Reynolds numbers and show that we get good agreement with references. Then, we demonstrate that the approach can be applied to free surface flows. Finally, we apply the new approach to micro-flow through a random porous medium with a different number of in- and outlets and demonstrate its benefits.

  6. Existence Result for the Kinetic Neutron Transport Problem with a General Albedo Boundary Condition

    NASA Astrophysics Data System (ADS)

    Sanchez, Richard; Bourhrara, Lahbib

    2011-09-01

    We present an existence result for the kinetic neutron transport equation with a general albedo boundary condition. The proof is constructive in the sense that we build a sequence that converges to the solution of the problem by iterating on the albedo term. Both nonhomogeneous and albedo boundary conditions are studied.

  7. Trickle-down boundary conditions in aeolian dune-field pattern formation

    NASA Astrophysics Data System (ADS)

    Ewing, R. C.; Kocurek, G.

    2015-12-01

    One the one hand, wind-blown dune-field patterns emerge within the overarching boundary conditions of climate, tectonics and eustasy implying the presence of these signals in the aeolian geomorphic and stratigraphic record. On the other hand, dune-field patterns are a poster-child of self-organization, in which autogenic processes give rise to patterned landscapes despite remarkable differences in the geologic setting (i.e., Earth, Mars and Titan). How important are climate, tectonics and eustasy in aeolian dune field pattern formation? Here we develop the hypothesis that, in terms of pattern development, dune fields evolve largely independent of the direct influence of 'system-scale' boundary conditions, such as climate, tectonics and eustasy. Rather, these boundary conditions set the stage for smaller-scale, faster-evolving 'event-scale' boundary conditions. This 'trickle-down' effect, in which system-scale boundary conditions indirectly influence the event scale boundary conditions provides the uniqueness and richness of dune-field patterned landscapes. The trickle-down effect means that the architecture of the stratigraphic record of dune-field pattern formation archives boundary conditions, which are spatially and temporally removed from the overarching geologic setting. In contrast, the presence of an aeolian stratigraphic record itself, reflects changes in system-scale boundary conditions that drive accumulation and preservation of aeolian strata.

  8. On the Boundary Condition Between Two Multiplying Media

    DOE R&D Accomplishments Database

    Friedman, F. L.; Wigner, E. P.

    1944-04-19

    The transition region between two parts of a pile which have different compositions is investigated. In the case where the moderator is the same in both parts of the pile, it is found that the diffusion constant times thermal neutron density plus diffusion constant times fast neutron density satisfies the usual pile equations everywhere, right to the boundary. More complicated formulae apply in a more general case.

  9. On global solutions for quasilinear one-dimensional parabolic problems with dynamical boundary conditions

    NASA Astrophysics Data System (ADS)

    Gvelesiani, Simon; Lippoth, Friedrich; Walker, Christoph

    2015-12-01

    We provide sufficient and almost optimal conditions for global existence of classical solutions in parabolic Hölder spaces to quasilinear one-dimensional parabolic problems with dynamical boundary conditions.

  10. Role of free-surface boundary conditions and nonlinearities in wave/boundary-layer and wake interaction

    NASA Astrophysics Data System (ADS)

    Choi, Jung-Eun

    1993-01-01

    In Part One of this two-part thesis, laminar and turbulent solutions are presented for the Stokes-wave/flat-plate boundary-layer and wake for small - large wave steepness, including exact and approximate treatments of the viscous free-surface boundary conditions. The macro-scale flow exhibits the wave-induced pressure-gradient effects described in a precursory work. For laminar flow, the micro-scale flow indicates that the free-surface boundary conditions have a profound influence over the boundary layer and near and intermediate wake: the wave elevation and slopes correlate with the depthwise velocity; the streamwise and transverse velocities and vorticity display large variations, including islands of maximum/minimum values, whereas the depthwise velocity and pressure indicate small variations; significant free-surface vorticity flux and complex vorticity transport are displayed; wave-induced effects normalized by wave steepness are larger for small steepness with the exception of wave-induced separation; order-of-magnitude estimates are confirmed; and appreciable errors are introduced through approximations to the free-surface boundary conditions. For turbulent flow, the results are similar, but preliminary due to the present uncertainty in appropriate treatment of the free-surface boundary conditions and meniscus boundary layer. In Part Two, Navier-Stokes, boundary-layer, and perturbation expansion solutions are presented for the model problem of a flat-plate boundary layer and wake with temporal, spatial, and traveling horizontal-wave external flows, which are characterized by Stokes-layer overshoots, phase angles, and streaming and nonlinearities. The temporal wave displays close agreement with previous studies and is useful for validation and placing the current work in technical perspective. The spatial wave indicates significantly increased magnitudes and complex nature (e.g., wake bias), which is attributed to nonlinearities associated with large

  11. Finite-size corrections in the Ising model with special boundary conditions

    NASA Astrophysics Data System (ADS)

    Izmailian, N. Sh.

    2010-11-01

    The Ising model in two dimensions with the special boundary conditions of Brascamp and Kunz (BK) is analyzed. We derive exact finite-size corrections for the free energy F of the critical ferromagnetic Ising model on the M×N square lattice with Brascamp-Kunz boundary conditions [H.J. Brascamp, H. Kunz, J. Math. Phys. 15 (1974) 66]. We show that finite-size corrections strongly depend not only on the boundary conditions but also on the shape and pattern of the lattice. In the limit N→∞ we obtain the expansion of the free energy and the inverse correlation lengths for infinitely long strip with BK boundary conditions. Our results are consistent with the conformal field theory prediction for the mixed boundary conditions.

  12. Structural acoustic control of plates with variable boundary conditions: design methodology.

    PubMed

    Sprofera, Joseph D; Cabell, Randolph H; Gibbs, Gary P; Clark, Robert L

    2007-07-01

    A method for optimizing a structural acoustic control system subject to variations in plate boundary conditions is provided. The assumed modes method is used to build a plate model with varying levels of rotational boundary stiffness to simulate the dynamics of a plate with uncertain edge conditions. A transducer placement scoring process, involving Hankel singular values, is combined with a genetic optimization routine to find spatial locations robust to boundary condition variation. Predicted frequency response characteristics are examined, and theoretically optimized results are discussed in relation to the range of boundary conditions investigated. Modeled results indicate that it is possible to minimize the impact of uncertain boundary conditions in active structural acoustic control by optimizing the placement of transducers with respect to those uncertainties.

  13. Neumann-Type Boundary Conditions for Hamilton-Jacobi Equations in Smooth Domains

    SciTech Connect

    Day, Martin V.

    2006-05-15

    Neumann or oblique derivative boundary conditions for viscosity solutions of Hamilton-Jacobi equations are considered. As developed by P.L. Lions, such boundary conditions are naturally associated with optimal control problems for which the state equations employ 'Skorokhod' or reflection dynamics to ensure that the state remains in a prescribed set, assumed here to have a smooth boundary. We develop connections between the standard formulation of viscosity boundary conditions and an alternative formulation using a naturally occurring discontinuous Hamiltonian which incorporates the reflection dynamics directly. (This avoids the dependence of such equivalence on existence and uniqueness results, which may not be available in some applications.) At points of differentiability, equivalent conditions for the boundary conditions are given in terms of the Hamiltonian and the geometry of the state trajectories using optimal controls.

  14. A convective-like energy-stable open boundary condition for simulations of incompressible flows

    NASA Astrophysics Data System (ADS)

    Dong, S.

    2015-12-01

    We present a new energy-stable open boundary condition, and an associated numerical algorithm, for simulating incompressible flows with outflow/open boundaries. This open boundary condition ensures the energy stability of the system, even when strong vortices or backflows occur at the outflow boundary. Under certain situations it can be reduced to a form that can be analogized to the usual convective boundary condition. One prominent feature of this boundary condition is that it provides a control over the velocity on the outflow/open boundary. This is not available with the other energy-stable open boundary conditions from previous works. Our numerical algorithm treats the proposed open boundary condition based on a rotational velocity-correction type strategy. It gives rise to a Robin-type condition for the discrete pressure and a Robin-type condition for the discrete velocity on the outflow/open boundary, respectively at the pressure and the velocity sub-steps. We present extensive numerical experiments on a canonical wake flow and a jet flow in open domain to test the effectiveness and performance of the method developed herein. Simulation results are compared with the experimental data as well as with other previous simulations to demonstrate the accuracy of the current method. Long-time simulations are performed for a range of Reynolds numbers, at which strong vortices and backflows occur at the outflow/open boundaries. The results show that our method is effective in overcoming the backflow instability, and that it allows for the vortices to discharge from the domain in a fairly natural fashion even at high Reynolds numbers.

  15. Open boundary conditions for the Diffuse Interface Model in 1-D

    NASA Astrophysics Data System (ADS)

    Desmarais, J. L.; Kuerten, J. G. M.

    2014-04-01

    New techniques are developed for solving multi-phase flows in unbounded domains using the Diffuse Interface Model in 1-D. They extend two open boundary conditions originally designed for the Navier-Stokes equations. The non-dimensional formulation of the DIM generalizes the approach to any fluid. The equations support a steady state whose analytical approximation close to the critical point depends only on temperature. This feature enables the use of detectors at the boundaries switching between conventional boundary conditions in bulk phases and a multi-phase strategy in interfacial regions. Moreover, the latter takes advantage of the steady state approximation to minimize the interface-boundary interactions. The techniques are applied to fluids experiencing a phase transition and where the interface between the phases travels through one of the boundaries. When the interface crossing the boundary is fully developed, the technique greatly improves results relative to cases where conventional boundary conditions can be used. Limitations appear when the interface crossing the boundary is not a stable equilibrium between the two phases: the terms responsible for creating the true balance between the phases perturb the interior solution. Both boundary conditions present good numerical stability properties: the error remains bounded when the initial conditions or the far field values are perturbed. For the PML, the influence of its main parameters on the global error is investigated to make a compromise between computational costs and maximum error. The approach can be extended to multiple spatial dimensions.

  16. Modeling mixed boundary conditions in a Hilbert space with the complex variable boundary element method (CVBEM).

    PubMed

    Johnson, Anthony N; Hromadka, T V

    2015-01-01

    The Laplace equation that results from specifying either the normal or tangential force equilibrium equation in terms of the warping functions or its conjugate can be modeled as a complex variable boundary element method or CVBEM mixed boundary problem. The CVBEM is a well-known numerical technique that can provide solutions to potential value problems in two or more dimensions by the use of an approximation function that is derived from the Cauchy Integral in complex analysis. This paper highlights three customizations to the technique.•A least squares approach to modeling the complex-valued approximation function will be compared and analyzed to determine if modeling error on the boundary can be reduced without the need to find and evaluated additional linearly independent complex functions.•The nodal point locations will be moved outside the problem domain.•Contour and streamline plots representing the warping function and its complementary conjugate are generated simultaneously from the complex-valued approximating function.

  17. Modeling mixed boundary conditions in a Hilbert space with the complex variable boundary element method (CVBEM)

    PubMed Central

    Johnson, Anthony N.; Hromadka, T.V.

    2015-01-01

    The Laplace equation that results from specifying either the normal or tangential force equilibrium equation in terms of the warping functions or its conjugate can be modeled as a complex variable boundary element method or CVBEM mixed boundary problem. The CVBEM is a well-known numerical technique that can provide solutions to potential value problems in two or more dimensions by the use of an approximation function that is derived from the Cauchy Integral in complex analysis. This paper highlights three customizations to the technique.•A least squares approach to modeling the complex-valued approximation function will be compared and analyzed to determine if modeling error on the boundary can be reduced without the need to find and evaluated additional linearly independent complex functions.•The nodal point locations will be moved outside the problem domain.•Contour and streamline plots representing the warping function and its complementary conjugate are generated simultaneously from the complex-valued approximating function. PMID:26151000

  18. Towards Perfectly Absorbing Boundary Conditions for Euler Equations

    NASA Technical Reports Server (NTRS)

    Hayder, M. Ehtesham; Hu, Fang Q.; Hussaini, M. Yousuff

    1997-01-01

    In this paper, we examine the effectiveness of absorbing layers as non-reflecting computational boundaries for the Euler equations. The absorbing-layer equations are simply obtained by splitting the governing equations in the coordinate directions and introducing absorption coefficients in each split equation. This methodology is similar to that used by Berenger for the numerical solutions of Maxwell's equations. Specifically, we apply this methodology to three physical problems shock-vortex interactions, a plane free shear flow and an axisymmetric jet- with emphasis on acoustic wave propagation. Our numerical results indicate that the use of absorbing layers effectively minimizes numerical reflection in all three problems considered.

  19. Variance reduction through robust design of boundary conditions for stochastic hyperbolic systems of equations

    SciTech Connect

    Nordström, Jan Wahlsten, Markus

    2015-02-01

    We consider a hyperbolic system with uncertainty in the boundary and initial data. Our aim is to show that different boundary conditions give different convergence rates of the variance of the solution. This means that we can with the same knowledge of data get a more or less accurate description of the uncertainty in the solution. A variety of boundary conditions are compared and both analytical and numerical estimates of the variance of the solution are presented. As an application, we study the effect of this technique on Maxwell's equations as well as on a subsonic outflow boundary for the Euler equations.

  20. A quenched study of the Schroedinger functional with chirally rotated boundary conditions: non-perturbative tuning

    SciTech Connect

    Gonzalez-Lopez, Jennifer; Jansen, Karl; Renner, Dru B.; Shindler, Andrea

    2013-02-01

    The use of chirally rotated boundary conditions provides a formulation of the Schroedinger functional that is compatible with automatic O(a) improvement of Wilson fermions up to O(a) boundary contributions. The elimination of bulk O(a) effects requires the non-perturbative tuning of the critical mass and one additional boundary counterterm. We present the results of such a tuning in a quenched setup for several values of the renormalized gauge coupling, from perturbative to non-perturbative regimes, and for a range of lattice spacings. We also check that the correct boundary conditions and symmetries are restored in the continuum limit.

  1. Comparison of Methods for Determining Boundary Layer Edge Conditions for Transition Correlations

    NASA Technical Reports Server (NTRS)

    Liechty, Derek S.; Berry, Scott A.; Hollis, Brian R.; Horvath, Thomas J.

    2003-01-01

    Data previously obtained for the X-33 in the NASA Langley Research Center 20-Inch Mach 6 Air Tunnel have been reanalyzed to compare methods for determining boundary layer edge conditions for use in transition correlations. The experimental results were previously obtained utilizing the phosphor thermography technique to monitor the status of the boundary layer downstream of discrete roughness elements via global heat transfer images of the X-33 windward surface. A boundary layer transition correlation was previously developed for this data set using boundary layer edge conditions calculated using an inviscid/integral boundary layer approach. An algorithm was written in the present study to extract boundary layer edge quantities from higher fidelity viscous computational fluid dynamic solutions to develop transition correlations that account for viscous effects on vehicles of arbitrary complexity. The boundary layer transition correlation developed for the X-33 from the viscous solutions are compared to the previous boundary layer transition correlations. It is shown that the boundary layer edge conditions calculated using an inviscid/integral boundary layer approach are significantly different than those extracted from viscous computational fluid dynamic solutions. The present results demonstrate the differences obtained in correlating transition data using different computational methods.

  2. New approximate boundary conditions for large eddy simulations of wall-bounded flows

    NASA Technical Reports Server (NTRS)

    Piomelli, Ugo; Ferziger, Joel; Moin, Parviz; Kim, John

    1989-01-01

    Two new approximate boundary conditions have been applied to the large eddy simulation of channel flow with and without transpiration. These new boundary conditions give more accurate results than those previously in use, and allow significant reduction of the required CPU time over simulations in which no-slip conditions are applied. Mean velocity profiles and turbulence intensities compare well both with experimental data and with the results of resolved simulations. The influence of the approximate boundary conditions remains confined near the point of application and does not affect the turbulence statistics in the core of the flow.

  3. Boundary conditions for simulations of oscillating bubbles using the non-linear acoustic approximation

    NASA Astrophysics Data System (ADS)

    King, J. R. C.; Ziolkowski, A. M.; Ruffert, M.

    2015-03-01

    We have developed a new boundary condition for finite volume simulations of oscillating bubbles. Our method uses an approximation to the motion outside the domain, based on the solution at the domain boundary. We then use this approximation to apply boundary conditions by defining incoming characteristic waves at the domain boundary. Our boundary condition is applicable in regions where the motion is close to spherically symmetric. We have tested our method on a range of one- and two-dimensional test cases. Results show good agreement with previous studies. The method allows simulations of oscillating bubbles for long run times (5 ×105 time steps with a CFL number of 0.8) on highly truncated domains, in which the boundary condition may be applied within 0.1% of the maximum bubble radius. Conservation errors due to the boundary conditions are found to be of the order of 0.1% after 105 time steps. The method significantly reduces the computational cost of fixed grid finite volume simulations of oscillating bubbles. Two-dimensional results demonstrate that highly asymmetric bubble features, such as surface instabilities and the formation of jets, may be captured on a small domain using this boundary condition.

  4. Inferring Lower Boundary Driving Conditions Using Vector Magnetic Field Observations

    NASA Technical Reports Server (NTRS)

    Schuck, Peter W.; Linton, Mark; Leake, James; MacNeice, Peter; Allred, Joel

    2012-01-01

    Low-beta coronal MHD simulations of realistic CME events require the detailed specification of the magnetic fields, velocities, densities, temperatures, etc., in the low corona. Presently, the most accurate estimates of solar vector magnetic fields are made in the high-beta photosphere. Several techniques have been developed that provide accurate estimates of the associated photospheric plasma velocities such as the Differential Affine Velocity Estimator for Vector Magnetograms and the Poloidal/Toroidal Decomposition. Nominally, these velocities are consistent with the evolution of the radial magnetic field. To evolve the tangential magnetic field radial gradients must be specified. In addition to estimating the photospheric vector magnetic and velocity fields, a further challenge involves incorporating these fields into an MHD simulation. The simulation boundary must be driven, consistent with the numerical boundary equations, with the goal of accurately reproducing the observed magnetic fields and estimated velocities at some height within the simulation. Even if this goal is achieved, many unanswered questions remain. How can the photospheric magnetic fields and velocities be propagated to the low corona through the transition region? At what cadence must we observe the photosphere to realistically simulate the corona? How do we model the magnetic fields and plasma velocities in the quiet Sun? How sensitive are the solutions to other unknowns that must be specified, such as the global solar magnetic field, and the photospheric temperature and density?

  5. Boundary conditions for Maxwell fields in Kerr-AdS spacetimes

    NASA Astrophysics Data System (ADS)

    Wang, Mengjie

    2016-05-01

    Perturbative methods are useful to study the interaction between black holes and test fields. The equation for a perturbation itself, however, is not complete to study such a composed system if we do not assign physically relevant boundary conditions. Recently we have proposed a new type of boundary conditions for Maxwell fields in Kerr-anti-de Sitter (Kerr-AdS) spacetimes, from the viewpoint that the AdS boundary may be regarded as a perfectly reflecting mirror, in the sense that energy flux vanishes asymptotically. In this paper, we prove explicitly that a vanishing energy flux leads to a vanishing angular momentum flux. Thus, these boundary conditions may be dubbed as vanishing flux boundary conditions.

  6. An implicit-iterative solution of the heat conduction equation with a radiation boundary condition

    NASA Technical Reports Server (NTRS)

    Williams, S. D.; Curry, D. M.

    1977-01-01

    For the problem of predicting one-dimensional heat transfer between conducting and radiating mediums by an implicit finite difference method, four different formulations were used to approximate the surface radiation boundary condition while retaining an implicit formulation for the interior temperature nodes. These formulations are an explicit boundary condition, a linearized boundary condition, an iterative boundary condition, and a semi-iterative boundary method. The results of these methods in predicting surface temperature on the space shuttle orbiter thermal protection system model under a variety of heating rates were compared. The iterative technique caused the surface temperature to be bounded at each step. While the linearized and explicit methods were generally more efficient, the iterative and semi-iterative techniques provided a realistic surface temperature response without requiring step size control techniques.

  7. MHD free convective boundary layer flow of a nanofluid past a flat vertical plate with Newtonian heating boundary condition.

    PubMed

    Uddin, Mohammed J; Khan, Waqar A; Ismail, Ahmed I

    2012-01-01

    Steady two dimensional MHD laminar free convective boundary layer flows of an electrically conducting Newtonian nanofluid over a solid stationary vertical plate in a quiescent fluid taking into account the Newtonian heating boundary condition is investigated numerically. A magnetic field can be used to control the motion of an electrically conducting fluid in micro/nano scale systems used for transportation of fluid. The transport equations along with the boundary conditions are first converted into dimensionless form and then using linear group of transformations, the similarity governing equations are developed. The transformed equations are solved numerically using the Runge-Kutta-Fehlberg fourth-fifth order method with shooting technique. The effects of different controlling parameters, namely, Lewis number, Prandtl number, buoyancy ratio, thermophoresis, Brownian motion, magnetic field and Newtonian heating on the flow and heat transfer are investigated. The numerical results for the dimensionless axial velocity, temperature and nanoparticle volume fraction as well as the reduced Nusselt and Sherwood number have been presented graphically and discussed. It is found that the rate of heat and mass transfer increase as Newtonian heating parameter increases. The dimensionless velocity and temperature distributions increase with the increase of Newtonian heating parameter. The results of the reduced heat transfer rate is compared for convective heating boundary condition and found an excellent agreement.

  8. MHD Free Convective Boundary Layer Flow of a Nanofluid past a Flat Vertical Plate with Newtonian Heating Boundary Condition

    PubMed Central

    Uddin, Mohammed J.; Khan, Waqar A.; Ismail, Ahmed I.

    2012-01-01

    Steady two dimensional MHD laminar free convective boundary layer flows of an electrically conducting Newtonian nanofluid over a solid stationary vertical plate in a quiescent fluid taking into account the Newtonian heating boundary condition is investigated numerically. A magnetic field can be used to control the motion of an electrically conducting fluid in micro/nano scale systems used for transportation of fluid. The transport equations along with the boundary conditions are first converted into dimensionless form and then using linear group of transformations, the similarity governing equations are developed. The transformed equations are solved numerically using the Runge-Kutta-Fehlberg fourth-fifth order method with shooting technique. The effects of different controlling parameters, namely, Lewis number, Prandtl number, buoyancy ratio, thermophoresis, Brownian motion, magnetic field and Newtonian heating on the flow and heat transfer are investigated. The numerical results for the dimensionless axial velocity, temperature and nanoparticle volume fraction as well as the reduced Nusselt and Sherwood number have been presented graphically and discussed. It is found that the rate of heat and mass transfer increase as Newtonian heating parameter increases. The dimensionless velocity and temperature distributions increase with the increase of Newtonian heating parameter. The results of the reduced heat transfer rate is compared for convective heating boundary condition and found an excellent agreement. PMID:23166688

  9. Inverse Lax-Wendroff procedure for numerical boundary conditions of convection-diffusion equations

    NASA Astrophysics Data System (ADS)

    Lu, Jianfang; Fang, Jinwei; Tan, Sirui; Shu, Chi-Wang; Zhang, Mengping

    2016-07-01

    We consider numerical boundary conditions for high order finite difference schemes for solving convection-diffusion equations on arbitrary geometry. The two main difficulties for numerical boundary conditions in such situations are: (1) the wide stencil of the high order finite difference operator requires special treatment for a few ghost points near the boundary; (2) the physical boundary may not coincide with grid points in a Cartesian mesh and may intersect with the mesh in an arbitrary fashion. For purely convection equations, the so-called inverse Lax-Wendroff procedure [28], in which we convert the normal derivatives into the time derivatives and tangential derivatives along the physical boundary by using the equations, has been quite successful. In this paper, we extend this methodology to convection-diffusion equations. It turns out that this extension is non-trivial, because totally different boundary treatments are needed for the diffusion-dominated and the convection-dominated regimes. We design a careful combination of the boundary treatments for the two regimes and obtain a stable and accurate boundary condition for general convection-diffusion equations. We provide extensive numerical tests for one- and two-dimensional problems involving both scalar equations and systems, including the compressible Navier-Stokes equations, to demonstrate the good performance of our numerical boundary conditions.

  10. On the resolvent of multidimensional operators with frequently changing boundary conditions in the case of the homogenized Dirichlet condition

    SciTech Connect

    Sharapov, T F

    2014-10-31

    We consider an elliptic operator in a multidimensional domain with frequently changing boundary conditions in the case when the homogenized operator contains the Dirichlet boundary condition. We prove the uniform resolvent convergence of the perturbed operator to the homogenized operator and obtain estimates for the rate of convergence. A complete asymptotic expansion is constructed for the resolvent when it acts on sufficiently smooth functions. Bibliography: 41 titles.

  11. Time dependent inflow-outflow boundary conditions for 2D acoustic systems

    NASA Technical Reports Server (NTRS)

    Watson, Willie R.; Myers, Michael K.

    1989-01-01

    An analysis of the number and form of the required inflow-outflow boundary conditions for the full two-dimensional time-dependent nonlinear acoustic system in subsonic mean flow is performed. The explicit predictor-corrector method of MacCormack (1969) is used. The methodology is tested on both uniform and sheared mean flows with plane and nonplanar sources. Results show that the acoustic system requires three physical boundary conditions on the inflow and one on the outflow boundary. The most natural choice for the inflow boundary conditions is judged to be a specification of the vorticity, the normal acoustic impedance, and a pressure gradient-density gradient relationship normal to the boundary. Specification of the acoustic pressure at the outflow boundary along with these inflow boundary conditions is found to give consistent reliable results. A set of boundary conditions developed earlier, which were intended to be nonreflecting is tested using the current method and is shown to yield unstable results for nonplanar acoustic waves.

  12. Second-Order Far Field Computational Boundary Conditions for Inviscid Duct Flow Problems

    DTIC Science & Technology

    1990-03-01

    COMPUTATIONAL BOUNDARY CONDITIONS INTERNAL FLOW COMPUTATIONS EULER METHODS 19. ABSTRACT (Continue on reverse if necessary and identify by block number...SOLUTIONS OF THE LINEARIZED, SECOND-ORDER EULER EQUATIONS. THE EULER EQUATIONS ARE LINEARIZED ABOUT A CONSTANT PRESSURE, RECTILINEAR FLOW C)NDITION...THE BOUNDARY PROCEDURE CAN BE USED WITH ANY NUMERICAL EULER SOLUTION METHOD AND ALLOWS COMPUTATIONAL BOUNDARIES TO BE LOCATED EXTREMELY CLOSE TO THE

  13. Magnetic Boundary Conditions at Non-Conducting Planetary Bodies: Applications to Ganymede

    NASA Astrophysics Data System (ADS)

    Saur, J.; Duling, S.; Seufert, M.; Wicht, J.

    2013-12-01

    The interaction of planetary bodies with their surrounding magnetized plasma can often be described with the magneto-hydrodynamic (MHD) equations, which are commonly solved by numerical models. For these models it is necessary to define physically correct boundary conditions. Many planetary bodies have electrically non-conductive surfaces, which do not allow electric current to penetrate their surfaces. Magnetic boundary conditions, which correctly consider that the associated radial electric current at the planetary surface is zero, are however difficult to implement because they include the curl of the magnetic field. Here we derive new boundary conditions for the magnetic field at non-conducting surfaces by a decomposition of the magnetic field in poloidal and toroidal components and their spherical harmonics expansions. We find that the toroidal part of the magnetic field needs to vanish at the surface of the isolator. For the spectral spherical harmonics coefficients of the poloidal part we derive a Cauchy boundary condition, which includes the Gauss coefficients of a possible intrinsic field. Our non-conducting boundary condition can thus additionally include intrinsic dynamo fields as well as induction fields within electrically conductive subsurface layers such as subsurface oceans. We implement the new boundary condition in the MHD simulation code ZEUS-MP using spherical geometry. We apply these new magnetic boundary conditions to a model for Ganymede's plasma environment. With this model we can describe the in-situ observations by the Galileo spacecraft and Hubble Space Telescope observations of Ganmyede's aurora very well.

  14. Surface boundary conditions for the numerical solution of the Euler equations

    NASA Technical Reports Server (NTRS)

    Dadone, A.; Grossman, B.

    1993-01-01

    We consider the implementation of boundary conditions at solid walls in inviscid Euler solutions by upwind, finite-volume methods. We review some current methods for the implementation of surface boundary conditions and examine their behavior for the problem of an oblique shock reflecting off a planar surface. We show the importance of characteristic boundary conditions for this problem and introduce a method of applying the classical flux-difference splitting of Roe as a characteristic boundary condition. Consideration of the equivalent problem of the intersection of two (equal and opposite) oblique shocks was very illuminating on the role of surface boundary conditions for an inviscid flow and led to the introduction of two new boundary-condition procedures, denoted as the symmetry technique and the curvature-corrected symmetry technique. Examples of the effects of the various surface boundary conditions considered are presented for the supersonic blunt body problem and the subcritical compressible flow over a circular cylinder. Dramatic advantages of the curvature-corrected symmetry technique over the other methods are shown, with regard to numerical entropy generation, total pressure loss, drag and grid convergence.

  15. Exploring the Boundary Conditions of the Redundancy Principle

    ERIC Educational Resources Information Center

    McCrudden, Matthew T.; Hushman, Carolyn J.; Marley, Scott C.

    2014-01-01

    This experiment investigated whether study of a scientific text and a visual display that contained redundant text segments would affect memory and transfer. The authors randomly assigned 42 students from a university in the southwestern United States in equal numbers to 1 of 2 conditions: (a) a redundant condition, in which participants studied a…

  16. Boundary conditions for the Baumgarte-Shapiro-Shibata-Nakamura formulation of Einstein's field equations

    SciTech Connect

    Nunez, Dario; Sarbach, Olivier

    2010-02-15

    We discuss the initial-boundary value problem for the Baumgarte-Shapiro-Shibata-Nakamura evolution system of Einstein's field equations which has been used extensively in numerical simulations of binary black holes and neutron stars. We specify nine boundary conditions for this system with the following properties: (i) they impose the momentum constraint at the boundary, which is shown to preserve all the constraints throughout evolution; (ii) they approximately control the incoming gravitational degrees of freedom by specifying the Weyl scalar {Psi}{sub 0} at the boundary; (iii) they control the gauge freedom by requiring a Neumann boundary condition for the lapse, by setting the normal component of the shift to zero, and by imposing a Sommerfeld-like condition on the tangential components of the shift; and (iv) they are shown to yield a well-posed problem in the limit of weak gravity. Possible numerical applications of our results are also discussed briefly.

  17. Wideband finite difference time domain implementation of surface impedance boundary conditions for good conductors

    NASA Technical Reports Server (NTRS)

    Beggs, John H.; Luebbers, Raymond J.; Kunz, Karl S.; Yee, Kane S.

    1991-01-01

    Surface impedance boundary conditions are used to reduce the solution volume during the analysis of scattering from lossy dielectric objects. In a finite difference solution, they also can be used to avoid using small cells, made necessary by shorter wavelengths in conducting media, throughout the solution volume. A one dimensional implementation is presented for a surface impedance boundary condition for good conductors in the Finite Difference Time Domain (FDTD) technique. In order to illustrate the FDTD surface impedance boundary condition, a planar air-lossy dielectric interface is considered.

  18. The PPP model of alternant cyclic polyenes with modified boundary conditions

    SciTech Connect

    Bendazzoli, G.L.; Evangelisti, S.

    1995-08-15

    The extension of the PPP Hamiltonian for alternant cyclic polyenes to noninteger values of the pseudomomentum by imposing modified boundary conditions is discussed in detail. It is shown that a computer program for periodic boundary conditions can be easily adapted to the new boundary conditions. Full CI computations are carried out for some low-lying states of the PPP model of alternant cyclic polyenes (CH){sub N} (N even) at half-filling. The energy values obtained by using periodic (Bloch) and antiperiodic (Moebius) orbitals are used to perform energy extrapolations for N {yields} {infinity}. 38 refs., 2 figs., 5 tabs.

  19. Solution of Poisson's Equation with Global, Local and Nonlocal Boundary Conditions

    ERIC Educational Resources Information Center

    Aliev, Nihan; Jahanshahi, Mohammad

    2002-01-01

    Boundary value problems (BVPs) for partial differential equations are common in mathematical physics. The differential equation is often considered in simple and symmetric regions, such as a circle, cube, cylinder, etc., with global and separable boundary conditions. In this paper and other works of the authors, a general method is used for the…

  20. An Existence Theorem for Fractional q-Difference Inclusions with Nonlocal Substrip Type Boundary Conditions

    PubMed Central

    Alsaedi, Ahmed; Ntouyas, Sotiris K.; Ahmad, Bashir

    2015-01-01

    By employing a nonlinear alternative for contractive maps, we investigate the existence of solutions for a boundary value problem of fractional q-difference inclusions with nonlocal substrip type boundary conditions. The main result is illustrated with the aid of an example. PMID:25629085

  1. Towards an effective non-reflective boundary condition for computational aeroacoustics

    NASA Astrophysics Data System (ADS)

    Gill, James; Fattah, Ryu; Zhang, Xin

    2017-03-01

    A generic, non-reflective zonal transverse characteristic boundary condition is described for computational aeroacoustics, which shows superior performance to existing non-reflective boundary conditions for two-dimensional linearized Euler simulations. The new condition is based on a characteristic non-reflective method, and also contains optimised use of transverse characteristic terms and a zonal forcing region. The performance of the new method and several existing non-reflective acoustic boundary conditions is quantitatively compared using a plane wave test case. The performance of buffer zone, perfectly matched layer, far-field, and characteristic non-reflective methods is compared, following an optimisation of the tuneable parameters in each method to give best performance. The study uses a high-order linearised Euler equation solver to assess non-reflective boundary conditions with a variety of cases. The performance is compared for downstream travelling acoustic waves with varying frequency and incident angle, and at various Mach numbers. The current study includes a more comprehensive evaluation than previous studies which used constant values of tuneable parameters or qualitative assessment methods. The new zonal transverse characteristic boundary condition is shown to give improved performance in comparison to the other tested outflow boundary conditions for two-dimensional linearized Euler simulations, and is also shown to give good performance when used as an inflow condition.

  2. Geomagnetic Secular Variation Prediction with Thermal Heterogeneous Boundary Conditions

    NASA Technical Reports Server (NTRS)

    Kuang, Weijia; Tangborn, Andrew; Jiang, Weiyuan

    2011-01-01

    It has long been conjectured that thermal heterogeneity at the core-mantle boundary (CMB) affects the geodynamo substantially. The observed two pairs of steady and strong magnetic flux lobes near the Polar Regions and the low secular variation in the Pacific over the past 400 years (and perhaps longer) are likely the consequences of this CMB thermal heterogeneity. There are several studies on the impact of the thermal heterogeneity with numerical geodynamo simulations. However, direct correlation between the numerical results and the observations is found very difficult, except qualitative comparisons of certain features in the radial component of the magnetic field at the CMB. This makes it difficult to assess accurately the impact of thermal heterogeneity on the geodynamo and the geomagnetic secular variation. We revisit this problem with our MoSST_DAS system in which geomagnetic data are assimilated with our geodynamo model to predict geomagnetic secular variations. In this study, we implement a heterogeneous heat flux across the CMB that is chosen based on the seismic tomography of the lowermost mantle. The amplitude of the heat flux (relative to the mean heat flux across the CMB) varies in the simulation. With these assimilation studies, we will examine the influences of the heterogeneity on the forecast accuracies, e.g. the accuracies as functions of the heterogeneity amplitude. With these, we could be able to assess the model errors to the true core state, and thus the thermal heterogeneity in geodynamo modeling.

  3. Generalized adjoint consistent treatment of wall boundary conditions for compressible flows

    NASA Astrophysics Data System (ADS)

    Hartmann, Ralf; Leicht, Tobias

    2015-11-01

    In this article, we revisit the adjoint consistency analysis of Discontinuous Galerkin discretizations of the compressible Euler and Navier-Stokes equations with application to the Reynolds-averaged Navier-Stokes and k- ω turbulence equations. Here, particular emphasis is laid on the discretization of wall boundary conditions. While previously only one specific combination of discretizations of wall boundary conditions and of aerodynamic force coefficients has been shown to give an adjoint consistent discretization, in this article we generalize this analysis and provide a discretization of the force coefficients for any consistent discretization of wall boundary conditions. Furthermore, we demonstrate that a related evaluation of the cp- and cf-distributions is required. The freedom gained in choosing the discretization of boundary conditions without loosing adjoint consistency is used to devise a new adjoint consistent discretization including numerical fluxes on the wall boundary which is more robust than the adjoint consistent discretization known up to now. While this work is presented in the framework of Discontinuous Galerkin discretizations, the insight gained is also applicable to (and thus valuable for) other discretization schemes. In particular, the discretization of integral quantities, like the drag, lift and moment coefficients, as well as the discretization of local quantities at the wall like surface pressure and skin friction should follow as closely as possible the discretization of the flow equations and boundary conditions at the wall boundary.

  4. High order local absorbing boundary conditions for acoustic waves in terms of farfield expansions

    NASA Astrophysics Data System (ADS)

    Villamizar, Vianey; Acosta, Sebastian; Dastrup, Blake

    2017-03-01

    We devise a new high order local absorbing boundary condition (ABC) for radiating problems and scattering of time-harmonic acoustic waves from obstacles of arbitrary shape. By introducing an artificial boundary S enclosing the scatterer, the original unbounded domain Ω is decomposed into a bounded computational domain Ω- and an exterior unbounded domain Ω+. Then, we define interface conditions at the artificial boundary S, from truncated versions of the well-known Wilcox and Karp farfield expansion representations of the exact solution in the exterior region Ω+. As a result, we obtain a new local absorbing boundary condition (ABC) for a bounded problem on Ω-, which effectively accounts for the outgoing behavior of the scattered field. Contrary to the low order absorbing conditions previously defined, the error at the artificial boundary induced by this novel ABC can be easily reduced to reach any accuracy within the limits of the computational resources. We accomplish this by simply adding as many terms as needed to the truncated farfield expansions of Wilcox or Karp. The convergence of these expansions guarantees that the order of approximation of the new ABC can be increased arbitrarily without having to enlarge the radius of the artificial boundary. We include numerical results in two and three dimensions which demonstrate the improved accuracy and simplicity of this new formulation when compared to other absorbing boundary conditions.

  5. A Boundary Mixture Approach to Violations of Conditional Independence

    ERIC Educational Resources Information Center

    Braeken, Johan

    2011-01-01

    Conditional independence is a fundamental principle in latent variable modeling and item response theory. Violations of this principle, commonly known as local item dependencies, are put in a test information perspective, and sharp bounds on these violations are defined. A modeling approach is proposed that makes use of a mixture representation of…

  6. On the Wave Equation with Hyperbolic Dynamical Boundary Conditions, Interior and Boundary Damping and Source

    NASA Astrophysics Data System (ADS)

    Vitillaro, Enzo

    2017-03-01

    The aim of this paper is to study the problem u_{tt}-Δ u+P(x,u_t)=f(x,u) quad & in (0,∞)×Ω, u=0 & on (0,∞)× Γ_0, u_{tt}+partial_ν u-Δ_Γ u+Q(x,u_t)=g(x,u)quad & on (0,∞)× Γ_1, u(0,x)=u_0(x),quad u_t(0,x)=u_1(x) & in overline Ω, where {Ω} is a open bounded subset of R^N with C 1 boundary ({N ≥ 2}), {Γ = partialΩ}, {(Γ0,Γ1)} is a measurable partition of {Γ}, {Δ_{Γ}} denotes the Laplace-Beltrami operator on {Γ}, {ν} is the outward normal to {Ω}, and the terms P and Q represent nonlinear damping terms, while f and g are nonlinear subcritical perturbations. In the paper a local Hadamard well-posedness result for initial data in the natural energy space associated to the problem is given. Moreover, when {Ω} is C 2 and {overline{Γ0} \\cap overline{Γ1} = emptyset}, the regularity of solutions is studied. Next a blow-up theorem is given when P and Q are linear and f and g are superlinear sources. Finally a dynamical system is generated when the source parts of f and g are at most linear at infinity, or they are dominated by the damping terms.

  7. Principal Eigenvalue Minimization for an Elliptic Problem with Indefinite Weight and Robin Boundary Conditions

    SciTech Connect

    Hintermueller, M.; Kao, C.-Y.; Laurain, A.

    2012-02-15

    This paper focuses on the study of a linear eigenvalue problem with indefinite weight and Robin type boundary conditions. We investigate the minimization of the positive principal eigenvalue under the constraint that the absolute value of the weight is bounded and the total weight is a fixed negative constant. Biologically, this minimization problem is motivated by the question of determining the optimal spatial arrangement of favorable and unfavorable regions for a species to survive. For rectangular domains with Neumann boundary condition, it is known that there exists a threshold value such that if the total weight is below this threshold value then the optimal favorable region is like a section of a disk at one of the four corners; otherwise, the optimal favorable region is a strip attached to the shorter side of the rectangle. Here, we investigate the same problem with mixed Robin-Neumann type boundary conditions and study how this boundary condition affects the optimal spatial arrangement.

  8. Influence of Boundary Conditions on Simulated U.S. Air Quality

    EPA Science Inventory

    One of the key inputs to regional-scale photochemical models frequently used in air quality planning and forecasting applications are chemical boundary conditions representing background pollutant concentrations originating outside the regional modeling domain. A number of studie...

  9. Evaluation of wall boundary condition parameters for gas-solids fluidized bed simulations

    SciTech Connect

    Li, Tingwen; Benyahia, Sofiane

    2013-10-01

    Wall boundary conditions for the solids phase have significant effects on numerical predictions of various gas-solids fluidized beds. Several models for the granular flow wall boundary condition are available in the open literature for numerical modeling of gas-solids flow. In this study, a model for specularity coefficient used in Johnson and Jackson boundary conditions by Li and Benyahia (AIChE Journal, 2012, 58, 2058-2068) is implemented in the open-source CFD code-MFIX. The variable specularity coefficient model provides a physical way to calculate the specularity coefficient needed by the partial-slip boundary conditions for the solids phase. Through a series of 2-D numerical simulations of bubbling fluidized bed and circulating fluidized bed riser, the model predicts qualitatively consistent trends to the previous studies. Furthermore, a quantitative comparison is conducted between numerical results of variable and constant specularity coefficients to investigate the effect of spatial and temporal variations in specularity coefficient.

  10. On the Ideal Boundary Condition in a General Toroidal Geometry for a Mixed Magnetic Field Representation

    SciTech Connect

    X. Z. Tang

    2000-12-18

    Subtleties of implementing the standard perfectly conducting wall boundary condition in a general toroidal geometry are clarified for a mixed scalar magnetic field representation. An iterative scheme based on Ohm's law is given.

  11. Simulating thermal boundary conditions of spin-lattice models with weighted averages

    NASA Astrophysics Data System (ADS)

    Wang, Wenlong

    2016-07-01

    Thermal boundary conditions have played an increasingly important role in revealing the nature of short-range spin glasses and is likely to be relevant also for other disordered systems. Diffusion method initializing each replica with a random boundary condition at the infinite temperature using population annealing has been used in recent large-scale simulations. However, the efficiency of this method can be greatly suppressed because of temperature chaos. For example, most samples have some boundary conditions that are completely eliminated from the population in the process of annealing at low temperatures. In this work, I study a weighted average method to solve this problem by simulating each boundary conditions separately and collect data using weighted averages. The efficiency of the two methods is studied using both population annealing and parallel tempering, showing that the weighted average method is more efficient and accurate.

  12. Bicategories for Boundary Conditions and for Surface Defects in 3-d TFT

    NASA Astrophysics Data System (ADS)

    Fuchs, Jürgen; Schweigert, Christoph; Valentino, Alessandro

    2013-07-01

    We analyze topological boundary conditions and topological surface defects in three-dimensional topological field theories of Reshetikhin-Turaev type based on arbitrary modular tensor categories. Boundary conditions are described by central functors that lift to trivializations in the Witt group of modular tensor categories. The bicategory of boundary conditions can be described through the bicategory of module categories over any such trivialization. A similar description is obtained for topological surface defects. Using string diagrams for bicategories we also establish a precise relation between special symmetric Frobenius algebras and Wilson lines involving special defects. We compare our results with previous work of Kapustin-Saulina and of Kitaev-Kong on boundary conditions and surface defects in abelian Chern-Simons theories and in Turaev-Viro type TFTs, respectively.

  13. On Korn's first inequality for tangential or normal boundary conditions with explicit constants

    NASA Astrophysics Data System (ADS)

    Bauer, Sebastian; Pauly, Dirk

    2016-12-01

    We will prove that for piecewise smooth and concave domains Korn's first inequality holds for vector fields satisfying homogeneous normal or tangential boundary conditions with explicit Korn constant square root of 2.

  14. An analysis of boundary condition effects on the thermomechanical modeling of the FSW process

    NASA Astrophysics Data System (ADS)

    Guedoiri, A.; Moufki, A.; Favier, V.; Zahrouni, H.

    2011-01-01

    The aim of the present work is to study the influence of thermal boundary conditions on the simulation of friction stir welding process "FSW". Generally, dimensions of the workpieces to be welded are very large and a very small zone surrounding the welding tool is modeled for the thermomechanical study of the process. This area, named box, should be small enough to reduce the computation time and large enough to minimize effects of boundary conditions. It is well known that during welding, the mixing zone is closed arround the tool; it is easily identified by analyzing the velocity field which is complex in contact interface with the tool and which tends rapidly to the tool traverse speed far from the tool. In the thermal analysis, the boundary conditions are not obvious since they depend on the welding parameters, on the workpiece dimensions and on its vicinity. We propose in this study a numerical strategy for determining the thermal boundary conditions on the box.

  15. Implementation of a Compressor Face Boundary Condition Based on Small Disturbances

    NASA Technical Reports Server (NTRS)

    Slater, John W.; Paynter, Gerald C.

    2000-01-01

    A compressor-face boundary condition that models the unsteady interactions of acoustic and convective velocity disturbances with a compressor has been implemented into a three-dimensional computational fluid dynamics code. Locally one-dimensional characteristics along with a small-disturbance model are used to compute the acoustic response as a function of the local stagger angle and the strength and direction of the disturbance. Simulations of the inviscid flow in a straight duct, a duct coupled to a compressor, and a supersonic inlet demonstrate the behavior of the boundary condition in relation to existing boundary conditions. Comparisons with experimental data show a large improvement in accuracy over existing boundary conditions in the ability to predict the reflected disturbance from the interaction of an acoustic disturbance with a compressor.

  16. A bridging technique to analyze the influence of boundary conditions on instability patterns

    SciTech Connect

    Hu Heng; Damil, Noureddine; Potier-Ferry, Michel

    2011-05-10

    In this paper, we present a new numerical technique that permits to analyse the effect of boundary conditions on the appearance of instability patterns. Envelope equations of Landau-Ginzburg type are classically used to predict pattern formation, but it is not easy to associate boundary conditions for these macroscopic models. Indeed, envelope equations ignore boundary layers that can be important, for instance in cases where the instability starts first near the boundary. In this work, the full model is considered close to the boundary, an envelope equation in the core and they are bridged by the Arlequin method . Simulation results are presented for the problem of buckling of long beams lying on a non-linear elastic foundation.

  17. Boundary conditions on faster-than-light transportation systems

    NASA Technical Reports Server (NTRS)

    Bennett, Gary L.; Knowles, H. B.

    1993-01-01

    In order to be consistent with current physical theories, any proposal of a faster-than light (FTL) transportation system must satisfy several critical conditions. It must predict the mass, space, and time dimensional changes predicted by relativity physics when velocity falls below the speed of light. It must also not violate causality, and remain consistent with quantum physics in the limit of microscopic systems. It is also essential that the proposal conserve energy.

  18. Wideband finite difference time domain implementation of surface impedance boundary conditions for good conductors

    NASA Technical Reports Server (NTRS)

    Beggs, John H.; Luebbers, Raymond J.; Kunz, Karl S.; Yee, Kane S.

    1991-01-01

    Surface impedance boundary conditions are employed to reduce the solution volume during the analysis of scattering from lossy dielectric objects. In a finite difference solution, they also can be utilized to avoid using small cells, made necessary by shorter wavelengths in conducting media, throughout the solution volume. A 1-D implementation for a surface impedance boundary condition for good conductors in the Finite Difference Time Domain (FDTD) technique.

  19. Unsteady Validation of a Mean Flow Boundary Condition for Computational Aeroacoustics

    NASA Technical Reports Server (NTRS)

    Hixon, R.; Zhen, F.; Nallasamy, M.; Sawyer, S> ; Dyson, R.

    2004-01-01

    In this work, a previously developed mean flow boundary condition will be validated for unsteady flows. The test cases will be several reference benchmark flows consisting of vortical gusts convecting in a uniform mean flow, as well as the more realistic case of a vortical gust impinging on a loaded 2D cascade. The results will verify that the mean flow boundary condition both imposes the desired mean flow as well as having little or no effect on the instantaneous unsteady solution.

  20. Towards Direct Simulations of Counterflow Flames with Consistent Numerical Differential-Algebraic Boundary Conditions

    DTIC Science & Technology

    2015-05-18

    Towards direct simulations of counterflow flames with consistent numerical differential-algebraic boundary conditions The views, opinions and/or...Research Triangle Park, NC 27709-2211 counterflow laminar flame model REPORT DOCUMENTATION PAGE 11. SPONSOR/MONITOR’S REPORT NUMBER(S) 10. SPONSOR...simulations of counterflow flames with consistent numerical differential-algebraic boundary conditions Report Title A new approach for the

  1. Design and Verification Methodology of Boundary Conditions for Finite Volume Schemes

    DTIC Science & Technology

    2012-07-01

    and Grossman advocate a curvature corrected symmetry condition for an inviscid wall [3]. Balakrishnan and Fernandez advocate a variety of other methods...boundary source terms is straightforward, generally requiring much less algebraic manipulation than interior source terms. A number of test cases...Meeting, Reno, NV, January 1986. [3] A. Dadone and B. Grossman . Surface boundary conditions for the numerical solution of the euler equations. AIAA

  2. Sobolev type equations of time-fractional order with periodical boundary conditions

    NASA Astrophysics Data System (ADS)

    Plekhanova, Marina

    2016-08-01

    The existence of a unique local solution for a class of time-fractional Sobolev type partial differential equations endowed by the Cauchy initial conditions and periodical with respect to every spatial variable boundary conditions on a parallelepiped is proved. General results are applied to study of the unique solvability for the initial boundary value problem to Benjamin-Bona-Mahony-Burgers and Allair partial differential equations.

  3. On pressure and velocity boundary conditions for the lattice Boltzmann BGK model

    SciTech Connect

    Zou, Q. |; He, X.

    1997-06-01

    Pressure (density) and velocity boundary conditions are studied for 2-D and 3-D lattice Boltzmann BGK models (LBGK) and a new method to specify these conditions is proposed. These conditions are constructed in consistency with the wall boundary condition, based on the idea of bounceback of the non-equilibrium distribution. When these conditions are used together with the incompressible LBGK model [J. Stat. Phys. {bold 81}, 35 (1995)] the simulation results recover the analytical solution of the plane Poiseuille flow driven by a pressure (density) difference. The half-way wall bounceback boundary condition is also used with the pressure (density) inlet/outlet conditions proposed in this paper and in Phys. Fluids {bold 8}, 2527 (1996) to study 2-D Poiseuille flow and 3-D square duct flow. The numerical results are approximately second-order accurate. The magnitude of the error of the half-way wall bounceback boundary condition is comparable with that of other published boundary conditions and it has better stability behavior. {copyright} {ital 1997 American Institute of Physics.}

  4. A hybrid FEM-BEM unified boundary condition with sub-cycling for electromagnetic radiation

    SciTech Connect

    Fasenfest, B; White, D; Stowell, M; Rieben, R; Sharpe, R; Madsen, N; Rockway, J; Champagne, N J; Jandhyala, V; Pingenot, J

    2006-01-12

    Hybrid solutions to time-domain electromagnetic problems offer many advantages when solving open-region scattering or radiation problems. Hybrid formulations use a finite-element or finite-difference discretization for the features of interest, then bound this region with a layer of planar boundary elements. The use of volume discretization allows for intricate features and many changes in material within the structure, while the boundary-elements provide a highly accurate radiating boundary condition. This concept has been implemented previously, using the boundary elements to set the E-field, H-field, or both for an FDTD grid, for example in [1][2][3], or as a mixed boundary condition for the second order wave equation solved by finite elements [4]. Further study has focused on using fast methods, such as the Plane Wave Time Domain method [3][4] to accelerate the BEM calculations. This paper details a hybrid solver using the coupled first-order equations for the E and H fields in the finite-element region. This formulation is explicit, with a restriction on the time step for stability. When this time step is used in conjunction with the boundary elements forming either a inhomogeneous Dirichlet or Neuman boundary condition on the finite-element mesh, late time instabilities occur. To combat this, a Unified Boundary Condition (UBC), similar to the one in [4] for the second-order wave equation, is used. Even when this UBC is used, the late time instabilities are merely delayed if standard testing in time is used. However, the late time instabilities can be removed by replacing centroid based time interpolation with quadrature point based time interpolation for the boundary elements, or by sub-cycling the boundary element portion of the formulation. This sub-cycling, used in [3] for FDTD to reduce complexity, is shown here to improve stability and overall accuracy of the technique.

  5. A stable penalty method for the compressible Navier-Stokes equations. 1: Open boundary conditions

    NASA Technical Reports Server (NTRS)

    Hesthaven, J. S.; Gottlieb, D.

    1994-01-01

    The purpose of this paper is to present asymptotically stable open boundary conditions for the numerical approximation of the compressible Navier-Stokes equations in three spatial dimensions. The treatment uses the conservation form of the Navier-Stokes equations and utilizes linearization and localization at the boundaries based on these variables. The proposed boundary conditions are applied through a penalty procedure, thus ensuring correct behavior of the scheme as the Reynolds number tends to infinity. The versatility of this method is demonstrated for the problem of a compressible flow past a circular cylinder.

  6. A finite element algorithm for high-lying eigenvalues with Neumann and Dirichlet boundary conditions

    NASA Astrophysics Data System (ADS)

    Báez, G.; Méndez-Sánchez, R. A.; Leyvraz, F.; Seligman, T. H.

    2014-01-01

    We present a finite element algorithm that computes eigenvalues and eigenfunctions of the Laplace operator for two-dimensional problems with homogeneous Neumann or Dirichlet boundary conditions, or combinations of either for different parts of the boundary. We use an inverse power plus Gauss-Seidel algorithm to solve the generalized eigenvalue problem. For Neumann boundary conditions the method is much more efficient than the equivalent finite difference algorithm. We checked the algorithm by comparing the cumulative level density of the spectrum obtained numerically with the theoretical prediction given by the Weyl formula. We found a systematic deviation due to the discretization, not to the algorithm itself.

  7. Continuous matrix product states with periodic boundary conditions and an application to atomtronics

    NASA Astrophysics Data System (ADS)

    Draxler, Damian; Haegeman, Jutho; Verstraete, Frank; Rizzi, Matteo

    2017-01-01

    We introduce a time evolution algorithm for one-dimensional quantum field theories with periodic boundary conditions. This is done by applying the Dirac-Frenkel time-dependent variational principle to the set of translational invariant continuous matrix product states with periodic boundary conditions. Moreover, the ansatz is accompanied with additional boundary degrees of freedom to study quantum impurity problems. The algorithm allows for a cutoff in the spectrum of the transfer matrix and thus has an efficient computational scaling. In particular we study the prototypical example of an atomtronic system—an interacting Bose gas rotating in a ring shaped trap in the presence of a localized barrier potential.

  8. ALmost EXact boundary conditions for transient Schrödinger–Poisson system

    SciTech Connect

    Bian, Lei; Pang, Gang; Tang, Shaoqiang; Arnold, Anton

    2016-05-15

    For the Schrödinger–Poisson system, we propose an ALmost EXact (ALEX) boundary condition to treat accurately the numerical boundaries. Being local in both space and time, the ALEX boundary conditions are demonstrated to be effective in suppressing spurious numerical reflections. Together with the Crank–Nicolson scheme, we simulate a resonant tunneling diode. The algorithm produces numerical results in excellent agreement with those in Mennemann et al. [1], yet at a much reduced complexity. Primary peaks in wave function profile appear as a consequence of quantum resonance, and should be considered in selecting the cut-off wave number for numerical simulations.

  9. Effect of different wall boundary conditions on the numerical simulation of bubbling fluidized beds

    NASA Astrophysics Data System (ADS)

    Haghgoo, Mohammad Reza; Bergstrom, Donald J.; Spiteri, Raymond J.

    2015-11-01

    There are distinct wall boundary conditions proposed in the literature for the particulate phase in the context of a continuum description of gas-particle flows. It is not yet clear how these different wall boundary conditions affect the simulated flow behavior, nor is it clear which are the most realistic. To investigate this issue, an Eulerian-Eulerian two-fluid model was used to investigate the effect of different particle-phase wall boundary conditions on the numerical prediction of bubbling/slugging gas-particle fluidized beds. Because the bed dynamics are strongly influenced by the motion of the bubbles, the impact of wall boundary conditions on the bubble statistics was examined specifically. In addition, the averaged field variables, such as the particle velocity, were compared to published experimental measurements. The comparison shows good agreement between the numerical results, generated by the Mfix code, and their experimental counterparts. It is found that the particle wall boundary condition does play a significant role in predicting the flow behavior. However, it appears that the influence of the wall boundary conditions is more significant for the instantaneous flow variables and bubble statistics than for the averaged quantities.

  10. Finite Element Based Structural Damage Detection Using Artificial Boundary Conditions

    DTIC Science & Technology

    2007-09-01

    ER, barp, shape, error, a_cp, modep , ap, % modelabelp, FOMABClabelp, FOMPLUSlabelp % abc_con, abc_conT % ABC, base % plus_con, plus_conT...error = round(rel_freqERROR(ER:ER+15)*100)/100; a_cp = 1; for modep = 1:3 %3 sets of modes per boundry condition ap = [a_cp...int2str(a_cp:a_cp+4); FOMABC = int2str(FOM_ABC5per(intervelp+ modep )); FOMABClabelp = sprintf(’System FOM = %s’, FOMABC

  11. Instanton-dyon ensembles with quarks with modified boundary conditions

    NASA Astrophysics Data System (ADS)

    Larsen, Rasmus; Shuryak, Edward

    2016-11-01

    We modify the quark periodicity condition on the thermal circle by the introduction of some phases—known also as "flavor holonomies"— different quark flavors. These phases provide a valuable tool, to be used for better understanding of deconfinement and chiral restoration phase transitions: by changing them, one can dramatically modify both phase transitions. In the language of instanton constituents—instanton-dyons or monopoles—changing the quark periodicity condition has a very direct explanation: the interplay of flavor and color holonomies can switch topological zero modes between various dyon types. The model we will study in detail, the so-called ZN c-symmetric QCD model with equal number of colors and flavors Nc=Nf=2 and special arrangement of flavor and color holonomies, ensures the "most democratic" setting, in which each quark flavor and each dyon type are in one-to-one correspondence. The usual QCD has the opposite "most exclusive" arrangement: all quarks are antiperiodic and, thus, all zero modes fall on only one—twisted or L —dyon type. As we show by ensemble simulation, deconfinement and chiral restoration phase transitions in these two models are dramatically different. In the usual QCD, both are smooth crossovers: but in the case of the Z2-symmetric model, deconfinement becomes a strong first-order transition, while chiral symmetry remains broken for all dyon densities studied. These results are in good correspondence with those from recent lattice simulations.

  12. Impact of Boundary Conditions on Pumping in a Fully Bounded Aquifer

    NASA Astrophysics Data System (ADS)

    Lu, C.; Xin, P.; Li, L.; Luo, J.

    2014-12-01

    The flow field may be affected by aquifer boundaries, when pumping in a small-scale aquifer or a long term pumping activity is required especially under a large pumping rate. Using potential theory, the image-well method and superposition principle, analytical solutions are derived for pumping in a fully bounded rectangular aquifer with five different boundary condition scenarios: (1) one constant-head boundary (in horizontal direction in plan view) and three impermeable boundaries, (2) two parallel constant-head boundaries (in horizontal direction) and two parallel impermeable boundaries (in vertical direction), (3) two pairs of orthogonal impermeable and constant-head boundaries, (4) three constant-head boundaries and one impermeable boundary, and (5) four constant-head boundaries. For each scenario, closed-form expressions are derived in three different types: (1) summation of the series in horizontal and vertical directions; (2) summation of the series in horizontal direction and exact potential in vertical direction, and (3) summation of the series in vertical direction and exact potential in horizontal direction. It is found that all the three types of closed-form expressions can produce an accurate potential for scenarios (3)-(5). For scenarios (1) and (2), by contrast, the third type closed-form expression can yield an accurate solution, while the second type close-form expression always generates an unacceptable solution. Therefore, the third type closed-form is recommended to solve the potential of a flow field created by a pumping well subjected to multiple impermeable and/or constant-head boundary conditions, due to its accuracy as well as computational efficiency.

  13. Small-charge underwater explosion bubble experiments under various boundary conditions

    NASA Astrophysics Data System (ADS)

    Cui, P.; Zhang, A. M.; Wang, S. P.

    2016-11-01

    Small-charge underwater explosion experiments were performed to investigate bubbles subjected to gravity and various boundary conditions, including single boundary (free surface and rigid wall boundary), combined boundaries of free surface and solid wall, solid wall boundaries with a circular opening, and resilient wall boundaries. With high speed camera and pressure sensors, the behavior of explosion bubbles was studied and features of associated pressure pulses were analyzed. Detailed image analysis on the final stages of bubble collapse was carried out and revealed a possible explanation for the weakening of pressure waves at bubble rebound as the bubble approaches a wall boundary. Certain features also indicate that the magnitude of the pressure peaks induced by bubble rebound is related to the shape of the bubble shape during collapse. Pressure pulses arising from the two types of bubble behavior, specifically the collision of an annular jet and the impact of a jet with the wall boundary, were measured. Other curious types of bubble behavior were found, including jetting induced by suction when a bubble collapses covering a circular opening on a solid wall, and bubble splitting in interaction with a resilient wall boundary.

  14. An energy absorbing far-field boundary condition for the elastic wave equation

    SciTech Connect

    Petersson, N A; Sjogreen, B

    2008-07-15

    The authors present an energy absorbing non-reflecting boundary condition of Clayton-Engquist type for the elastic wave equation together with a discretization which is stable for any ratio of compressional to shear wave speed. They prove stability for a second order accurate finite-difference discretization of the elastic wave equation in three space dimensions together with a discretization of the proposed non-reflecting boundary condition. The stability proof is based on a discrete energy estimate and is valid for heterogeneous materials. The proof includes all six boundaries of the computational domain where special discretizations are needed at the edges and corners. The stability proof holds also when a free surface boundary condition is imposed on some sides of the computational domain.

  15. Nonreflecting Far-Field Boundary Conditions for Unsteady Transonic Flow Computation

    NASA Technical Reports Server (NTRS)

    Kwak, D.

    1981-01-01

    The approximate nonreflecting far-field boundary condition, as proposed by Engquisi and Majda, is implemented In the computer code LTRAN2. This code solves the Implicit finite-difference representation of the small-disturbance equations for unsteady transonic flows about airfoils. The nonreflecting boundary condition and the description of the algorithm for Implementing these conditions In LTRAN2 tire discussed. Various cases re computed and compared with results from the older, more conventional procedures. One concludes that the nonreflecting far-field boundary approximation allows the far-field boundary to be located closer to the airfoil; this permits a decrease in the computer lime required to obtain the solution through the use of fewer mesh points.

  16. Nonreflecting boundary conditions for the complete unsteady transonic small-disturbance equation

    NASA Astrophysics Data System (ADS)

    Whitlow, W., Jr.; Seidel, D. A.

    1985-02-01

    Nonreflecting far-field boundary conditions that are consistent with the complete transonic small-disturbance (TSD) equations are derived. They are implemented in a new code for solving the complete TSD equation and are tested for a harmonically oscillating NACA 64A010 airfoil in transonic flow and for a flat-plate airfoil with a pulse in the angle of attack. Using the new boundary conditions on a relatively small grid, solutions for the airfoil that are obtained that agree with large-grid calculations, resulting in a 44 percent savings in computer time. Frequency responses for the flat plate show that most of the disturbances incident on the computational boundaries are absorbed by the boundary conditions.

  17. A direct approach to finding unknown boundary conditions in steady heat conduction

    NASA Technical Reports Server (NTRS)

    Martin, Thomas J.; Dulikravich, George S.

    1993-01-01

    The capability of the boundary element method (BEM) in determining thermal boundary conditions on surfaces of a conducting solid where such quantities are unknown was demonstrated. The method uses a non-iterative direct approach in solving what is usually called the inverse heat conduction problem (IHCP). Given any over-specified thermal boundary conditions such as a combination of temperature and heat flux on a surface where such data is readily available, the algorithm computes the temperature field within the object and any unknown thermal boundary conditions on surfaces where thermal boundary values are unavailable. A two-dimensional, steady-state BEM program was developed and was tested on several simple geometries where the analytic solution was known. Results obtained with the BEM were in excellent agreement with the analytic values. The algorithm is highly flexible in treating complex geometries, mixed thermal boundary conditions, and temperature-dependent material properties and is presently being extended to three-dimensional and unsteady heat conduction problems. The accuracy and reliability of this technique was very good but tended to deteriorate when the known surface conditions were only slightly over-specified and far from the inaccessible surface.

  18. Critical dense polymers with Robin boundary conditions, half-integer Kac labels and Z4 fermions

    NASA Astrophysics Data System (ADS)

    Pearce, Paul A.; Rasmussen, Jørgen; Tipunin, Ilya Yu.

    2014-12-01

    For general Temperley-Lieb loop models, including the logarithmic minimal models LM (p ,p‧) with p ,p‧ coprime integers, we construct an infinite family of Robin boundary conditions on the strip as linear combinations of Neumann and Dirichlet boundary conditions. These boundary conditions are Yang-Baxter integrable and allow loop segments to terminate on the boundary. Algebraically, the Robin boundary conditions are described by the one-boundary Temperley-Lieb algebra. Solvable critical dense polymers is the first member LM (1 , 2) of the family of logarithmic minimal models and has loop fugacity β = 0 and central charge c = - 2. Specialising to LM (1 , 2) with our Robin boundary conditions, we solve the model exactly on strips of arbitrary finite size N and extract the finite-size conformal corrections using an Euler-Maclaurin formula. The key to the solution is an inversion identity satisfied by the commuting double row transfer matrices. This inversion identity is established directly in the Temperley-Lieb algebra. We classify the eigenvalues of the double row transfer matrices using the physical combinatorics of the patterns of zeros in the complex spectral parameter plane and obtain finitised characters related to spaces of coinvariants of Z4 fermions. In the continuum scaling limit, the Robin boundary conditions are associated with irreducible Virasoro Verma modules with conformal weights Δ r , s -1/2 =1/32 (L2 - 4) where L = 2 s - 1 - 4 r, r ∈ Z, s ∈ N. These conformal weights populate a Kac table with half-integer Kac labels. Fusion of the corresponding modules with the generators of the Kac fusion algebra is examined and general fusion rules are proposed.

  19. Open boundary conditions for internal gravity wave modelling using polarization relations

    NASA Astrophysics Data System (ADS)

    Marsaleix, Patrick; Ulses, Caroline; Pairaud, Ivane; Herrmann, Marine Julie; Floor, Jochem Willem; Estournel, Claude; Auclair, Francis

    This paper proposes an original approach of the open boundary condition problem, within the framework of internal hydrostatic wave theory. These boundary conditions are based on the relations of polarization of internal waves. The method is presented progressively, beginning with a simple case (non-rotating regime, propagation direction normal to the open boundary), ending with a more general situation (rotating regime, multimodal & multi-dimensional propagations and variable background field). In the non-rotating case and as far as we assume that the direction of propagation is locally normal to the open boundary, the so-called PRM (polarization relation method) scheme can be seen as a three-dimensional version of the barotropic Flather boundary conditions. The discrete form of the scheme is detailed. Numerical stability issues proper to leap-frog time stepping are in particular discussed. It is shown that errors on phase speed prescribed in the boundary conditions can notably deteriorate radiation properties. The normal mode approach is introduced to identify coherent structures of propagation and their corresponding phase speed. A simple and robust multi-dimensional propagation scheme can easily be derived from polarization relations. The rotating case is more difficult but it is possible, to some extent, to get around the dependency of phase speed on wave frequency and to keep the non-rotating formulation of the PRM conditions almost unchanged. The PRM scheme being applied to field anomalies, the question of the background reference state is addressed. The latter can be used to introduce incoming waves across the open boundaries or, alternatively, to represent the low-frequency variability of the model itself. The consistency of the pressure and tracer boundary conditions is finally discussed.

  20. On the Nature of Boundary Conditions for Flows with Moving Free Surfaces

    NASA Astrophysics Data System (ADS)

    Renardy, Michael; Renardy, Yuriko

    1991-04-01

    We consider small perturbations of plane parallel flow between a wall and a moving free surface. The problem is posed on a rectangle with inflow and outflow boundaries. The usual boundary conditions are posed at the wall and the free surface, and the fluid satisfies the Navier-Stokes equations. We examine the nature of boundary conditions which can be imposed at the inflow and outflow boundaries in order to yield a well-posed problem. This question turns out to be more delicate than is generally appreciated. Depending on the precise situation and on the regularity required of the solution, boundary conditions at just one or both endpoints of the free surface need to be imposed. For example, we show that if the velocities at te inflow and outflow boundaries are prescribed, then the position of the free surface at the inflow boundary can be prescribed, but not at the outflow if an H1-solution is desired. Numerical simulations with the FIDAP package are used to illustrate our analytical results.

  1. Three Boundary Conditions for Computing the Fixed-Point Property in Binary Mixture Data.

    PubMed

    van Maanen, Leendert; Couto, Joaquina; Lebreton, Mael

    2016-01-01

    The notion of "mixtures" has become pervasive in behavioral and cognitive sciences, due to the success of dual-process theories of cognition. However, providing support for such dual-process theories is not trivial, as it crucially requires properties in the data that are specific to mixture of cognitive processes. In theory, one such property could be the fixed-point property of binary mixture data, applied-for instance- to response times. In that case, the fixed-point property entails that response time distributions obtained in an experiment in which the mixture proportion is manipulated would have a common density point. In the current article, we discuss the application of the fixed-point property and identify three boundary conditions under which the fixed-point property will not be interpretable. In Boundary condition 1, a finding in support of the fixed-point will be mute because of a lack of difference between conditions. Boundary condition 2 refers to the case in which the extreme conditions are so different that a mixture may display bimodality. In this case, a mixture hypothesis is clearly supported, yet the fixed-point may not be found. In Boundary condition 3 the fixed-point may also not be present, yet a mixture might still exist but is occluded due to additional changes in behavior. Finding the fixed-property provides strong support for a dual-process account, yet the boundary conditions that we identify should be considered before making inferences about underlying psychological processes.

  2. Solution of the three-dimensional Helmholtz equation with nonlocal boundary conditions

    NASA Technical Reports Server (NTRS)

    Hodge, Steve L.; Zorumski, William E.; Watson, Willie R.

    1995-01-01

    The Helmholtz equation is solved within a three-dimensional rectangular duct with a nonlocal radiation boundary condition at the duct exit plane. This condition accurately models the acoustic admittance at an arbitrarily-located computational boundary plane. A linear system of equations is constructed with second-order central differences for the Helmholtz operator and second-order backward differences for both local admittance conditions and the gradient term in the nonlocal radiation boundary condition. The resulting matrix equation is large, sparse, and non-Hermitian. The size and structure of the matrix makes direct solution techniques impractical; as a result, a nonstationary iterative technique is used for its solution. The theory behind the nonstationary technique is reviewed, and numerical results are presented for radiation from both a point source and a planar acoustic source. The solutions with the nonlocal boundary conditions are invariant to the location of the computational boundary, and the same nonlocal conditions are valid for all solutions. The nonlocal conditions thus provide a means of minimizing the size of three-dimensional computational domains.

  3. Radiation boundary condition and anisotropy correction for finite difference solutions of the Helmholtz equation

    NASA Technical Reports Server (NTRS)

    Tam, Christopher K. W.; Webb, Jay C.

    1994-01-01

    In this paper finite-difference solutions of the Helmholtz equation in an open domain are considered. By using a second-order central difference scheme and the Bayliss-Turkel radiation boundary condition, reasonably accurate solutions can be obtained when the number of grid points per acoustic wavelength used is large. However, when a smaller number of grid points per wavelength is used excessive reflections occur which tend to overwhelm the computed solutions. Excessive reflections are due to the incompability between the governing finite difference equation and the Bayliss-Turkel radiation boundary condition. The Bayliss-Turkel radiation boundary condition was developed from the asymptotic solution of the partial differential equation. To obtain compatibility, the radiation boundary condition should be constructed from the asymptotic solution of the finite difference equation instead. Examples are provided using the improved radiation boundary condition based on the asymptotic solution of the governing finite difference equation. The computed results are free of reflections even when only five grid points per wavelength are used. The improved radiation boundary condition has also been tested for problems with complex acoustic sources and sources embedded in a uniform mean flow. The present method of developing a radiation boundary condition is also applicable to higher order finite difference schemes. In all these cases no reflected waves could be detected. The use of finite difference approximation inevita bly introduces anisotropy into the governing field equation. The effect of anisotropy is to distort the directional distribution of the amplitude and phase of the computed solution. It can be quite large when the number of grid points per wavelength used in the computation is small. A way to correct this effect is proposed. The correction factor developed from the asymptotic solutions is source independent and, hence, can be determined once and for all. The

  4. Green's function of the heat equation with periodic and antiperiodic boundary conditions

    NASA Astrophysics Data System (ADS)

    Imanbaev, Nurlan; Erzhanov, Nurzhan

    2016-12-01

    In this work a non-local initial-boundary value problem for a non-homogeneous one-dimensional heat equation is con-sidered. The domain under consideration is a rectangle. The classical initial condition with respect to t is put. A non-local periodic boundary condition with respect to a spatial variable x is put. It is well-known that a solution of problem can be constructed in the form of convergent orthonormal series according to eigenfunctions of a spectral problem for an operator of multiple differentiation with periodic boundary conditions. Therefore Green's function can be also written in the form of an infinite series with respect to trigonometric functions (Fourier series). For classical first and second initial-boundary value problems there also exists a second representation of the Green's function by Jacobi function. In this paper we find the representation of the Green's function of the non-local initial-boundary value problem with periodic boundary conditions in the form of series according to exponents.

  5. Effect of thermal boundary condition on wall-bounded, stably-stratified turbulence

    NASA Astrophysics Data System (ADS)

    Flores, Oscar; Garcia-Villalba, Manuel

    2012-11-01

    The dynamics of stably stratified wall-bounded turbulent flows are of great importance for many engineering and geophysical problems. In some cases, like the stably stratified atmospheric boundary layer, it is unclear which is the most appropriate thermal boundary condition, i.e. constant temperature or constant flux at the ground. Here, we analyze the effect that this boundary condition has on the dynamics of turbulent motions in the near-wall region in the case of strong stable stratification. Two Direct Numerical Simulations of turbulent channels will be used, at Reτ =uτ h / ν = 560 and Riτ = Δρgh /ρ0uτ2 = 600 - 900 , which are described in detail in Flores & Riley (2011, Boundary-Layer Meteorol) and Garcia-Villalba & del Alamo (2011, Phys.Fluids). For this range of Reynolds and Richardson numbers, the near-wall region is intermittent, with patches of laminar flow embedded in the otherwise turbulent flow. It is in this regime where the differences between the constant temperature and the constant flux boundary conditions are expected to be larger, with the thermal boundary condition affecting how the local relaminarization of the flow takes place. This research has been supported by ARO, NSF and the German Research Foundation.

  6. Semi-analytical solution for the generalized absorbing boundary condition in molecular dynamics simulations

    NASA Astrophysics Data System (ADS)

    Lee, Chung-Shuo; Chen, Yan-Yu; Yu, Chi-Hua; Hsu, Yu-Chuan; Chen, Chuin-Shan

    2017-02-01

    We present a semi-analytical solution of a time-history kernel for the generalized absorbing boundary condition in molecular dynamics (MD) simulations. To facilitate the kernel derivation, the concept of virtual atoms in real space that can conform with an arbitrary boundary in an arbitrary lattice is adopted. The generalized Langevin equation is regularized using eigenvalue decomposition and, consequently, an analytical expression of an inverse Laplace transform is obtained. With construction of dynamical matrices in the virtual domain, a semi-analytical form of the time-history kernel functions for an arbitrary boundary in an arbitrary lattice can be found. The time-history kernel functions for different crystal lattices are derived to show the generality of the proposed method. Non-equilibrium MD simulations in a triangular lattice with and without the absorbing boundary condition are conducted to demonstrate the validity of the solution.

  7. Reflecting boundary conditions for classical molecular dynamics simulations of nonideal plasmas

    NASA Astrophysics Data System (ADS)

    Lavrinenko, Ya S.; Morozov, I. V.; Valuev, I. A.

    2016-11-01

    The influence of boundary conditions on results of the classical molecular dynamics simulations of nonideal electron-ion plasma is analyzed. A comprehensive study is performed for the convergence of per-particle potential energy and pressure with the number of particles using both the nearest image method (periodic boundaries) and harmonic reflective boundaries. As a result an error caused by finiteness of the simulation box is estimated. Moreover the electron oscillations given by the spectra of the current autocorrelation function are analyzed for both types of the boundary conditions. Nonideal plasmas with the nonideality parameter in range 0.26-2.6 is considered. To speed up the classical molecular dynamics simulations the graphics accelerators code is used.

  8. Buckling of stiffened shells with random initial imperfections, thickness and boundary conditions

    NASA Technical Reports Server (NTRS)

    Elishakoff, I.; Arbocz, J.; Starnes, J. H., Jr.

    1992-01-01

    The paper proposes a method to predict the buckling load of stiffened, composite shells reliably, where besides the randomness of the initial geometric imperfections also a random variation of the wall thickness and the uncertainty of the precise edge conditions is included in the analysis. The introduction of the variability in the thickness from shell to shell, in an ensemble of nominally identical shells, produced by the same manufacturing procedure is motivated by the growing realization of the importance of thickness variations by composite shells. The probabilistic treatment of the boundary conditions is dictated by the fact that 'true', deterministically specified boundary conditions are unlikely to be realizable in practice.

  9. On a Non-Reflecting Boundary Condition for Hyperbolic Conservation Laws

    NASA Technical Reports Server (NTRS)

    Loh, Ching Y.

    2003-01-01

    A non-reflecting boundary condition (NRBC) for practical computations in fluid dynamics and aeroacoustics is presented. The technique is based on the hyperbolicity of the Euler equation system and the first principle of plane (simple) wave propagation. The NRBC is simple and effective, provided the numerical scheme maintains locally a C(sup 1) continuous solution at the boundary. Several numerical examples in ID, 2D and 3D space are illustrated to demonstrate its robustness in practical computations.

  10. Far Field Numerical Boundary Conditions for Internal and Cascade Flow Computations

    DTIC Science & Technology

    1988-11-01

    for the treatment of the fa field boundary conditions, Verhoff and O’Neil (1984), to more ,,eneral formulations of the Euler equations and to cascade...4eometries. linearized solutions ,-f the Euler equations are developed for the perturbations from the tiniform free stream, for ducts and cascades...Fourier expansion in the direction al on tlie inlet or exit boundaries. Resul obtained from an Euler code are shown ftor duCts and cascadels , rompa rin

  11. Numerical Boundary Conditions for Specular Reflection in a Level-Sets-Based Wavefront Propagation Method

    DTIC Science & Technology

    2012-12-01

    then et∗ →0 as hl →0. This is essentially modifying the grid to include the point zb, and that modification could be different for each fixed x. But in...convergence rate, a rectangu- lar grid is used over the physical space. When the physical domain does not conform to the rectangular grid , appropriate...boundary conditions to represent reflection must be derived to apply at grid locations that are not coincident with the reflecting boundary. A related

  12. On a Non-Reflecting Boundary Condition for Hyperbolic Conservation Laws

    NASA Technical Reports Server (NTRS)

    Loh, Ching Y.

    2003-01-01

    A non-reflecting boundary condition (NRBC) for practical computations in fluid dynamics and aeroacoustics is presented. The technique is based on the first principle of non-reflecting, plane wave propagation and the hyperbolicity of the Euler equation system. The NRBC is simple and effective, provided the numerical scheme maintains locally a C(sup 1) continuous solution at the boundary. Several numerical examples in 1D, 2D, and 3D space are illustrated to demonstrate its robustness in practical computations.

  13. Spectrum of one BVP with discontinuities and spectral parameter in the boundary conditions

    NASA Astrophysics Data System (ADS)

    Aydemir, K.; Mukhtarov, O. Sh.; Olǧar, H.

    2016-04-01

    The aim this of paper is to investigate the spectral problem for the equation -(pu')'(x) + q(x)u(x) = λu(x), under eigen-dependent boundary conditions and supplementary transmission conditions at finite number interior points. By modifying some techniques of classical Sturm-Liouville theory and suggesting own approaches we esthabilish some properties of the eigenvalues and eigenfunction.

  14. Boundary conditions for plasma fluid models at the magnetic presheath entrance

    SciTech Connect

    Loizu, J.; Ricci, P.; Halpern, F. D.; Jolliet, S.

    2012-12-15

    The proper boundary conditions at the magnetic presheath entrance for plasma fluid turbulence models based on the drift approximation are derived, focusing on a weakly collisional plasma sheath with T{sub i} Much-Less-Than T{sub e} and a magnetic field oblique to a totally absorbing wall. First, the location of the magnetic presheath entrance is rigorously derived. Then boundary conditions at the magnetic presheath entrance are analytically deduced for v{sub ||i}, v{sub ||e}, n, {phi}, T{sub e}, and for the vorticity {omega}={nabla}{sub Up-Tack }{sup 2}{phi}. The effects of E Multiplication-Sign B and diamagnetic drifts on the boundary conditions are also investigated. Kinetic simulations are performed that confirm the analytical results. Finally, the new set of boundary conditions is implemented in a three-dimensional global fluid code for the simulation of plasma turbulence and, as an example, the results of a tokamak scrape-off layer simulation are discussed. The framework presented can be generalized to obtain boundary conditions at the magnetic presheath entrance in more complex scenarios.

  15. Supersonic far-field boundary conditions for transonic small-disturbance theory

    NASA Technical Reports Server (NTRS)

    Gibbons, Michael D.; Batina, John T.

    1989-01-01

    Characteristic far-field boundary conditions for supersonic freestream flow have been developed and implemented within a transonic small-disturbance code. The boundary conditions have been implemented within the CAP-TSD code which has been developed recently for aeroelastic analysis of complete aircraft configurations. These boundary conditions improve the accuracy of the solutions for supersonic freestream applications. They also allow the extent of the grid to be much smaller, thus providing savings in the computational time required to obtain solutions. Comparisons are shown between surface pressures computed using large and small grid extents for the NACA 0012 airfoil and the F-5 wing at various Mach numbers and angles of attack. Both steady and unsteady results are presented and comparisons are made with Euler results and with experimental data to assess the accuracy of the new far-field boundary conditions. Comparisons of these results show that the supersonic boundary conditions allow a much smaller grid to be used without losing accuracy.

  16. Integral Method of Boundary Characteristics in Solving the Stefan Problem: Dirichlet Condition

    NASA Astrophysics Data System (ADS)

    Kot, V. A.

    2016-09-01

    The integral method of boundary characteristics is considered as applied to the solution of the Stefan problem with a Dirichlet condition. On the basis of the multiple integration of the heat-conduction equation, a sequence of identical equalities with boundary characteristics in the form of n-fold integrals of the surface temperature has been obtained. It is shown that, in the case where the temperature profile is defined by an exponential polynomial and the Stefan condition is not fulfilled at a moving interphase boundary, the accuracy of solving the Stefan problem with a Dirichlet condition by the integral method of boundary characteristics is higher by several orders of magnitude than the accuracy of solving this problem by other known approximate methods and that the solutions of the indicated problem with the use of the fourth-sixth degree polynomials on the basis of the integral method of boundary characteristics are exact in essence. This method surpasses the known numerical methods by many orders of magnitude in the accuracy of calculating the position of the interphase boundary and is approximately equal to them in the accuracy of calculating the temperature profile.

  17. Constant-concentration boundary condition: Lessons from the HYDROCOIN variable-density groundwater benchmark problem

    USGS Publications Warehouse

    Konikow, L.F.; Sanford, W.E.; Campbell, P.J.

    1997-01-01

    In a solute-transport model, if a constant-concentration boundary condition is applied at a node in an active flow field, a solute flux can occur by both advective and dispersive processes. The potential for advective release is demonstrated by reexamining the Hydrologic Code Intercomparison (HYDROCOIN) project case 5 problem, which represents a salt dome overlain by a shallow groundwater system. The resulting flow field includes significant salinity and fluid density variations. Several independent teams simulated this problem using finite difference or finite element numerical models. We applied a method-of-characteristics model (MOCDENSE). The previous numerical implementations by HYDROCOIN teams of a constant-concentration boundary to represent salt release by lateral dispersion only (as stipulated in the original problem definition) was flawed because this boundary condition allows the release of salt into the flow field by both dispersion and advection. When the constant-concentration boundary is modified to allow salt release by dispersion only, significantly less salt is released into the flow field. The calculated brine distribution for case 5 depends very little on which numerical model is used, as long as the selected model is solving the proper equations. Instead, the accuracy of the solution depends strongly on the proper conceptualization of the problem, including the detailed design of the constant-concentration boundary condition. The importance and sensitivity to the manner of specification of this boundary does not appear to have been recognized previously in the analysis of this problem.

  18. Improving variational mass-consistent models of hydrodynamic flows via boundary conditions

    NASA Astrophysics Data System (ADS)

    Núñez, M. A.

    2012-04-01

    Variational mass-consistent models for the velocity field v have been used by mesoscale meteorological community to modeling the wind field from an observed field v 0 in a bounded region Ω with boundary Γ. Variational calculus reduces the problem to the solution of an elliptic equation for a Lagrange multiplier λ subject to Dirichlet Boundary Condition (DBC) on flow-through boundaries. In this work, it is shown that DBC decreases the regularity of λ and this in turn decreases the accuracy with which the velocity field satisfies the mass-balance. The boundary condition (BC) v · n = v T · ngiven by the true field v T on the whole boundary Γ, leads only to a Neumann boundary condition (NBC) for λ. Approximations of this BC are studied. Analytic and numerical results show that the velocity field U 0 obtained from v 0 by direct integration of the continuity equation, yields a NBC that improves significantly the fields obtained with DBC's.

  19. Conformal field theory of critical Casimir forces between surfaces with alternating boundary conditions in two dimensions

    NASA Astrophysics Data System (ADS)

    Dubail, J.; Santachiara, R.; Emig, T.

    2017-03-01

    Systems as diverse as binary mixtures and inclusions in biological membranes, and many more, can be described effectively by interacting spins. When the critical fluctuations in these systems are constrained by boundary conditions, critical Casimir forces (CCF) emerge. Here we analyze CCF between boundaries with alternating boundary conditions in two dimensions, employing conformal field theory (CFT). After presenting the concept of boundary changing operators, we specifically consider two different boundary configurations for a strip of critical Ising spins: (I) alternating equi-sized domains of up and down spins on both sides of the strip, with a possible lateral shift, and (II) alternating domains of up and down spins of different size on one side and homogeneously fixed spins on the other side of the strip. Asymptotic results for the CCF at small and large distances are derived. We introduce a novel modified Szegö formula for determinants of real antisymmetric block Toeplitz matrices to obtain the exact CCF and the corresponding scaling functions at all distances. We demonstrate the existence of a surface renormalization group flow between universal force amplitudes of different magnitude and sign. The Casimir force can vanish at a stable equilibrium position that can be controlled by parameters of the boundary conditions. Lateral Casimir forces assume a universal simple cosine form at large separations.

  20. An effective absorbing boundary condition for linear long-wave and linear dispersive-wave tsunami simulations

    NASA Astrophysics Data System (ADS)

    Maeda, Takuto; Tsushima, Hiroaki; Furumura, Takashi

    2016-04-01

    We numerically simulated the propagation of tsunami waves with finite difference methods by using perfectly matched layer (PML) boundary conditions to effectively eliminate artificial reflections from model boundaries. The PML method damps the tsunami height and velocity of seawater only in directions perpendicular to the boundary. Although the additional terms required to implement the PML conditions make the use of the PML technique difficult for linear dispersive tsunami waves, we have proposed an empirical extension of the PML method for modeling dispersive tsunami waves. Even for heterogeneous, realistic bathymetries, numerical tests demonstrated that the PML boundary condition dramatically decreased artificial reflections from model boundaries compared to the use of traditional boundary conditions. The use of PML boundary conditions for numerical modeling of tsunamis is especially useful because it facilitates use of the later phases of tsunamis that would otherwise be compromised by artifacts caused by reflections from model boundaries.

  1. Friction-term response to boundary-condition type in flow models

    USGS Publications Warehouse

    Schaffranek, R.W.; Lai, C.

    1996-01-01

    The friction-slope term in the unsteady open-channel flow equations is examined using two numerical models based on different formulations of the governing equations and employing different solution methods. The purposes of the study are to analyze, evaluate, and demonstrate the behavior of the term in a set of controlled numerical experiments using varied types and combinations of boundary conditions. Results of numerical experiments illustrate that a given model can respond inconsistently for the identical resistance-coefficient value under different types and combinations of boundary conditions. Findings also demonstrate that two models employing different dependent variables and solution methods can respond similarly for the identical resistance-coefficient value under similar types and combinations of boundary conditions. Discussion of qualitative considerations and quantitative experimental results provides insight into the proper treatment, evaluation, and significance of the friction-slope term, thereby offering practical guidelines for model implementation and calibration.

  2. Accuracy of the Frensley inflow boundary condition for Wigner equations in simulating resonant tunneling diodes

    SciTech Connect

    Jiang Haiyan; Cai Wei; Tsu, Raphael

    2011-03-01

    In this paper, the accuracy of the Frensley inflow boundary condition of the Wigner equation is analyzed in computing the I-V characteristics of a resonant tunneling diode (RTD). It is found that the Frensley inflow boundary condition for incoming electrons holds only exactly infinite away from the active device region and its accuracy depends on the length of contacts included in the simulation. For this study, the non-equilibrium Green's function (NEGF) with a Dirichlet to Neumann mapping boundary condition is used for comparison. The I-V characteristics of the RTD are found to agree between self-consistent NEGF and Wigner methods at low bias potentials with sufficiently large GaAs contact lengths. Finally, the relation between the negative differential conductance (NDC) of the RTD and the sizes of contact and buffer in the RTD is investigated using both methods.

  3. Scale effect of slip boundary condition at solid–liquid interface

    NASA Astrophysics Data System (ADS)

    Nagayama, Gyoko; Matsumoto, Takenori; Fukushima, Kohei; Tsuruta, Takaharu

    2017-03-01

    Rapid advances in microelectromechanical systems have stimulated the development of compact devices, which require effective cooling technologies (e.g., microchannel cooling). However, the inconsistencies between experimental and classical theoretical predictions for the liquid flow in microchannel remain unclarified. Given the larger surface/volume ratio of microchannel, the surface effects increase as channel scale decreases. Here we show the scale effect of the boundary condition at the solid–liquid interface on single-phase convective heat transfer characteristics in microchannels. We demonstrate that the deviation from classical theory with a reduction in hydraulic diameters is due to the breakdown of the continuum solid–liquid boundary condition. The forced convective heat transfer characteristics of single-phase laminar flow in a parallel-plate microchannel are investigated. Using the theoretical Poiseuille and Nusselt numbers derived under the slip boundary condition at the solid–liquid interface, we estimate the slip length and thermal slip length at the interface.

  4. Scale effect of slip boundary condition at solid–liquid interface

    PubMed Central

    Nagayama, Gyoko; Matsumoto, Takenori; Fukushima, Kohei; Tsuruta, Takaharu

    2017-01-01

    Rapid advances in microelectromechanical systems have stimulated the development of compact devices, which require effective cooling technologies (e.g., microchannel cooling). However, the inconsistencies between experimental and classical theoretical predictions for the liquid flow in microchannel remain unclarified. Given the larger surface/volume ratio of microchannel, the surface effects increase as channel scale decreases. Here we show the scale effect of the boundary condition at the solid–liquid interface on single-phase convective heat transfer characteristics in microchannels. We demonstrate that the deviation from classical theory with a reduction in hydraulic diameters is due to the breakdown of the continuum solid–liquid boundary condition. The forced convective heat transfer characteristics of single-phase laminar flow in a parallel-plate microchannel are investigated. Using the theoretical Poiseuille and Nusselt numbers derived under the slip boundary condition at the solid–liquid interface, we estimate the slip length and thermal slip length at the interface. PMID:28256536

  5. Perfectly matched layer absorbing boundary condition for nonlinear two-fluid plasma equations

    NASA Astrophysics Data System (ADS)

    Sun, X. F.; Jiang, Z. H.; Hu, X. W.; Zhuang, G.; Jiang, J. F.; Guo, W. X.

    2015-04-01

    Numerical instability occurs when coupled Maxwell equations and nonlinear two-fluid plasma equations are solved using finite difference method through parallel algorithm. Thus, a perfectly matched layer (PML) boundary condition is set to avoid the instability caused by velocity and density gradients between vacuum and plasma. A splitting method is used to first decompose governing equations to time-dependent nonlinear and linear equations. Then, a proper complex variable is used for the spatial derivative terms of the time-dependent nonlinear equation. Finally, with several auxiliary function equations, the governing equations of the absorbing boundary condition are derived by rewriting the frequency domain PML in the original physical space and time coordinates. Numerical examples in one- and two-dimensional domains show that the PML boundary condition is valid and effective. PML stability depends on the absorbing coefficient and thickness of absorbing layers.

  6. Boundary condition handling approaches for the model reduction of a vehicle frame

    NASA Astrophysics Data System (ADS)

    Xie, Qingxi; Zhang, Nong; Zhang, Bangji; Ji, Jinchen

    2016-06-01

    In order to apply model reduction technique to improve the computational efficiency for the large-scale FEM model of a vehicle, this paper presents the handling approaches for three widely-used boundary conditions, namely fixed boundary condition (FBC), prescribed motion (PSM) and coupling (COUP), respectively. It is found that iterated improved reduction system (IIRS) reduction method tends to generate better reduction approximation. Guyan method is not sensitive to the sequence of reduction and constraint under FBC, and can thus provide flexibility in handling different boundary conditions for the same system. As for PSM, 'constraint first' is recommended no matter which reduction method is used, and then separate reduction models can be coupled to form a new model with relative small dofs. By selecting appropriate master dofs for model reduction, the coupled model based on reduced models could produce same results as the original full one.

  7. Damping solitary wave under the second and third boundary condition of a viscous plasma

    NASA Astrophysics Data System (ADS)

    Li, G.; Ren, Y.-Q.

    2017-02-01

    In this paper, the solitary waves of a viscous plasma confined in a cylindrical pipe is investigated under two types of boundary condition. By using the reductive perturbation theory, a quasi-KdV equation is derived and a damping solitary wave is obtained. It is found that the damping rate increases with the viscosity coefficient of the plasma ν ' increasing and the radius of the cylindrical pipe R decreasing for second and third boundary condition. The magnitude of the damping rate is also dominated by boundary condition type. From the fact that the amplitude reduces rapidly when R approaches zero or ν ' approaches infinite, we confirm the existence of a damping solitary wave.

  8. Scale effect of slip boundary condition at solid-liquid interface.

    PubMed

    Nagayama, Gyoko; Matsumoto, Takenori; Fukushima, Kohei; Tsuruta, Takaharu

    2017-03-03

    Rapid advances in microelectromechanical systems have stimulated the development of compact devices, which require effective cooling technologies (e.g., microchannel cooling). However, the inconsistencies between experimental and classical theoretical predictions for the liquid flow in microchannel remain unclarified. Given the larger surface/volume ratio of microchannel, the surface effects increase as channel scale decreases. Here we show the scale effect of the boundary condition at the solid-liquid interface on single-phase convective heat transfer characteristics in microchannels. We demonstrate that the deviation from classical theory with a reduction in hydraulic diameters is due to the breakdown of the continuum solid-liquid boundary condition. The forced convective heat transfer characteristics of single-phase laminar flow in a parallel-plate microchannel are investigated. Using the theoretical Poiseuille and Nusselt numbers derived under the slip boundary condition at the solid-liquid interface, we estimate the slip length and thermal slip length at the interface.

  9. Euler calculations with embedded Cartesian grids and small-perturbation boundary conditions

    NASA Astrophysics Data System (ADS)

    Liao, W.; Koh, E. P. C.; Tsai, H. M.; Liu, F.

    2010-05-01

    This study examines the use of stationary Cartesian mesh for steady and unsteady flow computations. The surface boundary conditions are imposed by reflected points. A cloud of nodes in the vicinity of the surface is used to get a weighted average of the flow properties via a gridless least-squares technique. If the displacement of the moving surface from the original position is typically small, a small-perturbation boundary condition method can be used. To ensure computational efficiency, multigrid solution is made via a framework of embedded grids for local grid refinement. Computations of airfoil wing and wing-body test cases show the practical usefulness of the embedded Cartesian grids with the small-perturbation boundary conditions approach.

  10. A Formulation of Asymptotic and Exact Boundary Conditions Using Local Operators

    NASA Technical Reports Server (NTRS)

    Hagstrom, T.; Hariharan, S. I.

    1998-01-01

    In this paper we describe a systematic approach for constructing asymptotic boundary conditions for isotropic wave-like equations using local operators. The conditions take a recursive form with increasing order of accuracy. In three dimensions the recursion terminates and the resulting conditions are exact for solutions which are described by finite combinations of angular spherical harmonics. First, we develop the expansion for the two-dimensional wave equation and construct a sequence of easily implementable boundary conditions. We show that in three dimensions and analogous conditions are again easily implementable in addition to being exact. Also, we provide extensions of these ideas to hyperbolic systems. Namely, Maxwell's equations for TM waves are used to demonstrate the construction. Finally, we provide numerical examples to demonstrate the effectiveness of these conditions for a model problem governed by the wave equation.

  11. Development of stress boundary conditions in smoothed particle hydrodynamics (SPH) for the modeling of solids deformation

    NASA Astrophysics Data System (ADS)

    Douillet-Grellier, Thomas; Pramanik, Ranjan; Pan, Kai; Albaiz, Abdulaziz; Jones, Bruce D.; Williams, John R.

    2016-10-01

    This paper develops a method for imposing stress boundary conditions in smoothed particle hydrodynamics (SPH) with and without the need for dummy particles. SPH has been used for simulating phenomena in a number of fields, such as astrophysics and fluid mechanics. More recently, the method has gained traction as a technique for simulation of deformation and fracture in solids, where the meshless property of SPH can be leveraged to represent arbitrary crack paths. Despite this interest, application of boundary conditions within the SPH framework is typically limited to imposed velocity or displacement using fictitious dummy particles to compensate for the lack of particles beyond the boundary interface. While this is enough for a large variety of problems, especially in the case of fluid flow, for problems in solid mechanics there is a clear need to impose stresses upon boundaries. In addition to this, the use of dummy particles to impose a boundary condition is not always suitable or even feasibly, especially for those problems which include internal boundaries. In order to overcome these difficulties, this paper first presents an improved method for applying stress boundary conditions in SPH with dummy particles. This is then followed by a proposal of a formulation which does not require dummy particles. These techniques are then validated against analytical solutions to two common problems in rock mechanics, the Brazilian test and the penny-shaped crack problem both in 2D and 3D. This study highlights the fact that SPH offers a good level of accuracy to solve these problems and that results are reliable. This validation work serves as a foundation for addressing more complex problems involving plasticity and fracture propagation.

  12. Consistent boundary conditions at nonconducting surfaces of planetary bodies: Applications in a new Ganymede MHD model

    NASA Astrophysics Data System (ADS)

    Duling, Stefan; Saur, Joachim; Wicht, Johannes

    2014-06-01

    The interaction of planetary bodies with their surrounding magnetized plasma can often be described with the magnetohydrodynamic (MHD) equations, which are commonly solved by numerical models. For these models it is necessary to define physically correct boundary conditions for the plasma mass and energy density, the plasma velocity, and the magnetic field. Many planetary bodies have surfaces whose electrical conductivity is negligibly small and thus no electric current penetrates their surfaces. Magnetic boundary conditions, which consider that the associated radial electric current at the planetary surface is zero, are difficult to implement because they include the curl of the magnetic field. Here we derive new boundary conditions by a decomposition of the magnetic field in poloidal and toroidal parts. We find that the toroidal part of the magnetic field needs to vanish at the surface of the insulator. For the spherical harmonics coefficients of the poloidal part, we derive a Cauchy boundary condition, which also matches a possible intrinsic field by including its Gauss coefficients. Thus, we can additionally include planetary dynamo fields as well as time-variable induction fields within electrically conductive subsurface layers. We implement the nonconducting boundary condition in the MHD simulation code ZEUS-MP using spherical geometry and provide a numerical implementation in Fortran 90 as supporting information on the JGR website. We apply it to a model for Ganymede's plasma environment. Our model also includes a consistent set of boundary conditions for the other MHD variables density, velocity, and energy. With this model we can describe Galileo spacecraft observations in and around Ganymede's minimagnetosphere very well.

  13. The geoid constraint in global geodynamics: viscosity structure, mantle heterogeneity models and boundary conditions.

    NASA Astrophysics Data System (ADS)

    Thoraval, C.; Richards, M. A.

    1997-10-01

    The authors address several of the most straightforward problems inherent in geoid modelling, namely the issues of viscosity structure resolution, uncertainties in appropriate boundary conditions, and differences among mantle heterogeneity models. A robust feature of all models is a lower-mantle viscosity at least a factor of 30 greater than that of the upper mantle, but there is little resolution with regard to finer details such as lithospheric or uppermost mantle ("low-viscosity zone") viscosity. Ironically, free-slip boundary conditions result in the best fits to the geoid in all cases, but all boundary conditions exhibit predictable trade-offs with the uppermost-mantle viscosity. Models with a single viscosity layer representing the lower mantle yield similar dynamic topography estimates of the order of 700-1000 m in amplitude, regardless of the finer details of upper-mantle viscosity structure, boundary conditions or input heterogeneity models. Comparing mantle heterogeneity models based on two independent seismological determinations (Harvard and Berkeley models) and on the history of subduction, the authors find that these models are virtually indistinguishable regarding inferences of mantle viscosity structure and amplitude of dynamic topography, and in terms of the effects of different boundary conditions. Uncertainties concerning which type of boundary condition is appropriate are much more important than which mantle heterogeneity model is chosen. Given other uncertainties in modelling the geoid, particularly the strong effects due to lateral viscosity variations for intermediate (<10,000 km) wavelengths, the authors conclude that the class of dynamic geoid models explored so far cannot reliably elucidate the details of upper-mantle viscosity structure.

  14. Mathematical analysis of the Navier-Stokes equations with non standard boundary conditions

    NASA Technical Reports Server (NTRS)

    Tidriri, M. D.

    1995-01-01

    One of the major applications of the domain decomposition time marching algorithm is the coupling of the Navier-Stokes systems with Boltzmann equations in order to compute transitional flows. Another important application is the coupling of a global Navier-Stokes problem with a local one in order to use different modelizations and/or discretizations. Both of these applications involve a global Navier-Stokes system with nonstandard boundary conditions. The purpose of this work is to prove, using the classical Leray-Schauder theory, that these boundary conditions are admissible and lead to a well posed problem.

  15. Rayleigh-Ritz axial buckling analysis of single-walled carbon nanotubes with different boundary conditions

    NASA Astrophysics Data System (ADS)

    Ansari, R.; Sahmani, S.; Rouhi, H.

    2011-02-01

    Eringen's nonlocality is incorporated into the shell theory to include the small-scale effects on the axial buckling of single-walled carbon nanotubes (SWCNTs) with arbitrary boundary conditions. To this end, the Rayleigh-Ritz solution technique is implemented in conjunction with the set of beam functions as modal displacement functions. Then, molecular dynamics simulations are employed to obtain the critical buckling loads of armchair and zigzag SWCNTs, the results of which are matched with those of nonlocal shell model to extract the appropriate values of nonlocal parameter. It is found that in contrast to the chirality, boundary conditions have a considerable influence on the proper values of nonlocal parameter.

  16. Traffic flow of a roundabout crossing with an open boundary condition

    NASA Astrophysics Data System (ADS)

    Bai, Ke-Zhao; Tan, Hui-Li; Kong, Ling-Jiang; Liu, Mu-Ren

    2010-04-01

    This paper presents a cellular automaton traffic flow model with an open boundary condition to describe the traffic flow at a roundabout crossing with an inner roundabout lane and an outer roundabout lane. The simulation results show that the boundary condition, bottlenecks and the self-organization affect the traffic flow at the roundabout crossing. Because of the effect of bottlenecks, jams easily appear on the inner roundabout lane. To improve the capacity of the roundabout system, proper values of the enter probability α and the out probability β can be chosen.

  17. Topological quantum scattering under the influence of a nontrivial boundary condition

    NASA Astrophysics Data System (ADS)

    Mota, Herondy

    2016-04-01

    We consider the quantum scattering problem of a relativistic particle in (2 + 1)-dimensional cosmic string spacetime under the influence of a nontrivial boundary condition imposed on the solution of the Klein-Gordon equation. The solution is then shifted as consequence of the nontrivial boundary condition and the role of the phase shift is to produce an Aharonov-Bohm-like effect. We examine the connection between this phase shift and the electromagnetic and gravitational analogous of the Aharonov-Bohm effect and compare the present results with previous ones obtained in the literature, also considering non-relativistic cases.

  18. An Evaluation of Boundary Condition Specification for a Littoral Hydrodynamic Model

    DTIC Science & Technology

    2011-09-01

    from NCOM (blue) for 3 locations in the M2D model case. II. APPROACH Several comparisons of Delft3D model results were completed for a number...boundary conditions from OSU Tides (red) and time series boundary conditions from NCOM (blue) for 3 locations in the M2D model case. /; M2D and M3D...The M2D and M3D Delft3D applications cover approximately 33 square kilometers at a resolution of approximately 500 meters. The M2D model case is depth

  19. Higher Integrability of Solutions to Generalized Stokes System Under Perfect Slip Boundary Conditions

    NASA Astrophysics Data System (ADS)

    Mácha, Václav; Tichý, Jakub

    2014-10-01

    We prove an L q theory result for generalized Stokes system in a {{C}^{2,1}} domain complemented with the perfect slip boundary conditions and under Φ-growth conditions. Since the interior regularity was obtained in Diening and Kaplický (Manu Math 141:336-361, 2013), a regularity up to the boundary is an aim of this paper. In order to get the main result, we use Calderón-Zygmund theory and the method developed in Caffarelli and Peral (Ann Math 130:189-213, 1989). We obtain higher integrability of the first gradient of a solution.

  20. The sensitivity of numerically simulated climates to land-surface boundary conditions

    NASA Technical Reports Server (NTRS)

    Mintz, Y.

    1982-01-01

    Eleven sensitivity experiments that were made with general circulation models to see how land-surface boundary conditions can influence the rainfall, temperature, and motion fields of the atmosphere are discussed. In one group of experiments, different soil moistures or albedos are prescribed as time-invariant boundary conditions. In a second group, different soil moistures or different albedos are initially prescribed, and the soil moisture (but not the albedo) is allowed to change with time according to the governing equations for soil moisture. In a third group, the results of constant versus time-dependent soil moistures are compared.

  1. Role of Boundary Conditions in Monte Carlo Simulation of MEMS Devices

    NASA Technical Reports Server (NTRS)

    Nance, Robert P.; Hash, David B.; Hassan, H. A.

    1997-01-01

    A study is made of the issues surrounding prediction of microchannel flows using the direct simulation Monte Carlo method. This investigation includes the introduction and use of new inflow and outflow boundary conditions suitable for subsonic flows. A series of test simulations for a moderate-size microchannel indicates that a high degree of grid under-resolution in the streamwise direction may be tolerated without loss of accuracy. In addition, the results demonstrate the importance of physically correct boundary conditions, as well as possibilities for reducing the time associated with the transient phase of a simulation. These results imply that simulations of longer ducts may be more feasible than previously envisioned.

  2. On the choice of boundary conditions in continuum models of continental deformation

    NASA Technical Reports Server (NTRS)

    Wdowinski, Shimon; O'Connell, Richard J.

    1990-01-01

    Recent studies of continental deformation have treated the lithosphere as a viscous medium and investigated the time evolution of the deformation caused by tectonic and buoyancy forces. This paper examines the differences between (1) continuum models that keep velocity boundary conditions constant with time and (2) models that keep stress boundary conditions constant with time. These differences are demonstrated by using a simple example of a continental lithosphere that is subjected to horizontal compression. The results show that in (2) the indentation velocity decreases with time, while in (1) the indentation velocity remains constant with time.

  3. Verification Assessment of Flow Boundary Conditions for CFD Analysis of Supersonic Inlet Flows

    NASA Technical Reports Server (NTRS)

    Slater, John W.

    2002-01-01

    Boundary conditions for subsonic inflow, bleed, and subsonic outflow as implemented into the WIND CFD code are assessed with respect to verification for steady and unsteady flows associated with supersonic inlets. Verification procedures include grid convergence studies and comparisons to analytical data. The objective is to examine errors, limitations, capabilities, and behavior of the boundary conditions. Computational studies were performed on configurations derived from a "parameterized" supersonic inlet. These include steady supersonic flows with normal and oblique shocks, steady subsonic flow in a diffuser, and unsteady flow with the propagation and reflection of an acoustic disturbance.

  4. Bond and temperature chaos in spin glasses revealed through thermal boundary conditions

    NASA Astrophysics Data System (ADS)

    Wang, Wenlong; Jonathan Machta Collaboration; Helmut G. Katzgraber Collaboration

    Spin glasses are complex systems with rugged energy landscapes that exhibit chaotic behavior. Unfortunately, despite decades of study, there is still no clear understanding of the chaotic behavior found in these systems. The use of thermal boundary conditions has become a useful approach to study such phenomena. Here we discuss how to efficiently simulate bond and temperature chaos using thermal boundary conditions and population annealing Monte Carlo. We provide a simple scaling argument for bond and temperature chaos, and present numerical results of the scaling exponents. Similarities and differences of bond chaos and temperature chaos are also discussed. NSF DMR-120804.

  5. Air Flow Path Dynamics In The Vadose Zone Under Various Land Surface Climate Boundary Conditions

    NASA Astrophysics Data System (ADS)

    Illangasekare, T. H.; Sakaki, T.; Schulte, P. E.; Cihan, A.; Christ, J.

    2010-12-01

    Vapor intrusion (VI) refers to the transport of volatile chemical vapors from subsurface sources to surface and subsurface structures through the vadose zone. Because of the difference in pressure between the inside of the building and the subsurface soil pores, vapor can enter the building through cracks in the foundation, slab and walls and utility openings. The processes that govern the vapor transport in the heterogeneous subsurface “outside the home” are complex, and the sampling to assess potential pathways is subjected to spatial and temporal variability. Spatial variability is a result of a number of factors that include changing soil and soil moisture conditions. Temporal variability is a result of transient heat, wind, ambient pressure and a water flux boundary conditions at the land-atmospheric interface. Fluctuating water table conditions controlled by recharge, pumping, and stream-aquifer interactions will also contribute to the transient vapor flux generation at the sources. When the soil moisture changes as a result of precipitation events and other soil surface boundary conditions, the soil moisture content changes and hence the air permeability. Therefore, the primary pathways for the vapor are preferential channels that change with the transient soil moisture distribution. Both field and laboratory studies have shown that heterogeneity has a significant influence on soil moisture conditions in unsaturated soils. Uncertainties in vapor transport predictions have been attributed to heterogeneity and spatial variability in hydraulic properties. In this study, our goal was to determine the role of soil moisture variability on vapor transport and intrusion as affected by the climate driven boundary conditions on the land surface. A series of experiments were performed to generate a comprehensive data set to understand and evaluate how the spatial and temporal variability of soil moisture affected by the mass and heat flux boundary conditions on the

  6. The Sky is the Limit: Free Boundary Conditions in AdS3 Chern-Simons Theory

    NASA Astrophysics Data System (ADS)

    Apolo, Luis; Sundborg, Bo

    We test the effects of new diffeomorphism invariant boundary terms in SL(2,R)×SL(2,R) Chern-Simons theory. The gravitational interpretation corresponds to free AdS3 boundary conditions, without restrictions on the boundary geometry. The boundary theory is the theory of a string in a target AdS3. Its Virasoro conditions can eliminate ghosts. Generalisations to SL(N,R)×SL(N,R) higher spin theories and many other questions are still unexplored.

  7. Effects of Boundary Conditions and Flow on the Kink Instability in a Cylindrical Plasma Column

    SciTech Connect

    Furno, I; Intrator, T P; Lapenta, G; Dorf, L; Ryutov, D D

    2007-02-06

    An experimental investigation of the kink instability is presented in a linear plasma column where one end is line-tied to the plasma source, and the other end is not line-tied and therefore free to slide over the surface of the end-plate. This latter boundary condition is a result of plasma sheath resistance that insulates, at least partially, the plasma from the end-plate. The helical m = 1 kink mode is observed to grow when the plasma current exceeds a threshold and, close to the criticality, is characterized by an axial mode structure with maximum displacement at the free axial boundary. Azimuthal rotation of the mode is observed such that the helically kinked column always screws into the free axial boundary. The kink mode structure, rotation frequency and instability threshold are accurately reproduced by a recent kink theory [D. D. Ryutov, et al., Phys. Plasmas 13, 032105 (2006)], which includes axial plasma flow and one end of the plasma column that is free to move due to a perfect non-line-tying boundary condition which is experimentally verified. A brief review of the kink theory and its predictions for the boundary conditions relevant in the present experiments are presented.

  8. Numerical Study of Outlet Boundary Conditions for Unsteady Turbulent Internal Flows Using the NCC

    NASA Technical Reports Server (NTRS)

    Liu, Nan-Suey; Shih, Tsan-Hsing

    2009-01-01

    This paper presents the results of studies on the outlet boundary conditions for turbulent internal flow simulations. Several outlet boundary conditions have been investigated by applying the National Combustion Code (NCC) to the configuration of a LM6000 single injector flame tube. First of all, very large eddy simulations (VLES) have been performed using the partially resolved numerical simulation (PRNS) approach, in which both the nonlinear and linear dynamic subscale models were employed. Secondly, unsteady Reynolds averaged Navier- Stokes (URANS) simulations have also been performed for the same configuration to investigate the effects of different outlet boundary conditions in the context of URANS. Thirdly, the possible role of the initial condition is inspected by using three different initial flow fields for both the PRNS/VLES simulation and the URANS simulation. The same grid is used for all the simulations and the number of mesh element is about 0.5 million. The main purpose of this study is to examine the long-time behavior of the solution as determined by the imposed outlet boundary conditions. For a particular simulation to be considered as successful under the given initial and boundary conditions, the solution must be sustainable in a physically meaningful manner over a sufficiently long period of time. The commonly used outlet boundary condition for steady Reynolds averaged Navier-Stokes (RANS) simulation is a fixed pressure at the outlet with all the other dependent variables being extrapolated from the interior. The results of the present study suggest that this is also workable for the URANS simulation of the LM6000 injector flame tube. However, it does not work for the PRNS/VLES simulation due to the unphysical reflections of the pressure disturbances at the outlet boundary. This undesirable situation can be practically alleviated by applying a simple unsteady convection equation for the pressure disturbances at the outlet boundary. The

  9. Failure of the Ingard-Myers boundary condition for a lined duct: an experimental investigation.

    PubMed

    Renou, Ygaäl; Aurégan, Yves

    2011-07-01

    This paper deals with experimental investigation of the lined wall boundary condition in flow duct applications such as aircraft engine systems or automobile mufflers. A first experiment, based on a microphone array located in the liner test section, is carried out in order to extract the axial wavenumbers with the help of an "high-accurate" singular value decomposition Prony-like algorithm. The experimental axial wavenumbers are then used to provide the lined wall impedance for both downstream and upstream acoustic propagation by means of a straightforward impedance education method involving the classical Ingard-Myers boundary condition. The results show that the Ingard-Myers boundary condition fails to predict with accuracy the acoustic behavior in a lined duct with flow. An effective lined wall impedance, valid whatever the direction of acoustic propagation, can be suitably found from experimental axial wavenumbers and a modified version of the Ingard-Myers condition with the form inspired from a previous theoretical study [Aurégan et al., J. Acoust. Soc. Am. 109, 59-64 (2001)]. In a second experiment, the scattering matrix of the liner test section is measured and is then compared to the predicted scattering matrix using the multimodal approach and the lined wall impedances previously deduced. A large discrepancy is observed between the measured and the predicted scattering coefficients that confirms the poor accuracy provided from the Ingard-Myers boundary condition widely used in lined duct applications.

  10. Three Boundary Conditions for Computing the Fixed-Point Property in Binary Mixture Data

    PubMed Central

    Couto, Joaquina; Lebreton, Mael

    2016-01-01

    The notion of “mixtures” has become pervasive in behavioral and cognitive sciences, due to the success of dual-process theories of cognition. However, providing support for such dual-process theories is not trivial, as it crucially requires properties in the data that are specific to mixture of cognitive processes. In theory, one such property could be the fixed-point property of binary mixture data, applied–for instance- to response times. In that case, the fixed-point property entails that response time distributions obtained in an experiment in which the mixture proportion is manipulated would have a common density point. In the current article, we discuss the application of the fixed-point property and identify three boundary conditions under which the fixed-point property will not be interpretable. In Boundary condition 1, a finding in support of the fixed-point will be mute because of a lack of difference between conditions. Boundary condition 2 refers to the case in which the extreme conditions are so different that a mixture may display bimodality. In this case, a mixture hypothesis is clearly supported, yet the fixed-point may not be found. In Boundary condition 3 the fixed-point may also not be present, yet a mixture might still exist but is occluded due to additional changes in behavior. Finding the fixed-property provides strong support for a dual-process account, yet the boundary conditions that we identify should be considered before making inferences about underlying psychological processes. PMID:27893868

  11. A dual-pressure boundary condition for use in simulations of bifurcating conduits.

    PubMed

    Gin, Ron; Straatman, Anthony G; Steinman, David A

    2002-10-01

    A dual-pressure boundary condition has been developed for computational modelling of bifurcating conduits. The condition involves the imposition of a constant pressure on one branch while adjusting iteratively the pressure on the other branch until the desired flow division is obtained. The dual-pressure condition eliminates the need for specifying fully-developed flow conditions, which thereby enables significant reduction of the outlet branch lengths. The dual-pressure condition is suitable for both steady and time-periodic simulations of laminar or turbulent flows.

  12. Communication: Modeling charge-sign asymmetric solvation free energies with nonlinear boundary conditions

    SciTech Connect

    Bardhan, Jaydeep P.; Knepley, Matthew G.

    2014-10-07

    We show that charge-sign-dependent asymmetric hydration can be modeled accurately using linear Poisson theory after replacing the standard electric-displacement boundary condition with a simple nonlinear boundary condition. Using a single multiplicative scaling factor to determine atomic radii from molecular dynamics Lennard-Jones parameters, the new model accurately reproduces MD free-energy calculations of hydration asymmetries for: (i) monatomic ions, (ii) titratable amino acids in both their protonated and unprotonated states, and (iii) the Mobley “bracelet” and “rod” test problems [D. L. Mobley, A. E. Barber II, C. J. Fennell, and K. A. Dill, “Charge asymmetries in hydration of polar solutes,” J. Phys. Chem. B 112, 2405–2414 (2008)]. Remarkably, the model also justifies the use of linear response expressions for charging free energies. Our boundary-element method implementation demonstrates the ease with which other continuum-electrostatic solvers can be extended to include asymmetry.

  13. Grain boundary microchemistry and metallurgical characterization of Eurofer'97 after simulated service conditions

    NASA Astrophysics Data System (ADS)

    Fernández, P.; García-Mazarío, M.; Lancha, A. M.; Lapeña, J.

    2004-08-01

    The aim of this paper is to describe the microstructural investigations, the mechanical properties (hardness, tensile and charpy) and the grain boundary microchemistry studied by Auger electron spectroscopy (AES), of the Eurofer'97 steel aged in the range of temperatures from 400 to 600 °C up to 10 000 h. After these thermal aging treatments the steel showed a high microstructural stability, and similar values of hardness, ultimate tensile strength and 0.2% proof stress regardless of the material condition. A slight DBTT increase was observed in the material aged at 600 °C for 5000 and 10 000 h. The Auger results showed chromium enrichment at grain boundaries in all material conditions. In addition, phosphorus was detected at the grain boundaries after the aging treatments at 500 °C.

  14. Mixed boundary conditions for FFT-based homogenization at finite strains

    NASA Astrophysics Data System (ADS)

    Kabel, Matthias; Fliegener, Sascha; Schneider, Matti

    2016-02-01

    In this article we introduce a Lippmann-Schwinger formulation for the unit cell problem of periodic homogenization of elasticity at finite strains incorporating arbitrary mixed boundary conditions. Such problems occur frequently, for instance when validating computational results with tensile tests, where the deformation gradient in loading direction is fixed, as is the stress in the corresponding orthogonal plane. Previous Lippmann-Schwinger formulations involving mixed boundary can only describe tensile tests where the vector of applied force is proportional to a coordinate direction. Utilizing suitable orthogonal projectors we develop a Lippmann-Schwinger framework for arbitrary mixed boundary conditions. The resulting fixed point and Newton-Krylov algorithms preserve the positive characteristics of existing FFT-algorithms. We demonstrate the power of the proposed methods with a series of numerical examples, including continuous fiber reinforced laminates and a complex nonwoven structure of a long fiber reinforced thermoplastic, resulting in a speed-up of some computations by a factor of 1000.

  15. Elasto visco-plastic flow with special attention to boundary conditions

    NASA Technical Reports Server (NTRS)

    Shimazaki, Y.; Thompson, E. G.

    1981-01-01

    A simple but nontrivial steady-state creeping elasto visco-plastic (Maxwell fluid) radial flow problem is analyzed, with special attention given to the effects of the boundary conditions. Solutions are obtained through integration of a governing equation on stress using the Runge-Kutta method for initial value problems and finite differences for boundary value problems. A more general approach through the finite element method, an approach that solves for the velocity field rather than the stress field and that is applicable to a wide range of problems, is presented and tested using the radial flow example. It is found that steady-state flows of elasto visco-plastic materials are strongly influenced by the state of stress of material as it enters the region of interest. The importance of this boundary or initial condition in analyses involving materials coming into control volumes from unusual stress environments is emphasized.

  16. Communication: Modeling charge-sign asymmetric solvation free energies with nonlinear boundary conditions

    NASA Astrophysics Data System (ADS)

    Bardhan, Jaydeep P.; Knepley, Matthew G.

    2014-10-01

    We show that charge-sign-dependent asymmetric hydration can be modeled accurately using linear Poisson theory after replacing the standard electric-displacement boundary condition with a simple nonlinear boundary condition. Using a single multiplicative scaling factor to determine atomic radii from molecular dynamics Lennard-Jones parameters, the new model accurately reproduces MD free-energy calculations of hydration asymmetries for: (i) monatomic ions, (ii) titratable amino acids in both their protonated and unprotonated states, and (iii) the Mobley "bracelet" and "rod" test problems [D. L. Mobley, A. E. Barber II, C. J. Fennell, and K. A. Dill, "Charge asymmetries in hydration of polar solutes," J. Phys. Chem. B 112, 2405-2414 (2008)]. Remarkably, the model also justifies the use of linear response expressions for charging free energies. Our boundary-element method implementation demonstrates the ease with which other continuum-electrostatic solvers can be extended to include asymmetry.

  17. On the Navier-Stokes system with the Coulomb friction law boundary condition

    NASA Astrophysics Data System (ADS)

    Bălilescu, Loredana; San Martín, Jorge; Takahashi, Takéo

    2017-02-01

    We propose a new model for the motion of a viscous incompressible fluid. More precisely, we consider the Navier-Stokes system with a boundary condition governed by the Coulomb friction law. With this boundary condition, the fluid can slip on the boundary if the tangential component of the stress tensor is too large. We prove the existence and uniqueness of weak solution in the two-dimensional problem and the existence of at least one solution in the three-dimensional case, together with regularity properties and an energy estimate. We also propose a fully discrete scheme of our problem using the characteristic method, and we present numerical simulations in two physical examples.

  18. Development of an immersed boundary-phase field-lattice Boltzmann method for Neumann boundary condition to study contact line dynamics

    NASA Astrophysics Data System (ADS)

    Shao, J. Y.; Shu, C.; Chew, Y. T.

    2013-02-01

    The implementation of Neumann boundary condition in the framework of immersed boundary method (IBM) is presented in this paper to simulate contact line dynamics using a phase field-lattice Boltzmann method. Immersed boundary method [10] is known as an efficient algorithm for modelling fluid-solid interaction. Abundance of prominent works have been devoted to refine IBM [1,11,12]. However, they are mainly restricted to problems with Dirichlet boundary condition. Research that implements the Neumann boundary condition in IBM is very limited to the best of our knowledge. This deficiency significantly limits the application of IBM in computational fluid dynamics (CFD) since physical phenomena associated with Neumann boundary conditions are extremely diverse. The difficulty is attributed to the fact that implementation of Neumann boundary condition is much more complex than that of Dirichlet boundary condition. In the present work, we initiate the first endeavour to implement Neumann boundary condition in IBM with assistance of its physical interpretation rather than simple mathematical manipulation. Concretely speaking, rooted from physical conservation law, the Neumann boundary condition is considered as contribution of flux from the boundary to its relevant physical parameter in a control volume. Moreover, the link between the flux and its corresponding flow field variable is directly manipulated through the immersed boundary concept. In this way, the Neumann boundary conditions can be implemented in IBM. The developed method is applied together with phase field-lattice Boltzmann method to study contact line dynamics. The phase field method [27,39], which becomes increasingly popular in multiphase flow simulation, can efficiently capture complex interface topology and naturally resolve the contact line singularity. Meanwhile, the lattice Boltzmann method is known as an alternative to model fluid dynamics and holds good prospect to simulate multiphase flows with

  19. Fatigue crack damage detection using subharmonic component with nonlinear boundary condition

    NASA Astrophysics Data System (ADS)

    Wu, Weiliang; Shen, Yanfeng; Qu, Wenzhong; Xiao, Li; Giurgiutiu, Victor

    2015-03-01

    In recent years, researchers have focused on structural health monitoring (SHM) and damage detection techniques using nonlinear vibration and nonlinear ultrasonic methods. Fatigue cracks may exhibit contact acoustic nonlinearity (CAN) with distinctive features such as superharmonics and subharmonics in the power spectrum of the sensing signals. However, challenges have been noticed in the practical applications of the harmonic methods. For instance, superharmonics can also be generated by the piezoelectric transducers and the electronic equipment; super/subharmonics may also stem from the nonlinear boundary conditions such as structural fixtures and joints. It is hard to tell whether the nonlinear features come from the structural damage or the intrinsic nonlinear boundary conditions. The objective of this paper is to demonstrate the application of nonlinear ultrasonic subharmonic method for detecting fatigue cracks with nonlinear boundary conditions. The fatigue crack was qualitatively modeled as a single-degree-of-freedom (SDOF) system with non-classical hysteretic nonlinear interface forces at both sides of the crack surfaces. The threshold of subharmonic generation was studied, and the influence of crack interface parameters on the subharmonic resonance condition was investigated. The different threshold behaviors between the nonlinear boundary condition and the fatigue crack was found, which can be used to distinguish the source of nonlinear subharmonic features. To evaluate the proposed method, experiments of an aluminum plate with a fatigue crack were conducted to quantitatively verify the subharmonic resonance range. Two surface-bonded piezoelectric transducers were used to generate and receive ultrasonic wave signals. The fatigue damage was characterized in terms of a subharmonic damage index. The experimental results demonstrated that the subharmonic component of the sensing signal can be used to detect the fatigue crack and further distinguish it from

  20. Fatigue crack damage detection using subharmonic component with nonlinear boundary condition

    SciTech Connect

    Wu, Weiliang Qu, Wenzhong E-mail: xiaoli6401@126.com; Xiao, Li E-mail: xiaoli6401@126.com; Shen, Yanfeng Giurgiutiu, Victor

    2015-03-31

    In recent years, researchers have focused on structural health monitoring (SHM) and damage detection techniques using nonlinear vibration and nonlinear ultrasonic methods. Fatigue cracks may exhibit contact acoustic nonlinearity (CAN) with distinctive features such as superharmonics and subharmonics in the power spectrum of the sensing signals. However, challenges have been noticed in the practical applications of the harmonic methods. For instance, superharmonics can also be generated by the piezoelectric transducers and the electronic equipment; super/subharmonics may also stem from the nonlinear boundary conditions such as structural fixtures and joints. It is hard to tell whether the nonlinear features come from the structural damage or the intrinsic nonlinear boundary conditions. The objective of this paper is to demonstrate the application of nonlinear ultrasonic subharmonic method for detecting fatigue cracks with nonlinear boundary conditions. The fatigue crack was qualitatively modeled as a single-degree-of-freedom (SDOF) system with non-classical hysteretic nonlinear interface forces at both sides of the crack surfaces. The threshold of subharmonic generation was studied, and the influence of crack interface parameters on the subharmonic resonance condition was investigated. The different threshold behaviors between the nonlinear boundary condition and the fatigue crack was found, which can be used to distinguish the source of nonlinear subharmonic features. To evaluate the proposed method, experiments of an aluminum plate with a fatigue crack were conducted to quantitatively verify the subharmonic resonance range. Two surface-bonded piezoelectric transducers were used to generate and receive ultrasonic wave signals. The fatigue damage was characterized in terms of a subharmonic damage index. The experimental results demonstrated that the subharmonic component of the sensing signal can be used to detect the fatigue crack and further distinguish it from

  1. A laser Doppler system for the remote sensing of boundary layer winds in clear air conditions

    NASA Technical Reports Server (NTRS)

    Lawrence, T. R.; Krause, M. C.; Craven, C. E.; Morrison, L. K.; Thomson, J. A. L.; Cliff, W. C.; Huffaker, R. M.

    1975-01-01

    The system discussed uses a laser Doppler radar in combination with a velocity azimuth display mode of scanning to determine the three-dimensional wind field in the atmospheric boundary layer. An attractive feature of this CW monostatic system is that the ambient aerosol provides a 'sufficient' scattering target to permit operation under clear air conditions. Spatial resolution is achieved by focusing.

  2. LINKING ETA MODEL WITH THE COMMUNITY MULTISCALE AIR QUALITY (CMAQ) MODELING SYSTEM: OZONE BOUNDARY CONDITIONS

    EPA Science Inventory

    A prototype surface ozone concentration forecasting model system for the Eastern U.S. has been developed. The model system is consisting of a regional meteorological and a regional air quality model. It demonstrated a strong prediction dependence on its ozone boundary conditions....

  3. Sensitivity of Typhoon Track Predictions in a Regional Prediction System to Initial and Lateral Boundary Conditions

    DTIC Science & Technology

    2009-09-01

    less forecast skill due to a coarser res- olution. Miguez- Macho and Paegle (2000) suggest that accurate initial and lateral boundary conditions for a...nondeveloping ver- sus developing systems. J. Atmos. Sci., 38, 1132–1151. Miguez- Macho , G., and J. Paegle, 2000: Sensitivity of a global forecast model

  4. On a Mathematical Model with Noncompact Boundary Conditions Describing Bacterial Population

    NASA Astrophysics Data System (ADS)

    Boulanouar, Mohamed

    2013-04-01

    In this work, we are concerned with the well-posedness of a mathematical model describing a maturation-velocity structured bacterial population. Each bacterium is distinguished by its degree of maturity and its maturation velocity. The bacterial mitosis is mathematically described by noncompact boundary conditions. We show that the mathematical model is governed by a positive strongly continuous semigroup.

  5. Comparison of Extreme Pressure Additive Treat Rates in Soybean and Mineral Oils Under Boundary Lubrication Conditions

    Technology Transfer Automated Retrieval System (TEKTRAN)

    Traditionally, it is considered that, under boundary lubrication conditions, the reduction in friction and wear is mostly dependent on Extreme Pressure (EP) additives, rather than the basestock. However, several studies indicate that vegetable oils also contribute to the lubricity under this regime...

  6. Extragradient method for solving an optimal control problem with implicitly specified boundary conditions

    NASA Astrophysics Data System (ADS)

    Antipin, A. S.; Artem'eva, L. A.; Vasil'ev, F. P.

    2017-01-01

    An optimal control problem formulated as a system of linear ordinary differential equations with boundary conditions implicitly specified as a solution to a finite-dimensional minimization problem is considered. An extragradient method for solving this problem is proposed, and its convergence is studied.

  7. Local inhomogeneities in a Robertson-Walker background. II - Flux conditions at boundary surfaces

    NASA Astrophysics Data System (ADS)

    Lake, K.

    1980-12-01

    Energy flux conditions imposed on spherical boundary surfaces are examined. The zero-flux restriction, which is the hallmark of the standard Swiss cheese type construction, is relaxed. A class of locally inhomogeneous exact solutions to the Einstein equations which admit an effectively Newtonian accretion model is discussed.

  8. In-plane vibration analysis of annular plates with arbitrary boundary conditions.

    PubMed

    Shi, Xianjie; Shi, Dongyan; Qin, Zhengrong; Wang, Qingshan

    2014-01-01

    In comparison with the out-of-plane vibrations of annular plates, far less attention has been paid to the in-plane vibrations which may also play a vital important role in affecting the sound radiation from and power flows in a built-up structure. In this investigation, a generalized Fourier series method is proposed for the in-plane vibration analysis of annular plates with arbitrary boundary conditions along each of its edges. Regardless of the boundary conditions, the in-plane displacement fields are invariantly expressed as a new form of trigonometric series expansions with a drastically improved convergence as compared with the conventional Fourier series. All the unknown expansion coefficients are treated as the generalized coordinates and determined using the Rayleigh-Ritz technique. Unlike most of the existing studies, the presented method can be readily and universally applied to a wide spectrum of in-plane vibration problems involving different boundary conditions, varying material, and geometric properties with no need of modifying the basic functions or adapting solution procedures. Several numerical examples are presented to demonstrate the effectiveness and reliability of the current solution for predicting the in-plane vibration characteristics of annular plates subjected to different boundary conditions.

  9. Non-reflecting boundary conditions for the compressible Navier-Stokes equations

    NASA Technical Reports Server (NTRS)

    Abarbanel, S.; Bayliss, A.; Lustman, L.

    1986-01-01

    A small perturbation analysis, in the long wavelength regime, is used to obtain the downstream boundary condition for the pressure for the flow over a flat plate. The methodology is extendable to other geometries. Numerical results for high Reynolds number laminar flows show great improvement in convergence rate to steady state as well as the quality of the results.

  10. Artificial Boundary Conditions for the Numerical Simulation of Unsteady Electromagnetic Waves

    DTIC Science & Technology

    2003-01-01

    Tsynkov, V. I. Turchaninov , Long-time numerical computation of wave-type solutions driven by moving sources, Appl. Numer. Math. 38 (2001) 187–222. [2...V. S. Ryaben’kii, S. V. Tsynkov, V. I. Turchaninov , Global discrete artificial boundary conditions for time-dependent wave propagation, J. Comput

  11. Artificial Boundary Conditions for the Numerical Simulation of Unsteady Acoustic Waves

    DTIC Science & Technology

    2003-01-01

    Tsynkov, V. I. Turchaninov , Long-time numerical computation of wave-type solutions driven by moving sources, Appl. Numer. Math. 38 (2001) 187–222. [13...V. S. Ryaben’kii, S. V. Tsynkov, V. I. Turchaninov , Global discrete artificial boundary conditions for time-dependent wave propagation, J. Comput

  12. Damage detection of fatigue cracks under nonlinear boundary condition using subharmonic resonance.

    PubMed

    Zhang, Mengyang; Xiao, Li; Qu, Wenzhong; Lu, Ye

    2017-05-01

    In recent years, the nonlinear ultrasonic technique has been widely utilized for detecting fatigue crack, one of the most common forms of damage. However, one of limitations associated with this technique is that nonlinearities can be produced not only by damage but also by various intrinsic effects such as boundary conditions. The objective of this paper is to demonstrate the application of a nonlinear ultrasonic subharmonic method for detecting fatigue cracks with nonlinear boundary conditions. The fatigue crack was qualitatively modeled as two elastic, frictionless half spaces that enter into contact during vibration and where the contact obeys the basic Hertz contact law. The nonlinear ordinary differential equation drawn from the developed model was solved with the method of multiple scales. The threshold of subharmonic generation was studied. Different threshold behaviors between the nonlinear boundary condition and the fatigue crack were found that can be used to distinguish the source of nonlinear subharmonic features. To evaluate the proposed method, experiments using an aluminum plate with a fatigue crack were conducted to quantitatively verify the subharmonic resonance range. Two surface-bonded piezoelectric transducers were used to generate and receive ultrasonic wave signals. The experimental results demonstrated that the subharmonic component of the sensing signal could be used to detect the fatigue crack and further to distinguish it from inherent nonlinear boundary conditions.

  13. Prescribed mean curvature graphs with Neumann boundary conditions in some FLRW spacetimes

    NASA Astrophysics Data System (ADS)

    Mawhin, Jean; Torres, Pedro J.

    2016-12-01

    We identify a family of Friedmann-Lemaître-Robertson-Walker (FLRW) spacetimes such that the radially symmetric prescribed curvature problem with Neumann boundary condition is solvable on a ball of small radius. Such family contains some examples of interest in Cosmology.

  14. Effective conditions for the neutron flux density at axial boundaries of the core

    NASA Astrophysics Data System (ADS)

    Aristarkhova, E. A.; Malofeev, V. M.

    2016-12-01

    Analytical expressions for elements of the triangular matrix of effective conditions at the boundary of the core with a multiregion reflector are derived in the few-group diffusion approximation. The developed technique is verified using the example of fuel assemblies of a light-water reactor with an intermediate neutron spectrum.

  15. Construction of the Nuclear Effective Interaction from Energy Eigenstates and Boundary Conditions

    NASA Astrophysics Data System (ADS)

    McElvain, Kenneth; Haxton, Wick

    2017-01-01

    The original Harmonic Oscillator Based Effective Theory (HOBET) work by Haxton and Luu reduced H = T +VNN , with VNN a realistic potential, to Heff in a small basis defined by projection operator P while correctly including all scattering by H through an excluded space Q. Scattering by T is analytically included to all orders, leaving the ET expansion focused on the short range VNN. Results do not depend on the size P as the effect of scattering through Q is fully included, also distinguishing HOBET from other methods. In this talk we abandon VNN and determine the LECs of the ET expansion from energy levels and boundary conditions. In the infinite volume continuum case every energy is an eigenvalue of H with an associated scattering state. In the LQCD context boundary conditions are periodic. In either case the ET LECs can be determined from energy, boundary condition pairs. We show that the Cartesian HO ET LECs can be expressed in terms of the spherical ones, giving a spherical, infinite volume ET, bypassing the use of Luscher's method. The approach cleanly isolates operator mixing induced by the finite box, sequestering effects that vanish in the continuum limit in a Green's function constrained to match the boundary conditions. Supported by the DOE under contracts DE-SC00046548 and DE-AC02-98CH10886.

  16. Definition of boundary and initial conditions in the analysis of saturated ground-water flow systems - An introduction

    USGS Publications Warehouse

    Franke, O. Lehn; Reilly, Thomas E.; Bennett, Gordon D.

    1987-01-01

    Accurate definition of boundary and initial conditions is an essential part of conceptualizing and modeling ground-water flow systems. This report describes the properties of the seven most common boundary conditions encountered in ground-water systems and discusses major aspects of their application. It also discusses the significance and specification of initial conditions and evaluates some common errors in applying this concept to ground-water-system models. An appendix is included that discusses what the solution of a differential equation represents and how the solution relates to the boundary conditions defining the specific problem. This report considers only boundary conditions that apply to saturated ground-water systems.

  17. Conditions for the appearance of boundary modes in topological phases of Heisenberg spin ladders

    NASA Astrophysics Data System (ADS)

    Robinson, Neil; Atland, Alexander; Egger, Reinhold; Gergs, Nkilas; Konik, Robert; Li, Wei; Schuricht, Dirk; Tsvelik, Alexei; Weichselbaum, Andreas

    We consider the problem of delineating the necessary conditions for the appearance of boundary modes in extended SU (2) Heisenberg spin ladders. Specifically, we study Heisenberg ladders with rung exchange, J⊥, and ring exchange, JX, that admit a field theoretic description in terms of Majorana fermions in the continuum limit. In this description there are four Majorana fermions, arranged in a triplet and a singlet. This suggests there are four distinct phases, corresponding to the configurations of the signs of the triplet mt and singlet ms masses. We label these phases as: Haldane (mt > 0 ,ms < 0), rung singlet (mt < 0 ,ms > 0), VBS+ (mt ,ms > 0) and VBS- (mt ,ms < 0). Topologically, we find two of these phases support gapless boundary modes: the Haldane phase (the triplet forms a spin- 1 / 2 degree of freedom at the ends of the ladder) and the VBS+ phase, where all the Majorana fermions have gapless boundary modes. The absence of a gapless boundary mode in the rung singlet phase is surprising; we find that the singlet mode can become gapless if open boundary conditions are replaced with a continuous change in lattice parameters. We suggest a symmetry-allowed modification to the low-energy effective theory which may be responsible for this behavior.

  18. Grid resolution and turbulent inflow boundary condition recommendations for NPARC calculations

    NASA Technical Reports Server (NTRS)

    Georgiadis, Nicholas J.; Dudek, Julianne C.; Tierney, Thomas P.

    1995-01-01

    The effects of grid resolution and specification of turbulent inflow boundary conditions were examined using the NPARC code with the Baldwin-Lomax and Chien k-e turbulence models. Three benchmark turbulent test cases were calculated: two were wall bounded flows and the third was a compressible mixing layer. The wall bounded flows were essentially insensitive to axial grid density; however, the location of the first point off the wall had a substantial effect on flow solutions. It was determined that the first point off the wall must be in the laminar sublayer (y+ less than or equal to 5) for the entire boundary layer. For the compressible mixing layer cases, the axial grid density affected the capturing of oblique shock waves in the mixing region, but the overall mixing rate was not strongly dependent on grid resolution. In specifying the inflow turbulent boundary conditions, it was very important to match the boundary layer and momentum thicknesses of the two flows entering the mixing region; calculations obtained with smaller or no boundary layers resulted in substantially reduced mixing. The solutions were relatively insensitive to freestream turbulence level.

  19. Far-Field Boundary Conditions in Numerical Solutions of the Navier-Stokes Equations.

    DTIC Science & Technology

    2014-09-26

    nonlinear system of mixed parabolic- hyperbolic type in two space dimensions and time, with four independent variables must be solved in an exterior...conditions. * III THE NAVIER-STOKES EQUATIONS AND CHARACTERISTIC VARIABLES : We now begin our discussion of the equations of gas dynamics. We will neglect...8217 Far-Field Boundary Conditions in Numerical Solutions of the Navier-Stokes Equations L°O * (. P.J. McKenna LA. DTIC * E.LECTE Final Report AFOSR Grant

  20. The heat equation source determination for the case of non-smooth boundary and initial conditions

    NASA Astrophysics Data System (ADS)

    Solovi’ev, V. V.; Tkachenko, D. S.

    2017-01-01

    An inverse problem of reconstructing the source of a special kind for parabolic equations in a bounded region with smooth boundary is considered. Solutions are sought in the Holder classes. We prove an uniqueness criterion for the solution and sufficient conditions of Fredholm property of the task at hand. As a consequence of the sufficient conditions for existence and uniqueness of solution of the inhomogeneous inverse problems are found.

  1. Evaluation of Wall Boundary Conditions for Impedance Eduction Using a Dual-Source Method

    NASA Technical Reports Server (NTRS)

    Watson, W. R.; Jones, M. G.

    2012-01-01

    The accuracy of the Ingard-Myers boundary condition and a recently proposed modified Ingard-Myers boundary condition is evaluated for use in impedance eduction under the assumption of uniform mean flow. The evaluation is performed at three centerline Mach numbers, using data acquired in a grazing flow impedance tube, using both upstream and downstream propagating sound sources, and on a database of test liners for which the expected behavior of the impedance spectra is known. The test liners are a hard-wall insert consisting of 12.6 mm thick aluminum, a linear liner without a facesheet consisting of a number of small diameter but long cylindrical channels embedded in a ceramic material, and two conventional nonlinear liners consisting of a perforated facesheet bonded to a honeycomb core. The study is restricted to a frequency range for which only plane waves are cut on in the hard-wall sections of the flow impedance tube. The metrics used to evaluate each boundary condition are 1) how well it educes the same impedance for upstream and downstream propagating sources, and 2) how well it predicts the expected behavior of the impedance spectra over the Mach number range. The primary conclusions of the study are that the same impedance is educed for upstream and downstream propagating sources except at the highest Mach number, that an effective impedance based on both the upstream and downstream measurements is more accurate than an impedance based on the upstream or downstream data alone, and that the Ingard-Myers boundary condition with an effective impedance produces results similar to that achieved with the modified Ingard-Myers boundary condition.

  2. Boundary conditions for convergent radial tracer tests and effect of well bore mixing volume

    NASA Astrophysics Data System (ADS)

    Zlotnik, Vitaly A.; David Logan, J.

    Convergent radial flow tracer tests have a complex spatial nonaxial transport structure caused by the flow in the vicinity of the injection well and its finite mixing volume. The formulation of the boundary value problem, and especially the treatment of the boundary conditions at the injection well, is nontrivial. Hodgkinson and Lever [1983], Moench [1989, 1991], and Welty and Gelhar [1994] have developed different models and methods for the analysis of breakthrough curves in the extraction well. To extend interpretation techniques to breakthrough curves in the zone between injection and extraction wells, an analysis of conventional transport models is given, and improved boundary conditions are formulated for a convergent radial tracer test problem. The formulation of the boundary conditions is based upon a more detailed analysis of the kinematic flow structure and tracer mass balance in the neighborhood of the injection well. Two practical applications of revised boundary conditions for field data analysis are given. First, the note explains anomalous high well bore mixing volumes of injection wells found by Cady et al. [1993] and allows one to establish the role of mixing versus other processes (retardation, matrix diffusion, etc.). Second, it is shown that the improper use of Moench's [1989] model can produce bias in the characteristics of breakthrough curves in the extraction well under conditions that involve a significant mixing factor in the injection well. A numerical example indicates an error in peak concentrations on a breakthrough curve by as much as 70% and in peak arrival time by 10% for Peclet numbers Pe=102. The effect becomes slightly less significant for Pe=1.

  3. On the Exit Boundary Condition for One-Dimensional Calculations of Pulsed Detonation Engine Performance

    NASA Technical Reports Server (NTRS)

    Wilson, Jack; Paxson, Daniel E.

    2002-01-01

    In one-dimensional calculations of pulsed detonation engine (PDE) performance, the exit boundary condition is frequently taken to be a constant static pressure. In reality, for an isolated detonation tube, after the detonation wave arrives at the exit plane, there will be a region of high pressure, which will gradually return to ambient pressure as an almost spherical shock wave expands away from the exit, and weakens. Initially, the flow is supersonic, unaffected by external pressure, but later becomes subsonic. Previous authors have accounted for this situation either by assuming the subsonic pressure decay to be a relaxation phenomenon, or by running a two-dimensional calculation first, including a domain external to the detonation tube, and using the resulting exit pressure temporal distribution as the boundary condition for one-dimensional calculations. These calculations show that the increased pressure does affect the PDE performance. In the present work, a simple model of the exit process is used to estimate the pressure decay time. The planar shock wave emerging from the tube is assumed to transform into a spherical shock wave. The initial strength of the spherical shock wave is determined from comparison with experimental results. Its subsequent propagation, and resulting pressure at the tube exit, is given by a numerical blast wave calculation. The model agrees reasonably well with other, limited, results. Finally, the model was used as the exit boundary condition for a one-dimensional calculation of PDE performance to obtain the thrust wall pressure for a hydrogen-air detonation in tubes of length to diameter ratio (L/D) of 4, and 10, as well as for the original, constant pressure boundary condition. The modified boundary condition had no performance impact for values of L/D > 10, and moderate impact for L/D = 4.

  4. Dissipative particle dynamics simulation of flow generated by two rotating concentric cylinders: boundary conditions.

    PubMed

    Haber, S; Filipovic, N; Kojic, M; Tsuda, A

    2006-10-01

    The dissipative particle dynamics (DPD) method was used to simulate the flow in a system comprised of a fluid occupying the space between two cylinders rotating with equal angular velocities. The fluid, initially at rest, ultimately reaches a steady, linear velocity distribution (a rigid-body rotation). Since the induced flow field is solely associated with the no-slip boundary condition at the walls, we employed this system as a benchmark to examine the effect of bounce-back reflections, specular reflections, and Pivkin-Karniadakis no-slip boundary conditions, upon the steady-state velocity, density, and temperature distributions. An additional advantage of the foregoing system is that the fluid occupies inherently a finite bounded domain so that the results are affected by the prescribed no-slip boundary conditions only. Past benchmark systems such as Couette flow between two infinite parallel plates or Poiseuille flow in an infinitely long cylinder must employ artificial periodic boundary conditions at arbitrary upstream and downstream locations, a possible source of spurious effects. In addition, the effect of the foregoing boundary conditions on the time evolution of the simulated velocity profile was compared with that of the known, time-dependent analytical solution. It was shown that bounce-back reflection yields the best results for the velocity distributions with small fluctuations in density and temperature at the inner fluid domain and larger deviations near the walls. For the unsteady solutions a good fit is obtained if the DPD friction coefficient is proportional to the kinematic viscosity. Based on dimensional analysis and the numerical results a universal correlation is suggested between the friction coefficient and the kinematic viscosity.

  5. An Implementation of Hydrostatic Boundary Conditions for Variable Density Lattice Boltzmann Methods

    NASA Astrophysics Data System (ADS)

    Bardsley, K. J.; Thorne, D. T.; Lee, J. S.; Sukop, M. C.

    2006-12-01

    Lattice Boltzmann Methods (LBMs) have been under development for the last two decades and have become another capable numerical method for simulating fluid flow. Recent advances in lattice Boltzmann applications involve simulation of density-dependent fluid flow in closed (Dixit and Babu, 2006; D'Orazio et al., 2004) or periodic (Guo and Zhao, 2005) domains. However, standard pressure boundary conditions (BCs) are incompatible with concentration-dependent density flow simulations that use a body force for gravity. An implementation of hydrostatic BCs for use under these conditions is proposed here. The basis of this new implementation is an additional term in the pressure BC. It is derived to account for the incorporation of gravity as a body force and the effect of varying concentration in the fluid. The hydrostatic BC expands the potential of density-dependent LBM to simulate domains with boundaries other than the closed or periodic boundaries that have appeared in previous literature on LBM simulations. With this new implementation, LBM will be able to simulate complex concentration-dependent density flows, such as salt water intrusion in the classic Henry and Henry-Hilleke problems. This is demonstrated using various examples, beginning with a closed box system, and ending with a system containing two solid walls, one velocity boundary and one pressure boundary, as in the Henry problem. References Dixit, H. N., V. Babu, (2006), Simulation of high Rayleigh number natural convection in a square cavity using the lattice Boltzmann method, Int. J. Heat Mass Transfer, 49, 727-739. D'Orazio, A., M. Corcione, G.P. Celata, (2004), Application to natural convection enclosed flows of a lattice Boltzmann BGK model coupled with a general purpose thermal boundary conditions, Int. J. Thermal Sci., 43, 575-586. Gou, Z., T.S. Zhao, (2005), Lattice Boltzmann simulation of natural convection with temperature-dependant viscosity in a porous cavity, Numerical Heat Transfer, Part B

  6. Continuity and boundary conditions in thermodynamics: From Carnot's efficiency to efficiencies at maximum power

    NASA Astrophysics Data System (ADS)

    Ouerdane, H.; Apertet, Y.; Goupil, C.; Lecoeur, Ph.

    2015-07-01

    object of the article is thus to cover some of the milestones of thermodynamics, and show through the illustrative case of thermoelectric generators, our model heat engine, that the shift from Carnot's efficiency to efficienc ies at maximum power explains itself naturally as one considers continuity and boundary conditions carefully; indeed, as an adaptation of Friedrich Nietzche's quote, we may say that the thermodynamic demon is in the details. This article is supplemented with comments by J.M.R. Parrondo and a final reply by the authors.

  7. Stable boundary conditions and difference schemes for Navier-Stokes equations

    NASA Technical Reports Server (NTRS)

    Dutt, P.

    1985-01-01

    The Navier-Stokes equations can be viewed as an incompletely elliptic perturbation of the Euler equations. By using the entropy function for the Euler equations as a measure of energy for the Navier-Stokes equations, it was possible to obtain nonlinear energy estimates for the mixed initial boundary value problem. These estimates are used to derive boundary conditions which guarantee L2 boundedness even when the Reynolds number tends to infinity. Finally, a new difference scheme for modelling the Navier-Stokes equations in multidimensions for which it is possible to obtain discrete energy estimates exactly analogous to those we obtained for the differential equation was proposed.

  8. Boundary conditions for arbitrarily shaped and tightly focused laser pulses in electromagnetic codes

    NASA Astrophysics Data System (ADS)

    Thiele, Illia; Skupin, Stefan; Nuter, Rachel

    2016-09-01

    Investigation of laser matter interaction with electromagnetic codes requires to implement sources for the electromagnetic fields. A way to do so is to prescribe the fields at the numerical box boundaries in order to achieve the desired fields inside the numerical box. Here we show that the often used paraxial approximation can lead to unexpected field profiles with strong impact on the laser matter interaction results. We propose an efficient numerical algorithm to compute the required laser boundary conditions consistent with the Maxwell's equations for arbitrarily shaped, tightly focused laser pulses.

  9. Boundary conditions, gauge fixing ambiguities and exact expectation values in U(1) lattice gauge theory

    NASA Astrophysics Data System (ADS)

    Pinto, Carlos

    2016-03-01

    We analyze the interplay between gauge fixing and boundary conditions in two-dimensional U(1) lattice gauge theory. We show on the basis of a general argument that periodic boundary conditions result in an ill-defined weak coupling approximation but that the approximation can be made well-defined if the boundaries are fixed to zero. We confirm this result in the particular case of the Feynman gauge. We show that the zero momentum mode divergence in the propagator that appears in the Feynman gauge vanishes when the weak coupling approximation is well-defined. In addition we obtain exact results (for arbitrary coupling), including finite size corrections, for the partition function and for general one-point and two-point functions in the axial gauge under both periodic and zero boundary conditions and confirm these results numerically. The dependence of these objects on both lattice size and coupling constant is investigated using specific examples. These exact results may provide insight into similar gauge fixing issues in more complex models.

  10. A two-dimensional vibration analysis of piezoelectrically actuated microbeam with nonideal boundary conditions

    NASA Astrophysics Data System (ADS)

    Rezaei, M. P.; Zamanian, M.

    2017-01-01

    In this paper, the influences of nonideal boundary conditions (due to flexibility) on the primary resonant behavior of a piezoelectrically actuated microbeam have been studied, for the first time. The structure has been assumed to treat as an Euler-Bernoulli beam, considering the effects of geometric nonlinearity. In this work, the general nonideal supports have been modeled as a the combination of horizontal, vertical and rotational springs, simultaneously. Allocating particular values to the stiffness of these springs provides the mathematical models for the majority of boundary conditions. This consideration leads to use a two-dimensional analysis of the multiple scales method instead of previous works' method (one-dimensional analysis). If one neglects the nonideal effects, then this paper would be an effort to solve the two-dimensional equations of motion without a need of a combination of these equations using the shortening or stretching effect. Letting the nonideal effects equal to zero and comparing their results with the results of previous approaches have been demonstrated the accuracy of the two-dimensional solutions. The results have been identified the unique effects of constraining and stiffening of boundaries in horizontal, vertical and rotational directions. This means that it is inaccurate to suppose the nonideality of supports only in one or two of these directions like as previous works. The findings are of vital importance as a better prediction of the frequency response for the nonideal supports. Furthermore, the main findings of this effort can help to choose appropriate boundary conditions for desired systems.

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

    NASA Astrophysics Data System (ADS)

    Seo, Jongmin; Bose, Sanjeeb; Garcia-Mayoral, Ricardo; Mani, Ali

    2012-11-01

    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. Supported by the Office of Naval Research and the Kwanjeong Educational Scholarship Foundation.

  12. Program Code Generator for Cardiac Electrophysiology Simulation with Automatic PDE Boundary Condition Handling

    PubMed Central

    Punzalan, Florencio Rusty; Kunieda, Yoshitoshi; Amano, Akira

    2015-01-01

    Clinical and experimental studies involving human hearts can have certain limitations. Methods such as computer simulations can be an important alternative or supplemental tool. Physiological simulation at the tissue or organ level typically involves the handling of partial differential equations (PDEs). Boundary conditions and distributed parameters, such as those used in pharmacokinetics simulation, add to the complexity of the PDE solution. These factors can tailor PDE solutions and their corresponding program code to specific problems. Boundary condition and parameter changes in the customized code are usually prone to errors and time-consuming. We propose a general approach for handling PDEs and boundary conditions in computational models using a replacement scheme for discretization. This study is an extension of a program generator that we introduced in a previous publication. The program generator can generate code for multi-cell simulations of cardiac electrophysiology. Improvements to the system allow it to handle simultaneous equations in the biological function model as well as implicit PDE numerical schemes. The replacement scheme involves substituting all partial differential terms with numerical solution equations. Once the model and boundary equations are discretized with the numerical solution scheme, instances of the equations are generated to undergo dependency analysis. The result of the dependency analysis is then used to generate the program code. The resulting program code are in Java or C programming language. To validate the automatic handling of boundary conditions in the program code generator, we generated simulation code using the FHN, Luo-Rudy 1, and Hund-Rudy cell models and run cell-to-cell coupling and action potential propagation simulations. One of the simulations is based on a published experiment and simulation results are compared with the experimental data. We conclude that the proposed program code generator can be used to

  13. Program Code Generator for Cardiac Electrophysiology Simulation with Automatic PDE Boundary Condition Handling.

    PubMed

    Punzalan, Florencio Rusty; Kunieda, Yoshitoshi; Amano, Akira

    2015-01-01

    Clinical and experimental studies involving human hearts can have certain limitations. Methods such as computer simulations can be an important alternative or supplemental tool. Physiological simulation at the tissue or organ level typically involves the handling of partial differential equations (PDEs). Boundary conditions and distributed parameters, such as those used in pharmacokinetics simulation, add to the complexity of the PDE solution. These factors can tailor PDE solutions and their corresponding program code to specific problems. Boundary condition and parameter changes in the customized code are usually prone to errors and time-consuming. We propose a general approach for handling PDEs and boundary conditions in computational models using a replacement scheme for discretization. This study is an extension of a program generator that we introduced in a previous publication. The program generator can generate code for multi-cell simulations of cardiac electrophysiology. Improvements to the system allow it to handle simultaneous equations in the biological function model as well as implicit PDE numerical schemes. The replacement scheme involves substituting all partial differential terms with numerical solution equations. Once the model and boundary equations are discretized with the numerical solution scheme, instances of the equations are generated to undergo dependency analysis. The result of the dependency analysis is then used to generate the program code. The resulting program code are in Java or C programming language. To validate the automatic handling of boundary conditions in the program code generator, we generated simulation code using the FHN, Luo-Rudy 1, and Hund-Rudy cell models and run cell-to-cell coupling and action potential propagation simulations. One of the simulations is based on a published experiment and simulation results are compared with the experimental data. We conclude that the proposed program code generator can be used to

  14. Long-term behavior of reaction-diffusion equations with nonlocal boundary conditions on rough domains

    NASA Astrophysics Data System (ADS)

    Gal, Ciprian G.; Warma, Mahamadi

    2016-08-01

    We investigate the long term behavior in terms of finite dimensional global and exponential attractors, as time goes to infinity, of solutions to a semilinear reaction-diffusion equation on non-smooth domains subject to nonlocal Robin boundary conditions, characterized by the presence of fractional diffusion on the boundary. Our results are of general character and apply to a large class of irregular domains, including domains whose boundary is Hölder continuous and domains which have fractal-like geometry. In addition to recovering most of the existing results on existence, regularity, uniqueness, stability, attractor existence, and dimension, for the well-known reaction-diffusion equation in smooth domains, the framework we develop also makes possible a number of new results for all diffusion models in other non-smooth settings.

  15. Inhomogeneous Radiation Boundary Conditions Simulating Incoming Acoustic Waves for Computational Aeroacoustics

    NASA Technical Reports Server (NTRS)

    Tam, Christopher K. W.; Fang, Jun; Kurbatskii, Konstantin A.

    1996-01-01

    A set of nonhomogeneous radiation and outflow conditions which automatically generate prescribed incoming acoustic or vorticity waves and, at the same time, are transparent to outgoing sound waves produced internally in a finite computation domain is proposed. This type of boundary condition is needed for the numerical solution of many exterior aeroacoustics problems. In computational aeroacoustics, the computation scheme must be as nondispersive ans nondissipative as possible. It must also support waves with wave speeds which are nearly the same as those of the original linearized Euler equations. To meet these requirements, a high-order/large-stencil scheme is necessary The proposed nonhomogeneous radiation and outflow boundary conditions are designed primarily for use in conjunction with such high-order/large-stencil finite difference schemes.

  16. Swash zone boundary conditions derived from optical remote sensing of swash zone flow patterns

    NASA Astrophysics Data System (ADS)

    Power, H. E.; Holman, R. A.; Baldock, T. E.

    2011-06-01

    Optical remote sensing is used to measure flow patterns in the swash zone. Timestack images are analyzed to measure the asymmetry and the relative duration of the inflow into the swash zone. This varies significantly between individual swashes, contrary to the classical analytical swash model for runup induced by bores, which predicts a similar flow pattern for all events. For swash forced by breaking bores, the gradient of the x-t locus of flow reversal varies over a wide range and flow reversal can occur simultaneously across the whole swash zone. This variation of the gradient of the locus of flow reversal in x-t space can be parameterized in terms of a single free variable in recent solutions to the nonlinear shallow water equations, which fully defines the swash boundary inflow condition. Consistent with the theory, the horizontal runup, the swash period, and the swash similarity parameter were observed to be independent of the swash inflow conditions but the flow asymmetry is not. Only a weak correlation was observed between the swash boundary condition and the Iribarren number and beach slope. Conversely, the analysis suggests that the degree of swash-swash interaction does influence the swash boundary condition and the resulting internal flow kinematics. The variation in inflow conditions is expected to influence the magnitudes of the velocity moments within the swash zone and therefore sediment transport rates.

  17. Effects of non-ideal boundary conditions on the vibrations of a slightly curved micro beam

    NASA Astrophysics Data System (ADS)

    Sarı, Gözde; Pakdemirli, Mehmet

    2012-11-01

    Response of a slightly curved resonant microbeam having non-ideal boundary conditions is investigated. Non-ideal boundary conditions are formulated using perturbation theory. These non-ideal conditions allow for small deflection at the right end of the microbeam. The curvature is taken as a sinusoidal function of the spatial variable. The initial displacement is due to the geometry of the microbeam itself. They are produced intentionally to be curved or made curved by buckling straight beams through compressive axial loads. The model accounts for mid-plane stretching, an applied axial load and an AC harmonic force. The ends of the curved microbeam are on immovable simple supports. Immovable end conditions introduce integral type nonlinearity. The integro-differential equations of motion are solved analytically by means of direct application of the method of multiple scales (a perturbation method). The amplitude and phase modulation equations are derived for the case of primary resonances. The effect of curvature on the vibrations of the microbeam is examined. It is found that the effect of curvature is of softening type. The frequencies and mode shapes obtained are compared with the ideal boundary conditions case and the differences between them are contrasted on frequency response curves.

  18. The dynamic nature of the reconsolidation process and its boundary conditions: Evidence based on human tests.

    PubMed

    Fernández, Rodrigo S; Bavassi, Luz; Forcato, Cecilia; Pedreira, María E

    2016-04-01

    The reconsolidation process is the mechanism by which the strength and/or content of consolidated memories are updated. This process is triggered by the presentation of a reminder (training cues). It is not always possible to trigger the reconsolidation process. For example, memory age and strength are boundary conditions for the reconsolidation process. Here, we investigated the dynamic changes in these conditions. We propose that the boundary conditions of the reconsolidation process are not fixed and vary as a consequence of the interaction between memory features and reminder characteristics. To modify memory properties, participants received a threatening social protocol that improves memory acquisition or a control condition (fake, without social interaction) prior to learning pairs of meaningless syllables. To determine whether a strong young or old declarative memory undergoes the reconsolidation process, we used an interference task (a second list of pairs of meaningless syllables) to disrupt memory re-stabilization. To assess whether the older memory could be strengthened, we repeated the triggering of reconsolidation. Strong young or old memories modulated by a threatening experience could be interfered during reconsolidation and updated (strengthened) by reconsolidation. Rather than being fixed, boundary conditions vary according to the memory features (strong memory), which indicates the dynamic nature of the reconsolidation process. Our findings demonstrate that it is possible to modify these limits by recruiting the reconsolidation process and making it functionally operative again. This novel scenario opens the possibility to new therapeutically approaches that take into account the reconsolidation process.

  19. A database and tool for boundary conditions for regional air quality modeling: description and evaluation

    NASA Astrophysics Data System (ADS)

    Henderson, B. H.; Akhtar, F.; Pye, H. O. T.; Napelenok, S. L.; Hutzell, W. T.

    2013-09-01

    Transported air pollutants receive increasing attention as regulations tighten and global concentrations increase. The need to represent international transport in regional air quality assessments requires improved representation of boundary concentrations. Currently available observations are too sparse vertically to provide boundary information, particularly for ozone precursors, but global simulations can be used to generate spatially and temporally varying Lateral Boundary Conditions (LBC). This study presents a public database of global simulations designed and evaluated for use as LBC for air quality models (AQMs). The database covers the contiguous United States (CONUS) for the years 2000-2010 and contains hourly varying concentrations of ozone, aerosols, and their precursors. The database is complimented by a tool for configuring the global results as inputs to regional scale models (e.g., Community Multiscale Air Quality or Comprehensive Air quality Model with extensions). This study also presents an example application based on the CONUS domain, which is evaluated against satellite retrieved ozone vertical profiles. The results show performance is largely within uncertainty estimates for the Tropospheric Emission Spectrometer (TES) with some exceptions. The major difference shows a high bias in the upper troposphere along the southern boundary in January. This publication documents the global simulation database, the tool for conversion to LBC, and the fidelity of concentrations on the boundaries. This documentation is intended to support applications that require representation of long-range transport of air pollutants.

  20. An unstructured direct simulation Monte Carlo methodology with Kinetic-Moment inflow and outflow boundary conditions

    NASA Astrophysics Data System (ADS)

    Gatsonis, Nikolaos A.; Chamberlin, Ryan E.; Averkin, Sergey N.

    2013-01-01

    The mathematical and computational aspects of the direct simulation Monte Carlo on unstructured tetrahedral grids (U3DSMC) with a Kinetic-Moment (KM) boundary conditions method are presented. The algorithms for particle injection, particle loading, particle motion, and particle tracking are presented. The KM method applicable to a subsonic or supersonic inflow/outflow boundary, couples kinetic (particle) U3DSMC properties with fluid (moment) properties. The KM method obtains the number density, temperature and mean velocity needed to define the equilibrium, drifting Maxwellian distribution at a boundary. The moment component of KM is based on the local one dimensional inviscid (LODI) boundary conditions method consistent with the 5-moment compressible Euler equations. The kinetic component of KM is based on U3DSMC for interior properties and the equilibrium drifting Maxwellian at the boundary. The KM method is supplemented with a time-averaging procedure, allows for choices in sampling-cell procedures, minimizes fluctuations and accelerates the convergence in subsonic flows. Collision sampling in U3DSMC implements the no-time-counter method and includes elastic and inelastic collisions. The U3DSMC with KM boundary conditions is validated and verified extensively with simulations of subsonic nitrogen flows in a cylindrical tube with imposed inlet pressure and density and imposed outlet pressure. The simulations cover the regime from slip to free-molecular with inlet Knudsen numbers between 0.183 and 18.27 and resulting inlet Mach numbers between 0.037 and 0.027. The pressure and velocity profiles from U3DSMC-KM simulations are compared with analytical solutions obtained from first-order and second-order slip boundary conditions. Mass flow rates from U3DSMC-KM are compared with validated analytical solutions for the entire Knudsen number regime considered. Error and sensitivity analysis is performed and numerical fractional errors are in agreement with theoretical

  1. The influence of initial and surface boundary conditions on a model-generated January climatology

    NASA Technical Reports Server (NTRS)

    Wu, K. F.; Spar, J.

    1981-01-01

    The influence on a model-generated January climate of various surface boundary conditions, as well as initial conditions, was studied by using the GISS coarse-mesh climate model. Four experiments - two with water planets, one with flat continents, and one with mountains - were used to investigate the effects of initial conditions, and the thermal and dynamical effects of the surface on the model generated-climate. However, climatological mean zonal-symmetric sea surface temperature is used in all four runs over the model oceans. Moreover, zero ground wetness and uniform ground albedo except for snow are used in the last experiments.

  2. Inner boundary conditions for black hole initial data derived from isolated horizons

    NASA Astrophysics Data System (ADS)

    Jaramillo, José Luis; Gourgoulhon, Eric; Marugán, Guillermo A.

    2004-12-01

    We present a set of boundary conditions for solving the elliptic equations in the initial data problem for space-times containing a black hole, together with a number of constraints to be satisfied by the otherwise freely specifiable standard parameters of the conformal thin sandwich formulation. These conditions altogether are sufficient for the construction of a horizon that is instantaneously in equilibrium in the sense of the isolated horizons formalism. We then investigate the application of these conditions to the initial data problem of binary black holes and discuss the relation of our analysis with other proposals that exist in the literature.

  3. High-order Two-way Artificial Boundary Conditions for Nonlinear Wave Propagation with Backscattering

    NASA Technical Reports Server (NTRS)

    Fibich, Gadi; Tsynkov, Semyon

    2000-01-01

    When solving linear scattering problems, one typically first solves for the impinging wave in the absence of obstacles. Then, by linear superposition, the original problem is reduced to one that involves only the scattered waves driven by the values of the impinging field at the surface of the obstacles. In addition, when the original domain is unbounded, special artificial boundary conditions (ABCs) that would guarantee the reflectionless propagation of waves have to be set at the outer boundary of the finite computational domain. The situation becomes conceptually different when the propagation equation is nonlinear. In this case the impinging and scattered waves can no longer be separated, and the problem has to be solved in its entirety. In particular, the boundary on which the incoming field values are prescribed, should transmit the given incoming waves in one direction and simultaneously be transparent to all the outgoing waves that travel in the opposite direction. We call this type of boundary conditions two-way ABCs. In the paper, we construct the two-way ABCs for the nonlinear Helmholtz equation that models the laser beam propagation in a medium with nonlinear index of refraction. In this case, the forward propagation is accompanied by backscattering, i.e., generation of waves in the direction opposite to that of the incoming signal. Our two-way ABCs generate no reflection of the backscattered waves and at the same time impose the correct values of the incoming wave. The ABCs are obtained for a fourth-order accurate discretization to the Helmholtz operator; the fourth-order grid convergence is corroborated experimentally by solving linear model problems. We also present solutions in the nonlinear case using the two-way ABC which, unlike the traditional Dirichlet boundary condition, allows for direct calculation of the magnitude of backscattering.

  4. Measurements in Transitional Boundary Layers Under High Free-Stream Turbulence and Strong Acceleration Conditions

    NASA Technical Reports Server (NTRS)

    Volino, Ralph J.; Simon, Terrence W.

    1995-01-01

    Measurements from transitional, heated boundary layers along a concave-curved test wall are presented and discussed. A boundary layer subject to low free-stream turbulence intensity (FSTI), which contains stationary streamwise (Gortler) vortices, is documented. The low FSTI measurements are followed by measurements in boundary layers subject to high (initially 8%) free-stream turbulence intensity and moderate to strong streamwise acceleration. Conditions were chosen to simulate those present on the downstream half of the pressure side of a gas turbine airfoil. Mean flow characteristics as well as turbulence statistics, including the turbulent shear stress, turbulent heat flux, and turbulent Prandtl number, are documented. A technique called "octant analysis" is introduced and applied to several cases from the literature as well as to data from the present study. Spectral analysis was applied to describe the effects of turbulence scales of different sizes during transition. To the authors'knowledge, this is the first detailed documentation of boundary layer transition under such high free-stream turbulence conditions.

  5. Measurements in Separated and Transitional Boundary Layers Under Low-Pressure Turbine Airfoil Conditions

    NASA Technical Reports Server (NTRS)

    Volino, Ralph J.; Hultgren, Lennart .

    2000-01-01

    Detailed velocity measurements were made along a flat plate subject to the same dimensionless pressure gradient as the suction side of a modern low-pressure turbine airfoil. Reynolds numbers based on wetted plate length and nominal exit velocity were varied from 50,000 to 300,000, covering cruise to takeoff conditions. Low and high inlet free-stream turbulence intensities (0.2% and 7%) were set using passive grids. The location of boundary-layer separation does not depend strongly on the free-stream turbulence level or Reynolds number, as long as the boundary layer remains non-turbulent prior to separation. Strong acceleration prevents transition on the upstream part of the plate in all cases. Both free-stream turbulence and Reynolds number have strong effects on transition in the adverse pressure gradient region. Under low free-stream turbulence conditions transition is induced by instability waves in the shear layer of the separation bubble. Reattachment generally occurs at the transition start. At Re = 50,000 the separation bubble does not close before the trailing edge of the modeled airfoil. At higher Re, transition moves upstream, and the boundary layer reattaches. With high free-stream turbulence levels, transition appears to occur in a bypass mode, similar to that in attached boundary layers. Transition moves upstream, resulting in shorter separation regions. At Re above 200,000, transition begins before separation. Mean velocity, turbulence and intermittency profiles are presented.

  6. Defining boundary conditions for RANS predictions of urban flows using mesoscale simulations

    NASA Astrophysics Data System (ADS)

    Garcia Sanchez, Clara; Gorle, Catherine; van Beeck, Jeroen

    2015-11-01

    Pollutant dispersion and wind flows in urban canopies are major concerns for human health and energy, and the complex nature of the flow and transport processes remains a challenge when using Computational Fluid Dynamics (CFD) to predict wind flows. The definition of the inflow boundary condition in Reynolds-Averaged Navier-Stokes simulations (RANS) is one of the uncertainties that will strongly influence the prediction of the flow field, and thus, the dispersion pattern. The goal of the work presented is to define a methodology that improves the level of realism in the inflow condition for RANS simulations by accounting for larger mesoscale effects. The Weather Research and Forecasting model (WRF) is used to forecast mesoscale flow patterns, and two different approaches are used to define inflow conditions for the RANS simulations performed with OpenFOAM: 1) WRF variables such as local velocity magnitude, ABL height and friction velocity are directly interpolated onto the boundaries of the CFD domain; 2) WRF predictions for the geostrophic wind and friction velocity are applied as a forcing boundary condition. Simulations of the Joint Urban 2003 experimental campaign in Oklahoma City have been performed using both approaches and a comparison of the results will be presented.

  7. New Exact Solution of Dirac-Coulomb Equation with Exact Boundary Condition

    NASA Astrophysics Data System (ADS)

    Chen, Ruida

    2008-04-01

    It usually writes the boundary condition of the wave equation in the Coulomb field as a rough form without considering the size of the atomic nucleus. The rough expression brings on that the solutions of the Klein-Gordon equation and the Dirac equation with the Coulomb potential are divergent at the origin of the coordinates, also the virtual energies, when the nuclear charges number Z>137, meaning the original solutions do not satisfy the conditions for determining solution. Any divergences of the wave functions also imply that the probability density of the meson or the electron would rapidly increase when they are closing to the atomic nucleus. What it predicts is not a truth that the atom in ground state would rapidly collapse to the neutron-like. We consider that the atomic nucleus has definite radius and write the exact boundary condition for the hydrogen and hydrogen-like atom, then newly solve the radial Dirac-Coulomb equation and obtain a new exact solution without any mathematical and physical difficulties. Unexpectedly, the K value constructed by Dirac is naturally written in the barrier width or the equivalent radius of the atomic nucleus in solving the Dirac equation with the exact boundary condition, and it is independent of the quantum energy. Without any divergent wave function and the virtual energies, we obtain a new formula of the energy levels that is different from the Dirac formula of the energy levels in the Coulomb field.

  8. An Alternative Frictional Boundary Condition for Computational Fluid Dynamics Simulation of Friction Stir Welding

    NASA Astrophysics Data System (ADS)

    Chen, Gaoqiang; Feng, Zhili; Zhu, Yucan; Shi, Qingyu

    2016-09-01

    For better application of numerical simulation in optimization and design of friction stir welding (FSW), this paper presents a new frictional boundary condition at the tool/workpiece interface for computational fluid dynamics (CFD) modeling of FSW. The proposed boundary condition is based on an implementation of the Coulomb friction model. Using the new boundary condition, the CFD simulation yields non-uniform distribution of contact state over the tool/workpiece interface, as validated by the experimental weld macrostructure. It is found that interfacial sticking state is present over large area at the tool-workpiece interface, while significant interfacial sliding occurs at the shoulder periphery, the lower part of pin side, and the periphery of pin bottom. Due to the interfacial sticking, a rotating flow zone is found under the shoulder, in which fast circular motion occurs. The diameter of the rotating flow zone is smaller than the shoulder diameter, which is attributed to the presence of the interfacial sliding at the shoulder periphery. For the simulated welding condition, the heat generation due to friction and plastic deformation makes up 54.4 and 45.6% of the total heat generation rate, respectively. The simulated temperature field is validated by the good agreement to the experimental measurements.

  9. External Boundary Conditions for Three-Dimensional Problems of Computational Aerodynamics

    NASA Technical Reports Server (NTRS)

    Tsynkov, Semyon V.

    1997-01-01

    We consider an unbounded steady-state flow of viscous fluid over a three-dimensional finite body or configuration of bodies. For the purpose of solving this flow problem numerically, we discretize the governing equations (Navier-Stokes) on a finite-difference grid. The grid obviously cannot stretch from the body up to infinity, because the number of the discrete variables in that case would not be finite. Therefore, prior to the discretization we truncate the original unbounded flow domain by introducing some artificial computational boundary at a finite distance of the body. Typically, the artificial boundary is introduced in a natural way as the external boundary of the domain covered by the grid. The flow problem formulated only on the finite computational domain rather than on the original infinite domain is clearly subdefinite unless some artificial boundary conditions (ABC's) are specified at the external computational boundary. Similarly, the discretized flow problem is subdefinite (i.e., lacks equations with respect to unknowns) unless a special closing procedure is implemented at this artificial boundary. The closing procedure in the discrete case is called the ABC's as well. In this paper, we present an innovative approach to constructing highly accurate ABC's for three-dimensional flow computations. The approach extends our previous technique developed for the two-dimensional case; it employs the finite-difference counterparts to Calderon's pseudodifferential boundary projections calculated in the framework of the difference potentials method (DPM) by Ryaben'kii. The resulting ABC's appear spatially nonlocal but particularly easy to implement along with the existing solvers. The new boundary conditions have been successfully combined with the NASA-developed production code TLNS3D and used for the analysis of wing-shaped configurations in subsonic (including incompressible limit) and transonic flow regimes. As demonstrated by the computational experiments

  10. Sea slugs, subliminal pictures, and vegetative state patients: boundaries of consciousness in classical conditioning.

    PubMed

    Bekinschtein, Tristan A; Peeters, Moos; Shalom, Diego; Sigman, Mariano

    2011-01-01

    Classical (trace) conditioning is a specific variant of associative learning in which a neutral stimulus leads to the subsequent prediction of an emotionally charged or noxious stimulus after a temporal gap. When conditioning is concurrent with a distraction task, only participants who can report the relationship (the contingency) between stimuli explicitly show associative learning. This suggests that consciousness is a prerequisite for trace conditioning. We review and question three main controversies concerning this view. Firstly, virtually all animals, even invertebrate sea slugs, show this type of learning; secondly, unconsciously perceived stimuli may elicit trace conditioning; and thirdly, some vegetative state patients show trace learning. We discuss and analyze these seemingly contradictory arguments to find the theoretical boundaries of consciousness in classical conditioning. We conclude that trace conditioning remains one of the best measures to test conscious processing in the absence of explicit reports.

  11. Study on pure IL VIV of a free spanning pipeline under general boundary conditions

    NASA Astrophysics Data System (ADS)

    Xu, Wan-hai; Xu, Jing-yu; Wu, Ying-xiang; Ji, Chun-ning

    2017-03-01

    Pipeline spans may occur due to natural seabed irregularities or local scour of bed sediment. The pure in-line (IL) vortex-induced vibrations (VIV) analysis of the free spans is an important subject for design of pipeline in uneven seabed. The main objective of this paper is to analyze the characteristics of pure IL VIV of a free spanning pipeline under general boundary conditions. An IL wake oscillator model which can describe the coupling of pipeline structure and fluctuating drag is introduced and employed. The coupled partial differential equations of structure and wake are transformed into a set of ordinary differential equations using two-mode Galerkin method. Some case studies are presented and thoroughly discussed in order to investigate the effects of internal fluid, axial force and boundary conditions on the pure IL VIV.

  12. Combined solid and liquid lubrication of silicon nitride under boundary conditions

    NASA Astrophysics Data System (ADS)

    Ajayi, O. O.; Erdemir, A.; Hsieh, J. H.; Erck, R. A.; Fenske, G. R.

    1992-07-01

    The present study showed that an effective way of lubricating ceramic surfaces under boundary conditions both at room temperature and at high temperatures of 150 and 250 C was the combined effect of solid, i.e., soft metal-Ag, and liquid lubricants, i.e., polyol-ester-based synthetic oil. Compared to dry sliding of uncoated materials, oil-lubricated sliding of silver-coated silicon nitride surfaces resulted, for the conditions tested, in a decrease of the friction coefficient by a factor of 18 and of specific wear rate by more than four orders of magnitude. The Ag coating, which was formed in part by ion-beam-assisted deposition, was effective in preventing ceramic-to-ceramic contact under boundary-lubricated regimes. The only observed drawback was the occurrence of a chemical interaction between the Ag film and sulfur from the oil, which reduced the durability of the Ag film.

  13. Axisymmetric Stagnation-Point Flow with a General Slip Boundary Condition over a Lubricated Surface

    NASA Astrophysics Data System (ADS)

    Sajid, M.; K., Mahmood; Z., Abbas

    2012-02-01

    We investigate the axisymmetric stagnation-point flow of a viscous fluid over a lubricated surface by imposing a generalized slip condition at the fluid-fluid interface. The power law non-Newtonian fluid is considered as a lubricant. The lubrication layer is thin and assumed to have a variable thickness. The transformed nonlinear ordinary differential equation governing the flow is linearized using quasilinearization. The method of superposition is adopted to convert the boundary value problem into an initial value problem and the solution is obtained numerically by using the fourth-order Runge—Kutta method. The results are discussed to see the influence of pertinent parameters. The limiting cases of Navier and no-slip boundary conditions are obtained as the special cases and found to be in excellent agreement with the existing results in the literature.

  14. Drifts, boundary conditions and plasma convection on open magnetic field lines

    SciTech Connect

    Cohen, R. H.

    1998-11-20

    In a number of plasmas of practical interest, including the scrape-off layer of a tokamak with a divertor or toroidal limiter, some gas discharge devices, and in the vicinity of spacecraft, magnetic field lines intersect bounding surfaces at shallow angles. Under these circumstances a number of interesting and important effects arise. Drifts can compete with parallel flows in establishing the boundary conditions for plasma mass-flow and current (sheath current-voltage characteristics). We derive the mass-flow constraints including both poloidal and radial drifts, review the current boundary conditions, and survey the consequences, including along-field density and heat-flux asymmetries, convection created by a wavy surface, generation of electric fields and surface currents associated with shadows from surface structures, and modification of instability growth.

  15. A coupling strategy for nonlocal and local diffusion models with mixed volume constraints and boundary conditions

    SciTech Connect

    D'Elia, Marta; Perego, Mauro; Bochev, Pavel B.; Littlewood, David John

    2015-12-21

    We develop and analyze an optimization-based method for the coupling of nonlocal and local diffusion problems with mixed volume constraints and boundary conditions. The approach formulates the coupling as a control problem where the states are the solutions of the nonlocal and local equations, the objective is to minimize their mismatch on the overlap of the nonlocal and local domains, and the controls are virtual volume constraints and boundary conditions. When some assumptions on the kernel functions hold, we prove that the resulting optimization problem is well-posed and discuss its implementation using Sandia’s agile software components toolkit. As a result, the latter provides the groundwork for the development of engineering analysis tools, while numerical results for nonlocal diffusion in three-dimensions illustrate key properties of the optimization-based coupling method.

  16. High order optimal control of space trajectories with uncertain boundary conditions

    NASA Astrophysics Data System (ADS)

    Di Lizia, P.; Armellin, R.; Bernelli-Zazzera, F.; Berz, M.

    2014-01-01

    A high order optimal control strategy is proposed in this work, based on the use of differential algebraic techniques. In the frame of orbital mechanics, differential algebra allows to represent, by high order Taylor polynomials, the dependency of the spacecraft state on initial conditions and environmental parameters. The resulting polynomials can be manipulated to obtain the high order expansion of the solution of two-point boundary value problems. Since the optimal control problem can be reduced to a two-point boundary value problem, differential algebra is used to compute the high order expansion of the solution of the optimal control problem about a reference trajectory. Whenever perturbations in the nominal conditions occur, new optimal control laws for perturbed initial and final states are obtained by the mere evaluation of polynomials. The performances of the method are assessed on lunar landing, rendezvous maneuvers, and a low-thrust Earth-Mars transfer.

  17. Blow-up in p-Laplacian heat equations with nonlinear boundary conditions

    NASA Astrophysics Data System (ADS)

    Ding, Juntang; Shen, Xuhui

    2016-10-01

    In this paper, we investigate the blow-up of solutions to the following p-Laplacian heat equations with nonlinear boundary conditions: {l@{quad}l}(h(u))_t =nabla\\cdot(|nabla u|pnabla u)+k(t)f(u) &{in } Ω×(0,t^{*}), |nabla u|ppartial u/partial n=g(u) &on partialΩ×(0,t^{*}), u(x,0)=u0(x) ≥ 0 & {in } overline{Ω},. where {p ≥ 0} and {Ω} is a bounded convex domain in {RN}, {N ≥ 2} with smooth boundary {partialΩ}. By constructing suitable auxiliary functions and using a first-order differential inequality technique, we establish the conditions on the nonlinearities and data to ensure that the solution u( x, t) blows up at some finite time. Moreover, the upper and lower bounds for the blow-up time, when blow-up does occur, are obtained.

  18. Slip-flow boundary condition for straight walls in the lattice Boltzmann model.

    PubMed

    Szalmás, Lajos

    2006-06-01

    A slip-flow boundary condition has been developed in the lattice Boltzmann model combining an interpolation method and a simple slip boundary condition for straight walls placed at arbitrary distance from the last fluid node. An analytical expression has been derived to connect the model parameters with the slip velocity for Couette and Poiseuille flows in the nearly continuum limit. The proposed interpolation method ensures that the slip velocity is independent of the wall position in first order of the Knudsen number. Computer simulations have been carried out to validate the model. The Couette and Poiseuille flows agree with the analytical results to machine order. Numerical simulation of a moving square demonstrates the accuracy of the model for walls moving in both the tangential and normal directions.

  19. Stability of Interfacial Phase Growth in a Slab with Convective Boundary Conditions

    NASA Astrophysics Data System (ADS)

    Basu, Rahul

    2016-06-01

    The mass transport and energy equations for a semi-infinite porous slab are solved using similarity variables and closed form functions to describe freezing with remelt at the interface. Heat and mass balance analyses give a transcendental equation for the unknown interfacial freezing velocity for solving on the computer. The solutions for the temperature and mass concentration are decoupled and solved analytically. The solution for convective boundary conditions is compared with that for Dirichlet boundary conditions. The progressive development of the solution with material thickness and change of functional time dependence and effect on the stability of nucleation is outlined. A discussion with biological adaptation to extreme cold and possible evolution of molecules in heat transfer regimes is included in light of the above.

  20. Uncertain boundary condition Bayesian identification from experimental data: A case study on a cantilever beam

    NASA Astrophysics Data System (ADS)

    Ritto, T. G.; Sampaio, R.; Aguiar, R. R.

    2016-02-01

    In many mechanical applications (wind turbine tower, substructure joints, etc.), the stiffness of the boundary conditions is uncertain and might decrease with time, due to wear and/or looseness. In this paper, a torsional stiffness parameter is used to model the clamped side of a Timoshenko beam. The goal is to perform the identification with experimental data. To represent the decreasing stiffness of the clamped side, an experimental test rig is constructed, where several rubber layers are added to the clamped side, making it softer. Increasing the number of layers decreases the stiffness, thus representing a loss in the stiffness. The Bayesian approach is applied to update the probabilistic model related to the boundary condition (torsional stiffness parameter). The proposed Bayesian strategy worked well for the problem analyzed, where the experimental natural frequencies were within the 95% confidence limits of the computed natural frequencies probability density functions.

  1. One-dimensional diffusion problem with not strengthened regular boundary conditions

    NASA Astrophysics Data System (ADS)

    Orazov, I.; Sadybekov, M. A.

    2015-11-01

    In this paper we consider one family of problems simulating the determination of target components and density of sources from given values of the initial and final states. The mathematical statement of these problems leads to the inverse problem for the diffusion equation, where it is required to find not only a solution of the problem, but also its right-hand side that depends only on a spatial variable. One of specific features of the considered problems is that the system of eigenfunctions of the multiple differentiation operator subject to boundary conditions does not have the basis property. We prove the existence and uniqueness of classical solutions of the problem, solving the problem independently of whether the corresponding spectral problem (for the operator of multiple differentiation with not strengthened regular boundary conditions) has a basis of generalized eigenfunctions.

  2. Bleed-boundary conditions for numerically simulated mixed-compression supersonic inlet flow

    NASA Technical Reports Server (NTRS)

    Chyu, W. J.; Howe, G. W.; Shih, T. I-P.

    1992-01-01

    A numerical study was performed to investigate boundary conditions for bleed openings that are needed in the numerical simulation of critical flow through turbojet inlets with bleed. Nine different boundary conditions (BCs) were devised and examined. Of the BCs examined, three were able to stabilize the terminal shock near the inlet's throat. This numerical study was based on the ensemble-averaged, unsteady, three-dimensional, compressible Navier-Stokes equations closed by the Baldwin-Lomax algebraic turbulence model. Solutions to the Navier-Stokes equations were obtained by using a hybrid implicit-explicit method (Beam and Warming/MacCormack). The multiblock grid system used in the solution procedure was generated by solving a set of elliptic partial differential equations. Solutions obtained were compared with available experimental data.

  3. Stokesian dynamics of pill-shaped Janus particles with stick and slip boundary conditions

    NASA Astrophysics Data System (ADS)

    Sun, Qiang; Klaseboer, Evert; Khoo, Boo Cheong; Chan, Derek Y. C.

    2013-04-01

    We study the forces and torques experienced by pill-shaped Janus particles of different aspect ratios where half of the surface obeys the no-slip boundary condition and the other half obeys the Navier slip condition of varying slip lengths. Using a recently developed boundary integral formulation whereby the traditional singular behavior of this approach is removed analytically, we quantify the strength of the forces and torques experienced by such particles in a uniform flow field in the Stokes regime. Depending on the aspect ratio and the slip length, the force transverse to the flow direction can change sign. This is a novel property unique to the Janus nature of the particles.

  4. Global Artificial Boundary Conditions for Computation of External Flow Problems with Propulsive Jets

    NASA Technical Reports Server (NTRS)

    Tsynkov, Semyon; Abarbanel, Saul; Nordstrom, Jan; Ryabenkii, Viktor; Vatsa, Veer

    1998-01-01

    We propose new global artificial boundary conditions (ABC's) for computation of flows with propulsive jets. The algorithm is based on application of the difference potentials method (DPM). Previously, similar boundary conditions have been implemented for calculation of external compressible viscous flows around finite bodies. The proposed modification substantially extends the applicability range of the DPM-based algorithm. In the paper, we present the general formulation of the problem, describe our numerical methodology, and discuss the corresponding computational results. The particular configuration that we analyze is a slender three-dimensional body with boat-tail geometry and supersonic jet exhaust in a subsonic external flow under zero angle of attack. Similarly to the results obtained earlier for the flows around airfoils and wings, current results for the jet flow case corroborate the superiority of the DPM-based ABC's over standard local methodologies from the standpoints of accuracy, overall numerical performance, and robustness.

  5. Transparent Boundary Condition for Oseen-Frank Model. Application for NLC Cells With Patterned Electrodes

    NASA Astrophysics Data System (ADS)

    Orquín-Serrano, I.; Vijande, J.; Villatoro, F. R.; Ferrando, A.; Fernández de Córdoba, P.; Michinel, H.

    2015-04-01

    In the present work a novel application of Transparent Boundary Conditions (TBC) to nematic liquid crystal cells (NLCC) with planar alignment and a patterned electrode is studied. This device is attracting great interest since it allows soliton steering by optically and externally induced waveguides. We employ the continuum Oseen-Frank theory to find the tilt and twist angle distributions in the cell under the one-constant approximation. The electric field distribution takes into account the whole 2D permittivity tensor for the transverse coordinates. Standard finite difference time domain methods together with an iterative method is applied to find an approximate solution to our coupled problem. A novel class of TBC is used to correctly define the boundary for both the distortion angle problem and the electric field distribution when using patterned electrodes. Thus, we achieve an important decrease of computational needs when solving this kind of problems and we are also capable of exploring weak anchoring conditions for NLCC.

  6. Numerical simulation of hyperbolic heat conduction with convection boundary conditions and pulse heating effects

    NASA Technical Reports Server (NTRS)

    Glass, David E.; Tamma, Kumar K.; Railkar, Sudhir B.

    1989-01-01

    The paper describes the numerical simulation of hyperbolic heat conduction with convection boundary conditions. The effects of a step heat loading, a sudden pulse heat loading, and an internal heat source are considered in conjunction with convection boundary conditions. Two methods of solution are presened for predicting the transient behavior of the propagating thermal disturbances. In the first method, MacCormack's predictor-corrector method is employed for integrating the hyperbolic system of equations. Next, the transfinite element method, which employs specially tailored elements, is used for accurately representing the transient response of the propagating thermal wave fronts. The agreement between the results of various numerical test cases validate the representative behavior of the thermal wave fronts. Both methods represent hyperbolic heat conduction behavior by effectively modeling the sharp discontinuities of the propagating thermal disturbances.

  7. A coupling strategy for nonlocal and local diffusion models with mixed volume constraints and boundary conditions

    DOE PAGES

    D'Elia, Marta; Perego, Mauro; Bochev, Pavel B.; ...

    2015-12-21

    We develop and analyze an optimization-based method for the coupling of nonlocal and local diffusion problems with mixed volume constraints and boundary conditions. The approach formulates the coupling as a control problem where the states are the solutions of the nonlocal and local equations, the objective is to minimize their mismatch on the overlap of the nonlocal and local domains, and the controls are virtual volume constraints and boundary conditions. When some assumptions on the kernel functions hold, we prove that the resulting optimization problem is well-posed and discuss its implementation using Sandia’s agile software components toolkit. As a result,more » the latter provides the groundwork for the development of engineering analysis tools, while numerical results for nonlocal diffusion in three-dimensions illustrate key properties of the optimization-based coupling method.« less

  8. Hawking radiation from the Garfinkle-Horowitz-Strominger black hole, effective action, and covariant boundary condition

    SciTech Connect

    Gangopadhyay, Sunandan

    2008-03-15

    We exploit the expression for the anomalous (chiral) effective action to obtain the Hawking radiation from a Garfinkle-Horowitz-Strominger (stringy) black hole falling in the class of the most general spherically symmetric black holes ({radical}(-g){ne}1), using only covariant boundary conditions at the event horizon. The connection between the anomalous and the normal energy-momentum tensors is also established from the effective action approach.

  9. Open-ocean boundary conditions from interior data: Local and remote forcing of Massachusetts Bay

    USGS Publications Warehouse

    Bogden, P.S.; Malanotte-Rizzoli, P.; Signell, R.

    1996-01-01

    Massachusetts and Cape Cod Bays form a semienclosed coastal basin that opens onto the much larger Gulf of Maine. Subtidal circulation in the bay is driven by local winds and remotely driven flows from the gulf. The local-wind forced flow is estimated with a regional shallow water model driven by wind measurements. The model uses a gravity wave radiation condition along the open-ocean boundary. Results compare reasonably well with observed currents near the coast. In some offshore regions however, modeled flows are an order of magnitude less energetic than the data. Strong flows are observed even during periods of weak local wind forcing. Poor model-data comparisons are attributable, at least in part, to open-ocean boundary conditions that neglect the effects of remote forcing. Velocity measurements from within Massachusetts Bay are used to estimate the remotely forced component of the flow. The data are combined with shallow water dynamics in an inverse-model formulation that follows the theory of Bennett and McIntosh [1982], who considered tides. We extend their analysis to consider the subtidal response to transient forcing. The inverse model adjusts the a priori open-ocean boundary condition, thereby minimizing a combined measure of model-data misfit and boundary condition adjustment. A "consistency criterion" determines the optimal trade-off between the two. The criterion is based on a measure of plausibility for the inverse solution. The "consistent" inverse solution reproduces 56% of the average squared variation in the data. The local-wind-driven flow alone accounts for half of the model skill. The other half is attributable to remotely forced flows from the Gulf of Maine. The unexplained 44% comes from measurement errors and model errors that are not accounted for in the analysis. Copyright 1996 by the American Geophysical Union.

  10. Logarithmic interaction under periodic boundary conditions: closed form formulas for energy and forces

    NASA Astrophysics Data System (ADS)

    Tyagi, Sandeep

    A method is given to obtain closed form formulas for the energy and forces for an aggregate of charges interacting via a logarithmic interaction under periodic boundary conditions. The work done here is a generalization of Glasser's results [J. Math. Phys., 15, 188 (1974)] and is obtained with a different and simpler method than that by Stremler [J. Math. Phys., 45, 3584 (2004)]. The simplicity of the formulas derived here makes them extremely convenient in a computer simulation.

  11. Finite-size scaling and corrections in the Ising model with Brascamp-Kunz boundary conditions

    NASA Astrophysics Data System (ADS)

    Janke, W.; Kenna, R.

    2002-02-01

    The Ising model in two dimensions with the special boundary conditions of Brascamp and Kunz is analyzed. Leading and subdominant scaling behavior of the Fisher zeros are determined exactly. The exact finite-size scaling, with corrections, of the specific heat is determined both at critical and effective critical (pseudocritical) points. The shift exponents associated with the scaling of these effective critical points are not the same as the inverse correlation length critical exponent. All corrections to scaling are analytic.

  12. Radiative Squeezing Flow of Second Grade Fluid with Convective Boundary Conditions.

    PubMed

    Hayat, T; Jabeen, Sumaira; Shafiq, Anum; Alsaedi, A

    2016-01-01

    Influence of magnetohydrodynamic (MHD) flow between two parallel disks is considered. Heat transfer analysis is disclosed due to thermal radiation and convective boundary condition. Appropriate transformations are invoked to obtain the ordinary differential system. This system is solved using homotopic approach. Convergence of the obtained solution is discussed. Variations of embedded parameters into the governing problems are graphically discussed. Skin friction coefficient and Nusselt number are numerically computed and analyzed. It is noticed that temperature profile is increasing function of radiation parameter.

  13. Efficient finite element modeling of elastodynamic scattering with non-reflecting boundary conditions

    NASA Astrophysics Data System (ADS)

    Velichko, A.; Wilcox, P. D.

    2012-05-01

    An efficient technique for predicting the complete scattering behavior for an arbitrarily-shaped scatterer is presented. The spatial size of the modeling domain around the scatterer is as small as possible to minimize computational expense and a minimum number of models are executed. This model uses non-reflecting boundary conditions on the surface surrounding the scatterer which are non-local in space. Example results for 2D and 3D scattering in isotropic material and guided wave scattering are presented.

  14. Critical deflagration waves leading to detonation onset under different boundary conditions

    NASA Astrophysics Data System (ADS)

    Lin, Wei; Zhou, Jin; Fan, Xiao-Hua; Lin, Zhi-Yong

    2015-01-01

    High-speed turbulent critical deflagration waves before detonation onset in H2-air mixture propagated into a square cross section channel, which was assembled of optional rigid rough, rigid smooth, or flexible walls. The corresponding propagation characteristic and the influence of the wall boundaries on the propagation were investigated via high-speed shadowgraph and a high-frequency pressure sampling system. As a comprehensive supplement to the different walls effect investigation, the effect of porous absorbing walls on the detonation propagation was also investigated via smoke foils and the high-frequency pressure sampling system. Results are as follows. In the critical deflagration stage, the leading shock and the closely following turbulent flame front travel at a speed of nearly half the CJ detonation velocity. In the preheated zone, a zonary flame arises from the overlapping part of the boundary layer and the pressure waves, and then merges into the mainstream flame. Among these wall boundary conditions, the rigid rough wall plays a most positive role in the formation of the zonary flame and thus accelerates the transition of the deflagration to detonation (DDT), which is due to the boost of the boundary layer growth and the pressure wave reflection. Even though the flexible wall is not conducive to the pressure wave reflection, it brings out a faster boundary layer growth, which plays a more significant role in the zonary flame formation. Additionally, the porous absorbing wall absorbs the transverse wave and yields detonation decay and velocity deficit. After the absorbing wall, below some low initial pressure conditions, no re-initiation occurs and the deflagration propagates in critical deflagration for a relatively long distance. Project supported by the National Natural Science Foundation of China (Grant No. 51206182).

  15. [The Red Cross System for War Relief during the Second World War and Actual Conditions of Its Efforts in Burma].

    PubMed

    Kawahara, Yukari

    2015-12-01

    This paper aims to show the system for relief provided by the Japanese Red Cross relief units during the Second World War, as well as the actual activities of sixteen of its relief units dispatched to Burma. The Red Cross wartime relief efforts involved using personnel and funding prepared beforehand to provide aid to those injured in war, regardless of their status as ally or enemy. Thus they were able to receive support from the army in order to ensure safety and provide supplies. Nurses dispatched to Burma took care of many patients who suffered from malnutrition and physical injuries amidst the outbreak of infectious diseases typical of tropical areas, without sufficient replacement members. Base hospitals not meant for the front lines also came under attack, and the nurses' lives were thus in mortal danger. Of the 374 original members, 29 died or went missing in action.

  16. Barrier crossing with concentration boundary conditions in biological channels and chemical reactions

    NASA Astrophysics Data System (ADS)

    Barcilon, Victor; Chen, Duanpin; Eisenberg, Robert S.; Ratner, Mark A.

    1993-01-01

    Ions move into biological cells through pores in proteins called ionic channels, driven by gradients of potential and concentration imposed across the channel, impeded by potential barriers and friction within the pore. It is tempting to apply to channels the chemical theory of barrier crossing, but important issues must first be solved: Concentration boundary conditions must be used and flux must be predicted for applied potentials of all sizes and for barriers of all shapes, in particular, for low barriers. We use a macroscopic analysis to describe the flux as a convolution integral of a mathematically defined adjoint function, a Green's function. It so happens that the adjoint function also describes the first-passage time of a single particle moving between boundary conditions independent of concentration. The (experimentally observable) flux is computed from analytical formulas, from simulations of discrete random walks, and from simulations of the Langevin or reduced Langevin equations, with indistinguishable results. If the potential barrier has a single, large, parabolic peak, away from either boundary, an approximate expression reminiscent of Kramers' formula can be used to determine the flux. The fluxes predicted can be compared with measurements of current through single channels under a wide range of experimental conditions.

  17. Multiscale modelling as a tool to prescribe realistic boundary conditions for the study of surgical procedures.

    PubMed

    Laganà, K; Dubini, G; Migliavacca, F; Pietrabissa, R; Pennati, G; Veneziani, A; Quarteroni, A

    2002-01-01

    This work was motivated by the problems of analysing detailed 3D models of vascular districts with complex anatomy. It suggests an approach to prescribing realistic boundary conditions to use in order to obtain information on local as well as global haemodynamics. A method was developed which simultaneously solves Navier-Stokes equations for local information and a non-linear system of ordinary differential equations for global information. This is based on the principle that an anatomically detailed 3D model of a cardiovascular district can be achieved by using the finite element method. In turn the finite element method requires a specific boundary condition set. The approach outlined in this work is to include the system of ordinary differential equations in the boundary condition set. Such a multiscale approach was first applied to two controls: (i) a 3D model of a straight tube in a simple hydraulic network and (ii) a 3D model of a straight coronary vessel in a lumped-parameter model of the cardiovascular system. The results obtained are very close to the solutions available for the pipe geometry. This paper also presents preliminary results from the application of the methodology to a particular haemodynamic problem: namely the fluid dynamics of a systemic-to-pulmonary shunt in paediatric cardiac surgery.

  18. Applying Boundary Conditions Using a Time-Dependent Lagrangian for Modeling Laser-Plasma Interactions

    NASA Astrophysics Data System (ADS)

    Reyes, Jonathan; Shadwick, B. A.

    2016-10-01

    Modeling the evolution of a short, intense laser pulse propagating through an underdense plasma is of particular interest in the physics of laser-plasma interactions. Numerical models are typically created by first discretizing the equations of motion and then imposing boundary conditions. Using the variational principle of Chen and Sudan, we spatially discretize the Lagrangian density to obtain discrete equations of motion and a discrete energy conservation law which is exactly satisfied regardless of the spatial grid resolution. Modifying the derived equations of motion (e.g., enforcing boundary conditions) generally ruins energy conservation. However, time-dependent terms can be added to the Lagrangian which force the equations of motion to have the desired boundary conditions. Although some foresight is needed to choose these time-dependent terms, this approach provides a mechanism for energy to exit the closed system while allowing the conservation law to account for the loss. An appropriate time discretization scheme is selected based on stability analysis and resolution requirements. We present results using this variational approach in a co-moving coordinate system and compare such results to those using traditional second-order methods. This work was supported by the U. S. Department of Energy under Contract No. DE-SC0008382 and by the National Science Foundation under Contract No. PHY- 1104683.

  19. Boundary condition identification for a grid model by experimental and numerical dynamic analysis

    NASA Astrophysics Data System (ADS)

    Mao, Qiang; Devitis, John; Mazzotti, Matteo; Bartoli, Ivan; Moon, Franklin; Sjoblom, Kurt; Aktan, Emin

    2015-04-01

    There is a growing need to characterize unknown foundations and assess substructures in existing bridges. It is becoming an important issue for the serviceability and safety of bridges as well as for the possibility of partial reuse of existing infrastructures. Within this broader contest, this paper investigates the possibility of identifying, locating and quantifying changes of boundary conditions, by leveraging a simply supported grid structure with a composite deck. Multi-reference impact tests are operated for the grid model and modification of one supporting bearing is done by replacing a steel cylindrical roller with a roller of compliant material. Impact based modal analysis provide global modal parameters such as damped natural frequencies, mode shapes and flexibility matrix that are used as indicators of boundary condition changes. An updating process combining a hybrid optimization algorithm and the finite element software suit ABAQUS is presented in this paper. The updated ABAQUS model of the grid that simulates the supporting bearing with springs is used to detect and quantify the change of the boundary conditions.

  20. Perfectly Matched Layers versus discrete transparent boundary conditions in quantum device simulations

    SciTech Connect

    Mennemann, Jan-Frederik Jüngel, Ansgar

    2014-10-15

    Discrete transparent boundary conditions (DTBC) and the Perfectly Matched Layers (PML) method for the realization of open boundary conditions in quantum device simulations are compared, based on the stationary and time-dependent Schrödinger equation. The comparison includes scattering state, wave packet, and transient scattering state simulations in one and two space dimensions. The Schrödinger equation is discretized by a second-order Crank–Nicolson method in case of DTBC. For the discretization with PML, symmetric second-, fourth-, and sixth-order spatial approximations as well as Crank–Nicolson and classical Runge–Kutta time-integration methods are employed. In two space dimensions, a ring-shaped quantum waveguide device is simulated in the stationary and transient regime. As an application, a simulation of the Aharonov–Bohm effect in this device is performed, showing the excitation of bound states localized in the ring region. The numerical experiments show that the results obtained from PML are comparable to those obtained using DTBC, while keeping the high numerical efficiency and flexibility as well as the ease of implementation of the former method. -- Highlights: •In-depth comparison between discrete transparent boundary conditions (DTBC) and PML. •First 2-D transient scattering state simulations using DTBC. •First 2-D transient scattering state simulations of the Aharonov–Bohm effect.

  1. Variational multiscale enrichment method with mixed boundary conditions for elasto-viscoplastic problems

    NASA Astrophysics Data System (ADS)

    Zhang, Shuhai; Oskay, Caglar

    2015-04-01

    This manuscript presents the formulation and implementation of the variational multiscale enrichment (VME) method for the analysis of elasto-viscoplastic problems. VME is a global-local approach that allows accurate fine scale representation at small subdomains, where important physical phenomena are likely to occur. The response within far-fields is idealized using a coarse scale representation. The fine scale representation not only approximates the coarse grid residual, but also accounts for the material heterogeneity. A one-parameter family of mixed boundary conditions that range from Dirichlet to Neumann is employed to study the effect of the choice of the boundary conditions at the fine scale on accuracy. The inelastic material behavior is modeled using Perzyna type viscoplasticity coupled with flow stress evolution idealized by the Johnson-Cook model. Numerical verifications are performed to assess the performance of the proposed approach against the direct finite element simulations. The results of verification studies demonstrate that VME with proper boundary conditions accurately model the inelastic response accounting for material heterogeneity.

  2. Influence of seaward boundary condition on contaminant transport in unconfined coastal aquifers

    NASA Astrophysics Data System (ADS)

    Zhang, Q.; Volker, R. E.; Lockington, D. A.

    2001-06-01

    Contaminant transport in coastal aquifers is complicated partly due to the conditions at the seaward boundary including seawater intrusion and tidal variations of sea level. Their inclusion in modelling this system will be computationally expensive. Therefore, it will be instructive to investigate the consequence of simplifying the seaward boundary condition by neglecting the seawater density and tidal variations in numerical predictions of contaminant transport in this zone. This paper presents a comparison of numerical predictions for a simplified seaward boundary condition with experimental results for a corresponding realistic one including a saltwater interface and tidal variations. Different densities for contaminants are considered. The comparison suggests that the neglect of the seawater intrusion and tidal variations does not affect noticeably the overall migration rate of the plume before it reaches the saltwater interface. However, numerical prediction shows that a more dense contaminant travels further seaward and part of the solute mass exits under the sea if the seawater density is not included. This is not consistent with the experimental result, which shows that the contaminant travels upwards to the shoreline along the saltwater interface. Neglect of seawater density, therefore, will result in an underestimation of the exit rate of solute mass around the coastline and fictitious migration paths under the seabed. For a less dense contaminant, neglect of seawater density has little effect on numerical prediction of migration paths.

  3. Investigating TIME-GCM Atmospheric Tides for Different Lower Boundary Conditions

    NASA Astrophysics Data System (ADS)

    Haeusler, K.; Hagan, M. E.; Lu, G.; Forbes, J. M.; Zhang, X.; Doornbos, E.

    2013-12-01

    It has been recently established that atmospheric tides generated in the lower atmosphere significantly influence the geospace environment. In order to extend our knowledge of the various coupling mechanisms between the different atmospheric layers, we rely on model simulations. Currently there exist two versions of the Global Scale Wave Model (GSWM), i.e. GSWM02 and GSWM09, which are used as a lower boundary (ca. 30 km) condition for the Thermosphere-Ionosphere-Mesosphere-Electrodynamics General Circulation Model (TIME-GCM) and account for the upward propagating atmospheric tides that are generated in the troposphere and lower stratosphere. In this paper we explore the various TIME-GCM upper atmospheric tidal responses for different lower boundary conditions and compare the model diagnostics with tidal results from satellite missions such as TIMED, CHAMP, and GOCE. We also quantify the differences between results associated with GSWM02 and GSWM09 forcing and results of TIMEGCM simulations using Modern-Era Retrospective Analysis for Research and Application (MERRA) data as a lower boundary condition.

  4. Boundary conditions, dimensionality, topology and size dependence of the superconducting transition temperature

    NASA Astrophysics Data System (ADS)

    Fink, Herman J.; Haley, Stephen B.; Giuraniuc, Claudiu V.; Kozhevnikov, Vladimir F.; Indekeu, Joseph O.

    2005-11-01

    For various sample geometries (slabs, cylinders, spheres, hypercubes), de Gennes' boundary condition parameter b is used to study its effect upon the transition temperature Tc of a superconductor. For b > 0 the order parameter at the surface is decreased, and as a consequence Tc is reduced, while for b < 0 the order parameter at the surface is increased, thereby enhancing Tc of a specimen in zero magnetic field. Exact solutions, derived by Fink and Haley (Int. J. mod. Phys. B, 17, 2171 (2003)), of the order parameter of a slab of finite thickness as a function of temperature are presented, both for reduced and enhanced transition (nucleation) temperatures. At the nucleation temperature the order parameter approaches zero. This concise review closes with a link established between de Gennes' microscopic boundary condition and the Ginzburg-Landau phenomenological approach, and a discussion of some relevant experiments. For example, applying the boundary condition with b < 0 to tin whiskers elucidates the increase of Tc with strain.

  5. Rapid evaluation of mechanical boundary conditions using impedance based structural health monitoring

    NASA Astrophysics Data System (ADS)

    Kettle, Ryan A.; Anton, Steven R.

    2016-04-01

    Conventionally, structural health monitoring (SHM) has been primarily concerned with sensing, identifying, locating, and determining the severity of damage present in a structure that is in a static state. Instead, this study will investigate adapting the impedance SHM method to rapidly evaluate a mechanical system during a dynamic event. Also in contrast to conventional SHM, the objective is not to detect damage but instead to detect changes in the boundary conditions as they occur during a dynamic event. Rapid detection of changes in boundary conditions in highly dynamic environments has the potential to be used in a wide variety of applications, including the aerospace, civil, and mining industries. A key feature of this work will be the use of frequency ranges higher than what is typically used for SHM impedance measurements, in the range of several MHz. Using such high frequencies will allow for faster measurements of impedance, thus enabling the capture of variations in boundary conditions as they change during a dynamic event. An existing analytical model from the literature for electromechanical impedance based SHM will be utilized for this study.

  6. Constraint-preserving boundary conditions in the 3+1 first-order approach

    SciTech Connect

    Bona, C.; Bona-Casas, C.

    2010-09-15

    A set of energy-momentum constraint-preserving boundary conditions is proposed for the first-order Z4 case. The stability of a simple numerical implementation is tested in the linear regime (robust stability test), both with the standard corner and vertex treatment and with a modified finite-differences stencil for boundary points which avoids corners and vertices even in Cartesian-like grids. Moreover, the proposed boundary conditions are tested in a strong-field scenario, the Gowdy waves metric, showing the expected rate of convergence. The accumulated amount of energy-momentum constraint violations is similar or even smaller than the one generated by either periodic or reflection conditions, which are exact in the Gowdy waves case. As a side theoretical result, a new symmetrizer is explicitly given, which extends the parametric domain of symmetric hyperbolicity for the Z4 formalism. The application of these results to first-order Baumgarte-Shapiro-Shibata-Nakamura-like formalisms is also considered.

  7. A boundary condition to the Khokhlov-Zabolotskaya equation for modeling strongly focused nonlinear ultrasound fields

    SciTech Connect

    Rosnitskiy, P. Yuldashev, P. Khokhlova, V.

    2015-10-28

    An equivalent source model was proposed as a boundary condition to the nonlinear parabolic Khokhlov-Zabolotskaya (KZ) equation to simulate high intensity focused ultrasound (HIFU) fields generated by medical ultrasound transducers with the shape of a spherical shell. The boundary condition was set in the initial plane; the aperture, the focal distance, and the initial pressure of the source were chosen based on the best match of the axial pressure amplitude and phase distributions in the Rayleigh integral analytic solution for a spherical transducer and the linear parabolic approximation solution for the equivalent source. Analytic expressions for the equivalent source parameters were derived. It was shown that the proposed approach allowed us to transfer the boundary condition from the spherical surface to the plane and to achieve a very good match between the linear field solutions of the parabolic and full diffraction models even for highly focused sources with F-number less than unity. The proposed method can be further used to expand the capabilities of the KZ nonlinear parabolic equation for efficient modeling of HIFU fields generated by strongly focused sources.

  8. Boundary conditions, semigroups, quantum jumps, and the quantum arrow of time

    NASA Astrophysics Data System (ADS)

    Bohm, Arno

    2015-04-01

    Experiments on quantum systems are usually divided into preparation of states and the registration of observables. Using the traditional mathematical methods (the Hilbert space and Schwartz space of distribution theory), it is not possible to distinguish mathematically between observables and states. The Hilbert space as well as Schwartz space boundary conditions for the dynamical equations lead by mathematic theorems (Stone-von Neumann) to unitary group with —∞ < t < ∞. But in the experimental set-up, one clearly distinguishes between the preparation of a state and the registration of an observable in that state. Furthermore, a state must be prepared first before an observable can be measured in this state (causality). This suggests time asymmetric boundary conditions for the dynamical equations of quantum theory. Such boundary conditions have been provided by Hardy space in the Lax-Phillips theory for electromagnetic and acoustic scattering phenomena. The Paley-Wiener theorem for Hardy space then leads to semi-group and time asymmetry in quantum physics. It introduces a finite “beginning of time” t0 for a time asymmetric quantum theory, which have been observed as an ensemble of finite times t(i)0, the onset times of dark periods in the quantum jump experiments on a single ion.

  9. The wave equation with Wentzell-Robin boundary conditions on L-spaces

    NASA Astrophysics Data System (ADS)

    Keyantuo, Valentin; Warma, Mahamadi

    Let a∈W(0,1), a(x)⩾δ>0, b,c∈L(0,1) and consider the differential operator A formally given by Au=au+bu+cu. We prove in the first part that a realization of A with Wentzell-Robin boundary conditions on L(0,1)×C generates a cosine function for p∈[1,∞). In particular, we obtain that this realization of A generates a holomorphic C-semigroup of angle π/2 on the space L(0,1)×C. This solves an open problem by A. Favini, G.R. Goldstein, J.A. Goldstein, S. Romanelli and W. Arendt. Of crucial importance is the formulation of the boundary conditions. We show in the second part that if Ω:=(0, N⩾1, is the cube in R, then the Laplacian with pure Wentzell boundary conditions generates an α-times integrated cosine function on C(Ω¯) for any α⩾(N-1)/2.

  10. Buckling Analysis of Anti-Symmetric Cross-Ply Laminated Composite Plates Under Different Boundary Conditions

    NASA Astrophysics Data System (ADS)

    Adim, B.; Daouadji, T. Hassaine; Abbes, B.

    2016-11-01

    The buckling analysis of anti-symmetric cross-ply laminated composite plates under different boundary conditions is examined by using a refined higher order exponential shear deformation theory. The theory, which has strong similarity with classical plate theory in many aspects, accounts for a quadratic variation of the transverse shear strains across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. The number of independent unknowns in the present theory is four, as against five in other shear deformation theories. In this investigation, the equations of motion for simply supported thick laminated rectangular plates are derived and obtained through the use of Hamilton's principle. The closed-form solutions of anti-symmetric cross-ply and angle-ply laminates are obtained using Navier solution. Numerical results for critical buckling loads anti-symmetric cross-ply laminated composite plates are presented. The validity of the present study is demonstrated by comparison with other higher-order solutions reported in the literature. It can be concluded that the proposed theory is accurate and simple in solving the buckling behaviors of anti-symmetric cross-ply laminated composite plates under different boundary conditions

  11. Influence of seaward boundary condition on contaminant transport in unconfined coastal aquifers.

    PubMed

    Zhang, Q; Volker, R E; Lockington, D A

    2001-06-01

    Contaminant transport in coastal aquifers is complicated partly due to the conditions at the seaward boundary including seawater intrusion and tidal variations of sea level. Their inclusion in modelling this system will be computationally expensive. Therefore, it will be instructive to investigate the consequence of simplifying the seaward boundary condition by neglecting the seawater density and tidal variations in numerical predictions of contaminant transport in this zone. This paper presents a comparison of numerical predictions for a simplified seaward boundary condition with experimental results for a corresponding realistic one including a saltwater interface and tidal variations. Different densities for contaminants are considered. The comparison suggests that the neglect of the seawater intrusion and tidal variations does not affect noticeably the overall migration rate of the plume before it reaches the saltwater interface. However, numerical prediction shows that a more dense contaminant travels further seaward and part of the solute mass exits under the sea if the seawater density is not included. This is not consistent with the experimental result, which shows that the contaminant travels upwards to the shoreline along the saltwater interface. Neglect of seawater density, therefore, will result in an underestimation of the exit rate of solute mass around the coastline and fictitious migration paths under the seabed. For a less dense contaminant, neglect of seawater density has little effect on numerical prediction of migration paths.

  12. Optimisation methods for bathymetry and open boundary conditions in finite element model of ocean tides

    SciTech Connect

    Lyard, F.; Genco, M.L.

    1994-10-01

    A bidimensional, spectral in time, quasi-linearised hydrodynamic ocean tide model has been developed at the Institut de Mecanique de Grenoble. This model is derived from the classical shallow water equations by removing the velocity unknowns in the continuity equation, that leads to an elliptic, second-order differential equation where tide denivellation remains the only unknown quantity. The problem is solved in its variational formulation and the finite elements method is used to discretise the equations in the spatial domain with a Lagrange-P2 approximation. Bottom topography has to be known at the integration points of the elements. In the case of the large oceanic basins, a specific method, called the bathymetry optimisation method, is needed to correctly take into account the bottom topography inside the model. The accuracy of the model`s solutions is also strongly dependent on the quality of the open boundary conditions because of the elliptic characteristics of the problem. The optimisation method for open boundary conditions relies on the use of the in situ data available in the modelled domain. The aim of this paper is to present the basis of these optimisations of bathymetry and open boundary conditions. An illustration of the related improvements is presented on the North Atlantic Basin. 36 refs., 10 figs., 5 tabs.

  13. Implementation of Shifted Periodic Boundary Conditions in the Large-Scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) Software

    DTIC Science & Technology

    2015-08-01

    Atomic /Molecular Massively Parallel Simulator (LAMMPS) Software by N Scott Weingarten and James P Larentzos Approved for...0687 ● AUG 2015 US Army Research Laboratory Implementation of Shifted Periodic Boundary Conditions in the Large-Scale Atomic /Molecular...Shifted Periodic Boundary Conditions in the Large-Scale Atomic /Molecular Massively Parallel Simulator (LAMMPS) Software 5a. CONTRACT NUMBER 5b

  14. No-slip boundary conditions and forced flow in multiparticle collision dynamics.

    PubMed

    Bolintineanu, Dan S; Lechman, Jeremy B; Plimpton, Steven J; Grest, Gary S

    2012-12-01

    Multiparticle collision dynamics (MPCD) is a particle-based fluid simulation technique that is becoming increasingly popular for mesoscale fluid modeling. However, some confusion and conflicting results persist in literature regarding several important methodological details, in particular the enforcement of the no-slip condition and thermostatting in forced flow. These issues persist in simple flows past stationary boundaries, which we exclusively focus on here. We discuss the parametrization of MPCD fluids and its consequences for fluid-solid boundaries in great detail, and show that the method of virtual particles proposed by Lamura et al. and adopted by many others is required only for parameter choices that lead to viscosities dominated by collisional contributions. We test several implementations of the virtual particle method and discuss how to completely eliminate slip at stationary boundaries. We also show that stochastic boundary reflection rules are inherently problematic for forced flow and suggest a possible remedy. Finally, we discuss the most robust way to achieve forced flow and evaluate several thermostatting methods in the process. All discussion is limited to solid objects that do not move as a result of collisions with MPCD particles (i.e., walls). However, the results can be extended to solutes that experience forces and torques due to interactions with MPCD particles (e.g., colloids). The detailed analysis presented for this simple case provides the level of rigor and accuracy to the MPCD method required for the study of more complex systems.

  15. Simulation of Couette flow using conventional Burnett equations with modified slip boundary conditions

    NASA Astrophysics Data System (ADS)

    Liu, Hualin; Zhao, Wenwen; Chen, Weifang

    2016-11-01

    Gas or liquid flow through small channels has become more and more popular due to the micro-electro-mechanical systems (MEMS) fabrication technologies such as micro-motors, electrostatic comb-drive, micro-chromatographs, micro-actuators, micro-turbines and micro-pumps, etc. The flow conditions in and around these systems are always recognized as typical transitional regimes. Under these conditions, the mean free path of gas molecules approaches the characteristic scale of the micro-devices itself, and due to the little collisions the heat and momentum cannot equilibrate between the wall and fluids quickly. Couette flow is a simple and critical model in fluid dynamics which focuses on the mechanism of the heat transfer in shear-driven micro-cavities or micro-channels. Despite numerous work on the numerical solutions of the Couette flow, how to propose stable and accurate slip boundary conditions in rarefied flow conditions still remains to be elucidated. In this paper, converged solutions for steady-state micro Couette flows are obtained by using conventional Burnett equations with a set of modified slip boundary conditions. Instead of using the physical variables at the wall, the modified slip conditions use the variables at the edge of the Knudsen layer based on a physically plausible assumption in literature that Knudsen layer has a thickness only in the order of a mean free path and molecules are likely to travel without collision in this layer. Numerical results for non-dimensional wall shear stress and heat flux are compared with those of the DSMC solutions. Although there are not much improvement in the accuracy by using this modified slip conditions, the modified conditions perform much better than the unmodified slip conditions for numerical stabilization. All results show that the set of conventional Burnett equations with second order modified conditions are proved to be an appropriate model for the micro-Couette flows.

  16. Transient spatio-temporal dynamics of a diffusive plant-herbivore system with Neumann boundary conditions.

    PubMed

    Yu, Fang; Wang, Lin; Watmough, James

    2016-12-01

    In many existing predator-prey or plant-herbivore models, the numerical response is assumed to be proportional to the functional response. In this paper, without such an assumption, we consider a diffusive plant-herbivore system with Neumann boundary conditions. Besides stability of spatially homogeneous steady states, we also derive conditions for the occurrence of Hopf bifurcation and steady-state bifurcation and provide geometrical methods to locate the bifurcation values. We numerically explore the complex transient spatio-temporal behaviours induced by these bifurcations. A large variety of different types of transient behaviours including oscillations in one or both of space and time are observed.

  17. Boundary conditioning of capacitive MEMS devices through fabrication methods and operating environments

    NASA Astrophysics Data System (ADS)

    Muthukumaran, Packirisamy; Stiharu, Ion G.; Bhat, Rama B.

    2003-10-01

    This paper presents and applies the concept of micro-boundary conditioning to the design synthesis of microsystems in order to quantify the influence of inherent limitations of the fabrication process and the operating conditions on both static and dynamic behavior of microsystems. The predicted results on the static and dynamic behavior of a capacitive MEMS device, fabricated through MUMPs process, under the influence of the fabrication limitation and operating environment are presented along with the test results. The comparison between the predicted and experimental results shows a good agreement.

  18. Boundary conditions for probability density function transport equations in fluid mechanics.

    PubMed

    Valiño, Luis; Hierro, Juan

    2003-04-01

    The behavior of the probability density function (PDF) transport equation at the limits of the probability space is studied from the point of view of fluid mechanics. Different boundary conditions are considered depending on the nature of the variable considered (velocity, scalar, and position). A study of the implications of entrance and exit conditions is performed, showing that a new term should be added to the PDF transport equation to preserve normalization in some nonstationary processes. In practice, this term is taken into account naturally in particle methods. Finally, the existence of discontinuities at the limits is also investigated.

  19. Inverse scattering transform for the focusing nonlinear Schrödinger equation with nonzero boundary conditions

    SciTech Connect

    Biondini, Gino; Kovačič, Gregor

    2014-03-15

    The inverse scattering transform for the focusing nonlinear Schrödinger equation with non-zero boundary conditions at infinity is presented, including the determination of the analyticity of the scattering eigenfunctions, the introduction of the appropriate Riemann surface and uniformization variable, the symmetries, discrete spectrum, asymptotics, trace formulae and the so-called theta condition, and the formulation of the inverse problem in terms of a Riemann-Hilbert problem. In addition, the general behavior of the soliton solutions is discussed, as well as the reductions to all special cases previously discussed in the literature.

  20. Boundary and Interface Conditions for High Order Finite Difference Methods Applied to the Euler and Navier-Strokes Equations

    NASA Technical Reports Server (NTRS)

    Nordstrom, Jan; Carpenter, Mark H.

    1998-01-01

    Boundary and interface conditions for high order finite difference methods applied to the constant coefficient Euler and Navier-Stokes equations are derived. The boundary conditions lead to strict and strong stability. The interface conditions are stable and conservative even if the finite difference operators and mesh sizes vary from domain to domain. Numerical experiments show that the new conditions also lead to good results for the corresponding nonlinear problems.

  1. Exact finite-size corrections for the square-lattice Ising model with Brascamp-Kunz boundary conditions

    NASA Astrophysics Data System (ADS)

    Izmailian, N. Sh.; Oganesyan, K. B.; Hu, Chin-Kun

    2002-05-01

    Finite-size scaling, finite-size corrections, and boundary effects for critical systems have attracted much attention in recent years. Here we derive exact finite-size corrections for the free energy F and the specific heat C of the critical ferromagnetic Ising model on the M×2N square lattice with Brascamp-Kunz (BK) boundary conditions [J. Math. Phys. 15, 66 (1974)] and compare such results with those under toroidal boundary conditions. When the ratio ξ/2=(M+1)/2N is smaller than 1 the behaviors of finite-size corrections for C are quite different for BK and toroidal boundary conditions; when ln(ξ/2) is larger than 3, finite-size corrections for C in two boundary conditions approach the same values. In the limit N-->∞ we obtain the expansion of the free energy for infinitely long strip with BK boundary conditions. Our results are consistent with the conformal field theory prediction for the mixed boundary conditions by Cardy [Nucl. Phys. B 275, 200 (1986)] although the definitions of boundary conditions in two cases are different in one side of the long strip.

  2. Influence of boundary conditions on the solution of a hyperbolic thermoelasticity problem

    NASA Astrophysics Data System (ADS)

    Vitokhin, Evgeniy Yu.; Babenkov, Mikhail B.

    2017-03-01

    We consider a series of problems with a short laser impact on a thin metal layer accounting various boundary conditions of the first and second kind. The behavior of the material is modeled by the hyperbolic thermoelasticity of Lord-Shulman type. We obtain analytical solutions of the problems in the semi-coupled formulation and numerical solutions in the coupled formulation. Numerical solutions are compared with the analytical ones. The analytical solutions of the semi-coupled problems and numerical solutions of the coupled problems show qualitative match. The solutions of hyperbolic thermoelasticity problems are compared with those obtained in the frame of the classical thermoelasticity. It was determined that the most prominent difference between the classical and hyperbolic solutions arises in the problem with fixed boundaries and constant temperature on them. The smallest differences were observed in the problem with unconstrained, thermally insulated edges. It was shown that a cooling zone is observed if the boundary conditions of the first kind are given for the temperature. Analytical expressions for the velocities of the quasiacoustic and quasithermal fronts as well as the critical value for the attenuation coefficient of the excitation impulse are verified numerically.

  3. Boundary conditions for the solution of the three-dimensional Poisson equation in open metallic enclosures

    SciTech Connect

    Biswas, Debabrata; Singh, Gaurav; Kumar, Raghwendra

    2015-09-15

    Numerical solution of the Poisson equation in metallic enclosures, open at one or more ends, is important in many practical situations, such as high power microwave or photo-cathode devices. It requires imposition of a suitable boundary condition at the open end. In this paper, methods for solving the Poisson equation are investigated for various charge densities and aspect ratios of the open ends. It is found that a mixture of second order and third order local asymptotic boundary conditions is best suited for large aspect ratios, while a proposed non-local matching method, based on the solution of the Laplace equation, scores well when the aspect ratio is near unity for all charge density variations, including ones where the centre of charge is close to an open end or the charge density is non-localized. The two methods complement each other and can be used in electrostatic calculations where the computational domain needs to be terminated at the open boundaries of the metallic enclosure.

  4. Preconditioned characteristic boundary conditions for solution of the preconditioned Euler equations at low Mach number flows

    NASA Astrophysics Data System (ADS)

    Hejranfar, Kazem; Kamali-Moghadam, Ramin

    2012-06-01

    Preconditioned characteristic boundary conditions (BCs) are implemented at artificial boundaries for the solution of the two- and three-dimensional preconditioned Euler equations at low Mach number flows. The preconditioned compatibility equations and the corresponding characteristic variables (or the Riemann invariants) based on the characteristic forms of preconditioned Euler equations are mathematically derived for three preconditioners proposed by Eriksson, Choi and Merkle, and Turkel. A cell-centered finite volume Roe's method is used for the discretization of the preconditioned system of equations on unstructured meshes. The accuracy and performance of the preconditioned characteristic BCs applied at artificial boundaries are evaluated in comparison with the non-preconditioned characteristic BCs and the simplified BCs in computing steady low Mach number flows. The two-dimensional flow over the NACA0012 airfoil and three-dimensional flow over the hemispherical headform are computed and the results are obtained for different conditions and compared with the available numerical and experimental data. The sensitivity of the solution to the size of computational domain and the variation of the angle of attack for each type of BCs is also examined. Indications are that the preconditioned characteristic BCs implemented in the preconditioned system of Euler equations greatly enhance the convergence rate of the solution of low Mach number flows compared to the other two types of BCs.

  5. Blow-up problems for the heat equation with a local nonlinear Neumann boundary condition

    NASA Astrophysics Data System (ADS)

    Yang, Xin; Zhou, Zhengfang

    2016-09-01

    This paper estimates the blow-up time for the heat equation ut = Δu with a local nonlinear Neumann boundary condition: The normal derivative ∂ u / ∂ n =uq on Γ1, one piece of the boundary, while on the rest part of the boundary, ∂ u / ∂ n = 0. The motivation of the study is the partial damage to the insulation on the surface of space shuttles caused by high speed flying subjects. We show the finite time blow-up of the solution and estimate both upper and lower bounds of the blow-up time in terms of the area of Γ1. In many other work, they need the convexity of the domain Ω and only consider the problem with Γ1 = ∂ Ω. In this paper, we remove the convexity condition and only require ∂Ω to be C2. In addition, we deal with the local nonlinearity, namely Γ1 can be just part of ∂Ω.

  6. Derivation of matrix product states for the Heisenberg spin chain with open boundary conditions

    NASA Astrophysics Data System (ADS)

    Mei, Zhongtao; Bolech, C. J.

    2017-03-01

    Using the algebraic Bethe Ansatz, we derive a matrix product representation of the exact Bethe-Ansatz states of the six-vertex Heisenberg chain (either X X X or X X Z and spin-1/2 ) with open boundary conditions. In this representation, the components of the Bethe eigenstates are expressed as traces of products of matrices that act on a tensor product of auxiliary spaces. As compared to the matrix product states of the same Heisenberg chain but with periodic boundary conditions, the dimension of the exact auxiliary matrices is enlarged as if the conserved number of spin-flips considered would have been doubled. This result is generic for any non-nested integrable model, as is clear from our derivation, and we further show this by providing an additional example of the same matrix product state construction for a well-known model of a gas of interacting bosons. Counterintuitively, the matrices do not depend on the spatial coordinate despite the open boundaries, and thus they suggest generic ways of exploiting (emergent) translational invariance both for finite size and in the thermodynamic limit.

  7. The impedance problem of wave diffraction by a strip with higher order boundary conditions

    NASA Astrophysics Data System (ADS)

    Castro, L. P.; Simões, A. M.

    2013-10-01

    This work is devoted to analyse an impedance boundary-transmission problem for the Helmholtz equation originated by a problem of wave diffraction by an infinite strip with higher order imperfect boundary conditions. A constructive approach of operator relations is built, which allows a transparent interpretation of the problem in an operator theory framework. In particular, different types of operator relations are exhibited for different types of operators acting between Lebesgue and Sobolev spaces on a finite interval and the positive half-line. All this has consequences in the understanding of the structure of this type of problems. In particular, a Fredholm characterization of the problem is obtained in terms of the initial space order parameters. At the request of the author and the Proceedings Editor the above article has been replaced with a corrected version. The original PDF file supplied to AIP Publishing contained an error in the title of the article. The original title appeared as: "The Impedance Problem of Wave Diffraction by a trip with Higher Order Boundary Conditions." This article has been replaced and the title now appears correctly online. The corrected article was published on 8 November 2013.

  8. The impedance problem of wave diffraction by a strip with higher order boundary conditions

    SciTech Connect

    Castro, L. P.; Simões, A. M.

    2013-10-17

    This work is devoted to analyse an impedance boundary-transmission problem for the Helmholtz equation originated by a problem of wave diffraction by an infinite strip with higher order imperfect boundary conditions. A constructive approach of operator relations is built, which allows a transparent interpretation of the problem in an operator theory framework. In particular, different types of operator relations are exhibited for different types of operators acting between Lebesgue and Sobolev spaces on a finite interval and the positive half-line. All this has consequences in the understanding of the structure of this type of problems. In particular, a Fredholm characterization of the problem is obtained in terms of the initial space order parameters. At the request of the author and the Proceedings Editor the above article has been replaced with a corrected version. The original PDF file supplied to AIP Publishing contained an error in the title of the article. The original title appeared as: 'The Impedance Problem of Wave Diffraction by a trip with Higher Order Boundary Conditions.' This article has been replaced and the title now appears correctly online. The corrected article was published on 8 November 2013.

  9. Gibbons-Hawking boundary terms and junction conditions for higher-order brane gravity models

    SciTech Connect

    Balcerzak, Adam; Dabrowski, Mariusz P. E-mail: mpdabfz@wmf.univ.szczecin.pl

    2009-01-15

    We derive the most general junction conditions for the fourth-order brane gravity constructed of arbitrary functions of curvature invariants. We reduce these fourth-order theories to second order theories at the expense of introducing new scalar and tensor fields - the scalaron and the tensoron. In order to obtain junction conditions we apply the method of generalized Gibbons-Hawking boundary terms which are appended to the appropriate actions. After assuming the continuity of the scalaron and the tensoron on the brane, we recover junction conditions for such general brane universe models previously obtained by different methods. The derived junction conditions can serve studying the cosmological implications of the higher-order brane gravity models.

  10. Effect of Inflow Boundary Conditions on Hovering Tilt-Rotor Flows

    NASA Technical Reports Server (NTRS)

    Kaul, Upender K.

    2012-01-01

    A study on the effect of inflow turbulence boundary conditions on the local flow on and around a body in flight has been carried out. The study has been carried out using OVERFLOW2 flow solver using the default Spalart-Allmaras turbulence model in OVERFLOW. Many OVERFLOW turbulent flow simulations have been reported using the SA-fv3 model1 over the years. The present study demonstrates that the turbulence levels imposed as a boundary condition (b.c.) in the far-field as implemented in OVERFLOW are not correct. In fact, very low level of turbulence at the far-field boundary as implemented in OVERFLOW results in the SA-fv3 model predicting transition-like profiles on a given body. By choosing sufficiently high levels of the Reynolds number of turbulence, Rt, as a boundary condition, this anomalous behavior of SA-fv3 model is eliminated. Since numerous papers using OVERFLOW have been presented in the literature including that by the author2 using low level of inflow turbulence, it will be beneficial to the CFD community at large and in particular to the OVERFLOW community to understand this effect of the inflow b.c. in the SA-fv3 model. Various results reported over the years in domains such as high-lift applications, drag prediction applications and rotorcraft flow applications can be revisited using the new turbulence inflow boundary condition prescription as suggested in this study. It has been demonstrated in the literature that the effect of inflow turbulence level on the downstream development of flow is too important to be ignored. Demonstrative results are shown and compared with experiment for the case of hovering XV-15 rotor flow at a tip Reynolds number of 4.9 x 10(exp 6) and Mach number of 0.69 in Figs. 1 and 2 below. Fig. 1(a,b) shows skin friction predictions at radial station of r/R = 0.28 corresponding to 5 different inflow boundary conditions obtained with the SA-fv3 model. As the inflow turbulence is increased monotonically, from a value of Rt = 0

  11. Finite size effects in ferroelectric-semiconductor thin films under open-circuit electric boundary conditions

    SciTech Connect

    Eliseev, Eugene A.; Kalinin, Sergei V.; Morozovska, Anna N.

    2015-01-21

    General features of finite size effects in the ferroelectric-semiconductor film under open-circuit electric boundary conditions are analyzed using Landau-Ginzburg-Devonshire theory and continuum media electrostatics. The temperature dependence of the film critical thickness, spontaneous polarization and depolarization field profiles of the open-circuited films are found to be significantly different from the characteristics of short-circuited ones. In particular, we predict the re-entrant type transition boundary between the mono-domain and poly-domain ferroelectric states due to reduced internal screening efficiency and analyzed possible experimental scenarios created by this mechanism. Performed analysis is relevant for the quantitative description of free-standing ferroelectric films phase diagrams and polar properties. Also our results can be useful for the explanation of the scanning-probe microscopy experiments on free ferroelectric surfaces.

  12. Strong influence of periodic boundary conditions on lateral diffusion in lipid bilayer membranes

    NASA Astrophysics Data System (ADS)

    Camley, Brian A.; Lerner, Michael G.; Pastor, Richard W.; Brown, Frank L. H.

    2015-12-01

    The Saffman-Delbrück hydrodynamic model for lipid-bilayer membranes is modified to account for the periodic boundary conditions commonly imposed in molecular simulations. Predicted lateral diffusion coefficients for membrane-embedded solid bodies are sensitive to box shape and converge slowly to the limit of infinite box size, raising serious doubts for the prospects of using detailed simulations to accurately predict membrane-protein diffusivities and related transport properties. Estimates for the relative error associated with periodic boundary artifacts are 50% and higher for fully atomistic models in currently feasible simulation boxes. MARTINI simulations of LacY membrane protein diffusion and LacY dimer diffusion in DPPC membranes and lipid diffusion in pure DPPC bilayers support the underlying hydrodynamic model.

  13. Strong influence of periodic boundary conditions on lateral diffusion in lipid bilayer membranes

    SciTech Connect

    Camley, Brian A.; Lerner, Michael G.; Pastor, Richard W.; Brown, Frank L. H.

    2015-12-28

    The Saffman-Delbrück hydrodynamic model for lipid-bilayer membranes is modified to account for the periodic boundary conditions commonly imposed in molecular simulations. Predicted lateral diffusion coefficients for membrane-embedded solid bodies are sensitive to box shape and converge slowly to the limit of infinite box size, raising serious doubts for the prospects of using detailed simulations to accurately predict membrane-protein diffusivities and related transport properties. Estimates for the relative error associated with periodic boundary artifacts are 50% and higher for fully atomistic models in currently feasible simulation boxes. MARTINI simulations of LacY membrane protein diffusion and LacY dimer diffusion in DPPC membranes and lipid diffusion in pure DPPC bilayers support the underlying hydrodynamic model.

  14. Universal Dependence of the Mean Square Displacement in Equilibrium Point Vortex Systems without Boundary Conditions

    NASA Astrophysics Data System (ADS)

    Yoshida, Takeshi

    2009-02-01

    The diffusion processes of point vortex systems with no boundary are studied numerically and analytically. The mean square displacements in the radial direction are observed in equilibrium states corresponding to several parameters. It is shown that point vortex systems display an anomalous diffusion and that the mean square displacements exhibit a universal time dependence. The exponent of this time dependence corresponds to the results with circular boundary conditions reported by Kawahara and Nakanishi. On the other hand, the mean square displacement is dependent on system energy exponentially. The energy dependence of the mean square displacement is explained by the rough scaling theory. The probability distribution functions of the velocity field are also investigated numerically, and the results reinforce the theory of the dependence on system energy.

  15. Multi-component Cahn-Hilliard system with different boundary conditions in complex domains

    NASA Astrophysics Data System (ADS)

    Li, Yibao; Choi, Jung-Il; Kim, Junseok

    2016-10-01

    We propose an efficient phase-field model for multi-component Cahn-Hilliard (CH) systems in complex domains. The original multi-component Cahn-Hilliard system with a fixed phase is modified in order to make it suitable for complex domains in the Cartesian grid, along with contact angle or no mass flow boundary conditions on the complex boundaries. The proposed method uses a practically unconditionally gradient stable nonlinear splitting numerical scheme. Further, a nonlinear full approximation storage multigrid algorithm is used for solving semi-implicit formulations of the multi-component CH system, incorporated with an adaptive mesh refinement technique. The robustness of the proposed method is validated through various numerical simulations including multi-phase separations via spinodal decomposition, equilibrium contact angle problems, and multi-phase flows with a background velocity field in complex domains.

  16. Influence of boundary conditions and confinement on nonlocal effects in flows of wormlike micellar systems.

    PubMed

    Masselon, Chloé; Colin, Annie; Olmsted, Peter D

    2010-02-01

    In this paper we report on the influence of different geometric and boundary constraints on nonlocal (spatially inhomogeneous) effects in wormlike micellar systems. In a previous paper, nonlocal effects were observable by measuring the local rheological flow curves of micelles flowing in a microchannel under different pressure drops, which appeared to differ from the flow curve measured using conventional rheometry. Here we show that both the confinement and the boundary conditions can influence those nonlocal effects. The role of the nature of the surface is analyzed in detail using a simple scalar model that incorporates inhomogeneities, which captures the flow behavior in both wide and confined geometries. This leads to an estimate for the nonlocal "diffusion" coefficient (i.e., the shear curvature viscosity) which corresponds to a characteristic length from 1 to 10 microm.

  17. Finite size effects in ferroelectric-semiconductor thin films under open-circuit electric boundary conditions

    DOE PAGES

    Eliseev, Eugene A.; Kalinin, Sergei V.; Morozovska, Anna N.

    2015-01-21

    General features of finite size effects in the ferroelectric-semiconductor film under open-circuit electric boundary conditions are analyzed using Landau-Ginzburg-Devonshire theory and continuum media electrostatics. The temperature dependence of the film critical thickness, spontaneous polarization and depolarization field profiles of the open-circuited films are found to be significantly different from the characteristics of short-circuited ones. In particular, we predict the re-entrant type transition boundary between the mono-domain and poly-domain ferroelectric states due to reduced internal screening efficiency and analyzed possible experimental scenarios created by this mechanism. Performed analysis is relevant for the quantitative description of free-standing ferroelectric films phase diagrams andmore » polar properties. Also our results can be useful for the explanation of the scanning-probe microscopy experiments on free ferroelectric surfaces.« less

  18. The boundary conditions for simulations of a shake-table experiment on the seismic response of 3D slope

    NASA Astrophysics Data System (ADS)

    Tang, Liang; Cong, Shengyi; Ling, Xianzhang; Ju, Nengpan

    2017-01-01

    Boundary conditions can significantly affect a slope's behavior under strong earthquakes. To evaluate the importance of boundary conditions for finite element (FE) simulations of a shake-table experiment on the slope response, a validated three-dimensional (3D) nonlinear FE model is presented, and the numerical and experimental results are compared. For that purpose, the robust graphical user-interface "SlopeSAR", based on the open-source computational platform OpenSees, is employed, which simplifies the effort-intensive pre- and post-processing phases. The mesh resolution effect is also addressed. A parametric study is performed to evaluate the influence of boundary conditions on the FE model involving the boundary extent and three types of boundary conditions at the end faces. Generally, variations in the boundary extent produce inconsistent slope deformations. For the two end faces, fixing the y-direction displacement is not appropriate to simulate the shake-table experiment, in which the end walls are rigid and rough. In addition, the influence of the length of the 3D slope's top face and the width of the slope play an important role in the difference between two types of boundary conditions at the end faces (fixing the y-direction displacement and fixing the ( y, z) direction displacement). Overall, this study highlights that the assessment of a comparison between a simulation and an experimental result should be performed with due consideration to the effect of the boundary conditions.

  19. Flow Characteristics and Basal Boundary Condition for Daugaard-Jensen Gletscher, East Greenland

    NASA Astrophysics Data System (ADS)

    Perry, Thomas; Christoffersen, Poul; Dowdeswell, Julian; Palmer, Steven; Young, Duncan

    2014-05-01

    The recent acceleration of mass loss from the Greenland Ice Sheet can in part be attributed to the dynamic thinning and acceleration of its tidewater outlet glaciers. Many of these glaciers have been shown to exhibit sensitivity to conditions at their marine termini, where warm ocean currents promote ice front melting and retreat. However, these currents are confined to a northerly extent of 69N, and whilst remarkable change is seen to the south of this latitude, glaciers to the north are considerably more stable in terms of terminus position. Different environmental variables may thus control the flow characteristics of glaciers north of this well-defined geographical boundary. During 2011, high-resolution ice data was collected for Daugaard-Jensen Gletscher (71N) as part of the Greenland Outlet Glacier Geophysics (GrOGG) project. Remote sensing has confirmed its stability but few, if any, have applied an ice flow model to examine its ice dynamics in more detail. Here, the numerical Elmer-ICE model is applied to a new bed DEM in order to analyse flow characteristics and basal boundary conditions for Daugaard-Jensen Gletscher. The bed elevation of the inland part of the catchment was derived from Operation Icebridge and GrOGG ice thickness data, whilst the main glacier trunk was inferred through mass conservation calculations at a resolution of 100 m using TerraSAR-X velocity data. The latter was also used for 3D inverse modelling with Elmer-ICE, to analyse basal boundary conditions such as basal traction, sliding speed, frictional heating, and the basal melt rate. This is critical in accurately reproducing velocities and flow characteristics for the glacier, which is not always successful with a simple parameterisation in pure forward modelling. The new DEM offers considerable improvements in vertical accuracy and horizontal resolution compared to previous bed datasets created at the ice-sheet scale. Preliminary results indicate that two deep channels within the

  20. On the accurate long-time solution of the wave equation in exterior domains: Asymptotic expansions and corrected boundary conditions

    NASA Technical Reports Server (NTRS)

    Hagstrom, Thomas; Hariharan, S. I.; Maccamy, R. C.

    1993-01-01

    We consider the solution of scattering problems for the wave equation using approximate boundary conditions at artificial boundaries. These conditions are explicitly viewed as approximations to an exact boundary condition satisfied by the solution on the unbounded domain. We study the short and long term behavior of the error. It is provided that, in two space dimensions, no local in time, constant coefficient boundary operator can lead to accurate results uniformly in time for the class of problems we consider. A variable coefficient operator is developed which attains better accuracy (uniformly in time) than is possible with constant coefficient approximations. The theory is illustrated by numerical examples. We also analyze the proposed boundary conditions using energy methods, leading to asymptotically correct error bounds.