Mach's principle as boundary condition for Einstein's field equations
Mach principle as boundary condition for Einstein field equations
Wheeler, J. A.↗
SEARCH · Engineering Papers
Results for “BOUNDARY CONDITIONS”
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Multiple boundary condition test (MBCT) - Identification with mode shapes
The multiple boundary condition test (MBCT) approach is a ground test method to test a class of large flexible structures which cannot be ground tested by state-of-the-art test methods due to the adverse terrestrial environment. The ultimate objective of a ground test is considered to be the validation and update of a mathematical model of the structure. The research to date has indicated the MBCT does work on numerical simulations and on experimental laboratory hardware. To date only the eigenvalue has been used in the model correlation/update by inclusion of the information in the nonlinear terms resulting from the difference between the analytical and measured eigenvectors. This paper presents the results of utilizing additional information, namely the difference in the analytical and the test eigenvectors, in the validation and update of the mathematical model.
Kuo, C. P.↗
Unusual soft mode dynamics in ferroelectric PbTiO 3 , nanowire under different mechanical boundary conditions
Here, first-principles-based atomistic simulations are used to investigate equilibrium phases and soft mode dynamics in ultrathin ferroelectric PbTiO 3 nanowire with poor surface charge compensation subjected to a wide range of mechanical boundary conditions. The presence of the depolarizing field along the nanowire's transverse directions leads to the appearance of a unique high-frequency hard phonon mode that can be used to characterize electrical boundary conditions. This mode is insensitive to the mechanical load. Hydrostatic pressure was found to significantly influence the Curie point and ferroelectric soft modes in the nanowire. Uniaxial stress applied either along axial or transverse nanowire's direction is capable of inducing polydomain flux-closure phases that have a unique ``dynamical" fingerprint. In such phases the modes that originate from the soft modes of bulk PbTiO 3 become hard, which could open a way to potential identification of such nanodomain phases. In all cases, uniaxial stress significantly increases Curie temperature.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Calibration of hyperelastic constitutive models: the role of boundary conditions, search algorithms, and experimental variability
The calibration of hyperelastic constitutive models of soft tissue and tissue surrogates is often treated as an exercise in curve-fitting to the average experimental response, and many of the complicating factors such as experimental boundary conditions and data variability are ignored. Here, we focus on three questions that arise in this area: the ramifications of ignoring the experimental boundary conditions, the use of local optimizers, and the role of data variability. Using data from a uniaxial extension experiment on a tissue surrogate, we study how these three factors affect the calibration of isotropic hyperelastic constitutive models. Our results show that even with the simplest of constitutive models, it is necessary to look beyond a "good fit" to the average.
60 APPLIED LIFE SCIENCES↗
Time-dependent density functional theory with twist-averaged boundary conditions
Time-dependent density functional theory is widely used to describe excitations of many-fermion systems. In its many applications, three-dimensional (3D) coordinate-space representation is used, and infinitedomain calculations are limited to a finite volume represented by a spatial box. For finite quantum systems (atoms, molecules, nuclei, hadrons), the commonly used periodic or reflecting boundary conditions introduce spurious quantization of the continuum states and artificial reflections from boundary; hence, an incorrect treatment of evaporated particles. The finite-volume artifacts for finite systems can be practically cured by invoking an absorbing potential in a certain boundary region sufficiently far from the described system. However, such absorption cannot be applied in the calculations of infinite matter (crystal electrons, quantum fluids, neutron star crust), which suffer from unphysical effects stemming from a finite computational box used. Here, twist-averaged boundary conditions (TABC) have been used successfully to diminish the finite-volume effects. In this work, we extend TABC to time-dependent modes. We demonstrate that by using TABC, one can reduce finite-volume effects drastically without adding any additional parameters associated with absorption at large distances. Moreover, TABC are an obvious choice for time-dependent calculations for infinite systems. Furthermore, since TABC calculations for different twists can be performed independently, the method is trivially adapted to parallel computing.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Buckling of stiffened shells with random initial imperfections, thickness and boundary conditions
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.
Elishakoff, I.↗
Inverse scattering transform for the focusing nonlinear Schrödinger equation with nonzero boundary conditions
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.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
External Boundary Conditions for Three-Dimensional Problems of Computational Aerodynamics
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 and comparisons with the standard (local) methods, the DPM-based ABC's allow one to greatly reduce the size of the computational domain while still maintaining high accuracy of the numerical solution. Moreover, they may provide for a noticeable increase of the convergence rate of multigrid iterations.
Tsynkov, Semyon V.↗
Multiple boundary condition test (MBCT) approach to update mathematical models of large flexible structures
A major challenge to the structural dynamicist is to validate mathematical models of large space structures which cannot be ground tested because of its size and/or flexibility. The paper presents a Multiple Boundary Condition Test (MBCT) approach which allows a systematic validation of the mathematical model by performing a number of ground tests on a large structure with variable boundary conditions. A numerical simulation is presented which illustrates the validity of the MBCT including some of the potential limitations.
Wada, B. K.↗
Role of Boundary Conditions in Monte Carlo Simulation of MEMS Devices
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.
Nance, Robert P.↗
Theoretical analysis and numerical simulation for a hyperbolic equation with Dirichlet and acoustic boundary conditions
This paper is concerned with a theoretical and numerical study for the initial-boundary value problem for a linear hyperbolic equation with variable coefficient and acoustic boundary conditions. On the theoretical results, we prove the existence and uniqueness of global solutions, and the uniform stability of the total energy. Numerical simulations using the finite element method associated with the finite difference method are employed, for one-dimensional and two-dimensional cases, to validate the theoretical results. In addition, numerically the uniform decay rate for energy and the order of convergence of the approximate solution are also shown.
97 MATHEMATICS AND COMPUTING↗
On the prescription of boundary conditions for nonlocal Poisson's and peridynamics models
We introduce a technique to automatically convert local boundary conditions into nonlocal volume constraints for nonlocal Poisson’s and peridynamic models. The proposed strategy is based on the approximation of nonlocal Dirichlet or Neumann data with a local solution obtained by using available boundary, local data. The corresponding nonlocal solution converges quadratically to the local solution as the nonlocal horizon vanishes, making the proposed technique asymptotically compatible. The proposed conversion method does not have any geometry or dimensionality constraints and its computational cost is negligible, compared to the numerical solution of the nonlocal equation. The consistency of the method and its quadratic convergence with respect to the horizon is illustrated by several two-dimensional numerical experiments conducted by meshfree discretization for both the Poisson’s problem and the linear peridynamic solid model.
97 MATHEMATICS AND COMPUTING↗
Consistent Boundary Conditions for Multicomponent Real Gas Mixtures Based on Characteristic Waves
Previously developed characteristic-wave-based boundary conditions for multicomponent perfect gas mixtures are here extended to account for real gases.
transfer consistent boundary conditions real fluid↗
A boundary value “reservoir problem” and boundary conditions for multi-moment multifluid simulations of sheaths
Multifluid simulations of plasma sheaths are increasingly used to model a wide variety of problems in plasma physics ranging from global magnetospheric flows around celestial bodies to plasma–wall interactions in thrusters and fusion devices. For multifluid problems, accurate boundary conditions to model an absorbing wall that resolves a classical sheath remain an open research area. This work justifies the use of vacuum boundary conditions for absorbing walls to show comparable accuracy between a multifluid sheath and lower moments of a continuum-kinetic sheath.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
High-speed propeller noise predictions: Effects of boundary conditions used in blade loading calculations
The acoustics of an advanced single rotation SR-3 propeller at cruise conditions are studied employing a time-domain approach. The study evaluates the acoustic significance of the differences in blade pressures computed using nonreflecting rather than hard wall boundary conditions in the three-dimensional Euler code solution. The directivities of the harmonics of the blade passing frequency tone and the effects of chordwise loading on tone directivity are examined. The results show that the maximum difference in the computed sound pressure levels due to the use of blade pressure distributions obtained with the nonreflecting rather than the hard wall boundary conditions is about 1.5 dB. The blade passing frequency tone directivity obtained in the present study shows good agreement with jetstar flight data.
Nallasamy, M.↗
High-speed propeller noise predictions - Effects of boundary conditions used in blade loading calculations
The acoustics of an advanced single rotation SR-3 propeller at cruise conditions are studied employing a time-domain approach. The study evaluates the acoustic significance of the differences in blade pressures computed using nonreflecting rather than hard wall boundary conditions in the three-dimensional Euler code solution. The directivities of the harmonics of the blade passing frequency tone and the effects of chordwise loading on tone directivity are examined. The results show that the maximum difference in the computed sound pressure levels due to the use of blade pressure distributions obtained with the nonreflecting rather than the hard wall boundary conditions is about 1.5 dB. The blade passing frequency tone directivity obtained in the present study shows good agreement with jetstar flight data.
Nallasamy, M.↗
Representation and evolution of urban weather boundary conditions in downtown Chicago
Our study presents a novel computing technique for data exchange and coupling between a high-resolution weather simulation model and a building energy model, with a goal of evaluating the impact of urban weather boundary conditions on energy performance of urban buildings. The Weather Research and Forecasting (WRF) model is initialized with the operational High-Resolution Rapid Refresh (HRRR) dataset to provide hourly weather conditions over the Chicago region. We utilize the building footprint, land use, and building stock datasets to generate building energy models using EnergyPlus. We mapped the building exterior surfaces to local air nodes to import simulated microclimate data and to export buildings' heat emissions to their local environment. Preliminary experiments for a test area in Chicago show that predicted building cooling energy use differs by about 4.7% for the selected date when compared with simulations using TMY weather data and without considering the urban microclimate boundary conditions.
32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
Mathematical analysis of the Navier-Stokes equations with non standard boundary conditions
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.
Tidriri, M. D.↗