Well-posedness of the free boundary problem in compressible elastodynamics

NASA Astrophysics Data System (ADS)

Trakhinin, Yuri

2018-02-01

We study the free boundary problem for the flow of a compressible isentropic inviscid elastic fluid. At the free boundary moving with the velocity of the fluid particles the columns of the deformation gradient are tangent to the boundary and the pressure vanishes outside the flow domain. We prove the local-in-time existence of a unique smooth solution of the free boundary problem provided that among three columns of the deformation gradient there are two which are non-collinear vectors at each point of the initial free boundary. If this non-collinearity condition fails, the local-in-time existence is proved under the classical Rayleigh-Taylor sign condition satisfied at the first moment. By constructing an Hadamard-type ill-posedness example for the frozen coefficients linearized problem we show that the simultaneous failure of the non-collinearity condition and the Rayleigh-Taylor sign condition leads to Rayleigh-Taylor instability.

EDITORIAL: The nonstationary Casimir effect and quantum systems with moving boundaries

NASA Astrophysics Data System (ADS)

Barton, Gabriel; Dodonov, Victor V.; Man'ko, Vladimir I.

2005-03-01

This topical issue of Journal of Optics B: Quantum and Semiclassical Optics contains 16 contributions devoted to quantum systems with moving boundaries. In a broad sense, the papers continue the studies opened exactly 100 years ago by Einstein in his seminal work on the electrodynamics of moving bodies and the quantum nature of light. Another jubilee which we wish to celebrate by launching this issue is the 80th anniversary of the publication of two papers, where the first solutions of the classical Maxwell equations in a one-dimensional cavity with moving boundaries were obtained, by T H Havelock (1924 Some dynamical illustrations of the pressure of radiation and of adiabatic invariance Phil. Mag. 47 754-71) and by E L Nicolai (1925 On a dynamical illustration of the pressure of radiation Phil. Mag. 49 171-7). As was shown by Einstein, studying the fluctuations of the electromagnetic field inevitably leads one to its quantum (corpuscular) nature. Many papers in this issue deal with problems where moving boundaries produce parametric excitation of vacuum fluctuations of the field, which could result in several different observable effects, like the modification of the famous Casimir force, or the creation of real quanta from the vacuum. It is worth emphasizing that these phenomena, frequently referred to as nonstationary (or dynamical) Casimir effects, are no longer the province only of pure theorists: some experimental groups have already started long-term work aimed at observing such effects in the laboratory. Of course, many difficult problems remain to be resolved before this dream becomes reality. Several papers here show both important progress in this direction, and possible difficulties still to be tackled. Problems that have been considered include, in particular, decoherence, entanglement, and the roles of geometry and polarization. Other papers deal with fundamental problems like the Unruh effect, the interaction of accelerated relativistic atoms with radiation, vacuum friction, and so on. Solutions of some interesting problems of nonrelativistic quantum mechanics with time-dependent boundary conditions, including applications to Bose-Einstein condensates, can also be found here. Since nonstationary Casimir effects can exist not only for photons but for any other quanta (e.g., phonons in solids or in liquid helium), we believe the approaches and results presented in this collection will find interesting applications in other branches of physics too. One possible example might be the generation of squeezed and other 'nonclassical' states of different fields by time-dependent boundary conditions. Approximately half the contributed papers stem from talks at two recent conferences: the First International Workshop on Problems with Moving Boundaries, organized by Professor J Dittrich in Prague in October 2003, and the International Workshop on the Dynamical Casimir Effect, organized by Professor G Carugno in Padua in June 2004. We wish to thank all the authors and reviewers for their efforts in preparing high quality papers, which we hope will attract the attention of other researchers, and especially of young people, to the fascinating areas covered by this special issue.

The analytical solution of the problem of a shock focusing in a gas for one-dimensional case

NASA Astrophysics Data System (ADS)

Shestakovskaya, E. S.; Magazov, F. G.

2018-03-01

The analytical solution of the problem of an imploding shock wave in the vessel with an impermeable wall is constructed for the cases of planar, cylindrical and spherical symmetry. The negative velocity is set at the vessel boundary. The velocity of cold ideal gas is zero. At the initial time the shock spreads from this point into the center of symmetry. The boundary moves under the particular law which conforms to the movement of the shock. In Euler variables it moves but in Lagrangian variables its trajectory is a vertical line. Equations that determine the structure of the gas flow between the shock front and the boundary as a function of time and the Lagrangian coordinate as well as the dependence of the entropy on the shock wave velocity are obtained. Self-similar coefficients and corresponding critical values of self-similar coordinates were found for a wide range of adiabatic index. The problem is solved for Lagrangian coordinates.

Similarity solutions for unsteady free-convection flow from a continuous moving vertical surface

NASA Astrophysics Data System (ADS)

Abd-El-Malek, Mina B.; Kassem, Magda M.; Mekky, Mohammad L.

2004-03-01

The transformation group theoretic approach is applied to present an analysis of the problem of unsteady free convection flow over a continuous moving vertical sheet in an ambient fluid. The thermal boundary layer induced within a vertical semi-infinite layer of Boussinseq fluid by a constant heated bounding plate. The application of two-parameter groups reduces the number of independent variables by two, and consequently the system of governing partial differential equations with the boundary conditions reduces to a system of ordinary differential equations with appropriate boundary conditions. The obtained ordinary differential equations are solved analytically for the temperature and numerically for the velocity using the shooting method. Effect of Prandtl number on the thermal boundary-layer and velocity boundary-layer are studied and plotted in curves.

On mechanical waves and Doppler shifts from moving boundaries

DOE PAGES

Christov, Ivan C.; Christov, Christo I.

2017-02-01

We investigate the propagation of infinitesimal harmonic mechanical waves emitted from a boundary with variable velocity and arriving at a stationary observer. In the classical Doppler effect, X s(t)=vt is the location of the source with constant velocity v. In the present work, however, we consider a source co-located with a moving boundary x=X s(t), where X s(t) can have an arbitrary functional form. For ‘slowly moving’ boundaries (i.e., ones for which the timescale set by the mechanical motion is large in comparison to the inverse of the frequency of the emitted wave), we present a multiple-scale asymptotic analysis of the moving boundary problem for the linear wave equation. Here, we obtain a closed-form leading-order (with respect to the latter small parameter) solution and show that the variable velocity of the boundary results not only in frequency modulation but also in amplitude modulation of the received signal. Consequently, our results extend the applicability of two basic tenets of the theory of a moving source on a stationary domain, specifically that (i)more » $$.\\atop{x}_s$$ for non-uniform boundary motion can be inserted in place of the constant velocity v in the classical Doppler formula and (ii) that the non-uniform boundary motion introduces variability in the amplitude of the wave. The specific examples of decelerating and oscillatory boundary motion are worked out and illustrated.« less

Group solution for unsteady free-convection flow from a vertical moving plate subjected to constant heat flux

NASA Astrophysics Data System (ADS)

Kassem, M.

2006-03-01

The problem of heat and mass transfer in an unsteady free-convection flow over a continuous moving vertical sheet in an ambient fluid is investigated for constant heat flux using the group theoretical method. The nonlinear coupled partial differential equation governing the flow and the boundary conditions are transformed to a system of ordinary differential equations with appropriate boundary conditions. The obtained ordinary differential equations are solved numerically using the shooting method. The effect of Prandlt number on the velocity and temperature of the boundary-layer is plotted in curves. A comparison with previous work is presented.

An Adjoint-Based Approach to Study a Flexible Flapping Wing in Pitching-Rolling Motion

NASA Astrophysics Data System (ADS)

Jia, Kun; Wei, Mingjun; Xu, Min; Li, Chengyu; Dong, Haibo

2017-11-01

Flapping-wing aerodynamics, with advantages in agility, efficiency, and hovering capability, has been the choice of many flyers in nature. However, the study of bio-inspired flapping-wing propulsion is often hindered by the problem's large control space with different wing kinematics and deformation. The adjoint-based approach reduces largely the computational cost to a feasible level by solving an inverse problem. Facing the complication from moving boundaries, non-cylindrical calculus provides an easy extension of traditional adjoint-based approach to handle the optimization involving moving boundaries. The improved adjoint method with non-cylindrical calculus for boundary treatment is first applied on a rigid pitching-rolling plate, then extended to a flexible one with active deformation to further increase its propulsion efficiency. The comparison of flow dynamics with the initial and optimal kinematics and deformation provides a unique opportunity to understand the flapping-wing mechanism. Supported by AFOSR and ARL.

Computation of incompressible viscous flows through artificial heart devices with moving boundaries

NASA Technical Reports Server (NTRS)

Kiris, Cetin; Rogers, Stuart; Kwak, Dochan; Chang, I.-DEE

1991-01-01

The extension of computational fluid dynamics techniques to artificial heart flow simulations is illustrated. Unsteady incompressible Navier-Stokes equations written in 3-D generalized curvilinear coordinates are solved iteratively at each physical time step until the incompressibility condition is satisfied. The solution method is based on the pseudo compressibility approach and uses an implicit upwind differencing scheme together with the Gauss-Seidel line relaxation method. The efficiency and robustness of the time accurate formulation of the algorithm are tested by computing the flow through model geometries. A channel flow with a moving indentation is computed and validated with experimental measurements and other numerical solutions. In order to handle the geometric complexity and the moving boundary problems, a zonal method and an overlapping grid embedding scheme are used, respectively. Steady state solutions for the flow through a tilting disk heart valve was compared against experimental measurements. Good agreement was obtained. The flow computation during the valve opening and closing is carried out to illustrate the moving boundary capability.

Solution of internal ballistic problem for SRM with grain of complex shape during main firing phase

NASA Astrophysics Data System (ADS)

Kiryushkin, A. E.; Minkov, L. L.

2017-10-01

Solid rocket motor (SRM) internal ballistics problems are related to the problems with moving boundaries. The algorithm able to solve similar problems in axisymmetric formulation on Cartesian mesh with an arbitrary order of accuracy is considered in this paper. The base of this algorithm is the ghost point extrapolation using inverse Lax-Wendroff procedure. Level set method is used as an implicit representation of the domain boundary. As an example, the internal ballistics problem for SRM with umbrella type grain was solved during the main firing phase. In addition, flow parameters distribution in the combustion chamber was obtained for different time moments.

Superconvergent second order Cartesian method for solving free boundary problem for invadopodia formation

NASA Astrophysics Data System (ADS)

Gallinato, Olivier; Poignard, Clair

2017-06-01

In this paper, we present a superconvergent second order Cartesian method to solve a free boundary problem with two harmonic phases coupled through the moving interface. The model recently proposed by the authors and colleagues describes the formation of cell protrusions. The moving interface is described by a level set function and is advected at the velocity given by the gradient of the inner phase. The finite differences method proposed in this paper consists of a new stabilized ghost fluid method and second order discretizations for the Laplace operator with the boundary conditions (Dirichlet, Neumann or Robin conditions). Interestingly, the method to solve the harmonic subproblems is superconvergent on two levels, in the sense that the first and second order derivatives of the numerical solutions are obtained with the second order of accuracy, similarly to the solution itself. We exhibit numerical criteria on the data accuracy to get such properties and numerical simulations corroborate these criteria. In addition to these properties, we propose an appropriate extension of the velocity of the level-set to avoid any loss of consistency, and to obtain the second order of accuracy of the complete free boundary problem. Interestingly, we highlight the transmission of the superconvergent properties for the static subproblems and their preservation by the dynamical scheme. Our method is also well suited for quasistatic Hele-Shaw-like or Muskat-like problems.

A Conserving Discretization for the Free Boundary in a Two-Dimensional Stefan Problem

NASA Astrophysics Data System (ADS)

Segal, Guus; Vuik, Kees; Vermolen, Fred

1998-03-01

The dissolution of a disk-likeAl2Cuparticle is considered. A characteristic property is that initially the particle has a nonsmooth boundary. The mathematical model of this dissolution process contains a description of the particle interface, of which the position varies in time. Such a model is called a Stefan problem. It is impossible to obtain an analytical solution for a general two-dimensional Stefan problem, so we use the finite element method to solve this problem numerically. First, we apply a classical moving mesh method. Computations show that after some time steps the predicted particle interface becomes very unrealistic. Therefore, we derive a new method for the displacement of the free boundary based on the balance of atoms. This method leads to good results, also, for nonsmooth boundaries. Some numerical experiments are given for the dissolution of anAl2Cuparticle in anAl-Cualloy.

Resonances and vibrations in an elevator cable system due to boundary sway

NASA Astrophysics Data System (ADS)

Gaiko, Nick V.; van Horssen, Wim T.

2018-06-01

In this paper, an analytical method is presented to study an initial-boundary value problem describing the transverse displacements of a vertically moving beam under boundary excitation. The length of the beam is linearly varying in time, i.e., the axial, vertical velocity of the beam is assumed to be constant. The bending stiffness of the beam is assumed to be small. This problem may be regarded as a model describing the lateral vibrations of an elevator cable excited at its boundaries by the wind-induced building sway. Slow variation of the cable length leads to a singular perturbation problem which is expressed in slowly changing, time-dependent coefficients in the governing differential equation. By providing an interior layer analysis, infinitely many resonance manifolds are detected. Further, the initial-boundary value problem is studied in detail using a three-timescales perturbation method. The constructed formal approximations of the solutions are in agreement with the numerical results.

Two-phase Hele-Shaw flow with a moving contact line

DOE Office of Scientific and Technical Information (OSTI.GOV)

Weinstein, S.J.; Ungar, L.H.; Dussan, E.B.

1988-01-01

An asymptotic analysis is presented for Hele-Shaw viscous fingering with a moving contact line at flow rates. As in problems where a thin film is present instead of a contact line, the narrow gap limit is nonuniform, and interfacial boundary conditions valid for the Hele-Shaw equations must be determined in order to predict the flow field and interface shape. Many well-posed boundary-value problems can be identified, each corresponding to a different flow regime characterized by the relative sizes of the capillary number (dimensionless velocity) and the dimensionless gap width. These problems incorporate terms corresponding to the gapwise component of themore » interfacial curvature (the curvature in the cross-sectional view of the Hele-Shaw cell) and spanwise curvature (seen in the top view of the cell) in different ways. Nonunique interface solutions typically arise as in the analogous thin film problems. The relationships between the curvature terms, the spectra of allowable solutions, and the implications for stability are discussed.« less

Improvements to Level Set, Immersed Boundary methods for Interface Tracking

NASA Astrophysics Data System (ADS)

Vogl, Chris; Leveque, Randy

2014-11-01

It is not uncommon to find oneself solving a moving boundary problem under flow in the context of some application. Of particular interest is when the moving boundary exerts a curvature-dependent force on the liquid. Such a force arises when observing a boundary that is resistant to bending or has surface tension. Numerically speaking, stable numerical computation of the curvature can be difficult as it is often described in terms of high-order derivatives of either marker particle positions or of a level set function. To address this issue, the level set method is modified to track not only the position of the boundary, but the curvature as well. The definition of the signed-distance function that is used to modify the level set method is also used to develop an interpolation-free, closest-point method. These improvements are used to simulate a bending-resistant, inextensible boundary under shear flow to highlight area and volume conservation, as well as stable curvature calculation. Funded by a NSF MSPRF grant.

Quantum field between moving mirrors: A three dimensional example

NASA Technical Reports Server (NTRS)

Hacyan, S.; Jauregui, Roco; Villarreal, Carlos

1995-01-01

The scalar quantum field uniformly moving plates in three dimensional space is studied. Field equations for Dirichlet boundary conditions are solved exactly. Comparison of the resulting wavefunctions with their instantaneous static counterpart is performed via Bogolubov coefficients. Unlike the one dimensional problem, 'particle' creation as well as squeezing may occur. The time dependent Casimir energy is also evaluated.

High speed propeller acoustics and aerodynamics - A boundary element approach

NASA Technical Reports Server (NTRS)

Farassat, F.; Myers, M. K.; Dunn, M. H.

1989-01-01

The Boundary Element Method (BEM) is applied in this paper to the problems of acoustics and aerodynamics of high speed propellers. The underlying theory is described based on the linearized Ffowcs Williams-Hawkings equation. The surface pressure on the blade is assumed unknown in the aerodynamic problem. It is obtained by solving a singular integral equation. The acoustic problem is then solved by moving the field point inside the fluid medium and evaluating some surface and line integrals. Thus the BEM provides a powerful technique in calculation of high speed propeller aerodynamics and acoustics.

Transport of reacting solutes subject to a moving dissolution boundary: Numerical methods and solutions

USGS Publications Warehouse

Willis, Catherine; Rubin, Jacob

1987-01-01

A moving boundary problem which arises during transport with precipitation-dissolution reactions is solved by three different numerical methods. Two of these methods (one explicit and one implicit) are based on an integral formulation of mass balance and lead to an approximation of a weak solution. These methods are compared to a front-tracking scheme. Although the two approaches are conceptually different, the numerical solutions showed good agreement. As the ratio of dispersion to convection decreases, the methods based on the integral formulation become computationally more efficient. Specific reactions were modeled to examine the dependence of the system on the physical and chemical parameters. Although the water flow rate does not explicitly appear in the equation for the velocity of the moving boundary, the speed of the boundary depends more on the flux rate than on the dispersion coefficient. The discontinuity in the gradient of the solute concentration profile at the boundary increases with convection and with the initial concentration of the mineral. Our implicit method is extended to allow participation of the solutes in complexation reactions as well as the precipitation-dissolution reaction. This extension is easily made and does not change the basic method.

Moving charged particles in lattice Boltzmann-based electrokinetics

NASA Astrophysics Data System (ADS)

Kuron, Michael; Rempfer, Georg; Schornbaum, Florian; Bauer, Martin; Godenschwager, Christian; Holm, Christian; de Graaf, Joost

2016-12-01

The motion of ionic solutes and charged particles under the influence of an electric field and the ensuing hydrodynamic flow of the underlying solvent is ubiquitous in aqueous colloidal suspensions. The physics of such systems is described by a coupled set of differential equations, along with boundary conditions, collectively referred to as the electrokinetic equations. Capuani et al. [J. Chem. Phys. 121, 973 (2004)] introduced a lattice-based method for solving this system of equations, which builds upon the lattice Boltzmann algorithm for the simulation of hydrodynamic flow and exploits computational locality. However, thus far, a description of how to incorporate moving boundary conditions into the Capuani scheme has been lacking. Moving boundary conditions are needed to simulate multiple arbitrarily moving colloids. In this paper, we detail how to introduce such a particle coupling scheme, based on an analogue to the moving boundary method for the pure lattice Boltzmann solver. The key ingredients in our method are mass and charge conservation for the solute species and a partial-volume smoothing of the solute fluxes to minimize discretization artifacts. We demonstrate our algorithm's effectiveness by simulating the electrophoresis of charged spheres in an external field; for a single sphere we compare to the equivalent electro-osmotic (co-moving) problem. Our method's efficiency and ease of implementation should prove beneficial to future simulations of the dynamics in a wide range of complex nanoscopic and colloidal systems that were previously inaccessible to lattice-based continuum algorithms.

Discretization of three-dimensional free surface flows and moving boundary problems via elliptic grid methods based on variational principles

NASA Astrophysics Data System (ADS)

Fraggedakis, D.; Papaioannou, J.; Dimakopoulos, Y.; Tsamopoulos, J.

2017-09-01

A new boundary-fitted technique to describe free surface and moving boundary problems is presented. We have extended the 2D elliptic grid generator developed by Dimakopoulos and Tsamopoulos (2003) [19] and further advanced by Chatzidai et al. (2009) [18] to 3D geometries. The set of equations arises from the fulfillment of the variational principles established by Brackbill and Saltzman (1982) [21], and refined by Christodoulou and Scriven (1992) [22]. These account for both smoothness and orthogonality of the grid lines of tessellated physical domains. The elliptic-grid equations are accompanied by new boundary constraints and conditions which are based either on the equidistribution of the nodes on boundary surfaces or on the existing 2D quasi-elliptic grid methodologies. The capabilities of the proposed algorithm are first demonstrated in tests with analytically described complex surfaces. The sequence in which these tests are presented is chosen to help the reader build up experience on the best choice of the elliptic grid parameters. Subsequently, the mesh equations are coupled with the Navier-Stokes equations, in order to reveal the full potential of the proposed methodology in free surface flows. More specifically, the problem of gas assisted injection in ducts of circular and square cross-sections is examined, where the fluid domain experiences extreme deformations. Finally, the flow-mesh solver is used to calculate the equilibrium shapes of static menisci in capillary tubes.

An arbitrary boundary with ghost particles incorporated in coupled FEM-SPH model for FSI problems

NASA Astrophysics Data System (ADS)

Long, Ting; Hu, Dean; Wan, Detao; Zhuang, Chen; Yang, Gang

2017-12-01

It is important to treat the arbitrary boundary of Fluid-Structure Interaction (FSI) problems in computational mechanics. In order to ensure complete support condition and restore the first-order consistency near the boundary of Smoothed Particle Hydrodynamics (SPH) method for coupling Finite Element Method (FEM) with SPH model, a new ghost particle method is proposed by dividing the interceptive area of kernel support domain into subareas corresponding to boundary segments of structure. The ghost particles are produced automatically for every fluid particle at each time step, and the properties of ghost particles, such as density, mass and velocity, are defined by using the subareas to satisfy the boundary condition. In the coupled FEM-SPH model, the normal and shear forces from a boundary segment of structure to a fluid particle are calculated through the corresponding ghost particles, and its opposite forces are exerted on the corresponding boundary segment, then the momentum of the present method is conservation and there is no matching requirements between the size of elements and the size of particles. The performance of the present method is discussed and validated by several FSI problems with complex geometry boundary and moving boundary.

A Moving Mesh Finite Element Algorithm for Singular Problems in Two and Three Space Dimensions

NASA Astrophysics Data System (ADS)

Li, Ruo; Tang, Tao; Zhang, Pingwen

2002-04-01

A framework for adaptive meshes based on the Hamilton-Schoen-Yau theory was proposed by Dvinsky. In a recent work (2001, J. Comput. Phys.170, 562-588), we extended Dvinsky's method to provide an efficient moving mesh algorithm which compared favorably with the previously proposed schemes in terms of simplicity and reliability. In this work, we will further extend the moving mesh methods based on harmonic maps to deal with mesh adaptation in three space dimensions. In obtaining the variational mesh, we will solve an optimization problem with some appropriate constraints, which is in contrast to the traditional method of solving the Euler-Lagrange equation directly. The key idea of this approach is to update the interior and boundary grids simultaneously, rather than considering them separately. Application of the proposed moving mesh scheme is illustrated with some two- and three-dimensional problems with large solution gradients. The numerical experiments show that our methods can accurately resolve detail features of singular problems in 3D.

Flow simulations about steady-complex and unsteady moving configurations using structured-overlapped and unstructured grids

NASA Technical Reports Server (NTRS)

Newman, James C., III

1995-01-01

The limiting factor in simulating flows past realistic configurations of interest has been the discretization of the physical domain on which the governing equations of fluid flow may be solved. In an attempt to circumvent this problem, many Computational Fluid Dynamic (CFD) methodologies that are based on different grid generation and domain decomposition techniques have been developed. However, due to the costs involved and expertise required, very few comparative studies between these methods have been performed. In the present work, the two CFD methodologies which show the most promise for treating complex three-dimensional configurations as well as unsteady moving boundary problems are evaluated. These are namely the structured-overlapped and the unstructured grid schemes. Both methods use a cell centered, finite volume, upwind approach. The structured-overlapped algorithm uses an approximately factored, alternating direction implicit scheme to perform the time integration, whereas, the unstructured algorithm uses an explicit Runge-Kutta method. To examine the accuracy, efficiency, and limitations of each scheme, they are applied to the same steady complex multicomponent configurations and unsteady moving boundary problems. The steady complex cases consist of computing the subsonic flow about a two-dimensional high-lift multielement airfoil and the transonic flow about a three-dimensional wing/pylon/finned store assembly. The unsteady moving boundary problems are a forced pitching oscillation of an airfoil in a transonic freestream and a two-dimensional, subsonic airfoil/store separation sequence. Accuracy was accessed through the comparison of computed and experimentally measured pressure coefficient data on several of the wing/pylon/finned store assembly's components and at numerous angles-of-attack for the pitching airfoil. From this study, it was found that both the structured-overlapped and the unstructured grid schemes yielded flow solutions of comparable accuracy for these simulations. This study also indicated that, overall, the structured-overlapped scheme was slightly more CPU efficient than the unstructured approach.

On similarity solutions of a boundary layer problem with an upstream moving wall

NASA Technical Reports Server (NTRS)

Hussaini, M. Y.; Lakin, W. D.; Nachman, A.

1986-01-01

The problem of a boundary layer on a flat plate which has a constant velocity opposite in direction to that of the uniform mainstream is examined. It was previously shown that the solution of this boundary value problem is crucially dependent on the parameter which is the ratio of the velocity of the plate to the velocity of the free stream. In particular, it was proved that a solution exists only if this parameter does not exceed a certain critical value, and numerical evidence was adduced to show that this solution is nonunique. Using Crocco formulation the present work proves this nonuniqueness. Also considered are the analyticity of solutions and the derivation of upper bounds on the critical value of wall velocity parameter.

Adaptivity and smart algorithms for fluid-structure interaction

NASA Technical Reports Server (NTRS)

Oden, J. Tinsley

1990-01-01

This paper reviews new approaches in CFD which have the potential for significantly increasing current capabilities of modeling complex flow phenomena and of treating difficult problems in fluid-structure interaction. These approaches are based on the notions of adaptive methods and smart algorithms, which use instantaneous measures of the quality and other features of the numerical flowfields as a basis for making changes in the structure of the computational grid and of algorithms designed to function on the grid. The application of these new techniques to several problem classes are addressed, including problems with moving boundaries, fluid-structure interaction in high-speed turbine flows, flow in domains with receding boundaries, and related problems.

A space-time tensor formulation for continuum mechanics in general curvilinear, moving, and deforming coordinate systems

NASA Technical Reports Server (NTRS)

Avis, L. M.

1976-01-01

Tensor methods are used to express the continuum equations of motion in general curvilinear, moving, and deforming coordinate systems. The space-time tensor formulation is applicable to situations in which, for example, the boundaries move and deform. Placing a coordinate surface on such a boundary simplifies the boundary condition treatment. The space-time tensor formulation is also applicable to coordinate systems with coordinate surfaces defined as surfaces of constant pressure, density, temperature, or any other scalar continuum field function. The vanishing of the function gradient components along the coordinate surfaces may simplify the set of governing equations. In numerical integration of the equations of motion, the freedom of motion of the coordinate surfaces provides a potential for enhanced resolution of the continuum field function. An example problem of an incompressible, inviscid fluid with a top free surface is considered, where the surfaces of constant pressure (including the top free surface) are coordinate surfaces.

Moving boundary problems for a rarefied gas: Spatially one-dimensional case

NASA Astrophysics Data System (ADS)

Tsuji, Tetsuro; Aoki, Kazuo

2013-10-01

Unsteady flows of a rarefied gas in a full space caused by an oscillation of an infinitely wide plate in its normal direction are investigated numerically on the basis of the Bhatnagar-Gross-Krook (BGK) model of the Boltzmann equation. The paper aims at showing properties and difficulties inherent to moving boundary problems in kinetic theory of gases using a simple one-dimensional setting. More specifically, the following two problems are considered: (Problem I) the plate starts a forced harmonic oscillation (forced motion); (Problem II) the plate, which is subject to an external restoring force obeying Hooke’s law, is displaced from its equilibrium position and released (free motion). The physical interest in Problem I lies in the propagation of nonlinear acoustic waves in a rarefied gas, whereas that in Problem II in the decay rate of the oscillation of the plate. An accurate numerical method, which is capable of describing singularities caused by the oscillating plate, is developed on the basis of the method of characteristics and is applied to the two problems mentioned above. As a result, the unsteady behavior of the solution, such as the propagation of discontinuities and some weaker singularities in the molecular velocity distribution function, are clarified. Some results are also compared with those based on the existing method.

Quasi-stationary mechanics of elastic continua with bending stiffness wrapping on a pulley system

NASA Astrophysics Data System (ADS)

Kaczmarczyk, S.; Mirhadizadeh, S.

2016-05-01

In many engineering applications elastic continua such as ropes and belts often are subject to bending when they pass over pulleys / sheaves. In this paper the quasi-stationary mechanics of a cable-pulley system is studied. The cable is modelled as a moving Euler- Bernoulli beam. The distribution of tension is non-uniform along its span and due to the bending stiffness the contact points at the pulley-beam boundaries are not unknown. The system is described by a set of nonlinear ordinary differential equations with undetermined boundary conditions. The resulting nonlinear Boundary Value Problem (BVP) with unknown boundaries is solved by converting the problem into the ‘standard’ form defined over a fixed interval. Numerical results obtained for a range of typical configurations with relevant boundary conditions applied demonstrate that due to the effects of bending stiffness the angels of wrap are reduced and the span tensions are increased.

An adaptive gridless methodology in one dimension

DOE Office of Scientific and Technical Information (OSTI.GOV)

Snyder, N.T.; Hailey, C.E.

1996-09-01

Gridless numerical analysis offers great potential for accurately solving for flow about complex geometries or moving boundary problems. Because gridless methods do not require point connection, the mesh cannot twist or distort. The gridless method utilizes a Taylor series about each point to obtain the unknown derivative terms from the current field variable estimates. The governing equation is then numerically integrated to determine the field variables for the next iteration. Effects of point spacing and Taylor series order on accuracy are studied, and they follow similar trends of traditional numerical techniques. Introducing adaption by point movement using a spring analogymore » allows the solution method to track a moving boundary. The adaptive gridless method models linear, nonlinear, steady, and transient problems. Comparison with known analytic solutions is given for these examples. Although point movement adaption does not provide a significant increase in accuracy, it helps capture important features and provides an improved solution.« less

A numerical method for solving the 3D unsteady incompressible Navier Stokes equations in curvilinear domains with complex immersed boundaries

NASA Astrophysics Data System (ADS)

Ge, Liang; Sotiropoulos, Fotis

2007-08-01

A novel numerical method is developed that integrates boundary-conforming grids with a sharp interface, immersed boundary methodology. The method is intended for simulating internal flows containing complex, moving immersed boundaries such as those encountered in several cardiovascular applications. The background domain (e.g. the empty aorta) is discretized efficiently with a curvilinear boundary-fitted mesh while the complex moving immersed boundary (say a prosthetic heart valve) is treated with the sharp-interface, hybrid Cartesian/immersed-boundary approach of Gilmanov and Sotiropoulos [A. Gilmanov, F. Sotiropoulos, A hybrid cartesian/immersed boundary method for simulating flows with 3d, geometrically complex, moving bodies, Journal of Computational Physics 207 (2005) 457-492.]. To facilitate the implementation of this novel modeling paradigm in complex flow simulations, an accurate and efficient numerical method is developed for solving the unsteady, incompressible Navier-Stokes equations in generalized curvilinear coordinates. The method employs a novel, fully-curvilinear staggered grid discretization approach, which does not require either the explicit evaluation of the Christoffel symbols or the discretization of all three momentum equations at cell interfaces as done in previous formulations. The equations are integrated in time using an efficient, second-order accurate fractional step methodology coupled with a Jacobian-free, Newton-Krylov solver for the momentum equations and a GMRES solver enhanced with multigrid as preconditioner for the Poisson equation. Several numerical experiments are carried out on fine computational meshes to demonstrate the accuracy and efficiency of the proposed method for standard benchmark problems as well as for unsteady, pulsatile flow through a curved, pipe bend. To demonstrate the ability of the method to simulate flows with complex, moving immersed boundaries we apply it to calculate pulsatile, physiological flow through a mechanical, bileaflet heart valve mounted in a model straight aorta with an anatomical-like triple sinus.

Spark formation as a moving boundary process

NASA Astrophysics Data System (ADS)

Ebert, Ute

2006-03-01

The growth process of spark channels recently becomes accessible through complementary methods. First, I will review experiments with nanosecond photographic resolution and with fast and well defined power supplies that appropriately resolve the dynamics of electric breakdown [1]. Second, I will discuss the elementary physical processes as well as present computations of spark growth and branching with adaptive grid refinement [2]. These computations resolve three well separated scales of the process that emerge dynamically. Third, this scale separation motivates a hierarchy of models on different length scales. In particular, I will discuss a moving boundary approximation for the ionization fronts that generate the conducting channel. The resulting moving boundary problem shows strong similarities with classical viscous fingering. For viscous fingering, it is known that the simplest model forms unphysical cusps within finite time that are suppressed by a regularizing condition on the moving boundary. For ionization fronts, we derive a new condition on the moving boundary of mixed Dirichlet-Neumann type (φ=ɛnφ) that indeed regularizes all structures investigated so far. In particular, we present compact analytical solutions with regularization, both for uniformly translating shapes and for their linear perturbations [3]. These solutions are so simple that they may acquire a paradigmatic role in the future. Within linear perturbation theory, they explicitly show the convective stabilization of a curved front while planar fronts are linearly unstable against perturbations of arbitrary wave length. [1] T.M.P. Briels, E.M. van Veldhuizen, U. Ebert, TU Eindhoven. [2] C. Montijn, J. Wackers, W. Hundsdorfer, U. Ebert, CWI Amsterdam. [3] B. Meulenbroek, U. Ebert, L. Schäfer, Phys. Rev. Lett. 95, 195004 (2005).

An immersed boundary formulation for simulating high-speed compressible viscous flows with moving solids

NASA Astrophysics Data System (ADS)

Qu, Yegao; Shi, Ruchao; Batra, Romesh C.

2018-02-01

We present a robust sharp-interface immersed boundary method for numerically studying high speed flows of compressible and viscous fluids interacting with arbitrarily shaped either stationary or moving rigid solids. The Navier-Stokes equations are discretized on a rectangular Cartesian grid based on a low-diffusion flux splitting method for inviscid fluxes and conservative high-order central-difference schemes for the viscous components. Discontinuities such as those introduced by shock waves and contact surfaces are captured by using a high-resolution weighted essentially non-oscillatory (WENO) scheme. Ghost cells in the vicinity of the fluid-solid interface are introduced to satisfy boundary conditions on the interface. Values of variables in the ghost cells are found by using a constrained moving least squares method (CMLS) that eliminates numerical instabilities encountered in the conventional MLS formulation. The solution of the fluid flow and the solid motion equations is advanced in time by using the third-order Runge-Kutta and the implicit Newmark integration schemes, respectively. The performance of the proposed method has been assessed by computing results for the following four problems: shock-boundary layer interaction, supersonic viscous flows past a rigid cylinder, moving piston in a shock tube and lifting off from a flat surface of circular, rectangular and elliptic cylinders triggered by shock waves, and comparing computed results with those available in the literature.

The Stefan problem of solidification of ternary systems in the presence of moving phase transition regions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Alexandrov, D. V., E-mail: Dmitri.Alexandrov@usu.ru; Ivanov, A. A.

2009-05-15

The process of solidification of ternary systems in the presence of moving phase transition regions has been investigated theoretically in terms of the nonlinear equation of the liquidus surface. A mathematical model is developed and an approximate analytical solution to the Stefan problem is constructed for a linear temperature profile in two-phase zones. The temperature and impurity concentration distributions are determined, the solid-phase fractions in the phase transition regions are obtained, and the laws of motion of their boundaries are established. It is demonstrated that all boundaries move in accordance with the laws of direct proportionality to the square rootmore » of time, which is a general property of self-similar processes. It is substantiated that the concentration of an impurity of the substance undergoing a phase transition only in the cotectic zone increases in this zone and decreases in the main two-phase zone in which the other component of the substance undergoes a phase transition. In the process, the concentration reaches a maximum at the interface between the main two-phase zone and the cotectic two-phase zone. The revealed laws of motion of the outer boundaries of the entire phase transition region do not depend on the amount of the components under consideration and hold true for crystallization of a multicomponent system.« less

Segregation effects during solidification in weightless melts

NASA Technical Reports Server (NTRS)

Li, C.; Gershinsky, M.

1974-01-01

The generalized problem of determining the temperature and solute concentration profiles during directional solidification of binary alloys with surface evaporation was mathematically formulated. Realistic initial and boundary conditions were defined, and a computer program was developed and checked out. The programs computes the positions of two moving boundaries, evaporation and solidification, and their velocities. Temperature and solute concentration profiles in the semiinfinite material body at selected instances of time are also computed.

Slip effects on MHD flow and heat transfer of ferrofluids over a moving flat plate

NASA Astrophysics Data System (ADS)

Ramli, Norshafira; Ahmad, Syakila; Pop, Ioan

2017-08-01

In this study, the problem of MHD flow and heat transfer of ferrofluids over a moving flat plate with slip effect and uniform heat flux is considered. The governing ordinary differential equations are solved via shooting method. The effect of slip parameter on the dimensionless velocity, temperature, skin friction and Nusselt numbers are numerically studied for the three selected ferroparticles; magnetite (Fe3O4), cobalt ferrite (CoFe2O4) and Mn-Zn ferrite (Mn-ZnFe2O4) with water-based fluid. The results indicate that dual solutions exist for a plate moving towards the origin. It is found that the slip process delays the boundary layer separation. Moreover, the velocity and thermal boundary-layer thicknesses decrease in the first solution while increase with the increase of the value of slip parameters in second solution.

Level set immersed boundary method for gas-liquid-solid interactions with phase-change

NASA Astrophysics Data System (ADS)

Dhruv, Akash; Balaras, Elias; Riaz, Amir; Kim, Jungho

2017-11-01

We will discuss an approach to simulate the interaction between two-phase flows with phase changes and stationary/moving structures. In our formulation, the Navier-Stokes and heat advection-diffusion equations are solved on a block-structured grid using adaptive mesh refinement (AMR) along with sharp jump in pressure, velocity and temperature across the interface separating the different phases. The jumps are implemented using a modified Ghost Fluid Method (Lee et al., J. Comput. Physics, 344:381-418, 2017), and the interface is tracked with a level set approach. Phase transition is achieved by calculating mass flux near the interface and extrapolating it to the rest of the domain using a Hamilton-Jacobi equation. Stationary/moving structures are simulated with an immersed boundary formulation based on moving least squares (Vanella & Balaras, J. Comput. Physics, 228:6617-6628, 2009). A variety of canonical problems involving vaporization, film boiling and nucleate boiling is presented to validate the method and demonstrate the its formal accuracy. The robustness of the solver in complex problems, which are crucial in efficient design of heat transfer mechanisms for various applications, will also be demonstrated. Work supported by NASA, Grant NNX16AQ77G.

A Numerical Method for Solving the 3D Unsteady Incompressible Navier-Stokes Equations in Curvilinear Domains with Complex Immersed Boundaries.

PubMed

Ge, Liang; Sotiropoulos, Fotis

2007-08-01

A novel numerical method is developed that integrates boundary-conforming grids with a sharp interface, immersed boundary methodology. The method is intended for simulating internal flows containing complex, moving immersed boundaries such as those encountered in several cardiovascular applications. The background domain (e.g the empty aorta) is discretized efficiently with a curvilinear boundary-fitted mesh while the complex moving immersed boundary (say a prosthetic heart valve) is treated with the sharp-interface, hybrid Cartesian/immersed-boundary approach of Gilmanov and Sotiropoulos [1]. To facilitate the implementation of this novel modeling paradigm in complex flow simulations, an accurate and efficient numerical method is developed for solving the unsteady, incompressible Navier-Stokes equations in generalized curvilinear coordinates. The method employs a novel, fully-curvilinear staggered grid discretization approach, which does not require either the explicit evaluation of the Christoffel symbols or the discretization of all three momentum equations at cell interfaces as done in previous formulations. The equations are integrated in time using an efficient, second-order accurate fractional step methodology coupled with a Jacobian-free, Newton-Krylov solver for the momentum equations and a GMRES solver enhanced with multigrid as preconditioner for the Poisson equation. Several numerical experiments are carried out on fine computational meshes to demonstrate the accuracy and efficiency of the proposed method for standard benchmark problems as well as for unsteady, pulsatile flow through a curved, pipe bend. To demonstrate the ability of the method to simulate flows with complex, moving immersed boundaries we apply it to calculate pulsatile, physiological flow through a mechanical, bileaflet heart valve mounted in a model straight aorta with an anatomical-like triple sinus.

A Numerical Method for Solving the 3D Unsteady Incompressible Navier-Stokes Equations in Curvilinear Domains with Complex Immersed Boundaries

PubMed Central

Ge, Liang; Sotiropoulos, Fotis

2008-01-01

A novel numerical method is developed that integrates boundary-conforming grids with a sharp interface, immersed boundary methodology. The method is intended for simulating internal flows containing complex, moving immersed boundaries such as those encountered in several cardiovascular applications. The background domain (e.g the empty aorta) is discretized efficiently with a curvilinear boundary-fitted mesh while the complex moving immersed boundary (say a prosthetic heart valve) is treated with the sharp-interface, hybrid Cartesian/immersed-boundary approach of Gilmanov and Sotiropoulos [1]. To facilitate the implementation of this novel modeling paradigm in complex flow simulations, an accurate and efficient numerical method is developed for solving the unsteady, incompressible Navier-Stokes equations in generalized curvilinear coordinates. The method employs a novel, fully-curvilinear staggered grid discretization approach, which does not require either the explicit evaluation of the Christoffel symbols or the discretization of all three momentum equations at cell interfaces as done in previous formulations. The equations are integrated in time using an efficient, second-order accurate fractional step methodology coupled with a Jacobian-free, Newton-Krylov solver for the momentum equations and a GMRES solver enhanced with multigrid as preconditioner for the Poisson equation. Several numerical experiments are carried out on fine computational meshes to demonstrate the accuracy and efficiency of the proposed method for standard benchmark problems as well as for unsteady, pulsatile flow through a curved, pipe bend. To demonstrate the ability of the method to simulate flows with complex, moving immersed boundaries we apply it to calculate pulsatile, physiological flow through a mechanical, bileaflet heart valve mounted in a model straight aorta with an anatomical-like triple sinus. PMID:19194533

Simulation of blood flow through an artificial heart

NASA Technical Reports Server (NTRS)

Kiris, Cetin; Chang, I-Dee; Rogers, Stuart E.; Kwak, Dochan

1991-01-01

A numerical simulation of the incompressible viscous flow through a prosthetic tilting disk heart valve is presented in order to demonstrate the current capability to model unsteady flows with moving boundaries. Both steady state and unsteady flow calculations are done by solving the incompressible Navier-Stokes equations in 3-D generalized curvilinear coordinates. In order to handle the moving boundary problems, the chimera grid embedding scheme which decomposes a complex computational domain into several simple subdomains is used. An algebraic turbulence model for internal flows is incorporated to reach the physiological values of Reynolds number. Good agreement is obtained between the numerical results and experimental measurements. It is found that the tilting disk valve causes large regions of separated flow, and regions of high shear.

Remarks on Hierarchic Control for a Linearized Micropolar Fluids System in Moving Domains

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jesus, Isaías Pereira de, E-mail: isaias@ufpi.edu.br

We study a Stackelberg strategy subject to the evolutionary linearized micropolar fluids equations in domains with moving boundaries, considering a Nash multi-objective equilibrium (non necessarily cooperative) for the “follower players” (as is called in the economy field) and an optimal problem for the leader player with approximate controllability objective. We will obtain the following main results: the existence and uniqueness of Nash equilibrium and its characterization, the approximate controllability of the linearized micropolar system with respect to the leader control and the existence and uniqueness of the Stackelberg–Nash problem, where the optimality system for the leader is given.

Enriched reproducing kernel particle method for fractional advection-diffusion equation

NASA Astrophysics Data System (ADS)

Ying, Yuping; Lian, Yanping; Tang, Shaoqiang; Liu, Wing Kam

2018-06-01

The reproducing kernel particle method (RKPM) has been efficiently applied to problems with large deformations, high gradients and high modal density. In this paper, it is extended to solve a nonlocal problem modeled by a fractional advection-diffusion equation (FADE), which exhibits a boundary layer with low regularity. We formulate this method on a moving least-square approach. Via the enrichment of fractional-order power functions to the traditional integer-order basis for RKPM, leading terms of the solution to the FADE can be exactly reproduced, which guarantees a good approximation to the boundary layer. Numerical tests are performed to verify the proposed approach.

Three-dimensional numerical simulation for plastic injection-compression molding

NASA Astrophysics Data System (ADS)

Zhang, Yun; Yu, Wenjie; Liang, Junjie; Lang, Jianlin; Li, Dequn

2018-03-01

Compared with conventional injection molding, injection-compression molding can mold optical parts with higher precision and lower flow residual stress. However, the melt flow process in a closed cavity becomes more complex because of the moving cavity boundary during compression and the nonlinear problems caused by non-Newtonian polymer melt. In this study, a 3D simulation method was developed for injection-compression molding. In this method, arbitrary Lagrangian- Eulerian was introduced to model the moving-boundary flow problem in the compression stage. The non-Newtonian characteristics and compressibility of the polymer melt were considered. The melt flow and pressure distribution in the cavity were investigated by using the proposed simulation method and compared with those of injection molding. Results reveal that the fountain flow effect becomes significant when the cavity thickness increases during compression. The back flow also plays an important role in the flow pattern and redistribution of cavity pressure. The discrepancy in pressures at different points along the flow path is complicated rather than monotonically decreased in injection molding.

Estimation of the Thermal Process in the Honeycomb Panel by a Monte Carlo Method

NASA Astrophysics Data System (ADS)

Gusev, S. A.; Nikolaev, V. N.

2018-01-01

A new Monte Carlo method for estimating the thermal state of the heat insulation containing honeycomb panels is proposed in the paper. The heat transfer in the honeycomb panel is described by a boundary value problem for a parabolic equation with discontinuous diffusion coefficient and boundary conditions of the third kind. To obtain an approximate solution, it is proposed to use the smoothing of the diffusion coefficient. After that, the obtained problem is solved on the basis of the probability representation. The probability representation is the expectation of the functional of the diffusion process corresponding to the boundary value problem. The process of solving the problem is reduced to numerical statistical modelling of a large number of trajectories of the diffusion process corresponding to the parabolic problem. It was used earlier the Euler method for this object, but that requires a large computational effort. In this paper the method is modified by using combination of the Euler and the random walk on moving spheres methods. The new approach allows us to significantly reduce the computation costs.

An Immersed Boundary-Lattice Boltzmann Method for Simulating Particulate Flows

NASA Astrophysics Data System (ADS)

Zhang, Baili; Cheng, Ming; Lou, Jing

2013-11-01

A two-dimensional momentum exchange-based immersed boundary-lattice Boltzmann method developed by X.D. Niu et al. (2006) has been extended in three-dimensions for solving fluid-particles interaction problems. This method combines the most desirable features of the lattice Boltzmann method and the immersed boundary method by using a regular Eulerian mesh for the flow domain and a Lagrangian mesh for the moving particles in the flow field. The non-slip boundary conditions for the fluid and the particles are enforced by adding a force density term into the lattice Boltzmann equation, and the forcing term is simply calculated by the momentum exchange of the boundary particle density distribution functions, which are interpolated by the Lagrangian polynomials from the underlying Eulerian mesh. This method preserves the advantages of lattice Boltzmann method in tracking a group of particles and, at the same time, provides an alternative approach to treat solid-fluid boundary conditions. Numerical validations show that the present method is very accurate and efficient. The present method will be further developed to simulate more complex problems with particle deformation, particle-bubble and particle-droplet interactions.

Moving finite elements in 2-D

NASA Technical Reports Server (NTRS)

Gelinas, R. J.; Doss, S. K.; Vajk, J. P.; Djomehri, J.; Miller, K.

1983-01-01

The mathematical background regarding the moving finite element (MFE) method of Miller and Miller (1981) is discussed, taking into account a general system of partial differential equations (PDE) and the amenability of the MFE method in two dimensions to code modularization and to semiautomatic user-construction of numerous PDE systems for both Dirichlet and zero-Neumann boundary conditions. A description of test problem results is presented, giving attention to aspects of single square wave propagation, and a solution of the heat equation.

Moving International Technical Communication Forward: A World Englishes Approach

ERIC Educational Resources Information Center

Bokor, Michael Jarvis Kwadzo

2011-01-01

This article explores how the English language contributes to cross-boundary communication failure and establishes that there is an "English language problem" that has not been adequately addressed in preparing United States native English-speaking students for international technical communication tasks. For example, U.S. technical communication…

The Sedov Blast Wave as a Radial Piston Verification Test

DOE PAGES

Pederson, Clark; Brown, Bart; Morgan, Nathaniel

2016-06-22

The Sedov blast wave is of great utility as a verification problem for hydrodynamic methods. The typical implementation uses an energized cell of finite dimensions to represent the energy point source. We avoid this approximation by directly finding the effects of the energy source as a boundary condition (BC). Furthermore, the proposed method transforms the Sedov problem into an outward moving radial piston problem with a time-varying velocity. A portion of the mesh adjacent to the origin is removed and the boundaries of this hole are forced with the velocities from the Sedov solution. This verification test is implemented onmore » two types of meshes, and convergence is shown. Our results from the typical initial condition (IC) method and the new BC method are compared.« less

The penalty immersed boundary method and its application to aerodynamics

NASA Astrophysics Data System (ADS)

Kim, Yongsam

The Immersed Boundary (IB) method has been widely applied to problems involving a moving elastic boundary that is immersed in fluid and interacting with it. But most applications of the IB method have involved a massless elastic boundary. Extending the method to cover the case of a massive boundary has required spreading the boundary mass out onto the fluid grid and then solving the Navier-Stokes equations with a variable mass density. The variable mass density makes Fourier transform methods inapplicable, and requires a multigrid solver. Here we propose a new and simple way to give mass to the elastic boundary. The key idea of the method is to introduce two representations of each boundary: one is a massive boundary which does not interact with the fluid, and the other is messless and plays the same role as the boundary of the IB method with the massless assumption. Although they are almost the same, we allow these two representations of the boundary to be different as long as the gap between them is small. This can be ensured by connecting them with a stiff spring with a zero rest length which generates force acting on both boundaries and pulling them together. We call this the 'Penalty IB method'. It does not spread mass to the fluid grid, retains the use of Fourier transform methodology, and is easy to implement in the context of an existing IB method code for the massless case. This thesis introduces the Penalty IB method and applies it to several problems in which the mass of the boundary is important. These problems are filaments in a flowing soap film, flows past a cylinder, windsocks, flags, and parachutes.

Forecasting Natural Gas Prices Using Wavelets, Time Series, and Artificial Neural Networks

PubMed Central

2015-01-01

Following the unconventional gas revolution, the forecasting of natural gas prices has become increasingly important because the association of these prices with those of crude oil has weakened. With this as motivation, we propose some modified hybrid models in which various combinations of the wavelet approximation, detail components, autoregressive integrated moving average, generalized autoregressive conditional heteroskedasticity, and artificial neural network models are employed to predict natural gas prices. We also emphasize the boundary problem in wavelet decomposition, and compare results that consider the boundary problem case with those that do not. The empirical results show that our suggested approach can handle the boundary problem, such that it facilitates the extraction of the appropriate forecasting results. The performance of the wavelet-hybrid approach was superior in all cases, whereas the application of detail components in the forecasting was only able to yield a small improvement in forecasting performance. Therefore, forecasting with only an approximation component would be acceptable, in consideration of forecasting efficiency. PMID:26539722

Forecasting Natural Gas Prices Using Wavelets, Time Series, and Artificial Neural Networks.

PubMed

Jin, Junghwan; Kim, Jinsoo

2015-01-01

Following the unconventional gas revolution, the forecasting of natural gas prices has become increasingly important because the association of these prices with those of crude oil has weakened. With this as motivation, we propose some modified hybrid models in which various combinations of the wavelet approximation, detail components, autoregressive integrated moving average, generalized autoregressive conditional heteroskedasticity, and artificial neural network models are employed to predict natural gas prices. We also emphasize the boundary problem in wavelet decomposition, and compare results that consider the boundary problem case with those that do not. The empirical results show that our suggested approach can handle the boundary problem, such that it facilitates the extraction of the appropriate forecasting results. The performance of the wavelet-hybrid approach was superior in all cases, whereas the application of detail components in the forecasting was only able to yield a small improvement in forecasting performance. Therefore, forecasting with only an approximation component would be acceptable, in consideration of forecasting efficiency.

Asymptotic behaviour of Stokes flow in a thin domain with a moving rough boundary

PubMed Central

Fabricius, J.; Koroleva, Y. O.; Tsandzana, A.; Wall, P.

2014-01-01

We consider a problem that models fluid flow in a thin domain bounded by two surfaces. One of the surfaces is rough and moving, whereas the other is flat and stationary. The problem involves two small parameters ϵ and μ that describe film thickness and roughness wavelength, respectively. Depending on the ratio λ=ϵ/μ, three different flow regimes are obtained in the limit as both of them tend to zero. Time-dependent equations of Reynolds type are obtained in all three cases (Stokes roughness, Reynolds roughness and high-frequency roughness regime). The derivations of the limiting equations are based on formal expansions in the parameters ϵ and μ. PMID:25002820

2-D transmitral flows simulation by means of the immersed boundary method on unstructured grids

NASA Astrophysics Data System (ADS)

Denaro, F. M.; Sarghini, F.

2002-04-01

Interaction between computational fluid dynamics and clinical researches recently allowed a deeper understanding of the physiology of complex phenomena involving cardio-vascular mechanisms. The aim of this paper is to develop a simplified numerical model based on the Immersed Boundary Method and to perform numerical simulations in order to study the cardiac diastolic phase during which the left ventricle is filled with blood flowing from the atrium throughout the mitral valve. As one of the diagnostic problems to be faced by clinicians is the lack of a univocal definition of the diastolic performance from the velocity measurements obtained by Eco-Doppler techniques, numerical simulations are supposed to provide an insight both into the physics of the diastole and into the interpretation of experimental data. An innovative application of the Immersed Boundary Method on unstructured grids is presented, fulfilling accuracy requirements related to the development of a thin boundary layer along the moving immersed boundary. It appears that this coupling between unstructured meshes and the Immersed Boundary Method is a promising technique when a wide range of spatial scales is involved together with a moving boundary. Numerical simulations are performed in a range of physiological parameters and a qualitative comparison with experimental data is presented, in order to demonstrate that, despite the simplified model, the main physiological characteristics of the diastole are well represented. Copyright

Wetting boundary condition for the color-gradient lattice Boltzmann method: Validation with analytical and experimental data

NASA Astrophysics Data System (ADS)

Akai, Takashi; Bijeljic, Branko; Blunt, Martin J.

2018-06-01

In the color gradient lattice Boltzmann model (CG-LBM), a fictitious-density wetting boundary condition has been widely used because of its ease of implementation. However, as we show, this may lead to inaccurate results in some cases. In this paper, a new scheme for the wetting boundary condition is proposed which can handle complicated 3D geometries. The validity of our method for static problems is demonstrated by comparing the simulated results to analytical solutions in 2D and 3D geometries with curved boundaries. Then, capillary rise simulations are performed to study dynamic problems where the three-phase contact line moves. The results are compared to experimental results in the literature (Heshmati and Piri, 2014). If a constant contact angle is assumed, the simulations agree with the analytical solution based on the Lucas-Washburn equation. However, to match the experiments, we need to implement a dynamic contact angle that varies with the flow rate.

Regularization of moving boundaries in a laplacian field by a mixed Dirichlet-Neumann boundary condition: exact results.

PubMed

Meulenbroek, Bernard; Ebert, Ute; Schäfer, Lothar

2005-11-04

The dynamics of ionization fronts that generate a conducting body are in the simplest approximation equivalent to viscous fingering without regularization. Going beyond this approximation, we suggest that ionization fronts can be modeled by a mixed Dirichlet-Neumann boundary condition. We derive exact uniformly propagating solutions of this problem in 2D and construct a single partial differential equation governing small perturbations of these solutions. For some parameter value, this equation can be solved analytically, which shows rigorously that the uniformly propagating solution is linearly convectively stable and that the asymptotic relaxation is universal and exponential in time.

Open Rotor Computational Aeroacoustic Analysis with an Immersed Boundary Method

NASA Technical Reports Server (NTRS)

Brehm, Christoph; Barad, Michael F.; Kiris, Cetin C.

2016-01-01

Reliable noise prediction capabilities are essential to enable novel fuel efficient open rotor designs that can meet the community and cabin noise standards. Toward this end, immersed boundary methods have reached a level of maturity where more and more complex flow problems can be tackled with this approach. This paper demonstrates that our higher-order immersed boundary method provides the ability for aeroacoustic analysis of wake-dominated flow fields generated by a contra-rotating open rotor. This is the first of a kind aeroacoustic simulation of an open rotor propulsion system employing an immersed boundary method. In addition to discussing the methodologies of how to apply the immersed boundary method to this moving boundary problem, we will provide a detailed validation of the aeroacoustic analysis approach employing the Launch Ascent and Vehicle Aerodynamics (LAVA) solver. Two free-stream Mach numbers with M=0.2 and M=0.78 are considered in this analysis that are based on the nominally take-off and cruise flow conditions. The simulation data is compared to available experimental data and other computational results employing more conventional CFD methods. Spectral analysis is used to determine the dominant wave propagation pattern in the acoustic near-field.

Diffuse interface immersed boundary method for multi-fluid flows with arbitrarily moving rigid bodies

NASA Astrophysics Data System (ADS)

Patel, Jitendra Kumar; Natarajan, Ganesh

2018-05-01

We present an interpolation-free diffuse interface immersed boundary method for multiphase flows with moving bodies. A single fluid formalism using the volume-of-fluid approach is adopted to handle multiple immiscible fluids which are distinguished using the volume fractions, while the rigid bodies are tracked using an analogous volume-of-solid approach that solves for the solid fractions. The solution to the fluid flow equations are carried out using a finite volume-immersed boundary method, with the latter based on a diffuse interface philosophy. In the present work, we assume that the solids are filled with a "virtual" fluid with density and viscosity equal to the largest among all fluids in the domain. The solids are assumed to be rigid and their motion is solved using Newton's second law of motion. The immersed boundary methodology constructs a modified momentum equation that reduces to the Navier-Stokes equations in the fully fluid region and recovers the no-slip boundary condition inside the solids. An implicit incremental fractional-step methodology in conjunction with a novel hybrid staggered/non-staggered approach is employed, wherein a single equation for normal momentum at the cell faces is solved everywhere in the domain, independent of the number of spatial dimensions. The scalars are all solved for at the cell centres, with the transport equations for solid and fluid volume fractions solved using a high-resolution scheme. The pressure is determined everywhere in the domain (including inside the solids) using a variable coefficient Poisson equation. The solution to momentum, pressure, solid and fluid volume fraction equations everywhere in the domain circumvents the issue of pressure and velocity interpolation, which is a source of spurious oscillations in sharp interface immersed boundary methods. A well-balanced algorithm with consistent mass/momentum transport ensures robust simulations of high density ratio flows with strong body forces. The proposed diffuse interface immersed boundary method is shown to be discretely mass-preserving while being temporally second-order accurate and exhibits nominal second-order accuracy in space. We examine the efficacy of the proposed approach through extensive numerical experiments involving one or more fluids and solids, that include two-particle sedimentation in homogeneous and stratified environment. The results from the numerical simulations show that the proposed methodology results in reduced spurious force oscillations in case of moving bodies while accurately resolving complex flow phenomena in multiphase flows with moving solids. These studies demonstrate that the proposed diffuse interface immersed boundary method, which could be related to a class of penalisation approaches, is a robust and promising alternative to computationally expensive conformal moving mesh algorithms as well as the class of sharp interface immersed boundary methods for multibody problems in multi-phase flows.

Skin friction enhancement in a model problem of undulatory swimming

NASA Astrophysics Data System (ADS)

Ehrenstein, Uwe; Eloy, Christophe

2013-10-01

To calculate the energy costs of swimming, it is crucial to evaluate the drag force originating from skin friction. In this paper we examine the assumption, known as the 'Bone-Lighthill boundary-layer thinning hypothesis', that undulatory swimming motions induce a drag increase because of the compression of the boundary layer. Studying analytically an incoming flow along a flat plate moving at a normal velocity as a limit case of a yawed cylinder in uniform flow under the laminar boundary layer assumption, we demonstrate that the longitudinal drag scales as the square root of the normal velocity component. This analytical prediction is interpreted in the light of a three-dimensional numerical simulation result for a plate of finite length and width. An analogous two-dimensional Navier-Stokes problem by artificially accelerating the flow in a channel of finite height is proposed and solved numerically, showing the robustness of the analytical results. Solving the problem for an undulatory plate motion similar to fish swimming, we find a drag enhancement which can be estimated to be of the order of 20 %.

Switching moving boundary models for two-phase flow evaporators and condensers

NASA Astrophysics Data System (ADS)

Bonilla, Javier; Dormido, Sebastián; Cellier, François E.

2015-03-01

The moving boundary method is an appealing approach for the design, testing and validation of advanced control schemes for evaporators and condensers. When it comes to advanced control strategies, not only accurate but fast dynamic models are required. Moving boundary models are fast low-order dynamic models, and they can describe the dynamic behavior with high accuracy. This paper presents a mathematical formulation based on physical principles for two-phase flow moving boundary evaporator and condenser models which support dynamic switching between all possible flow configurations. The models were implemented in a library using the equation-based object-oriented Modelica language. Several integrity tests in steady-state and transient predictions together with stability tests verified the models. Experimental data from a direct steam generation parabolic-trough solar thermal power plant is used to validate and compare the developed moving boundary models against finite volume models.

Boundary states at reflective moving boundaries

NASA Astrophysics Data System (ADS)

Acosta Minoli, Cesar A.; Kopriva, David A.

2012-06-01

We derive and evaluate boundary states for Maxwell's equations, the linear, and the nonlinear Euler gas-dynamics equations to compute wave reflection from moving boundaries. In this study we use a Discontinuous Galerkin Spectral Element method (DGSEM) with Arbitrary Lagrangian-Eulerian (ALE) mapping for the spatial approximation, but the boundary states can be used with other methods, like finite volume schemes. We present four studies using Maxwell's equations, one for the linear Euler equations, and one more for the nonlinear Euler equations. These are: reflection of light from a plane mirror moving at constant velocity, reflection of light from a moving cylinder, reflection of light from a vibrating mirror, reflection of sound from a plane wall and dipole sound generation by an oscillating cylinder in an inviscid flow. The studies show that the boundary states preserve spectral convergence in the solution and in derived quantities like divergence and vorticity.

On the role of the frozen surface approximation in small wave-height perturbation theory for moving surfaces

NASA Astrophysics Data System (ADS)

Keiffer, Richard; Novarini, Jorge; Scharstein, Robert

2002-11-01

In the standard development of the small wave-height approximation (SWHA) perturbation theory for scattering from moving rough surfaces [e.g., E. Y. Harper and F. M. Labianca, J. Acoust. Soc. Am. 58, 349-364 (1975)] the necessity for any sort of frozen surface approximation is avoided by the replacement of the rough boundary by a flat (and static) boundary. In this paper, this seemingly fortuitous byproduct of the small wave-height approximation is examined and found to fail to fully agree with an analysis based on the kinematics of the problem. Specifically, the first-order correction term from standard perturbation approach predicts a scattered amplitude that depends on the source frequency, whereas the kinematics of the problem point to a scattered amplitude that depends on the scattered frequency. It is shown that a perturbation approach in which an explicit frozen surface approximation is made before the SWHA is invoked predicts (first-order) scattered amplitudes that are in agreement with the kinematic analysis. [Work supported by ONR/NRL (PE 61153N-32) and by grants of computer time DoD HPC Shared Resource Center at Stennis Space Center, MS.

The moving confluence route technology with WAD scheme for 3D hydrodynamic simulation in high altitude inland waters

NASA Astrophysics Data System (ADS)

Wang, Yonggui; Yang, Yinqun; Chen, Xiaolong; Engel, Bernard A.; Zhang, Wanshun

2018-04-01

For three-dimensional hydrodynamic simulations in inland waters, the rapid changes with moving boundary and various input conditions should be considered. Some models are developed with moving boundary but the dynamic change of discharges is unresolved or ignored. For better hydrodynamic simulation in inland waters, the widely used 3D model, ECOMSED, has been improved by moving confluence route (MCR) method with a wetting and drying scheme (WAD). The fixed locations of water and pollutants inputs from tributaries, point sources and non-point sources have been changed to dynamic confluence routes as the boundary moving. The improved model was applied in an inland water area, Qingshuihai reservoir, Kunming City, China, for a one-year hydrodynamic simulation. The results were verified by water level, flow velocity and water mass conservation. Detailed water level variation analysis and velocity field comparison at different times showed that the improved model has better performance for simulating the boundary moving phenomenon and moving discharges along with water level changing than the original one. The improved three-dimensional model is available for hydrodynamics simulation in water bodies where water boundary shifts along with change of water level and have various inlets.

On a Free Boundary Problem for the Curvature Flow with Driving Force

NASA Astrophysics Data System (ADS)

Guo, Jong-Shenq; Matano, Hiroshi; Shimojo, Masahiko; Wu, Chang-Hong

2016-03-01

We study a free boundary problem associated with the curvature dependent motion of planar curves in the upper half plane whose two endpoints slide along the horizontal axis with prescribed fixed contact angles. Our first main result concerns the classification of solutions; every solution falls into one of the three categories, namely, area expanding, area bounded and area shrinking types. We then study in detail the asymptotic behavior of solutions in each category. Among other things we show that solutions are asymptotically self-similar both in the area expanding and the area shrinking cases, while solutions converge to either a stationary solution or a traveling wave in the area bounded case. We also prove results on the concavity properties of solutions. One of the main tools of this paper is the intersection number principle, however in order to deal with solutions with free boundaries, we introduce what we call "the extended intersection number principle", which turns out to be exceedingly useful in handling curves with moving endpoints.

Open Rotor Computational Aeroacoustic Analysis with an Immersed Boundary Method

NASA Technical Reports Server (NTRS)

Brehm, Christoph; Barad, Michael F.; Kiris, Cetin C.

2016-01-01

Reliable noise prediction capabilities are essential to enable novel fuel efficient open rotor designs that can meet the community and cabin noise standards. Toward this end, immersed boundary methods have reached a level of maturity so that they are being frequently employed for specific real world applications within NASA. This paper demonstrates that our higher-order immersed boundary method provides the ability for aeroacoustic analysis of wake-dominated flow fields generated by highly complex geometries. This is the first of a kind aeroacoustic simulation of an open rotor propulsion system employing an immersed boundary method. In addition to discussing the peculiarities of applying the immersed boundary method to this moving boundary problem, we will provide a detailed aeroacoustic analysis of the noise generation mechanisms encountered in the open rotor flow. The simulation data is compared to available experimental data and other computational results employing more conventional CFD methods. The noise generation mechanisms are analyzed employing spectral analysis, proper orthogonal decomposition and the causality method.

Global stability analysis of axisymmetric boundary layer over a circular cylinder

NASA Astrophysics Data System (ADS)

Bhoraniya, Ramesh; Vinod, Narayanan

2018-05-01

This paper presents a linear global stability analysis of the incompressible axisymmetric boundary layer on a circular cylinder. The base flow is parallel to the axis of the cylinder at inflow boundary. The pressure gradient is zero in the streamwise direction. The base flow velocity profile is fully non-parallel and non-similar in nature. The boundary layer grows continuously in the spatial directions. Linearized Navier-Stokes (LNS) equations are derived for the disturbance flow quantities in the cylindrical polar coordinates. The LNS equations along with homogeneous boundary conditions forms a generalized eigenvalues problem. Since the base flow is axisymmetric, the disturbances are periodic in azimuthal direction. Chebyshev spectral collocation method and Arnoldi's iterative algorithm is used for the solution of the general eigenvalues problem. The global temporal modes are computed for the range of Reynolds numbers and different azimuthal wave numbers. The largest imaginary part of the computed eigenmodes is negative, and hence, the flow is temporally stable. The spatial structure of the eigenmodes shows that the disturbance amplitudes grow in size and magnitude while they are moving towards downstream. The global modes of axisymmetric boundary layer are more stable than that of 2D flat-plate boundary layer at low Reynolds number. However, at higher Reynolds number they approach 2D flat-plate boundary layer. Thus, the damping effect of transverse curvature is significant at low Reynolds number. The wave-like nature of the disturbance amplitudes is found in the streamwise direction for the least stable eigenmodes.

Effective matrix-free preconditioning for the augmented immersed interface method

NASA Astrophysics Data System (ADS)

Xia, Jianlin; Li, Zhilin; Ye, Xin

2015-12-01

We present effective and efficient matrix-free preconditioning techniques for the augmented immersed interface method (AIIM). AIIM has been developed recently and is shown to be very effective for interface problems and problems on irregular domains. GMRES is often used to solve for the augmented variable(s) associated with a Schur complement A in AIIM that is defined along the interface or the irregular boundary. The efficiency of AIIM relies on how quickly the system for A can be solved. For some applications, there are substantial difficulties involved, such as the slow convergence of GMRES (particularly for free boundary and moving interface problems), and the inconvenience in finding a preconditioner (due to the situation that only the products of A and vectors are available). Here, we propose matrix-free structured preconditioning techniques for AIIM via adaptive randomized sampling, using only the products of A and vectors to construct a hierarchically semiseparable matrix approximation to A. Several improvements over existing schemes are shown so as to enhance the efficiency and also avoid potential instability. The significance of the preconditioners includes: (1) they do not require the entries of A or the multiplication of AT with vectors; (2) constructing the preconditioners needs only O (log ⁡ N) matrix-vector products and O (N) storage, where N is the size of A; (3) applying the preconditioners needs only O (N) flops; (4) they are very flexible and do not require any a priori knowledge of the structure of A. The preconditioners are observed to significantly accelerate the convergence of GMRES, with heuristical justifications of the effectiveness. Comprehensive tests on several important applications are provided, such as Navier-Stokes equations on irregular domains with traction boundary conditions, interface problems in incompressible flows, mixed boundary problems, and free boundary problems. The preconditioning techniques are also useful for several other problems and methods.

Detecting Phase Boundaries in Hard-Sphere Suspensions

NASA Technical Reports Server (NTRS)

McDowell, Mark; Rogers, Richard B.; Gray, Elizabeth

2009-01-01

A special image-data-processing technique has been developed for use in experiments that involve observation, via optical microscopes equipped with electronic cameras, of moving boundaries between the colloidal-solid and colloidal-liquid phases of colloidal suspensions of monodisperse hard spheres. During an experiment, it is necessary to adjust the position of a microscope to keep the phase boundary within view. A boundary typically moves at a speed of the order of microns per hour. Because an experiment can last days or even weeks, it is impractical to require human intervention to keep the phase boundary in view. The present image-data-processing technique yields results within a computation time short enough to enable generation of automated-microscope-positioning commands to track the moving phase boundary

Three-dimensional local ALE-FEM method for fluid flow in domains containing moving boundaries/objects interfaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Carrington, David Bradley; Monayem, A. K. M.; Mazumder, H.

2015-03-05

A three-dimensional finite element method for the numerical simulations of fluid flow in domains containing moving rigid objects or boundaries is developed. The method falls into the general category of Arbitrary Lagrangian Eulerian methods; it is based on a fixed mesh that is locally adapted in the immediate vicinity of the moving interfaces and reverts to its original shape once the moving interfaces go past the elements. The moving interfaces are defined by separate sets of marker points so that the global mesh is independent of interface movement and the possibility of mesh entanglement is eliminated. The results is amore » fully robust formulation capable of calculating on domains of complex geometry with moving boundaries or devises that can also have a complex geometry without danger of the mesh becoming unsuitable due to its continuous deformation thus eliminating the need for repeated re-meshing and interpolation. Moreover, the boundary conditions on the interfaces are imposed exactly. This work is intended to support the internal combustion engines simulator KIVA developed at Los Alamos National Laboratories. The model's capabilities are illustrated through application to incompressible flows in different geometrical settings that show the robustness and flexibility of the technique to perform simulations involving moving boundaries in a three-dimensional domain.« less

Calculation of Water Entry Problem for Free-falling Bodies Using a Developed Cartesian Cut Cell Mesh

NASA Astrophysics Data System (ADS)

Wenhua, Wang; Yanying, Wang

2010-05-01

This paper describes the development of free surface capturing method on Cartesian cut cell mesh to water entry problem for free-falling bodies with body-fluid interaction. The incompressible Euler equations for a variable density fluid system are presented as governing equations and the free surface is treated as a contact discontinuity by using free surface capturing method. In order to be convenient for dealing with the problem with moving body boundary, the Cartesian cut cell technique is adopted for generating the boundary-fitted mesh around body edge by cutting solid regions out of a background Cartesian mesh. Based on this mesh system, governing equations are discretized by finite volume method, and at each cell edge inviscid flux is evaluated by means of Roe's approximate Riemann solver. Furthermore, for unsteady calculation in time domain, a time accurate solution is achieved by a dual time-stepping technique with artificial compressibility method. For the body-fluid interaction, the projection method of momentum equations and exact Riemann solution are applied in the calculation of fluid pressure on the solid boundary. Finally, the method is validated by test case of water entry for free-falling bodies.

Model creation of moving redox reaction boundary in agarose gel electrophoresis by traditional potassium permanganate method.

PubMed

Xie, Hai-Yang; Liu, Qian; Li, Jia-Hao; Fan, Liu-Yin; Cao, Cheng-Xi

2013-02-21

A novel moving redox reaction boundary (MRRB) model was developed for studying electrophoretic behaviors of analytes involving redox reaction on the principle of moving reaction boundary (MRB). Traditional potassium permanganate method was used to create the boundary model in agarose gel electrophoresis because of the rapid reaction rate associated with MnO(4)(-) ions and Fe(2+) ions. MRB velocity equation was proposed to describe the general functional relationship between velocity of moving redox reaction boundary (V(MRRB)) and concentration of reactant, and can be extrapolated to similar MRB techniques. Parameters affecting the redox reaction boundary were investigated in detail. Under the selected conditions, good linear relationship between boundary movement distance and time were obtained. The potential application of MRRB in electromigration redox reaction titration was performed in two different concentration levels. The precision of the V(MRRB) was studied and the relative standard deviations were below 8.1%, illustrating the good repeatability achieved in this experiment. The proposed MRRB model enriches the MRB theory and also provides a feasible realization of manual control of redox reaction process in electrophoretic analysis.

On the theory of polarization radiation in media with sharp boundaries

DOE Office of Scientific and Technical Information (OSTI.GOV)

Karlovets, D. V., E-mail: d.karlovets@gmail.com

2011-07-15

Polarization radiation generated when a point charge moves uniformly along a straight line in vacuum in the vicinity of media with a finite permittivity {epsilon}({omega}) = {epsilon} Prime + i{epsilon} Double-Prime and sharp boundaries is considered. A method is developed in which polarization radiation is represented as the field of the current induced in the substance by the field of the moving charge. The solution to the problem of radiation induced when a charge moves along the axis of a cylindrical vacuum channel in a thin screen with a finite radius and a finite permittivity is obtained. Depending on themore » parameters of the problem, this solution describes various types of radiation (Cherenkov, transition, and diffraction radiation). In particular, when the channel radius tends to zero and the outer radius of the screen tends to infinity, the expression derived for the emitted energy coincides with the known solution for transition radiation in a plate. In another particular case of ideal conductivity ({epsilon} Double-Prime {yields} {infinity}), the relevant formula coincides with the known results for diffraction radiation from a circular aperture in an infinitely thin screen. The solution is obtained to the problem of radiation generated when the charge flies near a thin rectangular screen with a finite permittivity. This solution describes the diffraction and Cherenkov mechanisms of radiation and takes into account possible multiple re-reflections of radiation in the screen. The solution to the problem of radiation generated when a particles flies near a thin grating consisting of a finite number of strips having a rectangular cross section and a finite permittivity and separated by vacuum gaps (Smith-Purcell radiation) is also obtained. In the special case of ideal conductivity, the expression derived for the emitted energy coincides with the known result in the model of surface currents.« less

Robust Surface Reconstruction via Laplace-Beltrami Eigen-Projection and Boundary Deformation

PubMed Central

Shi, Yonggang; Lai, Rongjie; Morra, Jonathan H.; Dinov, Ivo; Thompson, Paul M.; Toga, Arthur W.

2010-01-01

In medical shape analysis, a critical problem is reconstructing a smooth surface of correct topology from a binary mask that typically has spurious features due to segmentation artifacts. The challenge is the robust removal of these outliers without affecting the accuracy of other parts of the boundary. In this paper, we propose a novel approach for this problem based on the Laplace-Beltrami (LB) eigen-projection and properly designed boundary deformations. Using the metric distortion during the LB eigen-projection, our method automatically detects the location of outliers and feeds this information to a well-composed and topology-preserving deformation. By iterating between these two steps of outlier detection and boundary deformation, we can robustly filter out the outliers without moving the smooth part of the boundary. The final surface is the eigen-projection of the filtered mask boundary that has the correct topology, desired accuracy and smoothness. In our experiments, we illustrate the robustness of our method on different input masks of the same structure, and compare with the popular SPHARM tool and the topology preserving level set method to show that our method can reconstruct accurate surface representations without introducing artificial oscillations. We also successfully validate our method on a large data set of more than 900 hippocampal masks and demonstrate that the reconstructed surfaces retain volume information accurately. PMID:20624704

Theoretical study of air forces on an oscillating or steady thin wing in a supersonic main stream

NASA Technical Reports Server (NTRS)

Garrick, I E; Rubinow, S I

1947-01-01

A theoretical study, based on the linearized equations of motion for small disturbance, is made of the air forces on wings of general plan forms moving forward at a constant supersonic speed. The boundary problem is set up for both the harmonically oscillating and the steady conditions. Two types of boundary conditions are distinguished, which are designated "purely supersonic" and "mixed supersonic." the method is illustrated by applications to a number of examples for both the steady and the oscillating conditions. The purely supersonic case involves independence of action of the upper and lower surfaces of the airfoil and present analysis is mainly concerned with this case. A discussion is first given of the fundamental or elementary solution corresponding to a moving source. The solutions for the velocity potential are then synthesized by means of integration of the fundamental solution for the moving source. The method is illustrated by applications to a number of examples for both the steady and the oscillating cases and for various plan forms, including swept wings and rectangular and triangular plan forms. The special results of a number of authors are shown to be included in the analysis.

A sharp interface Cartesian grid method for viscous simulation of shocked particle-laden flows

NASA Astrophysics Data System (ADS)

Das, Pratik; Sen, Oishik; Jacobs, Gustaaf; Udaykumar, H. S.

2017-09-01

A Cartesian grid-based sharp interface method is presented for viscous simulations of shocked particle-laden flows. The moving solid-fluid interfaces are represented using level sets. A moving least-squares reconstruction is developed to apply the no-slip boundary condition at solid-fluid interfaces and to supply viscous stresses to the fluid. The algorithms developed in this paper are benchmarked against similarity solutions for the boundary layer over a fixed flat plate and against numerical solutions for moving interface problems such as shock-induced lift-off of a cylinder in a channel. The framework is extended to 3D and applied to calculate low Reynolds number steady supersonic flow over a sphere. Viscous simulation of the interaction of a particle cloud with an incident planar shock is demonstrated; the average drag on the particles and the vorticity field in the cloud are compared to the inviscid case to elucidate the effects of viscosity on momentum transfer between the particle and fluid phases. The methods developed will be useful for obtaining accurate momentum and heat transfer closure models for macro-scale shocked particulate flow applications such as blast waves and dust explosions.

Multi-resolution MPS method

NASA Astrophysics Data System (ADS)

Tanaka, Masayuki; Cardoso, Rui; Bahai, Hamid

2018-04-01

In this work, the Moving Particle Semi-implicit (MPS) method is enhanced for multi-resolution problems with different resolutions at different parts of the domain utilising a particle splitting algorithm for the finer resolution and a particle merging algorithm for the coarser resolution. The Least Square MPS (LSMPS) method is used for higher stability and accuracy. Novel boundary conditions are developed for the treatment of wall and pressure boundaries for the Multi-Resolution LSMPS method. A wall is represented by polygons for effective simulations of fluid flows with complex wall geometries and the pressure boundary condition allows arbitrary inflow and outflow, making the method easier to be used in flow simulations of channel flows. By conducting simulations of channel flows and free surface flows, the accuracy of the proposed method was verified.

Study of microwave drying of wet materials based on one-dimensional two-phase model

NASA Astrophysics Data System (ADS)

Salomatov, Vl V.; Karelin, V. A.

2017-11-01

Currently, microwave is one of the most interesting ways to conduct drying of dielectric materials, in particular coal. In this paper, two processes were considered - heating and drying. The temperature field of the coal semi-mass in the heating mode is found analytically strictly with the use of integral transformations. The drying process is formulated as a nonlinear Stephen problem with a moving boundary of the liquid-vapor phase transformation. The temperature distribution, speed and drying time in this mode are determined approximately analytically. Parametric analysis of the influence of the material and boundary conditions on the dynamics of warming up and drying is revealed.

Meshfree and efficient modeling of swimming cells

NASA Astrophysics Data System (ADS)

Gallagher, Meurig T.; Smith, David J.

2018-05-01

Locomotion in Stokes flow is an intensively studied problem because it describes important biological phenomena such as the motility of many species' sperm, bacteria, algae, and protozoa. Numerical computations can be challenging, particularly in three dimensions, due to the presence of moving boundaries and complex geometries; methods which combine ease of implementation and computational efficiency are therefore needed. A recently proposed method to discretize the regularized Stokeslet boundary integral equation without the need for a connected mesh is applied to the inertialess locomotion problem in Stokes flow. The mathematical formulation and key aspects of the computational implementation in matlab® or GNU Octave are described, followed by numerical experiments with biflagellate algae and multiple uniflagellate sperm swimming between no-slip surfaces, for which both swimming trajectories and flow fields are calculated. These computational experiments required minutes of time on modest hardware; an extensible implementation is provided in a GitHub repository. The nearest-neighbor discretization dramatically improves convergence and robustness, a key challenge in extending the regularized Stokeslet method to complicated three-dimensional biological fluid problems.

A DFFD simulation method combined with the spectral element method for solid-fluid-interaction problems

NASA Astrophysics Data System (ADS)

Chen, Li-Chieh; Huang, Mei-Jiau

2017-02-01

A 2D simulation method for a rigid body moving in an incompressible viscous fluid is proposed. It combines one of the immersed-boundary methods, the DFFD (direct forcing fictitious domain) method with the spectral element method; the former is employed for efficiently capturing the two-way FSI (fluid-structure interaction) and the geometric flexibility of the latter is utilized for any possibly co-existing stationary and complicated solid or flow boundary. A pseudo body force is imposed within the solid domain to enforce the rigid body motion and a Lagrangian mesh composed of triangular elements is employed for tracing the rigid body. In particular, a so called sub-cell scheme is proposed to smooth the discontinuity at the fluid-solid interface and to execute integrations involving Eulerian variables over the moving-solid domain. The accuracy of the proposed method is verified through an observed agreement of the simulation results of some typical flows with analytical solutions or existing literatures.

From the Nano- to the Macroscale - Bridging Scales for the Moving Contact Line Problem

NASA Astrophysics Data System (ADS)

Nold, Andreas; Sibley, David; Goddard, Benjamin; Kalliadasis, Serafim; Complex Multiscale Systems Team

2016-11-01

The moving contact line problem remains an unsolved fundamental problem in fluid mechanics. At the heart of the problem is its multiscale nature: a nanoscale region close to the solid boundary where the continuum hypothesis breaks down, must be resolved before effective macroscale parameters such as contact line friction and slip can be obtained. To capture nanoscale properties very close to the contact line and to establish a link to the macroscale behaviour, we employ classical density-functional theory (DFT), in combination with extended Navier-Stokes-like equations. Using simple models for viscosity and slip at the wall, we compare our computations with the Molecular Kinetic Theory, by extracting the contact line friction, depending on the imposed temperature of the fluid. A key fluid property captured by DFT is the fluid layering at the wall-fluid interface, which has a large effect on the shearing properties of a fluid. To capture this crucial property, we propose an anisotropic model for the viscosity, which also allows us to scrutinize the effect of fluid layering on contact line friction.

The Ffowcs Williams-Hawkings equation - Fifteen years of research

NASA Technical Reports Server (NTRS)

Farassat, F.

1986-01-01

The Ffowcs Williams-Hawkings equation governs the generation of sound in fluids in the presence of solid boundaries in motion. This equation is reviewed for situations where the linearization of the governing equations is allowed. In addition, research on the application of this equation to problems of aeroacoustic is briefly surveyed. Particular attention is given to the formulation of supersonic sources moving in uniform propeller-like motion.

Identification of a Flynn Effect in the NLSY: Moving from the Center to the Boundaries

ERIC Educational Resources Information Center

Rodgers, Joseph Lee; Wanstrom, Linda

2007-01-01

The Flynn Effect [Flynn, J. R. (1984). The mean IQ of Americans: Massive gains 1932 to 1978. Psychological Bulletin 95, 29-51.] is an increase in IQ of around 0.33 points per year, observed in developed (and some developing) countries during the past century. It emerges from problem solving and other non-verbal components of IQ. The cause has been…

Survival probability for a diffusive process on a growing domain

NASA Astrophysics Data System (ADS)

Simpson, Matthew J.; Sharp, Jesse A.; Baker, Ruth E.

2015-04-01

We consider the motion of a diffusive population on a growing domain, 0

Fluid Structure Interaction Techniques For Extrusion And Mixing Processes

NASA Astrophysics Data System (ADS)

Valette, Rudy; Vergnes, Bruno; Coupez, Thierry

2007-05-01

This work focuses on the development of numerical techniques devoted to the simulation of mixing processes of complex fluids such as twin-screw extrusion or batch mixing. In mixing process simulation, the absence of symmetry of the moving boundaries (the screws or the rotors) implies that their rigid body motion has to be taken into account by using a special treatment We therefore use a mesh immersion technique (MIT), which consists in using a P1+/P1-based (MINI-element) mixed finite element method for solving the velocity-pressure problem and then solving the problem in the whole barrel cavity by imposing a rigid motion (rotation) to nodes found located inside the so called immersed domain, each sub-domain (screw, rotor) being represented by a surface CAD mesh (or its mathematical equation in simple cases). The independent meshes are immersed into a unique background computational mesh by computing the distance function to their boundaries. Intersections of meshes are accounted for, allowing to compute a fill factor usable as for the VOF methodology. This technique, combined with the use of parallel computing, allows to compute the time-dependent flow of generalized Newtonian fluids including yield stress fluids in a complex system such as a twin screw extruder, including moving free surfaces, which are treated by a "level set" and Hamilton-Jacobi method.

Steam stripping of the unsaturated zone of contaminated sub-soils: The effect of diffusion/dispersion in the start-up phase

NASA Astrophysics Data System (ADS)

Brouwers, H. J. H.; Gilding, B. H.

2006-02-01

The unsteady process of steam stripping of the unsaturated zone of soils contaminated with volatile organic compounds (VOCs) is addressed. A model is presented. It accounts for the effects of water and contaminants remaining in vapour phase, as well as diffusion and dispersion of contaminants in this phase. The model has two components. The first is a one-dimensional description of the propagation of a steam front in the start-up phase. This is based on Darcy's law and conservation laws of mass and energy. The second component describes the transport of volatile contaminants. Taking the view that non-equilibrium between liquid and vapour phases exists, it accounts for evaporation, transport, and condensation at the front. This leads to a moving-boundary problem. The moving-boundary problem is brought into a fixed domain by a suitable transformation of the governing partial differential equations, and solved numerically. For a broad range of the governing dimensionless numbers, such as the Henry, Merkel and Péclet numbers, computational results are discussed. A mathematical asymptotic analysis supports this discussion. The range of parameter values for which the model is valid is investigated. Diffusion and dispersion are shown to be of qualitative importance, but to have little quantitative effect in the start-up phase.

Numerical simulation of low gravity draining. [computerized simulation of liquid sloshing in cylindrical tanks, and boundary value problems

NASA Technical Reports Server (NTRS)

Bizzell, G. D.; Crane, G. E.

1976-01-01

A boundary value problem was solved numerically for a liquid that is assumed to be inviscid and incompressible, having a motion that is irrotational and axisymmetric, and having a constant (5 degrees) solid-liquid contact angle. The avoidance of excessive mesh distortion, encountered with strictly Lagrangian or Eulerian kinematics, was achieved by introducing an auxiliary kinematic velocity field along the free surface in order to vary the trajectories used in integrating the ordinary differential equations simulating the moving boundary. The computation of the velocity potential was based upon a nonuniform triangular mesh which was automatically revised to varying depths to accommodate the motion of the free surface. These methods permitted calculation of draining induced axisymmetric slosh through the many (or fractional) finite amplitude oscillations that can occur depending upon the balance of draining, gravitational, and surface tension forces. Velocity fields, evolution of the free surface with time, and liquid residual volumes were computed for three and one half decades of Weber number and for two Bond numbers, tank fill levels, and drain radii. Comparisons with experimental data are very satisfactory.

Model of skin friction enhancement in undulatory swimming

NASA Astrophysics Data System (ADS)

Ehrenstein, Uwe; Eloy, Christophe

2012-11-01

To estimate the energetic cost of undulatory swimming, it is crucial to evaluate the drag forces originating from skin friction. This topic has been controversial for decades, some claiming that animals use ingenious mechanisms to reduce the drag and others hypothesizing that the undulatory motion induces a drag increase because of the compression of the boundary layers. In this paper, we examine this latter hypothesis, known as the ``Bone-Lighthill boundary-layer thinning hypothesis''. Considering a plate of section s moving perpendicular to itself at velocity U⊥ and applying the boundary-layer approximation for the incoming flow, the drag force per unit surface is shown to scale as √{U⊥ / s }. An analogous two-dimensional Navier-Stokes problem by artificially accelerating the flow in a channel of finite height is solved numerically, showing the robustness of the analytical results. Solving the problem for an undulatory plate motion similar to fish swimming, we find a drag enhancement which can be estimated to be of the order of 20 to 100%, depending on the geometry and the motion. M.J. Lighthill, Proc. R. Soc. Lond. B 179, 125 (1971).

An adaptive reconstruction for Lagrangian, direct-forcing, immersed-boundary methods

NASA Astrophysics Data System (ADS)

Posa, Antonio; Vanella, Marcos; Balaras, Elias

2017-12-01

Lagrangian, direct-forcing, immersed boundary (IB) methods have been receiving increased attention due to their robustness in complex fluid-structure interaction problems. They are very sensitive, however, on the selection of the Lagrangian grid, which is typically used to define a solid or flexible body immersed in a fluid flow. In the present work we propose a cost-efficient solution to this problem without compromising accuracy. Central to our approach is the use of isoparametric mapping to bridge the relative resolution requirements of Lagrangian IB, and Eulerian grids. With this approach, the density of surface Lagrangian markers, which is essential to properly enforce boundary conditions, is adapted dynamically based on the characteristics of the underlying Eulerian grid. The markers are not stored and the Lagrangian data-structure is not modified. The proposed scheme is implemented in the framework of a moving least squares reconstruction formulation, but it can be adapted to any Lagrangian, direct-forcing formulation. The accuracy and robustness of the approach is demonstrated in a variety of test cases of increasing complexity.

An immersed boundary method for modeling a dirty geometry data

NASA Astrophysics Data System (ADS)

Onishi, Keiji; Tsubokura, Makoto

2017-11-01

We present a robust, fast, and low preparation cost immersed boundary method (IBM) for simulating an incompressible high Re flow around highly complex geometries. The method is achieved by the dispersion of the momentum by the axial linear projection and the approximate domain assumption satisfying the mass conservation around the wall including cells. This methodology has been verified against an analytical theory and wind tunnel experiment data. Next, we simulate the problem of flow around a rotating object and demonstrate the ability of this methodology to the moving geometry problem. This methodology provides the possibility as a method for obtaining a quick solution at a next large scale supercomputer. This research was supported by MEXT as ``Priority Issue on Post-K computer'' (Development of innovative design and production processes) and used computational resources of the K computer provided by the RIKEN Advanced Institute for Computational Science.

Substructure method in high-speed monorail dynamic problems

NASA Astrophysics Data System (ADS)

Ivanchenko, I. I.

2008-12-01

The study of actions of high-speed moving loads on bridges and elevated tracks remains a topical problem for transport. In the present study, we propose a new method for moving load analysis of elevated tracks (monorail structures or bridges), which permits studying the interaction between two strained objects consisting of rod systems and rigid bodies with viscoelastic links; one of these objects is the moving load (monorail rolling stock), and the other is the carrying structure (monorail elevated track or bridge). The methods for moving load analysis of structures were developed in numerous papers [1-15]. At the first stage, when solving the problem about a beam under the action of the simplest moving load such as a moving weight, two fundamental methods can be used; the same methods are realized for other structures and loads. The first method is based on the use of a generalized coordinate in the expansion of the deflection in the natural shapes of the beam, and the problem is reduced to solving a system of ordinary differential equations with variable coefficients [1-3]. In the second method, after the "beam-weight" system is decomposed, just as in the problem with the weight impact on the beam [4], solving the problem is reduced to solving an integral equation for the dynamic weight reaction [6, 7]. In [1-3], an increase in the number of retained forms leads to an increase in the order of the system of equations; in [6, 7], difficulties arise when solving the integral equations related to the conditional stability of the step procedures. The method proposed in [9, 14] for beams and rod systems combines the above approaches and eliminates their drawbacks, because it permits retaining any necessary number of shapes in the deflection expansion and has a resolving system of equations with an unconditionally stable integration scheme and with a minimum number of unknowns, just as in the method of integral equations [6, 7]. This method is further developed for combined schemes modeling a strained elastic compound moving structure and a monorail elevated track. The problems of development of methods for dynamic analysis of monorails are very topical, especially because of increasing speeds of the rolling stock motion. These structures are studied in [16-18]. In the present paper, the above problem is solved by using the method for the moving load analysis and a step procedure of integration with respect to time, which were proposed in [9, 19], respectively. Further, these components are used to enlarge the possibilities of the substructure method in problems of dynamics. In the approach proposed for moving load analysis of structures, for a substructure (having the shape of a boundary element or a superelement) we choose an object moving at a constant speed (a monorail rolling stock); in this case, we use rod boundary elements of large length, which are gathered in a system modeling these objects. In particular, sets of such elements form a model of a monorail rolling stock, namely, carriage hulls, wheeled carts, elements of the wheel spring suspension, models of continuous beams of monorail ways and piers with foundations admitting emergency subsidence and unilateral links. These specialized rigid finite elements with linear and nonlinear links, included into the set of earlier proposed finite elements [14, 19], permit studying unsteady vibrations in the "monorail train-elevated track" (MTET) system taking into account various irregularities on the beam-rail, the pier emergency subsidence, and their elastic support by the basement. In this case, a high degree of the structure spatial digitization is obtained by using rods with distributed parameters in the analysis. The displacements are approximated by linear functions and trigonometric Fourier series, which, as was already noted, permits increasing the number of degrees of freedom of the system under study simultaneously preserving the order of the resolving system of equations. This approach permits studying the stress-strain state in the MTET system and determining accelerations at the desired points of the rolling stock. The proposed numerical procedure permits uniquely solving linear and nonlinear differential equations describing the operation of the model, which replaces the system by a monorail rolling stock consisting of several specialized mutually connected cars and a system of continuous beams on elastic inertial supports. This approach (based on the use of a moving substructure, which is also modeled by a system of boundary rod elements) permits maximally reducing the number of unknowns in the resolving system of equations at each step of its solution [11]. The authors of the preceding investigations of this problem, when studying the simultaneous vibrations of bridges and moving loads, considered only the case in which the rolling stock was represented by sufficiently complicated systems of rigid bodies connected by viscoelastic links [3-18] and the rolling stock motion was described by systems of ordinary differential equations. A specific characteristic of the proposed method is that it is convenient to derive the equations of motion of both the rolling stock and the bridge structure. The method [9, 14] permits obtaining the equations of interaction between the structures as two separate finite-element structures. Hence the researcher need not traditionally write out the system of equations of motion, for example, for the rolling stock (of cars) with finitely many degrees of freedom [3-18].We note several papers where simultaneous vibrations of an elastic moving load and an elastic carrying structure are considered in a rather narrow region and have a specific character. For example, the motion of an elastic rod along an elastic infinite rod on an elastic foundation is studied in [20], and the body of a car moving along a beam is considered as a rod with ten concentrated masses in [21].

Crossing and creating boundaries in healthcare innovation.

PubMed

Ingerslev, Karen

2016-06-20

Purpose - This paper reports from a qualitative case study of a change initiative undertaken in a Danish public hospital setting during national healthcare reforms. The purpose of this paper is to challenge understandings of innovations as defined by being value-adding per se. Whether the effects of attempting to innovate are positive or negative is in this paper regarded as a matter of empirical investigation. Design/methodology/approach - Narrative accounts of activities during the change initiative are analysed in order to elucidate the effects of framing the change initiative as innovation on which boundaries are created and crossed. Findings - Framing change initiatives as innovation leads to intended as well as unanticipated boundary crossings where healthcare practitioners from different organizations recognize a shared problem and task. It also leads to unintended boundary reinforcements between "us and them" that may exclude the perspectives of patients or stakeholders when confronting complex problems in healthcare. This boundary reinforcement can lead to further fragmentation of healthcare despite the stated intention to create more integrated services. Practical implications - The paper suggests that researchers as well as practitioners should not presume that intentions to innovate will by themselves enhance creativity and innovation. When analysing the intended, unintended as well as unanticipated consequences of framing change initiatives as innovation, researchers and practitioner gain nuanced knowledge about the effects of intending to innovate in complex settings such as healthcare. Originality/value - This paper suggests the need for an analytical move from studying the effects of innovation to studying the effects of framing complex problems as a call for innovation.

Solving of the coefficient inverse problems for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time data

NASA Astrophysics Data System (ADS)

Lukyanenko, D. V.; Shishlenin, M. A.; Volkov, V. T.

2018-01-01

We propose the numerical method for solving coefficient inverse problem for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time observation data based on the asymptotic analysis and the gradient method. Asymptotic analysis allows us to extract a priory information about interior layer (moving front), which appears in the direct problem, and boundary layers, which appear in the conjugate problem. We describe and implement the method of constructing a dynamically adapted mesh based on this a priory information. The dynamically adapted mesh significantly reduces the complexity of the numerical calculations and improve the numerical stability in comparison with the usual approaches. Numerical example shows the effectiveness of the proposed method.

A Review of Methods for Moving Boundary Problems

DTIC Science & Technology

2009-07-01

the bound- ary value problem for the eikonal equation: ‖∇u‖ = 1 for x ∈ Ω (29) u = 0 for x ∈ Γ (30) ERDC/CHL TR-09-10 8 where ‖ ‖ is the Euclidean norm...Solutions of the eikonal equation can in turn be characterized as steady state solutions of the initial value prob- lem ut + sgn(u0)(‖∇u‖ − 1) = 0...LS using the eikonal equation and use the NCI equation for the LS dynam- ics. The complete system of equations in weak form is ∫ Ω (‖∇u‖ − 1)wdV = 0

A Cartesian cut cell method for rarefied flow simulations around moving obstacles

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dechristé, G., E-mail: Guillaume.Dechriste@math.u-bordeaux1.fr; CNRS, IMB, UMR 5251, F-33400 Talence; Mieussens, L., E-mail: Luc.Mieussens@math.u-bordeaux1.fr

2016-06-01

For accurate simulations of rarefied gas flows around moving obstacles, we propose a cut cell method on Cartesian grids: it allows exact conservation and accurate treatment of boundary conditions. Our approach is designed to treat Cartesian cells and various kinds of cut cells by the same algorithm, with no need to identify the specific shape of each cut cell. This makes the implementation quite simple, and allows a direct extension to 3D problems. Such simulations are also made possible by using an adaptive mesh refinement technique and a hybrid parallel implementation. This is illustrated by several test cases, including amore » 3D unsteady simulation of the Crookes radiometer.« less

Analytical Solutions for an Escape Problem in a Disc with an Arbitrary Distribution of Exit Holes Along Its Boundary

NASA Astrophysics Data System (ADS)

Marshall, J. S.

2016-12-01

We analytically construct solutions for the mean first-passage time and splitting probabilities for the escape problem of a particle moving with continuous Brownian motion in a confining planar disc with an arbitrary distribution (i.e., of any number, size and spacing) of exit holes/absorbing sections along its boundary. The governing equations for these quantities are Poisson's equation with a (non-zero) constant forcing term and Laplace's equation, respectively, and both are subject to a mixture of homogeneous Neumann and Dirichlet boundary conditions. Our solutions are expressed as explicit closed formulae written in terms of a parameterising variable via a conformal map, using special transcendental functions that are defined in terms of an associated Schottky group. They are derived by exploiting recent results for a related problem of fluid mechanics that describes a unidirectional flow over "no-slip/no-shear" surfaces, as well as results from potential theory, all of which were themselves derived using the same theory of Schottky groups. They are exact up to the determination of a finite set of mapping parameters, which is performed numerically. Their evaluation also requires the numerical inversion of the parameterising conformal map. Computations for a series of illustrative examples are also presented.

Numerical methods for large-scale, time-dependent partial differential equations

NASA Technical Reports Server (NTRS)

Turkel, E.

1979-01-01

A survey of numerical methods for time dependent partial differential equations is presented. The emphasis is on practical applications to large scale problems. A discussion of new developments in high order methods and moving grids is given. The importance of boundary conditions is stressed for both internal and external flows. A description of implicit methods is presented including generalizations to multidimensions. Shocks, aerodynamics, meteorology, plasma physics and combustion applications are also briefly described.

Nonlinear dynamics of mushy layers induced by external stochastic fluctuations.

PubMed

Alexandrov, Dmitri V; Bashkirtseva, Irina A; Ryashko, Lev B

2018-02-28

The time-dependent process of directional crystallization in the presence of a mushy layer is considered with allowance for arbitrary fluctuations in the atmospheric temperature and friction velocity. A nonlinear set of mushy layer equations and boundary conditions is solved analytically when the heat and mass fluxes at the boundary between the mushy layer and liquid phase are induced by turbulent motion in the liquid and, as a result, have the corresponding convective form. Namely, the 'solid phase-mushy layer' and 'mushy layer-liquid phase' phase transition boundaries as well as the solid fraction, temperature and concentration (salinity) distributions are found. If the atmospheric temperature and friction velocity are constant, the analytical solution takes a parametric form. In the more common case when they represent arbitrary functions of time, the analytical solution is given by means of the standard Cauchy problem. The deterministic and stochastic behaviour of the phase transition process is analysed on the basis of the obtained analytical solutions. In the case of stochastic fluctuations in the atmospheric temperature and friction velocity, the phase transition interfaces (mushy layer boundaries) move faster than in the deterministic case. A cumulative effect of these noise contributions is revealed as well. In other words, when the atmospheric temperature and friction velocity fluctuate simultaneously due to the influence of different external processes and phenomena, the phase transition boundaries move even faster. This article is part of the theme issue 'From atomistic interfaces to dendritic patterns'.This article is part of the theme issue 'From atomistic interfaces to dendritic patterns'. © 2018 The Author(s).

CFD study of the flow pattern in an ultrasonic horn reactor: Introducing a realistic vibrating boundary condition.

PubMed

Rahimi, Masoud; Movahedirad, Salman; Shahhosseini, Shahrokh

2017-03-01

Recently, great attention has been paid to predict the acoustic streaming field distribution inside the sonoreactors, induced by high-power ultrasonic wave generator. The focus of this paper is to model an ultrasonic vibrating horn and study the induced flow pattern with a newly developed moving boundary condition. The numerical simulation utilizes the modified cavitation model along with the "mixture" model for turbulent flow (RNG, k-ε), and a moving boundary condition with an oscillating parabolic-logarithmic profile, applied to the horn tip. This moving-boundary provides the situation in which the center of the horn tip vibrates stronger than that of the peripheral regions. The velocity field obtained by computational fluid dynamic was in a reasonably good agreement with the PIV results. The moving boundary model is more accurate since it better approximates the movement of the horn tip in the ultrasonic assisted process. From an optimizing point of view, the model with the new moving boundary is more suitable than the conventional models for design purposes because the displacement magnitude of the horn tip is the only fitting parameter. After developing and validating the numerical model, the model was utilized to predict various quantities such as cavitation zone, pressure field and stream function that are not experimentally feasible to measure. Copyright © 2016 Elsevier B.V. All rights reserved.

A New Ghost Cell/Level Set Method for Moving Boundary Problems: Application to Tumor Growth

PubMed Central

Macklin, Paul

2011-01-01

In this paper, we present a ghost cell/level set method for the evolution of interfaces whose normal velocity depend upon the solutions of linear and nonlinear quasi-steady reaction-diffusion equations with curvature-dependent boundary conditions. Our technique includes a ghost cell method that accurately discretizes normal derivative jump boundary conditions without smearing jumps in the tangential derivative; a new iterative method for solving linear and nonlinear quasi-steady reaction-diffusion equations; an adaptive discretization to compute the curvature and normal vectors; and a new discrete approximation to the Heaviside function. We present numerical examples that demonstrate better than 1.5-order convergence for problems where traditional ghost cell methods either fail to converge or attain at best sub-linear accuracy. We apply our techniques to a model of tumor growth in complex, heterogeneous tissues that consists of a nonlinear nutrient equation and a pressure equation with geometry-dependent jump boundary conditions. We simulate the growth of glioblastoma (an aggressive brain tumor) into a large, 1 cm square of brain tissue that includes heterogeneous nutrient delivery and varied biomechanical characteristics (white matter, gray matter, cerebrospinal fluid, and bone), and we observe growth morphologies that are highly dependent upon the variations of the tissue characteristics—an effect observed in real tumor growth. PMID:21331304

Integral representations of solutions of the wave equation based on relativistic wavelets

NASA Astrophysics Data System (ADS)

Perel, Maria; Gorodnitskiy, Evgeny

2012-09-01

A representation of solutions of the wave equation with two spatial coordinates in terms of localized elementary ones is presented. Elementary solutions are constructed from four solutions with the help of transformations of the affine Poincaré group, i.e. with the help of translations, dilations in space and time and Lorentz transformations. The representation can be interpreted in terms of the initial-boundary value problem for the wave equation in a half-plane. It gives the solution as an integral representation of two types of solutions: propagating localized solutions running away from the boundary under different angles and packet-like surface waves running along the boundary and exponentially decreasing away from the boundary. Properties of elementary solutions are discussed. A numerical investigation of coefficients of the decomposition is carried out. An example of the decomposition of the field created by sources moving along a line with different speeds is considered, and the dependence of coefficients on speeds of sources is discussed.

Mass-conserved volumetric lattice Boltzmann method for complex flows with willfully moving boundaries.

PubMed

Yu, Huidan; Chen, Xi; Wang, Zhiqiang; Deep, Debanjan; Lima, Everton; Zhao, Ye; Teague, Shawn D

2014-06-01

In this paper, we develop a mass-conserved volumetric lattice Boltzmann method (MCVLBM) for numerically solving fluid dynamics with willfully moving arbitrary boundaries. In MCVLBM, fluid particles are uniformly distributed in lattice cells and the lattice Boltzmann equations deal with the time evolution of the particle distribution function. By introducing a volumetric parameter P(x,y,z,t) defined as the occupation of solid volume in the cell, we distinguish three types of lattice cells in the simulation domain: solid cell (pure solid occupation, P=1), fluid cell (pure fluid occupation, P=0), and boundary cell (partial solid and partial fluid, 0

Mechanisms in wing-in-ground effect aerodynamics

NASA Astrophysics Data System (ADS)

Jones, Marvin Alan

An aircraft in low-level flight experiences a large increase in lift and a marked reduction in drag, compared with flight at altitude. This phenomenon is termed the 'wing-in-ground' effect. In these circumstances a region of high pressure is created beneath the aerofoil, and a pressure difference is set up between its upper and lower surfaces. A pressure difference is not permitted at the trailing edge and therefore a mechanism must exist which allows the pressures above and below to adjust themselves to produce a continuous pressure field in the wake. It is the study of this mechanism and its role in the aerodynamics of low-level flight that forms the basis of our investigation. We begin in Chapter 2 by considering the flow past a thin aero-foil moving at moderate distances from the ground, the typical ground clearance a being of order unity. The aforementioned mechanism is introduced and described in detail in the context of this inviscid problem. Chapter 3 considers the same flow for large and small ground clearances and in the later case shows that the flow solution beneath the aerofoil takes on a particularly simple form. In this case the lift is shown to increase as a-1. In Chapter 4 we focus on the flow past the trailing edge of an aerofoil moving even nearer the ground, with the ground just outside the boundary layer. We show that in this case our asymptotic theory for small a is consistent with a 'triple-deck' approach to the problem which incorporates ground effects via a new pressure-displacement law. The triple-deck ground-interference problem is stated and solved. In Chapter 5 we investigate the case where the aerofoil is so near the ground that the ground is inside the boundary layer. Here the moving ground interacts with the aerofoil in a fully viscous way and the non-linear boundary layer equations hold along the entire length of the aerofoil. Again a pressure difference at the trailing edge is not permitted and this produces upstream adjustment back to the leading edge. Regions of reversed flow can occur and their effects, with regard to downforce production and racing car undertray design, are considered. In Chapter 6 we consider 'wing-in-tunnel' effects.

Moving overlapping grids with adaptive mesh refinement for high-speed reactive and non-reactive flow

NASA Astrophysics Data System (ADS)

Henshaw, William D.; Schwendeman, Donald W.

2006-08-01

We consider the solution of the reactive and non-reactive Euler equations on two-dimensional domains that evolve in time. The domains are discretized using moving overlapping grids. In a typical grid construction, boundary-fitted grids are used to represent moving boundaries, and these grids overlap with stationary background Cartesian grids. Block-structured adaptive mesh refinement (AMR) is used to resolve fine-scale features in the flow such as shocks and detonations. Refinement grids are added to base-level grids according to an estimate of the error, and these refinement grids move with their corresponding base-level grids. The numerical approximation of the governing equations takes place in the parameter space of each component grid which is defined by a mapping from (fixed) parameter space to (moving) physical space. The mapped equations are solved numerically using a second-order extension of Godunov's method. The stiff source term in the reactive case is handled using a Runge-Kutta error-control scheme. We consider cases when the boundaries move according to a prescribed function of time and when the boundaries of embedded bodies move according to the surface stress exerted by the fluid. In the latter case, the Newton-Euler equations describe the motion of the center of mass of the each body and the rotation about it, and these equations are integrated numerically using a second-order predictor-corrector scheme. Numerical boundary conditions at slip walls are described, and numerical results are presented for both reactive and non-reactive flows that demonstrate the use and accuracy of the numerical approach.

Transient analysis of bodies with moving boundaries using NASTRAN

NASA Technical Reports Server (NTRS)

Frye, J. W.

1975-01-01

A scheme is presented which allows the modeling of a moving boundary with NASTRAN NOLIN cards. Various aspects and limitations of the approach are explained. Recommendations are given as to the procedure to be used in implementing the method.

An immersed boundary-simplified sphere function-based gas kinetic scheme for simulation of 3D incompressible flows

NASA Astrophysics Data System (ADS)

Yang, L. M.; Shu, C.; Yang, W. M.; Wang, Y.; Wu, J.

2017-08-01

In this work, an immersed boundary-simplified sphere function-based gas kinetic scheme (SGKS) is presented for the simulation of 3D incompressible flows with curved and moving boundaries. At first, the SGKS [Yang et al., "A three-dimensional explicit sphere function-based gas-kinetic flux solver for simulation of inviscid compressible flows," J. Comput. Phys. 295, 322 (2015) and Yang et al., "Development of discrete gas kinetic scheme for simulation of 3D viscous incompressible and compressible flows," J. Comput. Phys. 319, 129 (2016)], which is often applied for the simulation of compressible flows, is simplified to improve the computational efficiency for the simulation of incompressible flows. In the original SGKS, the integral domain along the spherical surface for computing conservative variables and numerical fluxes is usually not symmetric at the cell interface. This leads the expression of numerical fluxes at the cell interface to be relatively complicated. For incompressible flows, the sphere at the cell interface can be approximately considered to be symmetric as shown in this work. Besides that, the energy equation is usually not needed for the simulation of incompressible isothermal flows. With all these simplifications, the simple and explicit formulations for the conservative variables and numerical fluxes at the cell interface can be obtained. Second, to effectively implement the no-slip boundary condition for fluid flow problems with complex geometry as well as moving boundary, the implicit boundary condition-enforced immersed boundary method [Wu and Shu, "Implicit velocity correction-based immersed boundary-lattice Boltzmann method and its applications," J. Comput. Phys. 228, 1963 (2009)] is introduced into the simplified SGKS. That is, the flow field is solved by the simplified SGKS without considering the presence of an immersed body and the no-slip boundary condition is implemented by the immersed boundary method. The accuracy and efficiency of the present scheme are validated by simulating the decaying vortex flow, flow past a stationary and rotating sphere, flow past a stationary torus, and flows over dragonfly flight.

Analytic Formulation and Numerical Implementation of an Acoustic Pressure Gradient Prediction

NASA Technical Reports Server (NTRS)

Lee, Seongkyu; Brentner, Kenneth S.; Farassat, F.; Morris, Philip J.

2008-01-01

Two new analytical formulations of the acoustic pressure gradient have been developed and implemented in the PSU-WOPWOP rotor noise prediction code. The pressure gradient can be used to solve the boundary condition for scattering problems and it is a key aspect to solve acoustic scattering problems. The first formulation is derived from the gradient of the Ffowcs Williams-Hawkings (FW-H) equation. This formulation has a form involving the observer time differentiation outside the integrals. In the second formulation, the time differentiation is taken inside the integrals analytically. This formulation avoids the numerical time differentiation with respect to the observer time, which is computationally more efficient. The acoustic pressure gradient predicted by these new formulations is validated through comparison with available exact solutions for a stationary and moving monopole sources. The agreement between the predictions and exact solutions is excellent. The formulations are applied to the rotor noise problems for two model rotors. A purely numerical approach is compared with the analytical formulations. The agreement between the analytical formulations and the numerical method is excellent for both stationary and moving observer cases.

Adaptive density trajectory cluster based on time and space distance

NASA Astrophysics Data System (ADS)

Liu, Fagui; Zhang, Zhijie

2017-10-01

There are some hotspot problems remaining in trajectory cluster for discovering mobile behavior regularity, such as the computation of distance between sub trajectories, the setting of parameter values in cluster algorithm and the uncertainty/boundary problem of data set. As a result, based on the time and space, this paper tries to define the calculation method of distance between sub trajectories. The significance of distance calculation for sub trajectories is to clearly reveal the differences in moving trajectories and to promote the accuracy of cluster algorithm. Besides, a novel adaptive density trajectory cluster algorithm is proposed, in which cluster radius is computed through using the density of data distribution. In addition, cluster centers and number are selected by a certain strategy automatically, and uncertainty/boundary problem of data set is solved by designed weighted rough c-means. Experimental results demonstrate that the proposed algorithm can perform the fuzzy trajectory cluster effectively on the basis of the time and space distance, and obtain the optimal cluster centers and rich cluster results information adaptably for excavating the features of mobile behavior in mobile and sociology network.

Local mesh adaptation technique for front tracking problems

NASA Astrophysics Data System (ADS)

Lock, N.; Jaeger, M.; Medale, M.; Occelli, R.

1998-09-01

A numerical model is developed for the simulation of moving interfaces in viscous incompressible flows. The model is based on the finite element method with a pseudo-concentration technique to track the front. Since a Eulerian approach is chosen, the interface is advected by the flow through a fixed mesh. Therefore, material discontinuity across the interface cannot be described accurately. To remedy this problem, the model has been supplemented with a local mesh adaptation technique. This latter consists in updating the mesh at each time step to the interface position, such that element boundaries lie along the front. It has been implemented for unstructured triangular finite element meshes. The outcome of this technique is that it allows an accurate treatment of material discontinuity across the interface and, if necessary, a modelling of interface phenomena such as surface tension by using specific boundary elements. For illustration, two examples are computed and presented in this paper: the broken dam problem and the Rayleigh-Taylor instability. Good agreement has been obtained in the comparison of the numerical results with theory or available experimental data.

Analytical solution of the problem of a shock wave in the collapsing gas in Lagrangian coordinates

NASA Astrophysics Data System (ADS)

Kuropatenko, V. F.; Shestakovskaya, E. S.

2016-10-01

It is proposed the exact solution of the problem of a convergent shock wave and gas dynamic compression in a spherical vessel with an impermeable wall in Lagrangian coordinates. At the initial time the speed of cold ideal gas is equal to zero, and a negative velocity is set on boundary of the sphere. When t > t0 the shock wave spreads from this point into the gas. The boundary of the sphere will move under the certain law correlated with the motion of the shock wave. The trajectories of the gas particles in Lagrangian coordinates are straight lines. The equations determining the structure of the gas flow between the shock front and gas border have been found as a function of time and Lagrangian coordinate. The dependence of the entropy on the velocity of the shock wave has been found too. For Lagrangian coordinates the problem is first solved. It is fundamentally different from previously known formulations of the problem of the self-convergence of the self-similar shock wave to the center of symmetry and its reflection from the center, which was built up for the infinite area in Euler coordinates.

Meshless Local Petrov-Galerkin Euler-Bernoulli Beam Problems: A Radial Basis Function Approach

NASA Technical Reports Server (NTRS)

Raju, I. S.; Phillips, D. R.; Krishnamurthy, T.

2003-01-01

A radial basis function implementation of the meshless local Petrov-Galerkin (MLPG) method is presented to study Euler-Bernoulli beam problems. Radial basis functions, rather than generalized moving least squares (GMLS) interpolations, are used to develop the trial functions. This choice yields a computationally simpler method as fewer matrix inversions and multiplications are required than when GMLS interpolations are used. Test functions are chosen as simple weight functions as in the conventional MLPG method. Compactly and noncompactly supported radial basis functions are considered. The non-compactly supported cubic radial basis function is found to perform very well. Results obtained from the radial basis MLPG method are comparable to those obtained using the conventional MLPG method for mixed boundary value problems and problems with discontinuous loading conditions.

Single particle nonlocality, geometric phases and time-dependent boundary conditions

NASA Astrophysics Data System (ADS)

Matzkin, A.

2018-03-01

We investigate the issue of single particle nonlocality in a quantum system subjected to time-dependent boundary conditions. We discuss earlier claims according to which the quantum state of a particle remaining localized at the center of an infinite well with moving walls would be specifically modified by the change in boundary conditions due to the wall’s motion. We first prove that the evolution of an initially localized Gaussian state is not affected nonlocally by a linearly moving wall: as long as the quantum state has negligible amplitude near the wall, the boundary motion has no effect. This result is further extended to related confined time-dependent oscillators in which the boundary’s motion is known to give rise to geometric phases: for a Gaussian state remaining localized far from the boundaries, the effect of the geometric phases is washed out and the particle dynamics shows no traces of a nonlocal influence that would be induced by the moving boundaries.

The metamorphoses of relativity

NASA Astrophysics Data System (ADS)

Staley, Richard

This talk will explore the ways that problems shifted and disciplinary boundaries changed around physicists' engagement with relational physics and relativistic thought, first in research dealing with physiology, psychology and geometry in the late nineteenth century and then (a better-known story) moving between physics, mathematics and geometry in the twentieth century. I hope to develop a richer approach for understanding the disciplinary and political significance of relativity, especially by considering in one framework the work of Engels, Mach, Einstein and Planck.

Domain Immersion Technique And Free Surface Computations Applied To Extrusion And Mixing Processes

NASA Astrophysics Data System (ADS)

Valette, Rudy; Vergnes, Bruno; Basset, Olivier; Coupez, Thierry

2007-04-01

This work focuses on the development of numerical techniques devoted to the simulation of mixing processes of complex fluids such as twin-screw extrusion or batch mixing. In mixing process simulation, the absence of symmetry of the moving boundaries (the screws or the rotors) implies that their rigid body motion has to be taken into account by using a special treatment. We therefore use a mesh immersion technique (MIT), which consists in using a P1+/P1-based (MINI-element) mixed finite element method for solving the velocity-pressure problem and then solving the problem in the whole barrel cavity by imposing a rigid motion (rotation) to nodes found located inside the so called immersed domain, each subdomain (screw, rotor) being represented by a surface CAD mesh (or its mathematical equation in simple cases). The independent meshes are immersed into a unique backgound computational mesh by computing the distance function to their boundaries. Intersections of meshes are accounted for, allowing to compute a fill factor usable as for the VOF methodology. This technique, combined with the use of parallel computing, allows to compute the time-dependent flow of generalized Newtonian fluids including yield stress fluids in a complex system such as a twin screw extruder, including moving free surfaces, which are treated by a "level set" and Hamilton-Jacobi method.

Visual memory for moving scenes.

PubMed

DeLucia, Patricia R; Maldia, Maria M

2006-02-01

In the present study, memory for picture boundaries was measured with scenes that simulated self-motion along the depth axis. The results indicated that boundary extension (a distortion in memory for picture boundaries) occurred with moving scenes in the same manner as that reported previously for static scenes. Furthermore, motion affected memory for the boundaries but this effect of motion was not consistent with representational momentum of the self (memory being further forward in a motion trajectory than actually shown). We also found that memory for the final position of the depicted self in a moving scene was influenced by properties of the optical expansion pattern. The results are consistent with a conceptual framework in which the mechanisms that underlie boundary extension and representational momentum (a) process different information and (b) both contribute to the integration of successive views of a scene while the scene is changing.

Validation of tsunami inundation model TUNA-RP using OAR-PMEL-135 benchmark problem set

NASA Astrophysics Data System (ADS)

Koh, H. L.; Teh, S. Y.; Tan, W. K.; Kh'ng, X. Y.

2017-05-01

A standard set of benchmark problems, known as OAR-PMEL-135, is developed by the US National Tsunami Hazard Mitigation Program for tsunami inundation model validation. Any tsunami inundation model must be tested for its accuracy and capability using this standard set of benchmark problems before it can be gainfully used for inundation simulation. The authors have previously developed an in-house tsunami inundation model known as TUNA-RP. This inundation model solves the two-dimensional nonlinear shallow water equations coupled with a wet-dry moving boundary algorithm. This paper presents the validation of TUNA-RP against the solutions provided in the OAR-PMEL-135 benchmark problem set. This benchmark validation testing shows that TUNA-RP can indeed perform inundation simulation with accuracy consistent with that in the tested benchmark problem set.

Nonlinear vibration of a traveling belt with non-homogeneous boundaries

NASA Astrophysics Data System (ADS)

Ding, Hu; Lim, C. W.; Chen, Li-Qun

2018-06-01

Free and forced nonlinear vibrations of a traveling belt with non-homogeneous boundary conditions are studied. The axially moving materials in operation are always externally excited and produce strong vibrations. The moving materials with the homogeneous boundary condition are usually considered. In this paper, the non-homogeneous boundaries are introduced by the support wheels. Equilibrium deformation of the belt is produced by the non-homogeneous boundaries. In order to solve the equilibrium deformation, the differential and integral quadrature methods (DIQMs) are utilized to develop an iterative scheme. The influence of the equilibrium deformation on free and forced nonlinear vibrations of the belt is explored. The DIQMs are applied to solve the natural frequencies and forced resonance responses of transverse vibration around the equilibrium deformation. The Galerkin truncation method (GTM) is utilized to confirm the DIQMs' results. The numerical results demonstrate that the non-homogeneous boundary conditions cause the transverse vibration to deviate from the straight equilibrium, increase the natural frequencies, and lead to coexistence of square nonlinear terms and cubic nonlinear terms. Moreover, the influence of non-homogeneous boundaries can be exacerbated by the axial speed. Therefore, non-homogeneous boundary conditions of axially moving materials especially should be taken into account.

General Solutions for Hydromagnetic Free Convection Flow over an Infinite Plate with Newtonian Heating, Mass Diffusion and Chemical Reaction

NASA Astrophysics Data System (ADS)

Fetecau, Constatin; Shah, Nehad Ali; Vieru, Dumitru

2017-12-01

The problem of hydromagnetic free convection flow over a moving infinite vertical plate with Newtonian heating, mass diffusion and chemical reaction in the presence of a heat source is completely solved. Radiative and porous effects are not taken into consideration but they can be immediately included by a simple rescaling of Prandtl number and magnetic parameter. Exact general solutions for the dimensionless velocity and concentration fields and the corresponding Sherwood number and skin friction coefficient are determined under integral form in terms of error function or complementary error function of Gauss. They satisfy all imposed initial and boundary conditions and can generate exact solutions for any problem with technical relevance of this type. As an interesting completion, uncommon in the literature, the differential equations which describe the thermal, concentration and momentum boundary layer, as well as the exact expressions for the thicknesses of thermal, concentration or velocity boundary layers were determined. Numerical results have shown that the thermal boundary layer thickness decreases for increasing values of Prandtl number and the concentration boundary layer thickness is decreasing with Schmidt number. Finally, for illustration, three special cases are considered and the influence of physical parameters on some fundamental motions is graphically underlined and discussed. The required time to reach the flow according with post-transient solution (the steady-state), for cosine/sine oscillating concentrations on the boundary is graphically determined. It is found that, the presence of destructive chemical reaction improves this time for increasing values of chemical reaction parameter.

The inverse problem for definition of the shape of a molten contact bridge

NASA Astrophysics Data System (ADS)

Kharin, Stanislav N.; Sarsengeldin, Merey M.

2017-09-01

The paper presents the results of investigation of bridging phenomenon occurring at opening of electrical contacts. The mathematical model describing the dynamics of metal molten bridge takes into account the Thomson effect. It is based on the system of partial differential equations for temperature and electrical fields of the bridge in the domain containing two moving unknown boundaries. One of them is an interface between liquid and solid zones of the bridge and should be found by the solution of the corresponding Stefan problem. The second free boundary corresponds to the shape of the visible part of a bridge. Its definition is an inverse problem, for which solution it is necessary to find minimum of the energy consuming for the formation of the shape of a quasi-stationary bridge. Three components of this energy, namely surface tension, pinch effect and gravitation, are defined by the functional which minimum gives the required shape of the bridge. The solution of corresponding variation problem is found by the reduction of the problem to the solution of the system of ordinary differential equations. Calculated values of the voltage of the bridge rupture for various metals are in a good agreement with the experimental data. The criteria responsible for the mechanism of molten bridge rupture are introduced in the paper.

Moving branes in the presence of background tachyon fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rezaei, Z., E-mail: z.rezaei@aut.ac.ir; Kamani, D., E-mail: kamani@aut.ac.ir

2011-12-15

We compute the boundary state associated with a moving Dp-brane in the presence of the open string tachyon field as a background field. The effect of the tachyon condensation on the boundary state is discussed. It leads to a boundary state associated with a lower-dimensional moving D-brane or a stationary instantonic D-brane. The former originates from condensation along the spatial directions and the latter comes from the temporal direction of the D-brane worldvolume. Using the boundary state, we also study the interaction amplitude between two arbitrary Dp{sub 1}- and Dp{sub 2}-branes. The long-range behavior of the amplitude is investigated, demonstratingmore » an obvious deviation from the conventional form, due to the presence of the background tachyon field.« less

Analysis and calculation of macrosegregation in a casting ingot, exhibits C and E

NASA Technical Reports Server (NTRS)

Poirier, D. R.; Maples, A. L.

1984-01-01

A computer model which describes the solidification of a binary metal alloy in an insulated rectangular mold with a temperature gradient is presented. A numerical technique, applicable to a broad class of moving boundary problems, was implemented therein. The solidification model described is used to calculate the macrosegregation within the solidified casting by coupling the equations for liquid flow in the solid/liquid or mushy zone with the energy equation for heat flow throughout the ingot and thermal convection in the bulk liquid portion. The rate of development of the solid can be automatically calculated by the model. Numerical analysis of such solidification parameters as enthalpy and boundary layer flow is displayed. On-line user interface and software documentation are presented.

On the Application of an Enthalpy Method to the Evolution of Fluvial Deltas Under Sea-Level Changes

NASA Astrophysics Data System (ADS)

Anderson, W.; Lorenzo-Trueba, J.; Voller, V. R.

2017-12-01

Fluvial deltas are composites of two primary sedimentary environments: a depositional fluvial region and an offshore region. The fluvial region is defined by two geomorphic moving boundaries: an alluvial-bedrock transition (ABT), which separates the sediment prism from the non-erodible bedrock basement, and the shoreline (SH), where the delta meets the ocean. The trajectories of these boundaries in time and space define the evolution of the shape of the sedimentary prism, and are often used as stratigraphic indicators, particularly in seismic studies, of changes in relative sea level and the identification of stratigraphic sequences. In order to better understand the relative role of sea-level variations, tectonics, and sediment supply on the evolution of these boundaries, we develop a forward stratigraphic model that captures the dynamic behavior of the fluvial surface and treats the SH and ABT as moving boundaries (i.e., internal boundaries whose location must be determined as part of the solution to the overall morphological evolution problem). This forward model extends a numerical technique from heat transfer (i.e., enthalpy method), previously applied to the evolution of sedimentary basins, to account for sea-level changes. The mathematics of the approach are verified by comparing predictions from the numerical model with both existing and newly developed closed form analytical solutions. Model results support previous work, which suggests that the migration of the ABT can respond very differently to the sea-level signal. This response depends on factors such as sediment supply and delta length, which can vary greatly between basins. These results can have important implications for the reconstruction of past sea-level changes from the stratigraphic record of sedimentary basins.

Extension of Kirchhoff's formula to radiation from moving surfaces

NASA Technical Reports Server (NTRS)

Farassat, F.; Myers, M. K.

1988-01-01

Kirchhoff's formula for radiation from a closed surface has been used recently for prediction of the noise of high speed rotors and propellers. Because the closed surface on which the boundary data are prescribed in these cases is in motion, an extension of Kirchhoff's formula to this condition is required. In this paper such a formula, obtained originally by Morgans for the interior problem, is derived for regions exterior to surfaces moving at speeds below the wave propagation speed by making use of some results of generalized function theory. It is shown that the usual Kirchhoff formula is a special case of the main result of the paper. The general result applies to a deformable surface. However, the special form it assumes for a rigid surface in motion is also noted. In addition, Morgans' result is further extended by showing that edge line integrals appear in the formula when applied to a surface that is piecewise smooth. Some possible areas of application of the formula to problems of current interest in aeroacoustics are discussed.

Extension of Kirchhoff's formula to radiation from moving surfaces

NASA Technical Reports Server (NTRS)

Farassat, F.; Myers, M. K.

1987-01-01

Kirchhoff's formula for radiation from a closed surface has been used recently for prediction of the noise of high speed rotors and propellers. Because the closed surface on which the boundary data are prescribed in these cases is in motion, an extension of Kirchhoff's formula to this condition is required. In this paper such a formula, obtained originally by Morgans for the interior problem, is derived for regions exterior to surfaces moving at speeds below the wave propagation speed by making use of some results of generalized function theory. It is shown that the usual Kirchhoff formula is a special case of the main result of the paper. The general result applies to a deformable surface. However, the special form it assumes for a rigid surface in motion is also noted. In addition, Morgans' result is further extended by showing that edge line integrals appear in the formula when applied to a surface that is piecewise smooth. Some possible areas of application of the formula to problems of current interest in aeroacoustics are discussed.

INTERNATIONAL CONFERENCE ON SEMICONDUCTOR INJECTION LASERS SELCO-87: Transient heat conduction in laser diodes

NASA Astrophysics Data System (ADS)

Enders, P.; Galley, J.

1988-11-01

The dynamics of heat transfer in stripe GaAlAs laser diodes is investigated by solving the linear diffusion equation for a quasitwo-dimensional multilayer structure. The calculations are rationalized drastically by the transfer matrix method and also using for the first time the asymptotes of the decay constants. Special attention is given to the convergence of the Fourier series. A comparison with experimental results reveals however that this is essentially the Stefan problem (with moving boundary conditions).

DOE Office of Scientific and Technical Information (OSTI.GOV)

Volkov, N. B.; Zubarev, N. M., E-mail: nick@iep.uran.ru; Zubareva, O. V.

Exact solutions are obtained for the problem of an equilibrium configuration of an uncharged cylindrical jet of a conducting liquid in a transverse electric field. The transverse cross section of the jet moving between two planar electrodes is deformed under the action of electrostatic forces (capillary forces play a stabilizing role). According to the solutions obtained, the initially circular cross section of the jet may be significantly (formally, unboundedly) stretched along the lines of forces of the field, and the boundaries of the jet asymptotically approach the electrodes.

A neural model of visual figure-ground segregation from kinetic occlusion.

PubMed

Barnes, Timothy; Mingolla, Ennio

2013-01-01

Freezing is an effective defense strategy for some prey, because their predators rely on visual motion to distinguish objects from their surroundings. An object moving over a background progressively covers (deletes) and uncovers (accretes) background texture while simultaneously producing discontinuities in the optic flow field. These events unambiguously specify kinetic occlusion and can produce a crisp edge, depth perception, and figure-ground segmentation between identically textured surfaces--percepts which all disappear without motion. Given two abutting regions of uniform random texture with different motion velocities, one region appears to be situated farther away and behind the other (i.e., the ground) if its texture is accreted or deleted at the boundary between the regions, irrespective of region and boundary velocities. Consequently, a region with moving texture appears farther away than a stationary region if the boundary is stationary, but it appears closer (i.e., the figure) if the boundary is moving coherently with the moving texture. A computational model of visual areas V1 and V2 shows how interactions between orientation- and direction-selective cells first create a motion-defined boundary and then signal kinetic occlusion at that boundary. Activation of model occlusion detectors tuned to a particular velocity results in the model assigning the adjacent surface with a matching velocity to the far depth. A weak speed-depth bias brings faster-moving texture regions forward in depth in the absence of occlusion (shearing motion). These processes together reproduce human psychophysical reports of depth ordering for key cases of kinetic occlusion displays. Copyright © 2012 Elsevier Ltd. All rights reserved.

Spin-3 topologically massive gravity

NASA Astrophysics Data System (ADS)

Chen, Bin; Long, Jiang; Wu, Jun-bao

2011-11-01

In this Letter, we study the spin-3 topologically massive gravity (TMG), paying special attention to its properties at the chiral point. We propose an action describing the higher spin fields coupled to TMG. We discuss the traceless spin-3 fluctuations around the AdS3 vacuum and find that there is an extra local massive mode, besides the left-moving and right-moving boundary massless modes. At the chiral point, such extra mode becomes massless and degenerates with the left-moving mode. We show that at the chiral point the only degrees of freedom in the theory are the boundary right-moving graviton and spin-3 field. We conjecture that spin-3 chiral gravity with generalized Brown-Henneaux boundary condition is holographically dual to 2D chiral CFT with classical W3 algebra and central charge cR = 3 l / G.

A Meshless Method Using Radial Basis Functions for Beam Bending Problems

NASA Technical Reports Server (NTRS)

Raju, I. S.; Phillips, D. R.; Krishnamurthy, T.

2004-01-01

A meshless local Petrov-Galerkin (MLPG) method that uses radial basis functions (RBFs) as trial functions in the study of Euler-Bernoulli beam problems is presented. RBFs, rather than generalized moving least squares (GMLS) interpolations, are used to develop the trial functions. This choice yields a computationally simpler method as fewer matrix inversions and multiplications are required than when GMLS interpolations are used. Test functions are chosen as simple weight functions as they are in the conventional MLPG method. Compactly and noncompactly supported RBFs are considered. Noncompactly supported cubic RBFs are found to be preferable. Patch tests, mixed boundary value problems, and problems with complex loading conditions are considered. Results obtained from the radial basis MLPG method are either of comparable or better accuracy than those obtained when using the conventional MLPG method.

A loosely-coupled scheme for the interaction between a fluid, elastic structure and poroelastic material

NASA Astrophysics Data System (ADS)

Bukač, M.

2016-05-01

We model the interaction between an incompressible, viscous fluid, thin elastic structure and a poroelastic material. The poroelastic material is modeled using the Biot's equations of dynamic poroelasticity. The fluid, elastic structure and the poroelastic material are fully coupled, giving rise to a nonlinear, moving boundary problem with novel energy estimates. We present a modular, loosely coupled scheme where the original problem is split into the fluid sub-problem, elastic structure sub-problem and poroelasticity sub-problem. An energy estimate associated with the stability of the scheme is derived in the case where one of the coupling parameters, β, is equal to zero. We present numerical tests where we investigate the effects of the material properties of the poroelastic medium on the fluid flow. Our findings indicate that the flow patterns highly depend on the storativity of the poroelastic material and cannot be captured by considering fluid-structure interaction only.

Comparison of Theoretical and Experimental Heat-Transfer Characteristics of Bodies of Revolution at Supersonic Speeds

NASA Technical Reports Server (NTRS)

Scherrer, Richard

1951-01-01

An investigation of the three important factors that determine convective heat-transfer characteristics at supersonic speeds, location boundary-layer transition, recovery factor, and heat-transfer parameter has been performed at Mach numbers from 1.49 to 1.18. The bodies of revolution that were tested had, in most cases, laminar boundary layers, and the test results have been compared with available theory. Boundary-layer transition was found to be affected by heat transfer. Adding heat to a laminar boundary layer caused transition to move forward on the test body, while removing heat caused transition to move rearward. These experimental results and the implications of boundary-layer-stability theory are in qualitative agreement.

Electromigration-induced void grain-boundary interactions: The mean time to failure for copper interconnects with bamboo and near-bamboo structures

NASA Astrophysics Data System (ADS)

Ogurtani, Tarik Omer; Oren, Ersin Emre

2004-12-01

A well-posed moving boundary-value problem, describing the dynamics of curved interfaces and surfaces associated with voids and/or cracks that are interacting with grain boundaries, is obtained. Extensive computer simulations are performed for void configuration evolution during intergranular motion, under the actions of capillary and electromigration forces in thin-film metallic interconnects with bamboo structures. The analysis of experimental data, utilizing the mean time to failure formulas derived in this paper, gives consistent values for the interface diffusion coefficients and enthalpies of voids. 5.85×10-5exp(-0.95eV/kT)m2s-1 is the value obtained for voids that form in the interior of the copper interconnects avoiding any surface contamination. 1.80×10-4exp(-1.20eV/kT)m2s-1 is obtained for those voids that nucleate either at triple junctions or at the grain-boundary technical surface intersections (grain-boundary groove), where the chemical impurities such as Si, O, S, and even C are segregated during the metallization and annealing processes and may act as trap centers for hopping vacancies.

Penalty methods for the numerical solution of American multi-asset option problems

NASA Astrophysics Data System (ADS)

Nielsen, Bjørn Fredrik; Skavhaug, Ola; Tveito, Aslak

2008-12-01

We derive and analyze a penalty method for solving American multi-asset option problems. A small, non-linear penalty term is added to the Black-Scholes equation. This approach gives a fixed solution domain, removing the free and moving boundary imposed by the early exercise feature of the contract. Explicit, implicit and semi-implicit finite difference schemes are derived, and in the case of independent assets, we prove that the approximate option prices satisfy some basic properties of the American option problem. Several numerical experiments are carried out in order to investigate the performance of the schemes. We give examples indicating that our results are sharp. Finally, the experiments indicate that in the case of correlated underlying assets, the same properties are valid as in the independent case.

Moving walls and geometric phases

DOE Office of Scientific and Technical Information (OSTI.GOV)

Facchi, Paolo, E-mail: paolo.facchi@ba.infn.it; INFN, Sezione di Bari, I-70126 Bari; Garnero, Giancarlo, E-mail: giancarlo.garnero@uniba.it

2016-09-15

We unveil the existence of a non-trivial Berry phase associated to the dynamics of a quantum particle in a one dimensional box with moving walls. It is shown that a suitable choice of boundary conditions has to be made in order to preserve unitarity. For these boundary conditions we compute explicitly the geometric phase two-form on the parameter space. The unboundedness of the Hamiltonian describing the system leads to a natural prescription of renormalization for divergent contributions arising from the boundary.

Real-time Fluorescence Polarization Microscopy of the Moving Boundary in Cross-Gradient SDS-PAGE

NASA Astrophysics Data System (ADS)

Hwang, Jeeseong; Giulian, Gary

2003-03-01

Real-time Fluorescence Polarization Microscopy of the Moving Boundary in Cross-Gradient SDS-PAGE Jeeseong Hwang, Jeffrey R. Krogmeier, Angela M. Bardo, Scott N. Goldie, Lori S. Goldner; Optical Technology Division, National Institute of Standards and Technology, Gaithersburg, MD 20899 Gary G. Giulian, Carl R. Merril; National Institute of Mental Health, National Institutes of Health, Bethesda, MD 20892 Sodium Dodecyl Sulfate Polyacrylamide Gel Electrophoresis (SDS-PAGE) is a popular method to separate proteins by their apparent molecular weight. However, it is a limited technique due, in part, to its low spatial resolution. In order to improve the resolution and to enhance the detection sensitivity of proteins separated by SDS-PAGE we are studying the detergent properties at the moving boundary of precast Tris-Tricine-Acetate cross-gradient gels using fluorescent cationic and pH indicating dyes. We have developed real-time full-field fluorescence polarization microscopy to monitor the dynamic fluorescence anisotropy from the cationic tetramethylindocarbocyanine dyes localized in the "extended stack", a concentrated detergent zone. We will present quantitative results of the fluorescence anisotropy. Our system is capable of analyzing local structures of the detergent molecules in the moving boundary of SDS-PAGE and the microenvironment(s) near the boundary. We will discuss the significance of these results and their potential role in enhanced protein separation.

SPLASH program for three dimensional fluid dynamics with free surface boundaries

NASA Astrophysics Data System (ADS)

Yamaguchi, A.

1996-05-01

This paper describes a three dimensional computer program SPLASH that solves Navier-Stokes equations based on the Arbitrary Lagrangian Eulerian (ALE) finite element method. SPLASH has been developed for application to the fluid dynamics problems including the moving boundary of a liquid metal cooled Fast Breeder Reactor (FBR). To apply SPLASH code to the free surface behavior analysis, a capillary model using a cubic Spline function has been developed. Several sample problems, e.g., free surface oscillation, vortex shedding development, and capillary tube phenomena, are solved to verify the computer program. In the analyses, the numerical results are in good agreement with the theoretical value or experimental observance. Also SPLASH code has been applied to an analysis of a free surface sloshing experiment coupled with forced circulation flow in a rectangular tank. This is a simplified situation of the flow field in a reactor vessel of the FBR. The computational simulation well predicts the general behavior of the fluid flow inside and the free surface behavior. Analytical capability of the SPLASH code has been verified in this study and the application to more practical problems such as FBR design and safety analysis is under way.

A novel spatial-temporal detection method of dim infrared moving small target

NASA Astrophysics Data System (ADS)

Chen, Zhong; Deng, Tao; Gao, Lei; Zhou, Heng; Luo, Song

2014-09-01

Moving small target detection under complex background in infrared image sequence is one of the major challenges of modern military in Early Warning Systems (EWS) and the use of Long-Range Strike (LRS). However, because of the low SNR and undulating background, the infrared moving small target detection is a difficult problem in a long time. To solve this problem, a novel spatial-temporal detection method based on bi-dimensional empirical mode decomposition (EMD) and time-domain difference is proposed in this paper. This method is downright self-data decomposition and do not rely on any transition kernel function, so it has a strong adaptive capacity. Firstly, we generalized the 1D EMD algorithm to the 2D case. In this process, the project has solved serial issues in 2D EMD, such as large amount of data operations, define and identify extrema in 2D case, and two-dimensional signal boundary corrosion. The EMD algorithm studied in this project can be well adapted to the automatic detection of small targets under low SNR and complex background. Secondly, considering the characteristics of moving target, we proposed an improved filtering method based on three-frame difference on basis of the original difference filtering in time-domain, which greatly improves the ability of anti-jamming algorithm. Finally, we proposed a new time-space fusion method based on a combined processing of 2D EMD and improved time-domain differential filtering. And, experimental results show that this method works well in infrared small moving target detection under low SNR and complex background.

Unsteady Aerodynamic Flow Control of Moving Platforms

DTIC Science & Technology

2014-05-29

aerodynamic forces and moments effected by fluidic actuation on the flow boundaries of stationary and moving platforms. Aerodynamic forces and...Control is effected fluidically by interactions of azimuthally- and streamwise-segmented individually-addressable synthetic jet actuators with...fundamental flow mechanisms that are associated with transitory aerodynamic forces and moments effected by fluidic actuation on the flow boundaries of

Single-pulse interference caused by temporal reflection at moving refractive-index boundaries

DOE Office of Scientific and Technical Information (OSTI.GOV)

Plansinis, Brent W.; Donaldson, William R.; Agrawal, Govind P.

Here, we show numerically and analytically that temporal reflections from a moving refractive-index boundary act as an analog of Lloyd’s mirror, allowing a single pulse to produce interference fringes in time as it propagates inside a dispersive medium. This interference can be viewed as the pulse interfering with a virtual pulse that is identical to the first, except for a π-phase shift. Furthermore, if a second moving refractive-index boundary is added to create the analog of an optical waveguide, a single pulse can be self-imaged or made to produce two or more pulses by adjusting the propagation length in amore » process similar to the Talbot effect.« less

Single-pulse interference caused by temporal reflection at moving refractive-index boundaries

DOE PAGES

Plansinis, Brent W.; Donaldson, William R.; Agrawal, Govind P.

2017-09-29

Here, we show numerically and analytically that temporal reflections from a moving refractive-index boundary act as an analog of Lloyd’s mirror, allowing a single pulse to produce interference fringes in time as it propagates inside a dispersive medium. This interference can be viewed as the pulse interfering with a virtual pulse that is identical to the first, except for a π-phase shift. Furthermore, if a second moving refractive-index boundary is added to create the analog of an optical waveguide, a single pulse can be self-imaged or made to produce two or more pulses by adjusting the propagation length in amore » process similar to the Talbot effect.« less

Hydrodynamic lubrication of rigid nonconformal contacts in combined rolling and normal motion

NASA Technical Reports Server (NTRS)

Ghosh, M. K.; Hamrock, B. J.; Brewe, D. E.

1984-01-01

A numerical solution to the problem of hydrodynamic lubrication of rigid point contacts with an isoviscous, incompressible lubricant was obtained. The hydrodynamic load-carrying capacity under unsteady (or dynamic) conditions arising from the combined effects of squeeze motion superposed upon the entraining motion was determined for both normal approach and separation. Superposed normal motion considerably increases net load-carrying capacity during normal approach and substantially reduces net load-carrying capacity during separation. Geometry was also found to have a significant influence on the dynamic load-carrying capacity. The ratio of dynamic to steady state load-carrying capacity increases with increasing geometry parameter for normal approach and decreases during separation. The cavitation (film rupture) boundary is also influenced significantly by the normal motion, moving downstream during approach and upstream during separation. For sufficiently high normal separation velocity the rupture boundary may even move upstream of the minimum-film-thickness position. Sixty-three cases were used to derive a functional relationship for the ratio of the dynamic to steady state load-carrying capacity in terms of the dimensionless normal velocity parameter (incorporating normal velocity, entraining velocity, and film thickness) and the geometry parameter.

Hydrodynamic lubrication of rigid nonconformal contacts in combined rolling and normal motion

NASA Technical Reports Server (NTRS)

Ghosh, M. K.; Hamrock, B. J.; Brewe, D.

1985-01-01

A numerical solution to the problem of hydrodynamic lubrication of rigid point contacts with an isoviscous, incompressible lubricant was obtained. The hydrodynamic load-carrying capacity under unsteady (or dynamic) conditions arising from the combined effects of squeeze motion superposed upon the entraining motion was determined for both normal approach and separation. Superposed normal motion considerably increases net load-carrying capacity during normal approach and substantially reduces net load-carrying capacity during separation. Geometry was also found to have a significant influence on the dynamic load-carrying capacity. The ratio of dynamic to steady state load-carrying capacity increases with increasing geometry parameter for normal approach and decreases during separation. The cavitation (film rupture) boundary is also influenced significantly by the normal motion, moving downstream during approach and upstream during separation. For sufficiently high normal separation velocity the rupture boundary may even move upstream of the minimum-film-thickness position. Sixty-three cases were used to derive a functional relationship for the ratio of the dynamic to steady state load-carrying capacity in terms of the dimensionless normal velocity parameter (incorporating normal velocity, entraining velocity, and film thickness) and the geometry parameter.

Knowledge mobilization in bridging patient-practitioner-researcher boundaries: A systematic integrative review protocol.

PubMed

Cowdell, Fiona; Booth, Andrew; Appleby, Ben

2017-11-01

To review published literature to identify when and how patients and healthcare practitioners have been involved in knowledge mobilization activity and the impact this may have had on their care. Improving patient outcomes, satisfaction and quality of care is increasingly reliant on shared decision-making between health professionals and patients. Knowledge mobilization, at its simplest: "moving knowledge to where it can be most useful" is a growing field of academic study. To date, it appears that much effort has focused on moving knowledge from researchers to healthcare practitioners. Knowledge mobilization to patients is currently under-researched. Integrative review. Methods of integrative review will be used to address the review problem. PRISMA guidelines were used as a general framework to guide structuring and reporting the review. Elements of method-specific reporting guidelines for specific streams of evidence will be used as required. This review will aim to provide a broad and deep understanding of patient-practitioner-researcher engagement in knowledge mobilization activity. This synthesis of the extant literature should offer insights into the optimum characteristics of methods for bridging patient-practitioner-researcher boundaries in knowledge mobilization action. © 2017 John Wiley & Sons Ltd.

Expected Reachability-Time Games

NASA Astrophysics Data System (ADS)

Forejt, Vojtěch; Kwiatkowska, Marta; Norman, Gethin; Trivedi, Ashutosh

In an expected reachability-time game (ERTG) two players, Min and Max, move a token along the transitions of a probabilistic timed automaton, so as to minimise and maximise, respectively, the expected time to reach a target. These games are concurrent since at each step of the game both players choose a timed move (a time delay and action under their control), and the transition of the game is determined by the timed move of the player who proposes the shorter delay. A game is turn-based if at any step of the game, all available actions are under the control of precisely one player. We show that while concurrent ERTGs are not always determined, turn-based ERTGs are positionally determined. Using the boundary region graph abstraction, and a generalisation of Asarin and Maler's simple function, we show that the decision problems related to computing the upper/lower values of concurrent ERTGs, and computing the value of turn-based ERTGs are decidable and their complexity is in NEXPTIME ∩ co-NEXPTIME.

Considerations on the moving contact-line singularity, with application to frictional drag on a slender drop

NASA Technical Reports Server (NTRS)

Durbin, P. A.

1988-01-01

It has previously been shown that the no-slip boundary conditions leads to a singularity at a moving contact line and that this presumes some form of slip. Present considerations on the energetics of slip due to shear stress lead to a yield stress boundary condition. A model for the distortion of the liquid state near solid boundaries gives a physical basis for this boundary condition. The yield stress condition is illustrated by an analysis of a slender drop rolling down an incline. That analysis provides a formula for the frictional drag resisting the drop movement. With the present boundary condition, the length of the slip region becomes a property of the fluid flow.

A reconstruction method of intra-ventricular blood flow using color flow ultrasound: a simulation study

NASA Astrophysics Data System (ADS)

Jang, Jaeseong; Ahn, Chi Young; Jeon, Kiwan; Choi, Jung-il; Lee, Changhoon; Seo, Jin Keun

2015-03-01

A reconstruction method is proposed here to quantify the distribution of blood flow velocity fields inside the left ventricle from color Doppler echocardiography measurement. From 3D incompressible Navier- Stokes equation, a 2D incompressible Navier-Stokes equation with a mass source term is derived to utilize the measurable color flow ultrasound data in a plane along with the moving boundary condition. The proposed model reflects out-of-plane blood flows on the imaging plane through the mass source term. For demonstrating a feasibility of the proposed method, we have performed numerical simulations of the forward problem and numerical analysis of the reconstruction method. First, we construct a 3D moving LV region having a specific stroke volume. To obtain synthetic intra-ventricular flows, we performed a numerical simulation of the forward problem of Navier-Stokes equation inside the 3D moving LV, computed 3D intra-ventricular velocity fields as a solution of the forward problem, projected the 3D velocity fields on the imaging plane and took the inner product of the 2D velocity fields on the imaging plane and scanline directional velocity fields for synthetic scanline directional projected velocity at each position. The proposed method utilized the 2D synthetic projected velocity data for reconstructing LV blood flow. By computing the difference between synthetic flow and reconstructed flow fields, we obtained the averaged point-wise errors of 0.06 m/s and 0.02 m/s for u- and v-components, respectively.

Tangle-Free Mesh Motion for Ablation Simulations

NASA Technical Reports Server (NTRS)

Droba, Justin

2016-01-01

Problems involving mesh motion-which should not be mistakenly associated with moving mesh methods, a class of adaptive mesh redistribution techniques-are of critical importance in numerical simulations of the thermal response of melting and ablative materials. Ablation is the process by which material vaporizes or otherwise erodes due to strong heating. Accurate modeling of such materials is of the utmost importance in design of passive thermal protection systems ("heatshields") for spacecraft, the layer of the vehicle that ensures survival of crew and craft during re-entry. In an explicit mesh motion approach, a complete thermal solve is first performed. Afterwards, the thermal response is used to determine surface recession rates. These values are then used to generate boundary conditions for an a posteriori correction designed to update the location of the mesh nodes. Most often, linear elastic or biharmonic equations are used to model this material response, traditionally in a finite element framework so that complex geometries can be simulated. A simple scheme for moving the boundary nodes involves receding along the surface normals. However, for all but the simplest problem geometries, evolution in time following such a scheme will eventually bring the mesh to intersect and "tangle" with itself, inducing failure. This presentation demonstrates a comprehensive and sophisticated scheme that analyzes the local geometry of each node with help from user-provided clues to eliminate the tangle and enable simulations on a wide-class of difficult problem geometries. The method developed is demonstrated for linear elastic equations but is general enough that it may be adapted to other modeling equations. The presentation will explicate the inner workings of the tangle-free mesh motion algorithm for both two and three-dimensional meshes. It will show abstract examples of the method's success, including a verification problem that demonstrates its accuracy and correctness. The focus of the presentation will be on the algorithm; specifics on how the techniques may be used in spacecraft design will be not discussed.

Fast algorithm for calculation of the moving tsunami wave height

NASA Astrophysics Data System (ADS)

Krivorotko, Olga; Kabanikhin, Sergey

2014-05-01

One of the most urgent problems of mathematical tsunami modeling is estimation of a tsunami wave height while a wave approaches to the coastal zone. There are two methods for solving this problem, namely, Airy-Green formula in one-dimensional case ° --- S(x) = S(0) 4 H(0)/H (x), and numerical solution of an initial-boundary value problem for linear shallow water equations ( { ηtt = div (gH (x,y)gradη), (x,y,t) ∈ ΩT := Ω ×(0,T); ( η|t=0 = q(x,y), ηt|t=0 = 0, (x,y ) ∈ Ω := (0,Lx)× (0,Ly ); (1) η|δΩT = 0. Here η(x,y,t) is the free water surface vertical displacement, H(x,y) is the depth at point (x,y), q(x,y) is the initial amplitude of a tsunami wave, S(x) is a moving tsunami wave height at point x. The main difficulty problem of tsunami modeling is a very big size of the computational domain ΩT. The calculation of the function η(x,y,t) of three variables in ΩT requires large computing resources. We construct a new algorithm to solve numerically the problem of determining the moving tsunami wave height which is based on kinematic-type approach and analytical representation of fundamental solution (2). The wave is supposed to be generated by the seismic fault of the bottom η(x,y,0) = g(y) ·θ(x), where θ(x) is a Heaviside theta-function. Let τ(x,y) be a solution of the eikonal equation 1 τ2x +τ2y = --, gH (x,y) satisfying initial conditions τ(0,y) = 0 and τx(0,y) = (gH (0,y))-1/2. Introducing new variables and new functions: ° -- z = τ(x,y), u(z,y,t) = ηt(x,y,t), b(z,y) = gH(x,y). We obtain an initial-boundary value problem in new variables from (1) ( 2 2 (2 bz- ) { utt = uzz + b uyy + 2b τyuzy + b(τxx + τyy) + 2b + 2bbyτy uz+ ( +2b(bzτy + by)uy, z,y- >2 0,t > 0,2 -1/2 u|t 0,t > 0. Then after some mathematical transformation we get the structure of the function u(x,y,t) in the form u(z,y,t) = S(z,y)·θ(t - z) + ˜u(z,y,t). (2) Here Å©(z,y,t) is a smooth function, S(z,y) is the solution of the problem: { S + b2τ S + (1b2(τ +τ )+ bz+ bb τ )S = 0, z,y > 0, z ygy(y)( 2-2 xx yy2 b)-1/2y y (3) S(0,y) = 2 b (0,y)- τy(0,y) , y > 0. Note that the problem (3) is two-dimensional which allows one to reduce the number of operations in 1.5 times. The algorithm makes it possible to calculate the moving tsunami wave height S(z,y) coming to a given point (z0,y0) as well as the arrival time. This work was supported by the Russian Foundation for Basic Research (project No. 12-01-00773 «Theory and Numerical Methods for Solving Combined Inverse Problems of Mathematical Physics») and interdisciplinary project of SB RAS 14 «Inverse Problems and Applications: Theory, Algorithms, Software».

Recalibration of the Palaeocene-Eocene boundary (P-E) using high precision U-Pb and Ar-Ar isotopic dating

NASA Astrophysics Data System (ADS)

Chambers, L.; Pringle, M.; Fitton, G.; Larsen, L. M.; Pedersen, A. K.; Parrish, R.

2003-04-01

In the current time scales (Cande and Kent, 95; Berggren et al, 95) the P-E Boundary is positioned at 55 Ma based primarily on the age of the -17 ash layer in Denmark. In the absence of a global stratigraphic section and point the boundary is an interval of 1 m.y. from 55.5 to 54.5 Ma that includes all of the different means of calibrating the boundary tie point, including the NP9/NP10 calcareous nannofossil zonal boundary, the planktonic foraminiferal P5/P6a zonal boundary, preliminary ages for the -17 and +19 ash layers (unpub.), the base of the London Clay Formation, and the δ13C spike. Here we present new Ar-Ar ages for the -17 and +19 ash layers in Denmark and combine this study with a calibration of the Ar-Ar with the U-Pb method. As Ar-Ar ages are relative to the known age of a standard or monitor, U-Pb ages on zircons from the same rocks from the British Tertiary Igneous Province provide an absolute age calibration for all of our Ar-Ar ages (including the monitors). An additional complication arises because the time scale is currently being revised (J. Ogg, Pers. Comm.). In the new time scale the P-E boundary will stay at 55 Ma and the K-T boundary will move by 0.5 m.y. to 65.5 Ma. Our results have a direct impact on the positioning of the P-E Boundary relative to the K-T boundary as definitive K-T tektite is used as one of our Ar-Ar standards. Ar-Ar ages and U-Pb ages for the same sample from the BTIP are indistinguishable when the ages used for the Ar-Ar monitor minerals are those recommended in Renne et al (98). This means that the K-T tektite is 65.78 ± 0.03 Ma, the -17 ash is 54.52 ± 0.05Ma, and the +19 ash is 54.04 ± 0.14 Ma. If the P-E boundary is taken to be between the -17 and +19 ash layers, as in DSDP Hole 550 (the ashes bracket the planktonic foraminiferal P5/P6a zonal boundary) then the current position at 55 Ma is too old. We therefore suggest that if the K-T boundary moves to 65.5 Ma, then the P-E boundary should not stay at 55 Ma, but move to 54.5 Ma (extending the Palaeocene by 1 m.y.). If the K-T boundary does not move by 0.5 m.y. then the P-E boundary would still have to move from its current position at 55 Ma and the ages used for the argon monitor minerals revised.

Dynamic ground-effect measurements on the F-15 STOL and Maneuver Technology Demonstrator (S/MTD) configuration

NASA Technical Reports Server (NTRS)

Kemmerly, Guy T.

1990-01-01

A moving-model ground-effect testing method was used to study the influence of rate-of-descent on the aerodynamic characteristics for the F-15 STOL and Maneuver Technology Demonstrator (S/MTD) configuration for both the approach and roll-out phases of landing. The approach phase was modeled for three rates of descent, and the results were compared to the predictions from the F-15 S/MTD simulation data base (prediction based on data obtained in a wind tunnel with zero rate of descent). This comparison showed significant differences due both to the rate of descent in the moving-model test and to the presence of the ground boundary layer in the wind tunnel test. Relative to the simulation data base predictions, the moving-model test showed substantially less lift increase in ground effect, less nose-down pitching moment, and less increase in drag. These differences became more prominent at the larger thrust vector angles. Over the small range of rates of descent tested using the moving-model technique, the effect of rate of descent on longitudinal aerodynamics was relatively constant. The results of this investigation indicate no safety-of-flight problems with the lower jets vectored up to 80 deg on approach. The results also indicate that this configuration could employ a nozzle concept using lower reverser vector angles up to 110 deg on approach if a no-flare approach procedure were adopted and if inlet reingestion does not pose a problem.

A dissipative particle dynamics method for arbitrarily complex geometries

NASA Astrophysics Data System (ADS)

Li, Zhen; Bian, Xin; Tang, Yu-Hang; Karniadakis, George Em

2018-02-01

Dissipative particle dynamics (DPD) is an effective Lagrangian method for modeling complex fluids in the mesoscale regime but so far it has been limited to relatively simple geometries. Here, we formulate a local detection method for DPD involving arbitrarily shaped geometric three-dimensional domains. By introducing an indicator variable of boundary volume fraction (BVF) for each fluid particle, the boundary of arbitrary-shape objects is detected on-the-fly for the moving fluid particles using only the local particle configuration. Therefore, this approach eliminates the need of an analytical description of the boundary and geometry of objects in DPD simulations and makes it possible to load the geometry of a system directly from experimental images or computer-aided designs/drawings. More specifically, the BVF of a fluid particle is defined by the weighted summation over its neighboring particles within a cutoff distance. Wall penetration is inferred from the value of the BVF and prevented by a predictor-corrector algorithm. The no-slip boundary condition is achieved by employing effective dissipative coefficients for liquid-solid interactions. Quantitative evaluations of the new method are performed for the plane Poiseuille flow, the plane Couette flow and the Wannier flow in a cylindrical domain and compared with their corresponding analytical solutions and (high-order) spectral element solution of the Navier-Stokes equations. We verify that the proposed method yields correct no-slip boundary conditions for velocity and generates negligible fluctuations of density and temperature in the vicinity of the wall surface. Moreover, we construct a very complex 3D geometry - the "Brown Pacman" microfluidic device - to explicitly demonstrate how to construct a DPD system with complex geometry directly from loading a graphical image. Subsequently, we simulate the flow of a surfactant solution through this complex microfluidic device using the new method. Its effectiveness is demonstrated by examining the rich dynamics of surfactant micelles, which are flowing around multiple small cylinders and stenotic regions in the microfluidic device without wall penetration. In addition to stationary arbitrary-shape objects, the new method is particularly useful for problems involving moving and deformable boundaries, because it only uses local information of neighboring particles and satisfies the desired boundary conditions on-the-fly.

A (137)Cs erosion model with moving boundary.

PubMed

Yin, Chuan; Ji, Hongbing

2015-12-01

A novel quantitative model of the relationship between diffused concentration changes and erosion rates using assessment of soil losses was developed. It derived from the analysis of surface soil (137)Cs flux variation under persistent erosion effect and based on the principle of geochemistry kinetics moving boundary. The new moving boundary model improves the basic simplified transport model (Zhang et al., 2008), and mainly applies to uniform rainfall areas which show a long-time soil erosion. The simulation results for this kind of erosion show under a long-time soil erosion, the influence of (137)Cs concentration will decrease exponentially with increasing depth. Using the new model fit to the measured (137)Cs depth distribution data in Zunyi site, Guizhou Province, China which has typical uniform rainfall provided a good fit with R(2) = 0.92. To compare the soil erosion rates calculated by the simple transport model and the new model, we take the Kaixian reference profile as example. The soil losses estimated by the previous simplified transport model are greater than those estimated by the new moving boundary model, which is consistent with our expectations. Copyright © 2015 Elsevier Ltd. All rights reserved.

A fast numerical method for ideal fluid flow in domains with multiple stirrers

NASA Astrophysics Data System (ADS)

Nasser, Mohamed M. S.; Green, Christopher C.

2018-03-01

A collection of arbitrarily-shaped solid objects, each moving at a constant speed, can be used to mix or stir ideal fluid, and can give rise to interesting flow patterns. Assuming these systems of fluid stirrers are two-dimensional, the mathematical problem of resolving the flow field—given a particular distribution of any finite number of stirrers of specified shape and speed—can be formulated as a Riemann-Hilbert (R-H) problem. We show that this R-H problem can be solved numerically using a fast and accurate algorithm for any finite number of stirrers based around a boundary integral equation with the generalized Neumann kernel. Various systems of fluid stirrers are considered, and our numerical scheme is shown to handle highly multiply connected domains (i.e. systems of many fluid stirrers) with minimal computational expense.

A framework for discrete stochastic simulation on 3D moving boundary domains

DOE PAGES

Drawert, Brian; Hellander, Stefan; Trogdon, Michael; ...

2016-11-14

We have developed a method for modeling spatial stochastic biochemical reactions in complex, three-dimensional, and time-dependent domains using the reaction-diffusion master equation formalism. In particular, we look to address the fully coupled problems that arise in systems biology where the shape and mechanical properties of a cell are determined by the state of the biochemistry and vice versa. To validate our method and characterize the error involved, we compare our results for a carefully constructed test problem to those of a microscale implementation. Finally, we demonstrate the effectiveness of our method by simulating a model of polarization and shmoo formationmore » during the mating of yeast. The method is generally applicable to problems in systems biology where biochemistry and mechanics are coupled, and spatial stochastic effects are critical.« less

Depth-color fusion strategy for 3-D scene modeling with Kinect.

PubMed

Camplani, Massimo; Mantecon, Tomas; Salgado, Luis

2013-12-01

Low-cost depth cameras, such as Microsoft Kinect, have completely changed the world of human-computer interaction through controller-free gaming applications. Depth data provided by the Kinect sensor presents several noise-related problems that have to be tackled to improve the accuracy of the depth data, thus obtaining more reliable game control platforms and broadening its applicability. In this paper, we present a depth-color fusion strategy for 3-D modeling of indoor scenes with Kinect. Accurate depth and color models of the background elements are iteratively built, and used to detect moving objects in the scene. Kinect depth data is processed with an innovative adaptive joint-bilateral filter that efficiently combines depth and color by analyzing an edge-uncertainty map and the detected foreground regions. Results show that the proposed approach efficiently tackles main Kinect data problems: distance-dependent depth maps, spatial noise, and temporal random fluctuations are dramatically reduced; objects depth boundaries are refined, and nonmeasured depth pixels are interpolated. Moreover, a robust depth and color background model and accurate moving objects silhouette are generated.

Minimal model of a cell connecting amoebic motion and adaptive transport networks.

PubMed

Gunji, Yukio-Pegio; Shirakawa, Tomohiro; Niizato, Takayuki; Haruna, Taichi

2008-08-21

A cell is a minimal self-sustaining system that can move and compute. Previous work has shown that a unicellular slime mold, Physarum, can be utilized as a biological computer based on cytoplasmic flow encapsulated by a membrane. Although the interplay between the modification of the boundary of a cell and the cytoplasmic flow surrounded by the boundary plays a key role in Physarum computing, no model of a cell has been developed to describe this interplay. Here we propose a toy model of a cell that shows amoebic motion and can solve a maze, Steiner minimum tree problem and a spanning tree problem. Only by assuming that cytoplasm is hardened after passing external matter (or softened part) through a cell, the shape of the cell and the cytoplasmic flow can be changed. Without cytoplasm hardening, a cell is easily destroyed. This suggests that cytoplasmic hardening and/or sol-gel transformation caused by external perturbation can keep a cell in a critical state leading to a wide variety of shapes and motion.

Flow produced by a free-moving floating magnet driven electromagnetically

NASA Astrophysics Data System (ADS)

Piedra, Saúl; Román, Joel; Figueroa, Aldo; Cuevas, Sergio

2018-04-01

The flow generated by a free-moving magnet floating in a thin electrolyte layer is studied experimentally and numerically. The magnet is dragged by a traveling vortex dipole produced by a Lorentz force created when a uniform dc current injected in the electrolyte interacts with the magnetic field of the same magnet. The problem represents a typical case of fluid-solid interaction but with a localized electromagnetic force promoting the motion. Classical wake flow structures are observed when the applied current varies in the range of 0.2 to 10 A. Velocity fields at the surface of the electrolyte are obtained for different flow conditions through particle image velocimetry. Quasi-two-dimensional numerical simulations, based on the immersed boundary technique that incorporates the fluid-solid interaction, reproduce satisfactorily the dynamics observed in the experiments.

Performance of flapping airfoil propulsion with LBM method and DMD analysis

NASA Astrophysics Data System (ADS)

Li, Bing-Hua; Huang, Xian-Wen; Zheng, Yao; Xie, Fang-Fang; Wang, Jing; Zou, Jian-Feng

2018-05-01

In this work, the performance of flapping airfoil propulsion at low Reynolds number of Re = 100-400 is studied numerically with the lattice Boltzmann method (LBM). Combined with immersed boundary method (IBM), the LBM has been widely used to simulate moving boundary problems. The influences of the reduced frequency on the plunging and pitching airfoil are explored. It is found that the leading-edge vertex separation and inverted wake structures are two main coherent structures, which dominate the flapping airfoil propulsion. However, the two structures play different roles in the flow and the combination effects on the propulsion need to be clarified. To do so, we adopt the dynamic mode decomposition (DMD) algorithm to reveal the underlying physics. The DMD has been proven to be very suitable for analyzing the complex transient systems like the vortex structure of flapping flight.

Nonlinear analysis of a model of vascular tumour growth and treatment

NASA Astrophysics Data System (ADS)

Tao, Youshan; Yoshida, Norio; Guo, Qian

2004-05-01

We consider a mathematical model describing the evolution of a vascular tumour in response to traditional chemotherapy. The model is a free boundary problem for a system of partial differential equations governing intratumoural drug concentration, cancer cell density and blood vessel density. Tumour cells consist of two types of competitive cells that have different proliferation rates and different sensitivities to drugs. The balance between cell proliferation and death generates a velocity field that drives tumour cell movement. The tumour surface is a moving boundary. The purpose of this paper is to establish a rigorous mathematical analysis of the model for studying the dynamics of intratumoural blood vessels and to explore drug dosage for the successful treatment of a tumour. We also study numerically the competitive effects of the two cell types on tumour growth.

A numerical method for electro-kinetic flow with deformable fluid interfaces

NASA Astrophysics Data System (ADS)

Booty, Michael; Ma, Manman; Siegel, Michael

2013-11-01

We consider two-phase flow of ionic fluids whose motion is driven by an imposed electric field. At a fluid interface, a screening cloud of ions develops and forms an electro-chemical double layer or Debye layer. The imposed field acts on this induced charge distribution, resulting in a strong slip flow near the interface. We formulate a ``hybrid'' or multiscale numerical method in the thin Debye layer limit that incorporates an asymptotic analysis of the electrostatic potential and fluid dynamics in the Debye layer into a boundary integral solution of the full moving boundary problem. Results of the method are presented that show time-dependent deformation and steady state drop interface shapes when the timescale for charge-up of the Debye layer is either much less than or comparable to the timescale of the flow.

Social Consequences of Nomadic Working: A Case Study in an Organization

NASA Astrophysics Data System (ADS)

Singh, Ramanjit; Wood-Harper, Trevor

This research study identified social challenges that knowledge workers in the Swedish organization TeliaSonera (Telia) face when utilizing wireless technologies to conduct work on the move. Upon collecting the relevant research data, five problem areas were identified: work and life balance, addiction, organizational involvement, nomadic work and control, and individual productivity. Each problem area was examined with the philosophical underpinning of socio-technical design principles. The results confirm that better role boundary management, self-discipline, work negotiation, and e-mail communication skills may be required for the knowledge workers to manage the demands of nomadic working. Similarly, rewarding nomadic work performance, building employee supervisor trust relations, and designing jobs that enhance work and life balance can be imperative.

Determining the Transference Number of H[superscript +](aq) by a Modified Moving Boundary Method: A Directed Study for the Undergraduate Physical Chemistry Laboratory

ERIC Educational Resources Information Center

Dabke, Rajeev B.; Gebeyehu, Zewdu; Padelford, Jonathan

2012-01-01

A directed study for the undergraduate physical chemistry laboratory for determining the transference number of H[superscript +](aq) using a modified moving boundary method is presented. The laboratory study combines Faraday's laws of electrolysis with mole ratios and the perfect gas equation. The volume of hydrogen gas produced at the cathode is…

A moving control volume method for smooth computation of hydrodynamic forces and torques on immersed bodies

NASA Astrophysics Data System (ADS)

Nangia, Nishant; Patankar, Neelesh A.; Bhalla, Amneet P. S.

2017-11-01

Fictitious domain methods for simulating fluid-structure interaction (FSI) have been gaining popularity in the past few decades because of their robustness in handling arbitrarily moving bodies. Often the transient net hydrodynamic forces and torques on the body are desired quantities for these types of simulations. In past studies using immersed boundary (IB) methods, force measurements are contaminated with spurious oscillations due to evaluation of possibly discontinuous spatial velocity of pressure gradients within or on the surface of the body. Based on an application of the Reynolds transport theorem, we present a moving control volume (CV) approach to computing the net forces and torques on a moving body immersed in a fluid. The approach is shown to be accurate for a wide array of FSI problems, including flow past stationary and moving objects, Stokes flow, and high Reynolds number free-swimming. The approach only requires far-field (smooth) velocity and pressure information, thereby suppressing spurious force oscillations and eliminating the need for any filtering. The proposed moving CV method is not limited to a specific IB method and is straightforward to implement within an existing parallel FSI simulation software. This work is supported by NSF (Award Numbers SI2-SSI-1450374, SI2-SSI-1450327, and DGE-1324585), the US Department of Energy, Office of Science, ASCR (Award Number DE-AC02-05CH11231), and NIH (Award Number HL117163).

The dimension split element-free Galerkin method for three-dimensional potential problems

NASA Astrophysics Data System (ADS)

Meng, Z. J.; Cheng, H.; Ma, L. D.; Cheng, Y. M.

2018-06-01

This paper presents the dimension split element-free Galerkin (DSEFG) method for three-dimensional potential problems, and the corresponding formulae are obtained. The main idea of the DSEFG method is that a three-dimensional potential problem can be transformed into a series of two-dimensional problems. For these two-dimensional problems, the improved moving least-squares (IMLS) approximation is applied to construct the shape function, which uses an orthogonal function system with a weight function as the basis functions. The Galerkin weak form is applied to obtain a discretized system equation, and the penalty method is employed to impose the essential boundary condition. The finite difference method is selected in the splitting direction. For the purposes of demonstration, some selected numerical examples are solved using the DSEFG method. The convergence study and error analysis of the DSEFG method are presented. The numerical examples show that the DSEFG method has greater computational precision and computational efficiency than the IEFG method.

Construction of optimum controls and trajectories of motion of the center of masses of a spacecraft equipped with the solar sail and low-thrust engine, using quaternions and Kustaanheimo-Stiefel variables

NASA Astrophysics Data System (ADS)

Sapunkov, Ya. G.; Chelnokov, Yu. N.

2014-11-01

The problem of optimum rendezvous of a controllable spacecraft (SC) with an uncontrollable spacecraft, moving over a Keplerian elliptic orbit in the gravitational field of the Sun, is considered. Control of the SC is performed using a solar sail and low-thrust engine. For solving the problem, the regular quaternion equations of the two-body problem with the Kustaanheimo-Stiefel variables and the Pontryagin maximum principle are used. The combined integral quality functional, which characterizes energy consumption for controllable SC transition from an initial to final state and the time spent for this transition, is used as a minimized functional. The differential boundary-value optimization problems are formulated, and their first integrals are found. Examples of numerical solution of problems are presented. The paper develops the application [1-6] of quaternion regular equations with the Kustaanheimo-Stiefel variables in the space flight mechanics.

Turbulent boundary layers over nonstationary plane boundaries

NASA Technical Reports Server (NTRS)

Roper, A. T.; Gentry, G. L., Jr.

1978-01-01

Methods of predicting integral parameters and skin friction coefficients of turbulent boundary layers developing over moving ground planes were evaluated. The three methods evaluated were: relative integral parameter method; relative power law method; and modified law of the wall method.

Tangle-Free Finite Element Mesh Motion for Ablation Problems

NASA Technical Reports Server (NTRS)

Droba, Justin

2016-01-01

In numerical simulations involving boundaries that evolve in time, the primary challenge is updating the computational mesh to reflect the physical changes in the domain. In particular, the fundamental objective for any such \\mesh motion" scheme is to maintain mesh quality and suppress unphysical geometric anamolies and artifacts. External to a physical process of interest, mesh motion is an added component that determines the specifics of how to move the mesh given certain limited information from the main system. This paper develops a set of boundary conditions designed to eliminate tangling and internal collision within the context of PDE-based mesh motion (linear elasticity). These boundary conditions are developed for two- and three-dimensional meshes. The paper presents detailed algorithms for commonly occuring topological scenarios and explains how to apply them appropriately. Notably, the techniques discussed herein make use of none of the specifics of any particular formulation of mesh motion and thus are more broadly applicable. The two-dimensional algorithms are validated by an extensive verification procedure. Finally, many examples of diverse geometries in both two- and three-dimensions are shown to showcase the capabilities of the tangle-free boundary conditions.

Adjustment of the problems of landslide GIS data

NASA Astrophysics Data System (ADS)

Uchiyama, S.; Doshida, S.; Oyagi, N.; Shimizu, F.; Inokuchi, T.

2012-12-01

Information on the distribution of landslides is a basic type of data used by countries for disaster prevention. Since 1972, 1:50,000 landslide maps have been produced at the Japanese National Research Institute for Earth Science and Disaster Prevention. From October 2000, the institute has been producing landslide GIS data and transmitting these data over the web. The area that has been published so far covers over 80% of Japan. Presently, the number of diagrams printed are 980 (March 2012). In addition, 350,000 landslide GIS data graphs have been digitized with the same diagrams as a base. Twelve years have passed since this GIS data acquisition program was launched, and in that time, several problems have been identified. These problems are listed below. 1) Scarps do not become polygonized. 2) Landslides which extend over the boundaries of the printed graphs are divided into separate elements. 3) When the time taken to read and interpret the landslide data differs, the shape of the landslides can vary between diagrams. 4) There have been cases of inaccurate positions and shapes in landslide GIS data produced since 2005. 5) Obvious mistakes are present in the attribute data. The causes of such problems are as follows: 1) Lack of technical examination at the time of the start of the production of the landslide GIS data. 2) Limitations of the landslide GIS data editing systems which were developed separately. 3) Program bugs which occur during the conversion of information input to an individual editing system into general-purpose GIS data. 4) Problems which arise during the process of the production of landslide GIS data. This project at the National Research Institute for Earth Science and Disaster Prevention is planned to be completed in 2013. By the end of the project, we hope to present a catalogue of all identified problems and formulate a plan to resolve them, and pass them on to the next generation.; Problems: For the diagram, scarps are presented by polylines and cannot be treated as polygons (topography area). Example of limitations of the individual editing system. Both the moving mass or scarp and other features are divided by the printing boundaries of the diagrams. Another example of the limitations of the editing system. When a scarp is present within the moving mass, the scarp area is hollowed out.

Role of Dynamic Nucleation at Moving Boundaries in Phase and Microstructure Selection

NASA Technical Reports Server (NTRS)

Karma, Alain; Trivedi, Rohit

1999-01-01

Solidification microstructures that form under steady-state growth conditions (cells, dendrites, regular eutectics, etc.) are reasonably well understood in comparison to other, more complex microstructures, which form under intrinsically non-steady-state growth conditions due to the competition between the nucleation and growth of several phases. Some important practical examples in this latter class include microstructures forming in peritectic systems in highly undercooled droplets, and in strip cast stainless steels. Prediction of phase and microstructure selection in these systems has been traditionally based on (1) heterogeneous nucleation on a static interface, and (2) comparing the relative growth rate of different phase/microstructures under steady-state growth conditions. The formation of new phases, however, occurs via nucleation on, or ahead of, a moving boundary. In addition, the actual selection process is controlled by a complex interaction between the nucleation process and the growth competition between the nuclei and the pre-existing phase under non-steady-state conditions. As a result, it is often difficult to predict which microstructure will form and which phases will be selected under prescribed processing conditions. This research addresses this critical role of nucleation at moving boundaries in the selection of phases and solidification microstructures through quantitative experiments and numerical modeling in peritectic systems. In order to create a well characterized system in which to study this problem, we focus on the directional solidification of hypo- and hyper-peritectic alloys in the two-phase region, imposing a large enough ratio of temperature gradient/growth rate (G/V(sub p)) to suppress the morphological instability of both the parent (alpha) and peritectic (Beta) phases, i.e. each phase alone would grow as a planar front. Our combined experimental and theoretical results show that, already in this simplified case, the growth competition of these two phases leads to a rich variety of microstructures that depend sensitively upon the relative importance of nucleation, diffusion, and convection.

Process modelling for materials preparation experiments

NASA Technical Reports Server (NTRS)

Rosenberger, Franz; Alexander, J. Iwan D.

1993-01-01

The main goals of the research under this grant consist of the development of mathematical tools and measurement of transport properties necessary for high fidelity modeling of crystal growth from the melt and solution, in particular, for the Bridgman-Stockbarger growth of mercury cadmium telluride (MCT) and the solution growth of triglycine sulphate (TGS). Of the tasks described in detail in the original proposal, two remain to be worked on: (1) development of a spectral code for moving boundary problems; and (2) diffusivity measurements on concentrated and supersaturated TGS solutions. Progress made during this seventh half-year period is reported.

Process modelling for materials preparation experiments

NASA Technical Reports Server (NTRS)

Rosenberger, Franz; Alexander, J. Iwan D.

1993-01-01

The main goals of the research consist of the development of mathematical tools and measurement of transport properties necessary for high fidelity modeling of crystal growth from the melt and solution, in particular for the Bridgman-Stockbarger growth of mercury cadmium telluride (MCT) and the solution growth of triglycine sulphate (TGS). Of the tasks described in detail in the original proposal, two remain to be worked on: development of a spectral code for moving boundary problems, and diffusivity measurements on concentrated and supersaturated TGS solutions. During this eighth half-year period, good progress was made on these tasks.

Process modelling for materials preparation experiments

NASA Technical Reports Server (NTRS)

Rosenberger, Franz; Alexander, J. Iwan D.

1992-01-01

The development is examined of mathematical tools and measurement of transport properties necessary for high fidelity modeling of crystal growth from the melt and solution, in particular for the Bridgman-Stockbarger growth of mercury cadmium telluride (MCT) and the solution growth of triglycine sulphate (TGS). The tasks include development of a spectral code for moving boundary problems, kinematic viscosity measurements on liquid MCT at temperatures close to the melting point, and diffusivity measurements on concentrated and supersaturated TGS solutions. A detailed description is given of the work performed for these tasks, together with a summary of the resulting publications and presentations.

Coiling of elastic rods from a geometric perspective

NASA Astrophysics Data System (ADS)

Jawed, Mohammad; Brun, Pierre-Thomas; Reis, Pedro

2015-03-01

We present results from a systematic numerical investigation of the pattern formation of coiling obtained when a slender elastic rod is deployed onto a moving substrate; a system known as the elastic sewing machine (ESM). The Discrete Elastic Rods method is employed to explore the parameter space, construct phase diagrams, identify their phase boundaries and characterize the morphology of the patterns. The nontrivial geometric nonlinearities are described in terms of the gravito-bending length and the deployment height. Our results are interpreted using a reduced geometric model for the evolution of the position of the contact point with the belt and the curvature of the rod in its neighborhood. This geometric model reproduces all of the coiling patterns of the ESM, which allows us to establish a universal link between our elastic problem and the analogous patterns obtained when depositing a viscous thread onto a moving surface; a well-known system referred to as the fluid mechanical sewing machine.

Moving mode shape function approach for spinning disk and asymmetric disc brake squeal

NASA Astrophysics Data System (ADS)

Kang, Jaeyoung

2018-06-01

The solution approach of an asymmetric spinning disk under stationary friction loads requires the mode shape function fixed in the disk in the assumed mode method when the equations of motion is described in the space-fixed frame. This model description will be termed the 'moving mode shape function approach' and it allows us to formulate the stationary contact load problem in both the axisymmetric and asymmetric disk cases. Numerical results show that the eigenvalues of the time-periodic axisymmetric disk system are time-invariant. When the axisymmetry of the disk is broken, the positive real parts of the eigenvalues highly vary with the rotation of the disk in the slow speeds in such application as disc brake squeal. By using the Floquet stability analysis, it is also shown that breaking the axisymmetry of the disc alters the stability boundaries of the system.

Effects of surface poisons on the oxidation of binary alloys

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hagan, P.S.; Polizzotti, R.S.; Luckman, G.

1985-10-01

A system of reaction-diffusion equations describing the oxidation of binary alloys in environments containing small amounts of surface poisons is analyzed. These poisons reduce the oxygen flux into the alloy, which causes the alloy to oxidize in two stages.During the initial stage, the oxidation reaction occurs in a stationary boundary layer at the alloy surface. Consequently, a thin zone containing a very high concentration of the metal oxide is created at the alloy surface. During the second stage, the oxidation reaction occurs in a moving boundary layer. This leads to a Stefan problem, which is analyzed by using asymptotic andmore » numerical techniques. By comparing the solutions to those of alloys in unpoisoned environments, it is concluded that surface poisons can lead to the formation of protective external oxide scales in alloys which would not normally form such scales. 11 references.« less

On simulation of no-slip condition in the method of discrete vortices

NASA Astrophysics Data System (ADS)

Shmagunov, O. A.

2017-10-01

When modeling flows of an incompressible fluid, it is convenient sometimes to use the method of discrete vortices (MDV), where the continuous vorticity field is approximated by a set of discrete vortex elements moving in the velocity field. The vortex elements have a clear physical interpretation, they do not require the construction of grids and are automatically adaptive, since they concentrate in the regions of greatest interest and successfully describe the flows of a non-viscous fluid. The possibility of using MDV in simulating flows of a viscous fluid was considered in the previous papers using the examples of flows past bodies with sharp edges with the no-penetration condition at solid boundaries. However, the appearance of vorticity on smooth boundaries requires the no-slip condition to be met when MDV is realized, which substantially complicates the initially simple method. In this connection, an approach is considered that allows solving the problem by simple means.

Flexibility of Event Boundaries in Autobiographical Memory

PubMed Central

Hohman, Timothy J.; Peynircioğlu, Zehra F.; Beason-Held, Lori L.

2014-01-01

Events have clear and consistent boundaries that are defined during perception in a manner that influences memory performance. The natural process of event segmentation shapes event definitions during perception, and appears to play a critical role in defining distinct episodic memories at encoding. However, the role of retrieval processes in modifying event definitions is not clear. We explored how such processes changed event boundary definitions at recall. In Experiment 1 we showed that distance from encoding is related to boundary flexibility. Participants were more likely to move self-reported event boundaries to include information reported beyond those boundaries when recalling more distant events compared to more recent events. In Experiment 2, we showed that age also influenced boundary flexibility. Older Age adults were more likely to move event boundaries than College Age adults, and the relationship between distance from encoding and boundary flexibility seen in Experiment 1 was present only in College Age and Middle Age adults. These results suggest that factors at retrieval have a direct impact on event definitions in memory and that, although episodic memories may be initially defined at encoding, these definitions are not necessarily maintained in long-term memory. PMID:22989194

Solvability and Regularity for an Elliptic System Prescribing the Curl, Divergence, and Partial Trace of a Vector Field on Sobolev-Class Domains

NASA Astrophysics Data System (ADS)

Cheng, C. H. Arthur; Shkoller, Steve

2017-09-01

We provide a self-contained proof of the solvability and regularity of a Hodge-type elliptic system, wherein the divergence and curl of a vector field u are prescribed in an open, bounded, Sobolev-class domain {Ω \\subseteq R^n}, and either the normal component {{u} \\cdot {N}} or the tangential components of the vector field {{u} × {N}} are prescribed on the boundary {partial Ω}. For {k > n/2}, we prove that u is in the Sobolev space {H^k+1(Ω)} if {Ω} is an {H^k+1}-domain, and the divergence, curl, and either the normal or tangential trace of u has sufficient regularity. The proof is based on a regularity theory for vector elliptic equations set on Sobolev-class domains and with Sobolev-class coefficients, and with a rather general set of Dirichlet and Neumann boundary conditions. The resulting regularity theory for the vector u is fundamental in the analysis of free-boundary and moving interface problems in fluid dynamics.

[Determination of total protein content in soya-bean milk via visual moving reaction boundary titration].

PubMed

Guo, Chengye; Wang, Houyu; Zhang, Lei; Fan, Liuyin; Cao, Chengxi

2013-11-01

A visual, rapid and accurate moving reaction boundary titration (MRBT) method was used for the determination of the total protein in soya-bean milk. During the process, moving reaction boundary (MRB) was formed by hydroxyl ions in the catholyte and soya-bean milk proteins immobilized in polyacrylamide gel (PAG), and an acid-base indicator was used to denote the boundary motion. The velocity of MRB has a relationship with protein concentration, which was used to obtain a standard curve. By paired t-test, there was no significant difference of the protein content between MRBT and Kjeldahl method at 95% confidence interval. The procedure of MRBT method required about 10 min, and it had linearity in the range of 2.0-14.0 g/L, low limit of detection (0.05 g/L), good precision (RSD of intra-day < 1.90% and inter-day < 4.39%), and high recoveries (97.41%-99.91%). In addition, non-protein nitrogen (NPN) such as melamine added into the soya-bean milk had weak influence on MRBT results.

Effect of rotation rate on the forces of a rotating cylinder: Simulation and control

NASA Technical Reports Server (NTRS)

Burns, John A.; Ou, Yuh-Roung

1993-01-01

In this paper we present numerical solutions to several optimal control problems for an unsteady viscous flow. The main thrust of this work is devoted to simulation and control of an unsteady flow generated by a circular cylinder undergoing rotary motion. By treating the rotation rate as a control variable, we can formulate two optimal control problems and use a central difference/pseudospectral transform method to numerically compute the optimal control rates. Several types of rotations are considered as potential controls, and we show that a proper synchronization of forcing frequency with the natural vortex shedding frequency can greatly influence the flow. The results here indicate that using moving boundary controls for such systems may provide a feasible mechanism for flow control.

Studies in nonlinear problems of energy. Final report

DOE Office of Scientific and Technical Information (OSTI.GOV)

Matkowsky, B.J.

1998-12-01

The author completed a successful research program on Nonlinear Problems of Energy, with emphasis on combustion and flame propagation. A total of 183 papers associated with the grant has appeared in the literature, and the efforts have twice been recognized by DOE`s Basic Science Division for Top Accomplishment. In the research program the author concentrated on modeling, analysis and computation of combustion phenomena, with particular emphasis on the transition from laminar to turbulent combustion. Thus he investigated the nonlinear dynamics and pattern formation in the successive stages of transition. He described the stability of combustion waves, and transitions to wavesmore » exhibiting progressively higher degrees of spatio-temporal complexity. Combustion waves are characterized by large activation energies, so that chemical reactions are significant only in thin layers, termed reaction zones. In the limit of infinite activation energy, the zones shrink to moving surfaces, termed fronts, which must be found during the course of the analysis, so that the problems are moving free boundary problems. The analytical studies were carried out for the limiting case with fronts, while the numerical studies were carried out for the case of finite, though large, activation energy. Accurate resolution of the solution in the reaction zone(s) is essential, otherwise false predictions of dynamical behavior are possible. Since the reaction zones move, and their location is not known a-priori, the author has developed adaptive pseudo-spectral methods, which have proven to be very useful for the accurate, efficient computation of solutions of combustion, and other, problems. The approach is based on a combination of analytical and numerical methods. The numerical computations built on and extended the information obtained analytically. Furthermore, the solutions obtained analytically served as benchmarks for testing the accuracy of the solutions determined computationally. Finally, the computational results suggested new analysis to be considered. A cumulative list of publications citing the grant make up the contents of this report.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schlanderer, Stefan C., E-mail: stefan.schlanderer@unimelb.edu.au; Weymouth, Gabriel D., E-mail: G.D.Weymouth@soton.ac.uk; Sandberg, Richard D., E-mail: richard.sandberg@unimelb.edu.au

This paper introduces a virtual boundary method for compressible viscous fluid flow that is capable of accurately representing moving bodies in flow and aeroacoustic simulations. The method is the compressible extension of the boundary data immersion method (BDIM, Maertens & Weymouth (2015), ). The BDIM equations for the compressible Navier–Stokes equations are derived and the accuracy of the method for the hydrodynamic representation of solid bodies is demonstrated with challenging test cases, including a fully turbulent boundary layer flow and a supersonic instability wave. In addition we show that the compressible BDIM is able to accurately represent noise radiation frommore » moving bodies and flow induced noise generation without any penalty in allowable time step.« less

Employee assistance programs.

PubMed

Austin, R L

1987-10-01

The substance abuser brings his problems to the workplace. Ninety-five percent or more of all individuals experiencing alcohol-or drug-related problems are either employed or the spouse or dependent of someone who is working. It is clear we are facing a problem which transcends the boundaries of the workplace. The result in the workplace, of course, is increased costs, lower productivity, more accidents on the job, but most importantly additional suffering for the individuals involved. It is important to remember that neither GM, the UAW, nor the IUE can be expected to accept responsibility for those individuals who have the ability to control their own "wellness" and productivity. Any joint union-management substance abuse program can only be a catalyst to help individuals confront their problems. Along with the other groups and institutions concerned with these problems, GM, in cooperation with the UAW, IUE, and the other unions that represent our employees, is trying to help individuals with addictive diseases confront and obtain treatment for their problems. We believe our programs are moving in the right direction and will continue to make progress.

Boundary-integral methods in elasticity and plasticity. [solutions of boundary value problems

NASA Technical Reports Server (NTRS)

Mendelson, A.

1973-01-01

Recently developed methods that use boundary-integral equations applied to elastic and elastoplastic boundary value problems are reviewed. Direct, indirect, and semidirect methods using potential functions, stress functions, and displacement functions are described. Examples of the use of these methods for torsion problems, plane problems, and three-dimensional problems are given. It is concluded that the boundary-integral methods represent a powerful tool for the solution of elastic and elastoplastic problems.

Detached eddy simulation for turbulent fluid-structure interaction of moving bodies using the constraint-based immersed boundary method

NASA Astrophysics Data System (ADS)

Nangia, Nishant; Bhalla, Amneet P. S.; Griffith, Boyce E.; Patankar, Neelesh A.

2016-11-01

Flows over bodies of industrial importance often contain both an attached boundary layer region near the structure and a region of massively separated flow near its trailing edge. When simulating these flows with turbulence modeling, the Reynolds-averaged Navier-Stokes (RANS) approach is more efficient in the former, whereas large-eddy simulation (LES) is more accurate in the latter. Detached-eddy simulation (DES), based on the Spalart-Allmaras model, is a hybrid method that switches from RANS mode of solution in attached boundary layers to LES in detached flow regions. Simulations of turbulent flows over moving structures on a body-fitted mesh incur an enormous remeshing cost every time step. The constraint-based immersed boundary (cIB) method eliminates this operation by placing the structure on a Cartesian mesh and enforcing a rigidity constraint as an additional forcing in the Navier-Stokes momentum equation. We outline the formulation and development of a parallel DES-cIB method using adaptive mesh refinement. We show preliminary validation results for flows past stationary bodies with both attached and separated boundary layers along with results for turbulent flows past moving bodies. This work is supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1324585.

The energy-release rate and “self-force” of dynamically expanding spherical and plane inclusion boundaries with dilatational eigenstrain

NASA Astrophysics Data System (ADS)

Markenscoff, Xanthippi; Ni, Luqun

2010-01-01

In the context of the linear theory of elasticity with eigenstrains, the radiated field including inertia effects of a spherical inclusion with dilatational eigenstrain radially expanding is obtained on the basis of the dynamic Green's function, and one of the half-space inclusion boundary (with dilatational eigenstrain) moving from rest in general subsonic motion is obtained by a limiting process from the spherically expanding inclusion as the radius tends to infinity while the eigenstrain remains constrained, and this is the minimum energy solution. The global energy-release rate required to move the plane inclusion boundary and to create an incremental region of eigenstrain is defined analogously to the one for moving cracks and dislocations and represents the mechanical rate of work needed to be provide for the expansion of the inclusion. The calculated value, which is the "self-force" of the expanding inclusion, has a static component plus a dynamic one depending only on the current value of the velocity, while in the case of the spherical boundary, there is an additional contribution accounting for the jump in the strain at the farthest part at the back of the inclusion having the time to reach the front boundary, thus making the dynamic "self-force" history dependent.

Issues associated with Galilean invariance on a moving solid boundary in the lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Peng, Cheng; Geneva, Nicholas; Guo, Zhaoli; Wang, Lian-Ping

2017-01-01

In lattice Boltzmann simulations involving moving solid boundaries, the momentum exchange between the solid and fluid phases was recently found to be not fully consistent with the principle of local Galilean invariance (GI) when the bounce-back schemes (BBS) and the momentum exchange method (MEM) are used. In the past, this inconsistency was resolved by introducing modified MEM schemes so that the overall moving-boundary algorithm could be more consistent with GI. However, in this paper we argue that the true origin of this violation of Galilean invariance (VGI) in the presence of a moving solid-fluid interface is due to the BBS itself, as the VGI error not only exists in the hydrodynamic force acting on the solid phase, but also in the boundary force exerted on the fluid phase, according to Newton's Third Law. The latter, however, has so far gone unnoticed in previously proposed modified MEM schemes. Based on this argument, we conclude that the previous modifications to the momentum exchange method are incomplete solutions to the VGI error in the lattice Boltzmann method (LBM). An implicit remedy to the VGI error in the LBM and its limitation is then revealed. To address the VGI error for a case when this implicit remedy does not exist, a bounce-back scheme based on coordinate transformation is proposed. Numerical tests in both laminar and turbulent flows show that the proposed scheme can effectively eliminate the errors associated with the usual bounce-back implementations on a no-slip solid boundary, and it can maintain an accurate momentum exchange calculation with minimal computational overhead.

The looped adhesive strip: An example of coplanar delamination interaction

NASA Technical Reports Server (NTRS)

Bottega, W. J.

1990-01-01

The phenomenon of peeling and debonding of thin layers is a subject of interest to those concerned with adhesives, thin films, and layered materials. In recent years much attention has been focused on such problems as a result of increased interest and application of advanced composites and thin film coatings. A related problem which is of interest for its own sake but also represents a simple example of a tangled adhesive strip and of coplanar delamination interaction, is the problem of a looped adhesive strip. This is the subject of the present study. Researchers consider here the problem of an elastic strip which possesses an adherend on (at least) one of its surfaces. If the strip is deformed so that two portions of such a surface are brought into contact, a position of the strip becomes bonded and a loop is formed. Researchers are interested in determining the equilibrium configuration of such a strip and investigating the behavior of the strip when its edges are pulled apart. The problem is approached as a moving interior boundary problem in the calculus of variations with the strip modeled as an inextensible elastica and the bond strength characterized by its surface energy. A Griffith type energy criterion is employed for debonding, and solutions corresponding to the problem of interest obtained. The solution obtained will be seen to predict the interesting phenomenon of bond point propagation, as well as the more standard peeling type behavior. Numerical results demonstrating the phenomena of interest are presented as well and will be seen to reveal both stable and unstable propagation of the boundaries of the bonded portion of the strip, depending upon the loading conditions.

A Gaussian Mixture Model-based continuous Boundary Detection for 3D sensor networks.

PubMed

Chen, Jiehui; Salim, Mariam B; Matsumoto, Mitsuji

2010-01-01

This paper proposes a high precision Gaussian Mixture Model-based novel Boundary Detection 3D (BD3D) scheme with reasonable implementation cost for 3D cases by selecting a minimum number of Boundary sensor Nodes (BNs) in continuous moving objects. It shows apparent advantages in that two classes of boundary and non-boundary sensor nodes can be efficiently classified using the model selection techniques for finite mixture models; furthermore, the set of sensor readings within each sensor node's spatial neighbors is formulated using a Gaussian Mixture Model; different from DECOMO [1] and COBOM [2], we also formatted a BN Array with an additional own sensor reading to benefit selecting Event BNs (EBNs) and non-EBNs from the observations of BNs. In particular, we propose a Thick Section Model (TSM) to solve the problem of transition between 2D and 3D. It is verified by simulations that the BD3D 2D model outperforms DECOMO and COBOM in terms of average residual energy and the number of BNs selected, while the BD3D 3D model demonstrates sound performance even for sensor networks with low densities especially when the value of the sensor transmission range (r) is larger than the value of Section Thickness (d) in TSM. We have also rigorously proved its correctness for continuous geometric domains and full robustness for sensor networks over 3D terrains.

A Numerical Study of Three Moving-Grid Methods for One-Dimensional Partial Differential Equations Which Are Based on the Method of Lines

NASA Astrophysics Data System (ADS)

Furzeland, R. M.; Verwer, J. G.; Zegeling, P. A.

1990-08-01

In recent years, several sophisticated packages based on the method of lines (MOL) have been developed for the automatic numerical integration of time-dependent problems in partial differential equations (PDEs), notably for problems in one space dimension. These packages greatly benefit from the very successful developments of automatic stiff ordinary differential equation solvers. However, from the PDE point of view, they integrate only in a semiautomatic way in the sense that they automatically adjust the time step sizes, but use just a fixed space grid, chosen a priori, for the entire calculation. For solutions possessing sharp spatial transitions that move, e.g., travelling wave fronts or emerging boundary and interior layers, a grid held fixed for the entire calculation is computationally inefficient, since for a good solution this grid often must contain a very large number of nodes. In such cases methods which attempt automatically to adjust the sizes of both the space and the time steps are likely to be more successful in efficiently resolving critical regions of high spatial and temporal activity. Methods and codes that operate this way belong to the realm of adaptive or moving-grid methods. Following the MOL approach, this paper is devoted to an evaluation and comparison, mainly based on extensive numerical tests, of three moving-grid methods for 1D problems, viz., the finite-element method of Miller and co-workers, the method published by Petzold, and a method based on ideas adopted from Dorfi and Drury. Our examination of these three methods is aimed at assessing which is the most suitable from the point of view of retaining the acknowledged features of reliability, robustness, and efficiency of the conventional MOL approach. Therefore, considerable attention is paid to the temporal performance of the methods.

Moving Particles Through a Finite Element Mesh

PubMed Central

Peskin, Adele P.; Hardin, Gary R.

1998-01-01

We present a new numerical technique for modeling the flow around multiple objects moving in a fluid. The method tracks the dynamic interaction between each particle and the fluid. The movements of the fluid and the object are directly coupled. A background mesh is designed to fit the geometry of the overall domain. The mesh is designed independently of the presence of the particles except in terms of how fine it must be to track particles of a given size. Each particle is represented by a geometric figure that describes its boundary. This figure overlies the mesh. Nodes are added to the mesh where the particle boundaries intersect the background mesh, increasing the number of nodes contained in each element whose boundary is intersected. These additional nodes are then used to describe and track the particle in the numerical scheme. Appropriate element shape functions are defined to approximate the solution on the elements with extra nodes. The particles are moved through the mesh by moving only the overlying nodes defining the particles. The regular finite element grid remains unchanged. In this method, the mesh does not distort as the particles move. Instead, only the placement of particle-defining nodes changes as the particles move. Element shape functions are updated as the nodes move through the elements. This method is especially suited for models of moderate numbers of moderate-size particles, where the details of the fluid-particle coupling are important. Both the complications of creating finite element meshes around appreciable numbers of particles, and extensive remeshing upon movement of the particles are simplified in this method. PMID:28009377

Feature extraction and classification algorithms for high dimensional data

NASA Technical Reports Server (NTRS)

Lee, Chulhee; Landgrebe, David

1993-01-01

Feature extraction and classification algorithms for high dimensional data are investigated. Developments with regard to sensors for Earth observation are moving in the direction of providing much higher dimensional multispectral imagery than is now possible. In analyzing such high dimensional data, processing time becomes an important factor. With large increases in dimensionality and the number of classes, processing time will increase significantly. To address this problem, a multistage classification scheme is proposed which reduces the processing time substantially by eliminating unlikely classes from further consideration at each stage. Several truncation criteria are developed and the relationship between thresholds and the error caused by the truncation is investigated. Next an approach to feature extraction for classification is proposed based directly on the decision boundaries. It is shown that all the features needed for classification can be extracted from decision boundaries. A characteristic of the proposed method arises by noting that only a portion of the decision boundary is effective in discriminating between classes, and the concept of the effective decision boundary is introduced. The proposed feature extraction algorithm has several desirable properties: it predicts the minimum number of features necessary to achieve the same classification accuracy as in the original space for a given pattern recognition problem; and it finds the necessary feature vectors. The proposed algorithm does not deteriorate under the circumstances of equal means or equal covariances as some previous algorithms do. In addition, the decision boundary feature extraction algorithm can be used both for parametric and non-parametric classifiers. Finally, some problems encountered in analyzing high dimensional data are studied and possible solutions are proposed. First, the increased importance of the second order statistics in analyzing high dimensional data is recognized. By investigating the characteristics of high dimensional data, the reason why the second order statistics must be taken into account in high dimensional data is suggested. Recognizing the importance of the second order statistics, there is a need to represent the second order statistics. A method to visualize statistics using a color code is proposed. By representing statistics using color coding, one can easily extract and compare the first and the second statistics.

A finite element computation of turbulent boundary layer flows with an algebraic stress turbulence model

NASA Technical Reports Server (NTRS)

Kim, Sang-Wook; Chen, Yen-Sen

1988-01-01

An algebraic stress turbulence model and a computational procedure for turbulent boundary layer flows which is based on the semidiscrete Galerkin FEM are discussed. In the algebraic stress turbulence model, the eddy viscosity expression is obtained from the Reynolds stress turbulence model, and the turbulent kinetic energy dissipation rate equation is improved by including a production range time scale. Good agreement with experimental data is found for the examples of a fully developed channel flow, a fully developed pipe flow, a flat plate boundary layer flow, a plane jet exhausting into a moving stream, a circular jet exhausting into a moving stream, and a wall jet flow.

Unsteady Boundary-Layer Flow over Jerked Plate Moving in a Free Stream of Viscoelastic Fluid

PubMed Central

Mehmood, Ahmer; Ali, Asif; Saleem, Najma

2014-01-01

This study aims to investigate the unsteady boundary-layer flow of a viscoelastic non-Newtonian fluid over a flat surface. The plate is suddenly jerked to move with uniform velocity in a uniform stream of non-Newtonian fluid. Purely analytic solution to governing nonlinear equation is obtained. The solution is highly accurate and valid for all values of the dimensionless time 0 ≤ τ < ∞. Flow properties of the viscoelastic fluid are discussed through graphs. PMID:24892060

Global conservation model for a mushy region over a moving substrate

NASA Astrophysics Data System (ADS)

Kyselica, J.; Šimkanin, J.

2018-03-01

We study solidification over a cool substrate moving with a relative velocity with respect to the rest of the fluid. A mathematical model based on global conservation of solute is presented. The explicit solutions of the governing equations are found and analysed via the asymptotic methods. The assessment of how the boundary-layer flow influences the physical characteristics of the mushy region is given, together with the discussion of a possible connection with the solidification at the inner core boundary.

Supercomputing Aspects for Simulating Incompressible Flow

NASA Technical Reports Server (NTRS)

Kwak, Dochan; Kris, Cetin C.

2000-01-01

The primary objective of this research is to support the design of liquid rocket systems for the Advanced Space Transportation System. Since the space launch systems in the near future are likely to rely on liquid rocket engines, increasing the efficiency and reliability of the engine components is an important task. One of the major problems in the liquid rocket engine is to understand fluid dynamics of fuel and oxidizer flows from the fuel tank to plume. Understanding the flow through the entire turbo-pump geometry through numerical simulation will be of significant value toward design. One of the milestones of this effort is to develop, apply and demonstrate the capability and accuracy of 3D CFD methods as efficient design analysis tools on high performance computer platforms. The development of the Message Passage Interface (MPI) and Multi Level Parallel (MLP) versions of the INS3D code is currently underway. The serial version of INS3D code is a multidimensional incompressible Navier-Stokes solver based on overset grid technology, INS3D-MPI is based on the explicit massage-passing interface across processors and is primarily suited for distributed memory systems. INS3D-MLP is based on multi-level parallel method and is suitable for distributed-shared memory systems. For the entire turbo-pump simulations, moving boundary capability and efficient time-accurate integration methods are built in the flow solver, To handle the geometric complexity and moving boundary problems, an overset grid scheme is incorporated with the solver so that new connectivity data will be obtained at each time step. The Chimera overlapped grid scheme allows subdomains move relative to each other, and provides a great flexibility when the boundary movement creates large displacements. Two numerical procedures, one based on artificial compressibility method and the other pressure projection method, are outlined for obtaining time-accurate solutions of the incompressible Navier-Stokes equations. The performance of the two methods is compared by obtaining unsteady solutions for the evolution of twin vortices behind a flat plate. Calculated results are compared with experimental and other numerical results. For an unsteady flow, which requires small physical time step, the pressure projection method was found to be computationally efficient since it does not require any subiteration procedure. It was observed that the artificial compressibility method requires a fast convergence scheme at each physical time step in order to satisfy the incompressibility condition. This was obtained by using a GMRES-ILU(0) solver in present computations. When a line-relaxation scheme was used, the time accuracy was degraded and time-accurate computations became very expensive.

Force-free magnetic fields - The magneto-frictional method

NASA Technical Reports Server (NTRS)

Yang, W. H.; Sturrock, P. A.; Antiochos, S. K.

1986-01-01

The problem under discussion is that of calculating magnetic field configurations in which the Lorentz force j x B is everywhere zero, subject to specified boundary conditions. We choose to represent the magnetic field in terms of Clebsch variables in the form B = grad alpha x grad beta. These variables are constant on any field line so that each field line is labeled by the corresponding values of alpha and beta. When the field is described in this way, the most appropriate choice of boundary conditions is to specify the values of alpha and beta on the bounding surface. We show that such field configurations may be calculated by a magneto-frictional method. We imagine that the field lines move through a stationary medium, and that each element of magnetic field is subject to a frictional force parallel to and opposing the velocity of the field line. This concept leads to an iteration procedure for modifying the variables alpha and beta, that tends asymptotically towards the force-free state. We apply the method first to a simple problem in two rectangular dimensions, and then to a problem of cylindrical symmetry that was previously discussed by Barnes and Sturrock (1972). In one important respect, our new results differ from the earlier results of Barnes and Sturrock, and we conclude that the earlier article was in error.

High-Order Moving Overlapping Grid Methodology in a Spectral Element Method

NASA Astrophysics Data System (ADS)

Merrill, Brandon E.

A moving overlapping mesh methodology that achieves spectral accuracy in space and up to second-order accuracy in time is developed for solution of unsteady incompressible flow equations in three-dimensional domains. The targeted applications are in aerospace and mechanical engineering domains and involve problems in turbomachinery, rotary aircrafts, wind turbines and others. The methodology is built within the dual-session communication framework initially developed for stationary overlapping meshes. The methodology employs semi-implicit spectral element discretization of equations in each subdomain and explicit treatment of subdomain interfaces with spectrally-accurate spatial interpolation and high-order accurate temporal extrapolation, and requires few, if any, iterations, yet maintains the global accuracy and stability of the underlying flow solver. Mesh movement is enabled through the Arbitrary Lagrangian-Eulerian formulation of the governing equations, which allows for prescription of arbitrary velocity values at discrete mesh points. The stationary and moving overlapping mesh methodologies are thoroughly validated using two- and three-dimensional benchmark problems in laminar and turbulent flows. The spatial and temporal global convergence, for both methods, is documented and is in agreement with the nominal order of accuracy of the underlying solver. Stationary overlapping mesh methodology was validated to assess the influence of long integration times and inflow-outflow global boundary conditions on the performance. In a turbulent benchmark of fully-developed turbulent pipe flow, the turbulent statistics are validated against the available data. Moving overlapping mesh simulations are validated on the problems of two-dimensional oscillating cylinder and a three-dimensional rotating sphere. The aerodynamic forces acting on these moving rigid bodies are determined, and all results are compared with published data. Scaling tests, with both methodologies, show near linear strong scaling, even for moderately large processor counts. The moving overlapping mesh methodology is utilized to investigate the effect of an upstream turbulent wake on a three-dimensional oscillating NACA0012 extruded airfoil. A direct numerical simulation (DNS) at Reynolds Number 44,000 is performed for steady inflow incident upon the airfoil oscillating between angle of attack 5.6° and 25° with reduced frequency k=0.16. Results are contrasted with subsequent DNS of the same oscillating airfoil in a turbulent wake generated by a stationary upstream cylinder.

The use of MACSYMA for solving elliptic boundary value problems

NASA Technical Reports Server (NTRS)

Thejll, Peter; Gilbert, Robert P.

1990-01-01

A boundary method is presented for the solution of elliptic boundary value problems. An approach based on the use of complete systems of solutions is emphasized. The discussion is limited to the Dirichlet problem, even though the present method can possibly be adapted to treat other boundary value problems.

Global Discrete Artificial Boundary Conditions for Time-Dependent Wave Propagation

NASA Technical Reports Server (NTRS)

Ryabenkii, V. S.; Tsynkov, S. V.; Turchaninov, V. I.; Bushnell, Dennis M. (Technical Monitor)

2001-01-01

We construct global artificial boundary conditions (ABCs) for the numerical simulation of wave processes on unbounded domains using a special non-deteriorating algorithm that has been developed previously for the long-term computation of wave-radiation solutions. The ABCs are obtained directly for the discrete formulation of the problem; in so doing, neither a rational approximation of 'non-reflecting kernels,' nor discretization of the continuous boundary conditions is required. The extent of temporal nonlocality of the new ABCs appears fixed and limited; in addition, the ABCs can handle artificial boundaries of irregular shape on regular grids with no fitting/adaptation needed and no accuracy loss induced. The non-deteriorating algorithm, which is the core of the new ABCs is inherently three-dimensional, it guarantees temporally uniform grid convergence of the solution driven by a continuously operating source on arbitrarily long time intervals, and provides unimprovable linear computational complexity with respect to the grid dimension. The algorithm is based on the presence of lacunae, i.e., aft fronts of the waves, in wave-type solutions in odd-dimension spaces, It can, in fact, be built as a modification on top of any consistent and stable finite-difference scheme, making its grid convergence uniform in time and at the same time keeping the rate of convergence the same as that of the non-modified scheme. In the paper, we delineate the construction of the global lacunae-based ABCs in the framework of a discretized wave equation. The ABCs are obtained for the most general formulation of the problem that involves radiation of waves by moving sources (e.g., radiation of acoustic waves by a maneuvering aircraft). We also present systematic numerical results that corroborate the theoretical design properties of the ABCs' algorithm.

Global Discrete Artificial Boundary Conditions for Time-Dependent Wave Propagation

NASA Astrophysics Data System (ADS)

Ryaben'kii, V. S.; Tsynkov, S. V.; Turchaninov, V. I.

2001-12-01

We construct global artificial boundary conditions (ABCs) for the numerical simulation of wave processes on unbounded domains using a special nondeteriorating algorithm that has been developed previously for the long-term computation of wave-radiation solutions. The ABCs are obtained directly for the discrete formulation of the problem; in so doing, neither a rational approximation of “nonreflecting kernels” nor discretization of the continuous boundary conditions is required. The extent of temporal nonlocality of the new ABCs appears fixed and limited; in addition, the ABCs can handle artificial boundaries of irregular shape on regular grids with no fitting/adaptation needed and no accuracy loss induced. The nondeteriorating algorithm, which is the core of the new ABCs, is inherently three-dimensional, it guarantees temporally uniform grid convergence of the solution driven by a continuously operating source on arbitrarily long time intervals and provides unimprovable linear computational complexity with respect to the grid dimension. The algorithm is based on the presence of lacunae, i.e., aft fronts of the waves, in wave-type solutions in odd-dimensional spaces. It can, in fact, be built as a modification on top of any consistent and stable finite-difference scheme, making its grid convergence uniform in time and at the same time keeping the rate of convergence the same as that of the unmodified scheme. In this paper, we delineate the construction of the global lacunae-based ABCs in the framework of a discretized wave equation. The ABCs are obtained for the most general formulation of the problem that involves radiation of waves by moving sources (e.g., radiation of acoustic waves by a maneuvering aircraft). We also present systematic numerical results that corroborate the theoretical design properties of the ABC algorithm.

Electrolyte system strategies for anionic ITP with ESI-MS detection. 3. The ITP spacer technique in moving-boundary systems and configurations with two self-maintained ITP subsystems.

PubMed

Gebauer, Petr; Malá, Zdena; Boček, Petr

2014-03-01

This contribution is the third part of the project on strategies used in the selection and tuning of electrolyte systems for anionic ITP with ESI-MS detection. The strategy presented here is based on the creation of self-maintained ITP subsystems in moving-boundary systems and describes two new principal approaches offering physical separation of analyte zones from their common ITP stack and/or simultaneous selective stacking of two different analyte groups. Both strategic directions are based on extending the number of components forming the electrolyte system by adding a third suitable anion. The first method is the application of the spacer technique to moving-boundary anionic ITP systems, the second method is a technique utilizing a moving-boundary ITP system in which two ITP subsystems exist and move with mutually different velocities. It is essential for ESI detection that both methods can be based on electrolyte systems containing only several simple chemicals, such as simple volatile organic acids (formic and acetic) and their ammonium salts. The properties of both techniques are defined theoretically and discussed from the viewpoint of their applicability to trace analysis by ITP-ESI-MS. Examples of system design for selected model separations of preservatives and pharmaceuticals illustrate the validity of the theoretical model and application potential of the proposed techniques by both computer simulations and experiments. Both new methods enhance the application range of ITP-MS and may be beneficial particularly for complex multicomponent samples or for analytes with identical molecular mass. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

A Linear-Elasticity Solver for Higher-Order Space-Time Mesh Deformation

NASA Technical Reports Server (NTRS)

Diosady, Laslo T.; Murman, Scott M.

2018-01-01

A linear-elasticity approach is presented for the generation of meshes appropriate for a higher-order space-time discontinuous finite-element method. The equations of linear-elasticity are discretized using a higher-order, spatially-continuous, finite-element method. Given an initial finite-element mesh, and a specified boundary displacement, we solve for the mesh displacements to obtain a higher-order curvilinear mesh. Alternatively, for moving-domain problems we use the linear-elasticity approach to solve for a temporally discontinuous mesh velocity on each time-slab and recover a continuous mesh deformation by integrating the velocity. The applicability of this methodology is presented for several benchmark test cases.

Transient response in granular quasi-two-dimensional bounded heap flow.

PubMed

Xiao, Hongyi; Ottino, Julio M; Lueptow, Richard M; Umbanhowar, Paul B

2017-10-01

We study the transition between steady flows of noncohesive granular materials in quasi-two-dimensional bounded heaps by suddenly changing the feed rate. In both experiments and simulations, the primary feature of the transition is a wedge of flowing particles that propagates downstream over the rising free surface with a wedge front velocity inversely proportional to the square root of time. An additional longer duration transient process continues after the wedge front reaches the downstream wall. The entire transition is well modeled as a moving boundary problem with a diffusionlike equation derived from local mass balance and a local relation between the flux and the surface slope.

Lubrication theory for a random fibrous medium

NASA Astrophysics Data System (ADS)

Mirbod, Parisa; Andreopoulos, Yiannis; Weinbaum, Sheldon

2007-11-01

In the classical theory for a slipper bearing one examines the relative motion of an inclined planar surface and a horizontal planar surface. The solution for the pressure distribution and lift force are independent of which boundary is moving and there is an optimum tilt k=h1/h2=2.2 for maximum lift. This symmetry is lost if the intervening space is filled with a soft porous fibrous material. In this paper the generalized Reynolds equation derived in Feng and Weinbaum (2000) J. Fluid Mech. 422:281 is extended to treat a random fiber matrix satisfying the widely used Carman-Kozeny equation. We show that the solutions are strikingly different depending on whether a) the inclined upper boundary moves or b) the upper boundary is stationary and the horizontal lower boundary moves beneath it. The behavior depends critically on the value of the dimensionless fiber interaction layer thickness α=H/√Kp . In a) the pressure and lift force increase as 2̂ and asymptotically approach a limiting behavior for large values of α since the fluid is pushed forward by the tilt of the upper boundary. In b) the pressure and lift force decay as &-2circ; since the fiber interaction layer thickness decreases and the amount of fluid dragged though the fluid gap decreases as α increases and vanishes for α>> 1.

A visual detection of protein content based on titration of moving reaction boundary electrophoresis.

PubMed

Wang, Hou-Yu; Guo, Cheng-Ye; Guo, Chen-Gang; Fan, Liu-Yin; Zhang, Lei; Cao, Cheng-Xi

2013-04-24

A visual electrophoretic titration method was firstly developed from the concept of moving reaction boundary (MRB) for protein content analysis. In the developed method, when the voltage was applied, the hydroxide ions in the cathodic vessel moved towards the anode, and neutralized the carboxyl groups of protein immobilized via highly cross-linked polyacrylamide gel (PAG), generating a MRB between the alkali and the immobilized protein. The boundary moving velocity (V(MRB)) was as a function of protein content, and an acid-base indicator was used to denote the boundary displacement. As a proof of concept, standard model proteins and biological samples were chosen for the experiments to study the feasibility of the developed method. The experiments revealed that good linear calibration functions between V(MRB) and protein content (correlation coefficients R>0.98). The experiments further demonstrated the following merits of developed method: (1) weak influence of non-protein nitrogen additives (e.g., melamine) adulterated in protein samples, (2) good agreement with the classic Kjeldahl method (R=0.9945), (3) fast measuring speed in total protein analysis of large samples from the same source, and (4) low limit of detection (0.02-0.15 mg mL(-1) for protein content), good precision (R.S.D. of intra-day less than 1.7% and inter-day less than 2.7%), and high recoveries (105-107%). Crown Copyright © 2013. Published by Elsevier B.V. All rights reserved.

An adaptive discretization of incompressible flow using a multitude of moving Cartesian grids

NASA Astrophysics Data System (ADS)

English, R. Elliot; Qiu, Linhai; Yu, Yue; Fedkiw, Ronald

2013-12-01

We present a novel method for discretizing the incompressible Navier-Stokes equations on a multitude of moving and overlapping Cartesian grids each with an independently chosen cell size to address adaptivity. Advection is handled with first and second order accurate semi-Lagrangian schemes in order to alleviate any time step restriction associated with small grid cell sizes. Likewise, an implicit temporal discretization is used for the parabolic terms including Navier-Stokes viscosity which we address separately through the development of a method for solving the heat diffusion equations. The most intricate aspect of any such discretization is the method used in order to solve the elliptic equation for the Navier-Stokes pressure or that resulting from the temporal discretization of parabolic terms. We address this by first removing any degrees of freedom which duplicately cover spatial regions due to overlapping grids, and then providing a discretization for the remaining degrees of freedom adjacent to these regions. We observe that a robust second order accurate symmetric positive definite readily preconditioned discretization can be obtained by constructing a local Voronoi region on the fly for each degree of freedom in question in order to obtain both its stencil (logically connected neighbors) and stencil weights. Internal curved boundaries such as at solid interfaces are handled using a simple immersed boundary approach which is directly applied to the Voronoi mesh in both the viscosity and pressure solves. We independently demonstrate each aspect of our approach on test problems in order to show efficacy and convergence before finally addressing a number of common test cases for incompressible flow with stationary and moving solid bodies.

Hydrodynamic and Thermal Slip Effect on Double-Diffusive Free Convective Boundary Layer Flow of a Nanofluid Past a Flat Vertical Plate in the Moving Free Stream

PubMed Central

Khan, Waqar A.; Uddin, Md Jashim; Ismail, A. I. Md.

2013-01-01

The effects of hydrodynamic and thermal slip boundary conditions on the double-diffusive free convective flow of a nanofluid along a semi-infinite flat solid vertical plate are investigated numerically. It is assumed that free stream is moving. The governing boundary layer equations are non-dimensionalized and transformed into a system of nonlinear, coupled similarity equations. The effects of the controlling parameters on the dimensionless velocity, temperature, solute and nanofluid concentration as well as on the reduced Nusselt number, reduced Sherwood number and the reduced nanoparticle Sherwood number are investigated and presented graphically. To the best of our knowledge, the effects of hydrodynamic and thermal slip boundary conditions have not been investigated yet. It is found that the reduced local Nusselt, local solute and the local nanofluid Sherwood numbers increase with hydrodynamic slip and decrease with thermal slip parameters. PMID:23533566

Calculation of steady and unsteady transonic flow using a Cartesian mesh and gridless boundary conditions with application to aeroelasticity

NASA Astrophysics Data System (ADS)

Kirshman, David

A numerical method for the solution of inviscid compressible flow using an array of embedded Cartesian meshes in conjunction with gridless surface boundary conditions is developed. The gridless boundary treatment is implemented by means of a least squares fitting of the conserved flux variables using a cloud of nodes in the vicinity of the surface geometry. The method allows for accurate treatment of the surface boundary conditions using a grid resolution an order of magnitude coarser than required of typical Cartesian approaches. Additionally, the method does not suffer from issues associated with thin body geometry or extremely fine cut cells near the body. Unlike some methods that consider a gridless (or "meshless") treatment throughout the entire domain, multi-grid acceleration can be effectively incorporated and issues associated with global conservation are alleviated. The "gridless" surface boundary condition provides for efficient and simple problem set up since definition of the body geometry is generated independently from the field mesh, and automatically incorporated into the field discretization of the domain. The applicability of the method is first demonstrated for steady flow of single and multi-element airfoil configurations. Using this method, comparisons with traditional body-fitted grid simulations reveal that steady flow solutions can be obtained accurately with minimal effort associated with grid generation. The method is then extended to unsteady flow predictions. In this application, flow field simulations for the prescribed oscillation of an airfoil indicate excellent agreement with experimental data. Furthermore, it is shown that the phase lag associated with shock oscillation is accurately predicted without the need for a deformable mesh. Lastly, the method is applied to the prediction of transonic flutter using a two-dimensional wing model, in which comparisons with moving mesh simulations yield nearly identical results. As a result, applicability of the method to transient and vibrating fluid-structure interaction problems is established in which the requirement for a deformable mesh is eliminated.

A numerical solution of a singular boundary value problem arising in boundary layer theory.

PubMed

Hu, Jiancheng

2016-01-01

In this paper, a second-order nonlinear singular boundary value problem is presented, which is equivalent to the well-known Falkner-Skan equation. And the one-dimensional third-order boundary value problem on interval [Formula: see text] is equivalently transformed into a second-order boundary value problem on finite interval [Formula: see text]. The finite difference method is utilized to solve the singular boundary value problem, in which the amount of computational effort is significantly less than the other numerical methods. The numerical solutions obtained by the finite difference method are in agreement with those obtained by previous authors.

Compressor airfoil tip clearance optimization system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Little, David A.; Pu, Zhengxiang

2015-08-18

A compressor airfoil tip clearance optimization system for reducing a gap between a tip of a compressor airfoil and a radially adjacent component of a turbine engine is disclosed. The turbine engine may include ID and OD flowpath boundaries configured to minimize compressor airfoil tip clearances during turbine engine operation in cooperation with one or more clearance reduction systems that are configured to move the rotor assembly axially to reduce tip clearance. The configurations of the ID and OD flowpath boundaries enhance the effectiveness of the axial movement of the rotor assembly, which includes movement of the ID flowpath boundary.more » During operation of the turbine engine, the rotor assembly may be moved axially to increase the efficiency of the turbine engine.« less

On The Determination of Shadow Boundaries and Relevant Eigenrays For Sound Propagation In Stratified Moving Media

NASA Technical Reports Server (NTRS)

Mcaninch, Gerry L.; Heath, Stephanie L.

2006-01-01

The eiconal and ray equations for a stratified moving medium are analyzed to determine which rays connect a source located at an altitude z = z(sub s) to an observer on the ground plane. The characteristics of all available rays are ascertained. Further, the rays which determine the shadow boundary are found. Thus, the shadow boundary may be easily calculated and any observers for which an eigenray does not exist eliminated from further consideration. Therefore, the analysis may be applied to save computer time in two ways. First, rays that do not reach the ground may be eliminated before they are traced, and observers for which no eigenray exists may be eliminated from consideration.

Techniques and computations for mapping plot clusters that straddle stand boundaries

Treesearch

Charles T. Scott; William A. Bechtold

1995-01-01

Many regional (extensive) forest surveys use clusters of subplots or prism points to reduce survey costs. Two common methods of handling clusters that straddle stand boundaries entail: (1) moving all subplots into a single forest cover type, or (2)"averaging" data across multiple conditions without regard to the boundaries. these methods result in biased...

The Boundary Function Method. Fundamentals

NASA Astrophysics Data System (ADS)

Kot, V. A.

2017-03-01

The boundary function method is proposed for solving applied problems of mathematical physics in the region defined by a partial differential equation of the general form involving constant or variable coefficients with a Dirichlet, Neumann, or Robin boundary condition. In this method, the desired function is defined by a power polynomial, and a boundary function represented in the form of the desired function or its derivative at one of the boundary points is introduced. Different sequences of boundary equations have been set up with the use of differential operators. Systems of linear algebraic equations constructed on the basis of these sequences allow one to determine the coefficients of a power polynomial. Constitutive equations have been derived for initial boundary-value problems of all the main types. With these equations, an initial boundary-value problem is transformed into the Cauchy problem for the boundary function. The determination of the boundary function by its derivative with respect to the time coordinate completes the solution of the problem.

Long-Time Numerical Integration of the Three-Dimensional Wave Equation in the Vicinity of a Moving Source

NASA Technical Reports Server (NTRS)

Ryabenkii, V. S.; Turchaninov, V. I.; Tsynkov, S. V.

1999-01-01

We propose a family of algorithms for solving numerically a Cauchy problem for the three-dimensional wave equation. The sources that drive the equation (i.e., the right-hand side) are compactly supported in space for any given time; they, however, may actually move in space with a subsonic speed. The solution is calculated inside a finite domain (e.g., sphere) that also moves with a subsonic speed and always contains the support of the right-hand side. The algorithms employ a standard consistent and stable explicit finite-difference scheme for the wave equation. They allow one to calculate tile solution for arbitrarily long time intervals without error accumulation and with the fixed non-growing amount of tile CPU time and memory required for advancing one time step. The algorithms are inherently three-dimensional; they rely on the presence of lacunae in the solutions of the wave equation in oddly dimensional spaces. The methodology presented in the paper is, in fact, a building block for constructing the nonlocal highly accurate unsteady artificial boundary conditions to be used for the numerical simulation of waves propagating with finite speed over unbounded domains.

A multiple-time-scale turbulence model based on variable partitioning of turbulent kinetic energy spectrum

NASA Technical Reports Server (NTRS)

Kim, S.-W.; Chen, C.-P.

1987-01-01

A multiple-time-scale turbulence model of a single point closure and a simplified split-spectrum method is presented. In the model, the effect of the ratio of the production rate to the dissipation rate on eddy viscosity is modeled by use of the multiple-time-scales and a variable partitioning of the turbulent kinetic energy spectrum. The concept of a variable partitioning of the turbulent kinetic energy spectrum and the rest of the model details are based on the previously reported algebraic stress turbulence model. Example problems considered include: a fully developed channel flow, a plane jet exhausting into a moving stream, a wall jet flow, and a weakly coupled wake-boundary layer interaction flow. The computational results compared favorably with those obtained by using the algebraic stress turbulence model as well as experimental data. The present turbulence model, as well as the algebraic stress turbulence model, yielded significantly improved computational results for the complex turbulent boundary layer flows, such as the wall jet flow and the wake boundary layer interaction flow, compared with available computational results obtained by using the standard kappa-epsilon turbulence model.

A multiple-time-scale turbulence model based on variable partitioning of the turbulent kinetic energy spectrum

NASA Technical Reports Server (NTRS)

Kim, S.-W.; Chen, C.-P.

1989-01-01

A multiple-time-scale turbulence model of a single point closure and a simplified split-spectrum method is presented. In the model, the effect of the ratio of the production rate to the dissipation rate on eddy viscosity is modeled by use of the multiple-time-scales and a variable partitioning of the turbulent kinetic energy spectrum. The concept of a variable partitioning of the turbulent kinetic energy spectrum and the rest of the model details are based on the previously reported algebraic stress turbulence model. Example problems considered include: a fully developed channel flow, a plane jet exhausting into a moving stream, a wall jet flow, and a weakly coupled wake-boundary layer interaction flow. The computational results compared favorably with those obtained by using the algebraic stress turbulence model as well as experimental data. The present turbulence model, as well as the algebraic stress turbulence model, yielded significantly improved computational results for the complex turbulent boundary layer flows, such as the wall jet flow and the wake boundary layer interaction flow, compared with available computational results obtained by using the standard kappa-epsilon turbulence model.

Boundary control by displacement at one end of a string and the integral condition on the other

NASA Astrophysics Data System (ADS)

Attaev, Anatoly Kh.

2017-09-01

For a one-dimensional wave equation we study the problem of finding such boundary controls that makes a string move from an arbitrary specified initial state to an arbitrary specified final state. The control is applied at the left end of the string while the nonlocal displacement is at the right end. Necessary and sufficient conditions are established for the functions determining the initial and final state of the string. An explicit analytical form of the boundary control is obtained as well as the minimum time T = l for this control. In case when T = l - ɛ, 0 < ɛ < l, i.e. T < l it is shown the initial values u(x, 0) = ϕ(x) and ut (x, 0) = ψ(x) cannot be set arbitrary. Moreover, if ɛ < l/2, hence the functions ϕ(x) and ψ(x) are linearly dependent on any segment of finite length either in the segment [0, ɛ], or in [l-ɛ, l]. Suppose ɛ ≥ l/2, then functions ϕ(x) and ψ(x) are linearly dependent on any segment of finite length in the segment [0, l].

The complex variable boundary element method: Applications in determining approximative boundaries

USGS Publications Warehouse

Hromadka, T.V.

1984-01-01

The complex variable boundary element method (CVBEM) is used to determine approximation functions for boundary value problems of the Laplace equation such as occurs in potential theory. By determining an approximative boundary upon which the CVBEM approximator matches the desired constant (level curves) boundary conditions, the CVBEM is found to provide the exact solution throughout the interior of the transformed problem domain. Thus, the acceptability of the CVBEM approximation is determined by the closeness-of-fit of the approximative boundary to the study problem boundary. ?? 1984.

Response of plasma facing components in Tokamaks due to intense energy deposition using Particle-In-Cell (PIC) methods

NASA Astrophysics Data System (ADS)

Genco, Filippo

Damage to plasma-facing components (PFC) due to various plasma instabilities is still a major concern for the successful development of fusion energy and represents a significant research obstacle in the community. It is of great importance to fully understand the behavior and lifetime expectancy of PFC under both low energy cycles during normal events and highly energetic events as disruptions, Edge-Localized Modes (ELM), Vertical Displacement Events (VDE), and Run-away electron (RE). The consequences of these high energetic dumps with energy fluxes ranging from 10 MJ/m2 up to 200 MJ/m 2 applied in very short periods (0.1 to 5 ms) can be catastrophic both for safety and economic reasons. Those phenomena can cause a) large temperature increase in the target material b) consequent melting, evaporation and erosion losses due to the extremely high heat fluxes c) possible structural damage and permanent degradation of the entire bulk material with probable burnout of the coolant tubes; d) plasma contamination, transport of target material into the chamber far from where it was originally picked. The modeling of off-normal events such as Disruptions and ELMs requires the simultaneous solution of three main problems along time: a) the heat transfer in the plasma facing component b) the interaction of the produced vapor from the surface with the incoming plasma particles c) the transport of the radiation produced in the vapor-plasma cloud. In addition the moving boundaries problem has to be considered and solved at the material surface. Considering the carbon divertor as target, the moving boundaries are two since for the given conditions, carbon doesn't melt: the plasma front and the moving eroded material surface. The current solution methods for this problem use finite differences and moving coordinates system based on the Crank-Nicholson method and Alternating Directions Implicit Method (ADI). Currently Particle-In-Cell (PIC) methods are widely used for solving complex dynamics problems involving distorted plasma hydrodynamic problems and plasma physics. The PIC method solves the hydrodynamic equations solving all field equations tracking at the same time "sample particles" or pseudo-particles (representative of the much more numerous real ones) as the move under the influence of diffusion or magnetic force. The superior behavior of the PIC techniques over the more classical Lagrangian finite difference methods stands in the fact that detailed information about the particles are available at all times as well as mass and momentum transport values are constantly provided. This allows with a relative small number of particles to well describe the behavior of plasma even in presence of highly distorted flows without losing accuracy. The radiation transport equation is solved at each time step calculating for each cell the opacity and emissivity coefficients. Photon radiation continuum and line fluxes are also calculated per the entire domain and provide useful information for the entire energetic calculation of the system which in the end provides the total values of erosion and lifetime of the target material. In this thesis, a new code named HEIGHTS-PIC code has been created and modified using a new approach of the PIC technique to solve the three physics problems involved integrating each of them as a continuum providing insight on the plasma behavior, evolution along time and physical understanding of the very complex phenomena taking place. The results produced with the models are compared with the well-known and benchmarked HEIGHTS package and also with existing experimental results especially produced in Russia at the TRINITI facility. Comparisons with LASER experiments are also discussed.

Exact solutions for sound radiation from a moving monopole above an impedance plane.

PubMed

Ochmann, Martin

2013-04-01

The acoustic field of a monopole source moving with constant velocity at constant height above an infinite locally reacting plane can be expressed in analytical form by combining the Lorentz transformation with the method of superimposing complex or real point sources. For a plane with masslike response, the solution in Lorentz space consists of a superposition of monopoles only and therefore, does not differ in principle from the solution for the corresponding stationary boundary value problem. However, by considering a frequency independent surface impedance, e.g., with pure absorbing behavior, the half-space Green's function is now comprised of not only a line of monopoles but also of dipoles. For certain field points at a special line g, this solution can be written explicitly by using an exponential integral. For arbitrary field points, the method of stationary phase leads to an asymptotic solution for the reflection coefficient which agrees with prior results from the literature.

The solution of the Elrod algorithm for a dynamically loaded journal bearing using multigrid techniques

NASA Technical Reports Server (NTRS)

Woods, Claudia M.; Brewe, David E.

1988-01-01

A numerical solution to a theoretical model of vapor cavitation in a dynamically loaded journal bearing is developed utilizing a multigrid iteration technique. The method is compared with a noniterative approach in terms of computational time and accuracy. The computational model is based on the Elrod algorithm, a control volume approach to the Reynolds equation which mimics the Jakobsson-Floberg and Olsson cavitation theory. Besides accounting for a moving cavitation boundary and conservation of mass at the boundary, it also conserves mass within the cavitated region via a smeared mass or striated flow extending to both surfaces in the film gap. The mixed nature of the equations (parabolic in the full film zone and hyperbolic in the cavitated zone) coupled with the dynamic aspects of the problem create interesting difficulties for the present solution approach. Emphasis is placed on the methods found to eliminate solution instabilities. Excellent results are obtained for both accuracy and reduction of computational time.

The solution of the Elrod algorithm for a dynamically loaded journal bearing using multigrid techniques

NASA Technical Reports Server (NTRS)

Woods, C. M.; Brewe, D. E.

1989-01-01

A numerical solution to a theoretical model of vapor cavitation in a dynamically loaded journal bearing is developed utilizing a multigrid iteration technique. The method is compared with a noniterative approach in terms of computational time and accuracy. The computational model is based on the Elrod algorithm, a control volume approach to the Reynolds equation which mimics the Jakobsson-Floberg and Olsson cavitation theory. Besides accounting for a moving cavitation boundary and conservation of mass at the boundary, it also conserves mass within the cavitated region via a smeared mass or striated flow extending to both surfaces in the film gap. The mixed nature of the equations (parabolic in the full film zone and hyperbolic in the cavitated zone) coupled with the dynamic aspects of the problem create interesting difficulties for the present solution approach. Emphasis is placed on the methods found to eliminate solution instabilities. Excellent results are obtained for both accuracy and reduction of computational time.

The use of multigrid techniques in the solution of the Elrod algorithm for a dynamically loaded journal bearing. M.S. Thesis. Final Report

NASA Technical Reports Server (NTRS)

Woods, Claudia M.

1988-01-01

A numerical solution to a theoretical model of vapor cavitation in a dynamically loaded journal bearing is developed, utilizing a multigrid iterative technique. The code is compared with a presently existing direct solution in terms of computational time and accuracy. The model is based on the Elrod algorithm, a control volume approach to the Reynolds equation which mimics the Jakobssen-Floberg and Olsson cavitation theory. Besides accounting for a moving cavitation boundary and conservation of mass at the boundary, it also conserves mass within the cavitated region via liquid striations. The mixed nature of the equations (elliptic in the full film zone and nonelliptic in the cavitated zone) coupled with the dynamic aspects of the problem create interesting difficulties for the present solution approach. Emphasis is placed on the methods found to eliminate solution instabilities. Excellent results are obtained for both accuracy and reduction of computational time.

Large-aspect-ratio limit of neoclassical transport theory.

PubMed

Wong, S K; Chan, V S

2003-06-01

This paper presents a comprehensive description of neoclassical transport theory in the banana regime for large-aspect-ratio flux surfaces of arbitrary shapes. The method of matched-asymptotic expansions is used to obtain analytical solutions for plasma distribution functions and to compute transport coefficients. The method provides justification for retaining only the part of the Fokker-Planck operator that involves the second derivative with respect to the cosine of the pitch angle for the trapped and barely circulating particles. It leads to a simple equation for the freely circulating particles with boundary conditions that embody a discontinuity separating particles moving in opposite directions. Corrections to the transport coefficients are obtained by generalizing an existing boundary layer analysis. The system of moment and field equations is consistently taken in the cylinder limit, which facilitates the discussion of the treatment of dynamical constraints. It is shown that the nonlocal nature of Ohm's law in neoclassical theory renders the mathematical problem of plasma transport with changing flux surfaces nonstandard.

Scalar discrete nonlinear multipoint boundary value problems

NASA Astrophysics Data System (ADS)

Rodriguez, Jesus; Taylor, Padraic

2007-06-01

In this paper we provide sufficient conditions for the existence of solutions to scalar discrete nonlinear multipoint boundary value problems. By allowing more general boundary conditions and by imposing less restrictions on the nonlinearities, we obtain results that extend previous work in the area of discrete boundary value problems [Debra L. Etheridge, Jesus Rodriguez, Periodic solutions of nonlinear discrete-time systems, Appl. Anal. 62 (1996) 119-137; Debra L. Etheridge, Jesus Rodriguez, Scalar discrete nonlinear two-point boundary value problems, J. Difference Equ. Appl. 4 (1998) 127-144].

Error analysis of finite difference schemes applied to hyperbolic initial boundary value problems

NASA Technical Reports Server (NTRS)

Skollermo, G.

1979-01-01

Finite difference methods for the numerical solution of mixed initial boundary value problems for hyperbolic equations are studied. The reported investigation has the objective to develop a technique for the total error analysis of a finite difference scheme, taking into account initial approximations, boundary conditions, and interior approximation. Attention is given to the Cauchy problem and the initial approximation, the homogeneous problem in an infinite strip with inhomogeneous boundary data, the reflection of errors in the boundaries, and two different boundary approximations for the leapfrog scheme with a fourth order accurate difference operator in space.

A level-set method for two-phase flows with moving contact line and insoluble surfactant

NASA Astrophysics Data System (ADS)

Xu, Jian-Jun; Ren, Weiqing

2014-04-01

A level-set method for two-phase flows with moving contact line and insoluble surfactant is presented. The mathematical model consists of the Navier-Stokes equation for the flow field, a convection-diffusion equation for the surfactant concentration, together with the Navier boundary condition and a condition for the dynamic contact angle derived by Ren et al. (2010) [37]. The numerical method is based on the level-set continuum surface force method for two-phase flows with surfactant developed by Xu et al. (2012) [54] with some cautious treatment for the boundary conditions. The numerical method consists of three components: a flow solver for the velocity field, a solver for the surfactant concentration, and a solver for the level-set function. In the flow solver, the surface force is dealt with using the continuum surface force model. The unbalanced Young stress at the moving contact line is incorporated into the Navier boundary condition. A convergence study of the numerical method and a parametric study are presented. The influence of surfactant on the dynamics of the moving contact line is illustrated using examples. The capability of the level-set method to handle complex geometries is demonstrated by simulating a pendant drop detaching from a wall under gravity.

Numerical Boundary Conditions for Computational Aeroacoustics Benchmark Problems

NASA Technical Reports Server (NTRS)

Tam, Chritsopher K. W.; Kurbatskii, Konstantin A.; Fang, Jun

1997-01-01

Category 1, Problems 1 and 2, Category 2, Problem 2, and Category 3, Problem 2 are solved computationally using the Dispersion-Relation-Preserving (DRP) scheme. All these problems are governed by the linearized Euler equations. The resolution requirements of the DRP scheme for maintaining low numerical dispersion and dissipation as well as accurate wave speeds in solving the linearized Euler equations are now well understood. As long as 8 or more mesh points per wavelength is employed in the numerical computation, high quality results are assured. For the first three categories of benchmark problems, therefore, the real challenge is to develop high quality numerical boundary conditions. For Category 1, Problems 1 and 2, it is the curved wall boundary conditions. For Category 2, Problem 2, it is the internal radiation boundary conditions inside the duct. For Category 3, Problem 2, they are the inflow and outflow boundary conditions upstream and downstream of the blade row. These are the foci of the present investigation. Special nonhomogeneous radiation boundary conditions that generate the incoming disturbances and at the same time allow the outgoing reflected or scattered acoustic disturbances to leave the computation domain without significant reflection are developed. Numerical results based on these boundary conditions are provided.

Existence and non-uniqueness of similarity solutions of a boundary-layer problem

NASA Technical Reports Server (NTRS)

Hussaini, M. Y.; Lakin, W. D.

1986-01-01

A Blasius boundary value problem with inhomogeneous lower boundary conditions f(0) = 0 and f'(0) = - lambda with lambda strictly positive was considered. The Crocco variable formulation of this problem has a key term which changes sign in the interval of interest. It is shown that solutions of the boundary value problem do not exist for values of lambda larger than a positive critical value lambda. The existence of solutions is proven for 0 lambda lambda by considering an equivalent initial value problem. It is found however that for 0 lambda lambda, solutions of the boundary value problem are nonunique. Physically, this nonuniqueness is related to multiple values of the skin friction.

Existence and non-uniqueness of similarity solutions of a boundary layer problem

NASA Technical Reports Server (NTRS)

Hussaini, M. Y.; Lakin, W. D.

1984-01-01

A Blasius boundary value problem with inhomogeneous lower boundary conditions f(0) = 0 and f'(0) = - lambda with lambda strictly positive was considered. The Crocco variable formulation of this problem has a key term which changes sign in the interval of interest. It is shown that solutions of the boundary value problem do not exist for values of lambda larger than a positive critical value lambda. The existence of solutions is proven for 0 lambda lambda by considering an equivalent initial value problem. It is found however that for 0 lambda lambda, solutions of the boundary value problem are nonunique. Physically, this nonuniqueness is related to multiple values of the skin friction.

Vibration analysis of beams traversed by uniform partially distributed moving masses

NASA Astrophysics Data System (ADS)

Esmailzadeh, E.; Ghorashi, M.

1995-07-01

An investigation into the dynamic behavior of beams with simply supported boundary conditions, carrying either uniform partially distributed moving masses or forces, has been carried out. The present analysis in its general form may well be applied to beams with various boundary conditions. However, the results from the computer simulation model given in this paper are for beams with simply supported end conditions. Results from the numerical solutions of the differential equations of motion are shown graphically and their close agreement, in some extreme cases, with those published previously by the authors is demonstrated. It is shown that the inertial effect of the moving mass is of importance in the dynamic behavior of such structures. Moreover, when considering the maximum deflection for the mid-span of the beam, the critical speeds of the moving load have been evaluated. It is also verified that the length of the distributed moving mass affects the dynamic response considerably. These effects are shown to be of significant practical importance when designing beam-type structures such as long suspension and railway bridges.

APPLICATION OF FLOW SIMULATION FOR EVALUATION OF FILLING-ABILITY OF SELF-COMPACTING CONCRETE

NASA Astrophysics Data System (ADS)

Urano, Shinji; Nemoto, Hiroshi; Sakihara, Kohei

In this paper, MPS method was applied to fluid an alysis of self-compacting concrete. MPS method is one of the particle method, and it is suitable for the simulation of moving boundary or free surface problems and large deformation problems. The constitutive equation of self-compacting concrete is assumed as bingham model. In order to investigate flow Stoppage and flow speed of self-compacting concrete, numerical analysis examples of slump flow and L-flow test were performed. In addition, to evaluate verification of compactability of self-compacting concrete, numerical analys is examples of compaction at the part of CFT diaphragm were performed. As a result, it was found that the MPS method was suitable for the simulation of compaction of self-compacting concrete, and a just appraisal was obtained by setting shear strain rate of flow-limit πc and limitation point of segregation.

The US/Mexico Border: A Binational Approach to Framing Challenges and Constructing Solutions for Improving Farmworkers’ Lives

PubMed Central

Rosales, Cecilia; Ortega, Maria Isabel; De Zapien, Jill Guernsey; Paniagua, Alma Delia Contreras; Zapien, Antonio; Ingram, Maia; Aranda, Patricia

2012-01-01

Mexican migrant and seasonal farmworkers in the US-Mexico border region face health hazards and occupational risks and are becoming commonly known in the public health literature. According to several studies, farmworkers have high levels of chronic diseases such as diabetes and respiratory problems, are at risk for infectious diseases, and experience among the highest incidences of work-related injuries of any profession. The findings from two studies are considered and presented with the objective of contributing to an overall understanding of migrant farmworkers as a workforce moving across national boundaries and affected by the work environments and health stressors both shared and unique to each context. We propose a binational approach to comprehensively address the health problems and socioeconomic challenges faced by migrant and seasonal farmworkers. In this paper we present the results of two distinct but complementary studies of farmworker health on the Arizona-Sonora border. PMID:22829796

Stability of Contact Lines in Fluids: 2D Stokes Flow

NASA Astrophysics Data System (ADS)

Guo, Yan; Tice, Ian

2018-02-01

In an effort to study the stability of contact lines in fluids, we consider the dynamics of an incompressible viscous Stokes fluid evolving in a two-dimensional open-top vessel under the influence of gravity. This is a free boundary problem: the interface between the fluid in the vessel and the air above (modeled by a trivial fluid) is free to move and experiences capillary forces. The three-phase interface where the fluid, air, and solid vessel wall meet is known as a contact point, and the angle formed between the free interface and the vessel is called the contact angle. We consider a model of this problem that allows for fully dynamic contact points and angles. We develop a scheme of a priori estimates for the model, which then allow us to show that for initial data sufficiently close to equilibrium, the model admits global solutions that decay to equilibrium exponentially quickly.

Comparison of two methods of numerical tracking of the soil contamination dynamics during a leak from a pipeline

NASA Astrophysics Data System (ADS)

Kosterina, E. A.

2018-01-01

The situation of leakage of a polluting liquid from a longitudinal crack of the pipeline lying on the ground surface is considered. The two-dimensional nonstationary mathematical model is based on the mass balance equation in terms of pressure, which is satisfied in a domain with an unknown moving boundary. This area corresponds to the area of contaminated zone. A function characterizing the region of action of the equation is introduced, which makes it possible to obtain the formulation of the problem in a fixed domain. Two types of finite-difference approximation of the problem statement are proposed. They differ by approximation of the convective term. Counter-current approximation and approximation along characteristics are used. The results of computational experiments, which are in favor of using the method of characteristics, are presented. The methods application is illustrated by an example of spread of oil pollution.

A numerical algorithm for MHD of free surface flows at low magnetic Reynolds numbers

NASA Astrophysics Data System (ADS)

Samulyak, Roman; Du, Jian; Glimm, James; Xu, Zhiliang

2007-10-01

We have developed a numerical algorithm and computational software for the study of magnetohydrodynamics (MHD) of free surface flows at low magnetic Reynolds numbers. The governing system of equations is a coupled hyperbolic-elliptic system in moving and geometrically complex domains. The numerical algorithm employs the method of front tracking and the Riemann problem for material interfaces, second order Godunov-type hyperbolic solvers, and the embedded boundary method for the elliptic problem in complex domains. The numerical algorithm has been implemented as an MHD extension of FronTier, a hydrodynamic code with free interface support. The code is applicable for numerical simulations of free surface flows of conductive liquids or weakly ionized plasmas. The code has been validated through the comparison of numerical simulations of a liquid metal jet in a non-uniform magnetic field with experiments and theory. Simulations of the Muon Collider/Neutrino Factory target have also been discussed.

NOR-USA Scientific Traverse of East Antarctica: Science and Logistics on a Three-Month Expedition Across Antarctica's Farthest Frontier

NASA Technical Reports Server (NTRS)

Albert, Mary R.

2012-01-01

Dr. Albert's current research is centered on transfer processes in porous media, including air-snow exchange in the Polar Regions and in soils in temperate areas. Her research includes field measurements, laboratory experiments, and theoretical modeling. Mary conducts field and laboratory measurements of the physical properties of natural terrain surfaces, including permeability, microstructure, and thermal conductivity. Mary uses the measurements to examine the processes of diffusion and advection of heat, mass, and chemical transport through snow and other porous media. She has developed numerical models for investigation of a variety of problems, from interstitial transport to freezing of flowing liquids. These models include a two-dimensional finite element code for air flow with heat, water vapor, and chemical transport in porous media, several multidimensional codes for diffusive transfer, as well as a computational fluid dynamics code for analysis of turbulent water flow in moving-boundary phase change problems.

Element free Galerkin formulation of composite beam with longitudinal slip

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ahmad, Dzulkarnain; Mokhtaram, Mokhtazul Haizad; Badli, Mohd Iqbal

2015-05-15

Behaviour between two materials in composite beam is assumed partially interact when longitudinal slip at its interfacial surfaces is considered. Commonly analysed by the mesh-based formulation, this study used meshless formulation known as Element Free Galerkin (EFG) method in the beam partial interaction analysis, numerically. As meshless formulation implies that the problem domain is discretised only by nodes, the EFG method is based on Moving Least Square (MLS) approach for shape functions formulation with its weak form is developed using variational method. The essential boundary conditions are enforced by Langrange multipliers. The proposed EFG formulation gives comparable results, after beenmore » verified by analytical solution, thus signify its application in partial interaction problems. Based on numerical test results, the Cubic Spline and Quartic Spline weight functions yield better accuracy for the EFG formulation, compares to other proposed weight functions.« less

Precipitation of low energy electrons at high latitudes: Effects of substorms, interplanetary magnetic field and dipole tilt angle

NASA Technical Reports Server (NTRS)

Burch, J. L.

1972-01-01

Data from the auroral particles experiment on OGO-4 were used to study effects of substorm activity, interplanetary magnetic field latitutde, and dipole tilt angle on high-latitude precipitation of 700 eV electrons. It was found that: (1) The high-latitude zone of 700 eV electron precipitation in late evening and early morning hours moves equatorward by 5 to 10 deg during substorms. (2) The low-latitude boundary of polar cusp electron precipitation at 9 to 15 hours MLT also moves equatorward by several degrees during substorms and, in the absence of significant substorm activity, after a period of southward interplanetary magnetic field. (3) With times containing substorm activity or a southward interplanetary magnetic field eliminated, the low-latitude boundary of polar cusp electron precipitation is found to move by approximately 4 deg over the total yearly range of tilt angles. At maximum winter and summer conditions the invariant latitude of the boundary is shown to shift by approximately -3 deg and +1 deg respectively from its equinox location.

The free versus fixed geodetic boundary value problem for different combinations of geodetic observables

NASA Astrophysics Data System (ADS)

Grafarend, E. W.; Heck, B.; Knickmeyer, E. H.

1985-03-01

Various formulations of the geodetic fixed and free boundary value problem are presented, depending upon the type of boundary data. For the free problem, boundary data of type astronomical latitude, astronomical longitude and a pair of the triplet potential, zero and first-order vertical gradient of gravity are presupposed. For the fixed problem, either the potential or gravity or the vertical gradient of gravity is assumed to be given on the boundary. The potential and its derivatives on the boundary surface are linearized with respect to a reference potential and a reference surface by Taylor expansion. The Eulerian and Lagrangean concepts of a perturbation theory of the nonlinear geodetic boundary value problem are reviewed. Finally the boundary value problems are solved by Hilbert space techniques leading to new generalized Stokes and Hotine functions. Reduced Stokes and Hotine functions are recommended for numerical reasons. For the case of a boundary surface representing the topography a base representation of the solution is achieved by solving an infinite dimensional system of equations. This system of equations is obtained by means of the product-sum-formula for scalar surface spherical harmonics with Wigner 3j-coefficients.

Optimal Paths in Gliding Flight

NASA Astrophysics Data System (ADS)

Wolek, Artur

Underwater gliders are robust and long endurance ocean sampling platforms that are increasingly being deployed in coastal regions. This new environment is characterized by shallow waters and significant currents that can challenge the mobility of these efficient (but traditionally slow moving) vehicles. This dissertation aims to improve the performance of shallow water underwater gliders through path planning. The path planning problem is formulated for a dynamic particle (or "kinematic car") model. The objective is to identify the path which satisfies specified boundary conditions and minimizes a particular cost. Several cost functions are considered. The problem is addressed using optimal control theory. The length scales of interest for path planning are within a few turn radii. First, an approach is developed for planning minimum-time paths, for a fixed speed glider, that are sub-optimal but are guaranteed to be feasible in the presence of unknown time-varying currents. Next the minimum-time problem for a glider with speed controls, that may vary between the stall speed and the maximum speed, is solved. Last, optimal paths that minimize change in depth (equivalently, maximize range) are investigated. Recognizing that path planning alone cannot overcome all of the challenges associated with significant currents and shallow waters, the design of a novel underwater glider with improved capabilities is explored. A glider with a pneumatic buoyancy engine (allowing large, rapid buoyancy changes) and a cylindrical moving mass mechanism (generating large pitch and roll moments) is designed, manufactured, and tested to demonstrate potential improvements in speed and maneuverability.

Developments in boundary element methods - 2

NASA Astrophysics Data System (ADS)

Banerjee, P. K.; Shaw, R. P.

This book is a continuation of the effort to demonstrate the power and versatility of boundary element methods which began in Volume 1 of this series. While Volume 1 was designed to introduce the reader to a selected range of problems in engineering for which the method has been shown to be efficient, the present volume has been restricted to time-dependent problems in engineering. Boundary element formulation for melting and solidification problems in considered along with transient flow through porous elastic media, applications of boundary element methods to problems of water waves, and problems of general viscous flow. Attention is given to time-dependent inelastic deformation of metals by boundary element methods, the determination of eigenvalues by boundary element methods, transient stress analysis of tunnels and caverns of arbitrary shape due to traveling waves, an analysis of hydrodynamic loads by boundary element methods, and acoustic emissions from submerged structures.

An iterative kernel based method for fourth order nonlinear equation with nonlinear boundary condition

NASA Astrophysics Data System (ADS)

Azarnavid, Babak; Parand, Kourosh; Abbasbandy, Saeid

2018-06-01

This article discusses an iterative reproducing kernel method with respect to its effectiveness and capability of solving a fourth-order boundary value problem with nonlinear boundary conditions modeling beams on elastic foundations. Since there is no method of obtaining reproducing kernel which satisfies nonlinear boundary conditions, the standard reproducing kernel methods cannot be used directly to solve boundary value problems with nonlinear boundary conditions as there is no knowledge about the existence and uniqueness of the solution. The aim of this paper is, therefore, to construct an iterative method by the use of a combination of reproducing kernel Hilbert space method and a shooting-like technique to solve the mentioned problems. Error estimation for reproducing kernel Hilbert space methods for nonlinear boundary value problems have yet to be discussed in the literature. In this paper, we present error estimation for the reproducing kernel method to solve nonlinear boundary value problems probably for the first time. Some numerical results are given out to demonstrate the applicability of the method.

A model problem for estimation of moving-film time relaxation at sudden change of boundary conditions

NASA Astrophysics Data System (ADS)

Smirnovsky, Alexander A.; Eliseeva, Viktoria O.

2018-05-01

The study of the film flow occurred under the influence of a gas slug flow is of definite interest in heat and mass transfer during the motion of a coolant in the second circuit of a nuclear water-water reactor. Thermohydraulic codes are usually used for analysis of the such problems in which the motion of the liquid film and the vapor is modeled on the basis of a one-dimensional balance equations. Due to a greater inertia of the liquid film motion, film flow parameters changes with a relaxation compared with gas flow. We consider a model problem of film flow under the influence of friction from gas slug flow neglecting such effects as wave formation, droplet breakage and deposition on the film surface, evaporation and condensation. Such a problem is analogous to the well-known problems of Couette and Stokes flows. An analytical solution has been obtained for laminar flow. Numerical RANS-based simulation of turbulent flow was performed using OpenFOAM. It is established that the relaxation process is almost self-similar. This fact opens a possibility of obtaining valuable correlations for the relaxation time.

Probabilistic Open Set Recognition

NASA Astrophysics Data System (ADS)

Jain, Lalit Prithviraj

Real-world tasks in computer vision, pattern recognition and machine learning often touch upon the open set recognition problem: multi-class recognition with incomplete knowledge of the world and many unknown inputs. An obvious way to approach such problems is to develop a recognition system that thresholds probabilities to reject unknown classes. Traditional rejection techniques are not about the unknown; they are about the uncertain boundary and rejection around that boundary. Thus traditional techniques only represent the "known unknowns". However, a proper open set recognition algorithm is needed to reduce the risk from the "unknown unknowns". This dissertation examines this concept and finds existing probabilistic multi-class recognition approaches are ineffective for true open set recognition. We hypothesize the cause is due to weak adhoc assumptions combined with closed-world assumptions made by existing calibration techniques. Intuitively, if we could accurately model just the positive data for any known class without overfitting, we could reject the large set of unknown classes even under this assumption of incomplete class knowledge. For this, we formulate the problem as one of modeling positive training data by invoking statistical extreme value theory (EVT) near the decision boundary of positive data with respect to negative data. We provide a new algorithm called the PI-SVM for estimating the unnormalized posterior probability of class inclusion. This dissertation also introduces a new open set recognition model called Compact Abating Probability (CAP), where the probability of class membership decreases in value (abates) as points move from known data toward open space. We show that CAP models improve open set recognition for multiple algorithms. Leveraging the CAP formulation, we go on to describe the novel Weibull-calibrated SVM (W-SVM) algorithm, which combines the useful properties of statistical EVT for score calibration with one-class and binary support vector machines. Building from the success of statistical EVT based recognition methods such as PI-SVM and W-SVM on the open set problem, we present a new general supervised learning algorithm for multi-class classification and multi-class open set recognition called the Extreme Value Local Basis (EVLB). The design of this algorithm is motivated by the observation that extrema from known negative class distributions are the closest negative points to any positive sample during training, and thus should be used to define the parameters of a probabilistic decision model. In the EVLB, the kernel distribution for each positive training sample is estimated via an EVT distribution fit over the distances to the separating hyperplane between positive training sample and closest negative samples, with a subset of the overall positive training data retained to form a probabilistic decision boundary. Using this subset as a frame of reference, the probability of a sample at test time decreases as it moves away from the positive class. Possessing this property, the EVLB is well-suited to open set recognition problems where samples from unknown or novel classes are encountered at test. Our experimental evaluation shows that the EVLB provides a substantial improvement in scalability compared to standard radial basis function kernel machines, as well as P I-SVM and W-SVM, with improved accuracy in many cases. We evaluate our algorithm on open set variations of the standard visual learning benchmarks, as well as with an open subset of classes from Caltech 256 and ImageNet. Our experiments show that PI-SVM, WSVM and EVLB provide significant advances over the previous state-of-the-art solutions for the same tasks.

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.

Motion of 1/3⟨111⟩ dislocations on Σ3 {112} twin boundaries in nanotwinned copper

NASA Astrophysics Data System (ADS)

Lu, N.; Du, K.; Lu, L.; Ye, H. Q.

2014-01-01

The atomic structure of Σ3 {112} ITBs in nanotwinned Cu is investigated by using aberration-corrected high resolution transmission electron microscopy (HRTEM) and in situ HRTEM observations. The Σ3 {112} ITBs are consisted of periodically repeated three partial dislocations. The in situ HRTEM results show that 1/3[111] partial dislocation moves on the Σ3 {112} incoherent twin boundary (ITB), which was accompanied by a migration of the ITB. A dislocation reaction mechanism is proposed for the motion of 1/3[111] Frank partial dislocation, in which the 1/3[111] partial dislocation exchanges its position with twin boundary dislocations in sequence. In this way, the 1/3[111] dislocation can move on the incoherent twin boundary in metals with low stacking fault energy. Meanwhile, the ITB will migrate in its normal direction accordingly. These results provide insight into the reaction mechanism of 1/3[111] dislocations and ITBs and the associated migration of ITBs.

On solvability of boundary value problems for hyperbolic fourth-order equations with nonlocal boundary conditions of integral type

NASA Astrophysics Data System (ADS)

Popov, Nikolay S.

2017-11-01

Solvability of some initial-boundary value problems for linear hyperbolic equations of the fourth order is studied. A condition on the lateral boundary in these problems relates the values of a solution or the conormal derivative of a solution to the values of some integral operator applied to a solution. Nonlocal boundary-value problems for one-dimensional hyperbolic second-order equations with integral conditions on the lateral boundary were considered in the articles by A.I. Kozhanov. Higher-dimensional hyperbolic equations of higher order with integral conditions on the lateral boundary were not studied earlier. The existence and uniqueness theorems of regular solutions are proven. The method of regularization and the method of continuation in a parameter are employed to establish solvability.

A multiphysics 3D model of tissue growth under interstitial perfusion in a tissue-engineering bioreactor.

PubMed

Nava, Michele M; Raimondi, Manuela T; Pietrabissa, Riccardo

2013-11-01

The main challenge in engineered cartilage consists in understanding and controlling the growth process towards a functional tissue. Mathematical and computational modelling can help in the optimal design of the bioreactor configuration and in a quantitative understanding of important culture parameters. In this work, we present a multiphysics computational model for the prediction of cartilage tissue growth in an interstitial perfusion bioreactor. The model consists of two separate sub-models, one two-dimensional (2D) sub-model and one three-dimensional (3D) sub-model, which are coupled between each other. These sub-models account both for the hydrodynamic microenvironment imposed by the bioreactor, using a model based on the Navier-Stokes equation, the mass transport equation and the biomass growth. The biomass, assumed as a phase comprising cells and the synthesised extracellular matrix, has been modelled by using a moving boundary approach. In particular, the boundary at the fluid-biomass interface is moving with a velocity depending from the local oxygen concentration and viscous stress. In this work, we show that all parameters predicted, such as oxygen concentration and wall shear stress, by the 2D sub-model with respect to the ones predicted by the 3D sub-model are systematically overestimated and thus the tissue growth, which directly depends on these parameters. This implies that further predictive models for tissue growth should take into account of the three dimensionality of the problem for any scaffold microarchitecture.

Mixed boundary value problems in mechanics

NASA Technical Reports Server (NTRS)

Erdogan, F.

1975-01-01

Certain boundary value problems were studied over a domain D which may contain the point at infinity and may be multiply connected. Contours forming the boundary are assumed to consist of piecewise smooth arcs. Mixed boundary value problems are those with points of flux singularity on the boundary; these are points on the surface, either side of which at least one of the differential operator has different behavior. The physical system was considered to be described by two quantities, the potential and the flux type quantities. Some of the examples that were illustrated included problems in potential theory and elasticity.

Towards Flange-to-Flange Turbopump Simulations for Liquid Rocket Engines

NASA Technical Reports Server (NTRS)

Kiris, Cetin; Williams, Robert

2000-01-01

The primary objective of this research is to support the design of liquid rocket systems for the Advanced Space Transportation System. Since the space launch systems in the near future are likely to rely on liquid rocket engines, increasing the efficiency and reliability of the engine components is an important task. One of the major problems in the liquid rocket engine is to understand fluid dynamics of fuel and oxidizer flows from the fuel tank to plume. Understanding the flow through the entire turbopump geometry through numerical simulation will be of significant value toward design. This will help to improve safety of future space missions. One of the milestones of this effort is to develop, apply and demonstrate the capability and accuracy of 3D CFD methods as efficient design analysis tools on high performance computer platforms. The development of the MPI and MLP versions of the INS3D code is currently underway. The serial version of INS3D code is a multidimensional incompressible Navier-Stokes solver based on overset grid technology. INS3D-MPI is based on the explicit massage-passing interface across processors and is primarily suited for distributed memory systems. INS3D-MLP is based on multi-level parallel method and is suitable for distributed-shared memory systems. For the entire turbopump simulations, moving boundary capability and an efficient time-accurate integration methods are build in the flow solver. To handle the geometric complexity and moving boundary problems, overset grid scheme is incorporated with the solver that new connectivity data will be obtained at each time step. The Chimera overlapped grid scheme allows subdomains move relative to each other, and provides a great flexibility when the boundary movement creates large displacements. The performance of the two time integration schemes for time-accurate computations is investigated. For an unsteady flow which requires small physical time step, the pressure projection method was found to be computationally efficient since it does not require any subiterations procedure. It was observed that the artificial compressibility method requires a fast convergence scheme at each physical time step in order to satisfy incompressibility condition. This was obtained by using a GMRES-ILU(0) solver in our computations. When a line-relaxation scheme was used, the time accuracy was degraded and time-accurate computations became very expensive. The current geometry for the LOX boost turbopump has various rotating and stationary components, such as inducer, stators, kicker, hydrolic turbine, where the flow is extremely unsteady. Figure 1 shows the geometry and computed surface pressure of the inducer. The inducer and the hydrolic turbine rotate in different rotational speed.

Mesoscale observational analysis of lifting mechanism of a warm-sector convective system producing the maximal daily precipitation in China mainland during pre-summer rainy season of 2015

NASA Astrophysics Data System (ADS)

Wu, Mengwen; Luo, Yali

2016-08-01

A long-lived, quasi-stationary mesoscale convective system (MCS) producing extreme rainfall (maximum of 542 mm) over the eastern coastal area of Guangdong Province on 20 May 2015 is analyzed by using high-resolution surface observations, sounding data, and radar measurements. New convective cells are continuously initiated along a mesoscale boundary at the surface, leading to formation and maintenance of the quasi-linear-shaped MCS from about 2000 BT 19 to 1200 BT 20 May. The boundary is originally formed between a cold dome generated by previous convection and southwesterly flow from the ocean carrying higher equivalent potential temperature ( θ e) air. The boundary is subsequently maintained and reinforced by the contrast between the MCS-generated cold outflow and the oceanic higher- θ e air. The cold outflow is weak (wind speed ≤ 5 m s -1), which is attributable to the characteristic environmental conditions, i.e., high humidity in the lower troposphere and weak horizontal winds in the middle and lower troposphere. The low speed of the cold outflow is comparable to that of the near surface southerly flow from the ocean, resulting in very slow southward movement of the boundary. The boundary features temperature contrasts of 2-3°C and is roughly 500-m deep. Despite its shallowness, the boundary appears to exert a profound influence on continuous convection initiation because of the very low level of free convection and small convection inhibition of the near surface oceanic air, building several parallel rainbands (of about 50-km length) that move slowly eastward along the MCS and produce about 80% of the total rainfall. Another MCS moves into the area from the northwest and merges with the local MCS at about 1200 BT. The cold outflow subsequently strengthens and the boundary moves more rapidly toward the southeast, leading to end of the event in 3 h.

Induced rotational motion with nonabutting inducing and induced stimuli: implications regarding two forms of induced motion.

PubMed

Reinhardt-Rutland, A H

2003-07-01

Induced motion is the illusory motion of a static stimulus in the opposite direction to a moving stimulus. Two types of induced motion have been distinguished: (a) when the moving stimulus is distant from the static stimulus and undergoes overall displacement, and (b) when the moving stimulus is pattern viewed within fixed boundaries that abut the static stimulus. Explanations of the 1st type of induced motion refer to mediating phenomena, such as vection, whereas the 2nd type is attributed to local processing by motion-sensitive neurons. The present research was directed to a display that elicited induced rotational motion with the characteristics of both types of induced motion: the moving stimulus lay within fixed boundaries, but the inducing and induced stimuli were distant from each other. The author investigated the properties that distinguished the two types of induced motion. In 3 experiments, induced motion persisted indefinitely, interocular transfer of the aftereffect of induced motion was limited to about 20%, and the time-course of the aftereffect of induced motion could not be attributed to vection. Those results were consistent with fixed-boundary induced motion. However, they could not be explained by local processing. Instead, the results might reflect the detection of object motion within a complex flow-field that resulted from the observer's motion.

Fast and selective determination of total protein in milk powder via titration of moving reaction boundary electrophoresis.

PubMed

Guo, Cheng-ye; Wang, Hou-yu; Liu, Xiao-ping; Fan, Liu-yin; Zhang, Lei; Cao, Cheng-xi

2013-05-01

In this paper, moving reaction boundary titration (MRBT) was developed for rapid and accurate quantification of total protein in infant milk powder, from the concept of moving reaction boundary (MRB) electrophoresis. In the method, the MRB was formed by the hydroxide ions and the acidic residues of milk proteins immobilized via cross-linked polyacrylamide gel (PAG), an acid-base indicator was used to denote the boundary motion. As a proof of concept, we chose five brands of infant milk powders to study the feasibility of MRBT method. The calibration curve of MRB velocity versus logarithmic total protein content of infant milk powder sample was established based on the visual signal of MRB motion as a function of logarithmic milk protein content. Weak influence of nonprotein nitrogen (NPN) reagents (e.g., melamine and urea) on MRBT method was observed, due to the fact that MRB was formed with hydroxide ions and the acidic residues of captured milk proteins, rather than the alkaline residues or the NPN reagents added. The total protein contents in infant milk powder samples detected via the MRBT method were in good agreement with those achieved by the classic Kjeldahl method. In addition, the developed method had much faster measuring speed compared with the Kjeldahl method. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

The Need to Proactively Develop Flexible, Adaptable Plans for Logistics

DTIC Science & Technology

2013-03-01

operational reach.6 The deployment and distribution capability moves forces 4 and logistic support globally and on time meeting the required...forcing function, as supplies were moving efficiently through Pakistan. The northern routes were more expensive, so there was not a keen interest in...products to State valuing relationships more than rank.22 Clarifying the boundaries of what combatant commanders could do to move the agenda along

Positivity and Almost Positivity of Biharmonic Green's Functions under Dirichlet Boundary Conditions

NASA Astrophysics Data System (ADS)

Grunau, Hans-Christoph; Robert, Frédéric

2010-03-01

In general, for higher order elliptic equations and boundary value problems like the biharmonic equation and the linear clamped plate boundary value problem, neither a maximum principle nor a comparison principle or—equivalently—a positivity preserving property is available. The problem is rather involved since the clamped boundary conditions prevent the boundary value problem from being reasonably written as a system of second order boundary value problems. It is shown that, on the other hand, for bounded smooth domains {Ω subsetmathbb{R}^n} , the negative part of the corresponding Green’s function is “small” when compared with its singular positive part, provided {n≥q 3} . Moreover, the biharmonic Green’s function in balls {Bsubsetmathbb{R}^n} under Dirichlet (that is, clamped) boundary conditions is known explicitly and is positive. It has been known for some time that positivity is preserved under small regular perturbations of the domain, if n = 2. In the present paper, such a stability result is proved for {n≥q 3}.

Internationalization in German Academic Libraries: Moving beyond North American Perspectives

ERIC Educational Resources Information Center

Bordonaro, Karen; Rauchmann, Sabine

2015-01-01

This paper explores how internationalization is understood and experienced in German academic libraries. Its main purpose is to move the discussion of internationalization in academic libraries beyond the boundaries of English-speaking North America by investigating a European perspective. Its secondary purpose is to investigate the role of…

Numerical methods for stiff systems of two-point boundary value problems

NASA Technical Reports Server (NTRS)

Flaherty, J. E.; Omalley, R. E., Jr.

1983-01-01

Numerical procedures are developed for constructing asymptotic solutions of certain nonlinear singularly perturbed vector two-point boundary value problems having boundary layers at one or both endpoints. The asymptotic approximations are generated numerically and can either be used as is or to furnish a general purpose two-point boundary value code with an initial approximation and the nonuniform computational mesh needed for such problems. The procedures are applied to a model problem that has multiple solutions and to problems describing the deformation of thin nonlinear elastic beam that is resting on an elastic foundation.

Global plate motion frames: Toward a unified model

NASA Astrophysics Data System (ADS)

Torsvik, Trond H.; Müller, R. Dietmar; van der Voo, Rob; Steinberger, Bernhard; Gaina, Carmen

2008-09-01

Plate tectonics constitutes our primary framework for understanding how the Earth works over geological timescales. High-resolution mapping of relative plate motions based on marine geophysical data has followed the discovery of geomagnetic reversals, mid-ocean ridges, transform faults, and seafloor spreading, cementing the plate tectonic paradigm. However, so-called "absolute plate motions," describing how the fragments of the outer shell of the Earth have moved relative to a reference system such as the Earth's mantle, are still poorly understood. Accurate absolute plate motion models are essential surface boundary conditions for mantle convection models as well as for understanding past ocean circulation and climate as continent-ocean distributions change with time. A fundamental problem with deciphering absolute plate motions is that the Earth's rotation axis and the averaged magnetic dipole axis are not necessarily fixed to the mantle reference system. Absolute plate motion models based on volcanic hot spot tracks are largely confined to the last 130 Ma and ideally would require knowledge about the motions within the convecting mantle. In contrast, models based on paleomagnetic data reflect plate motion relative to the magnetic dipole axis for most of Earth's history but cannot provide paleolongitudes because of the axial symmetry of the Earth's magnetic dipole field. We analyze four different reference frames (paleomagnetic, African fixed hot spot, African moving hot spot, and global moving hot spot), discuss their uncertainties, and develop a unifying approach for connecting a hot spot track system and a paleomagnetic absolute plate reference system into a "hybrid" model for the time period from the assembly of Pangea (˜320 Ma) to the present. For the last 100 Ma we use a moving hot spot reference frame that takes mantle convection into account, and we connect this to a pre-100 Ma global paleomagnetic frame adjusted 5° in longitude to smooth the reference frame transition. Using plate driving force arguments and the mapping of reconstructed large igneous provinces to core-mantle boundary topography, we argue that continental paleolongitudes can be constrained with reasonable confidence.

Higher modes of the Orr-Sommerfeld problem for boundary layer flows

NASA Technical Reports Server (NTRS)

Lakin, W. D.; Grosch, C. E.

1983-01-01

The discrete spectrum of the Orr-Sommerfeld problem of hydrodynamic stability for boundary layer flows in semi-infinite regions is examined. Related questions concerning the continuous spectrum are also addressed. Emphasis is placed on the stability problem for the Blasius boundary layer profile. A general theoretical result is given which proves that the discrete spectrum of the Orr-Sommerfeld problem for boundary layer profiles (U(y), 0,0) has only a finite number of discrete modes when U(y) has derivatives of all orders. Details are given of a highly accurate numerical technique based on collocation with splines for the calculation of stability characteristics. The technique includes replacement of 'outer' boundary conditions by asymptotic forms based on the proper large parameter in the stability problem. Implementation of the asymptotic boundary conditions is such that there is no need to make apriori distinctions between subcases of the discrete spectrum or between the discrete and continuous spectrums. Typical calculations for the usual Blasius problem are presented.

Interaction of aerodynamic noise with laminar boundary layers in supersonic wind tunnels

NASA Technical Reports Server (NTRS)

Schopper, M. R.

1984-01-01

The interaction between incoming aerodynamic noise and the supersonic laminar boundary layer is studied. The noise field is modeled as a Mach wave radiation field consisting of discrete waves emanating from coherent turbulent entities moving downstream within the supersonic turbulent boundary layer. The individual disturbances are likened to miniature sonic booms and the laminar boundary layer is staffed by the waves as the sources move downstream. The mean, autocorrelation, and power spectral density of the field are expressed in terms of the wave shapes and their average arrival rates. Some consideration is given to the possible appreciable thickness of the weak shock fronts. The emphasis in the interaction analysis is on the behavior of the shocklets in the noise field. The shocklets are shown to be focused by the laminar boundary layer in its outer region. Borrowing wave propagation terminology, this region is termed the caustic region. Using scaling laws from sonic boom work, focus factors at the caustic are estimated to vary from 2 to 6 for incoming shocklet strengths of 1 to .01 percent of the free stream pressure level. The situation regarding experimental evidence of the caustic region is reviewed.

Fixing a Reference Frame to a Moving and Deforming Continent

NASA Astrophysics Data System (ADS)

Blewitt, G.; Kreemer, C.; Hammond, W. C.

2016-12-01

The U.S. National Spatial Reference System will be modernized in 2022. A foundational component will be a geocentric reference frame fixed to the North America tectonic plate. Here we address challenges of fixing a reference frame to a moving and deforming continent. Scientific applications motivate that we fix the frame with a scale consistent with the SI system, an origin that coincides with the Earth system's center of mass, and with axes attached to the rigidly rotating interior of the North America plate. Realizing the scale and origin is now achieved to < 0.5 mm/yr by combining space-geodetic techniques (SLR, VLBI, GPS, and DORIS) in the global system, ITRS. To realize the no-net rotation condition, the complexity of plate boundary deformation demands that we only select GPS stations far from plate boundaries. Another problem is that velocity uncertainties in models of glacial isostatic adjustment (GIA) are significant compared to uncertainties in observed velocities. GIA models generally agree that far-field horizontal velocities tend to be directed toward/away from Hudson Bay, depending on mantle viscosity, with uncertain sign and magnitude of velocity. Also in the far field, strain rates tend to be small beyond the peripheral bulge ( US-Canada border). Thus the Earth's crust in the US east of the Rockies may appear to be rigid, even if this region moves relative to plate motion. This can affect Euler vector estimation, with implications (pros and cons) on scientific interpretation. Our previous approach [ref. 1] in defining the NA12 frame was to select a core set of 30 stations east of the Rockies and south of the U.S.-Canada border that satisfy strict criteria on position time series quality. The resulting horizontal velocities have an RMS of 0.3 mm/yr, quantifying a combination of plate rigidity and accuracy. However, this does not rule out possible common-mode motion arising from GIA. For the development of new frame NA16, we consider approaches to this problem. We also apply new techniques including the MIDAS robust velocity estimator [ref. 2] and "GPS Imaging" of vertical motions and strain rates (Fig. 1), which together could assist in better defining "stable North America".[1] Blewitt et al. (2013). J. Geodyn. 72, 11-24, doi:10.1016/j.jog.2013.08.004[2] Blewitt et al. (2016). JGR 121, doi:10.1002/2015JB012552

Adaptive and dynamic meshing methods for numerical simulations

NASA Astrophysics Data System (ADS)

Acikgoz, Nazmiye

For the numerical simulation of many problems of engineering interest, it is desirable to have an automated mesh adaption tool capable of producing high quality meshes with an affordably low number of mesh points. This is important especially for problems, which are characterized by anisotropic features of the solution and require mesh clustering in the direction of high gradients. Another significant issue in meshing emerges in the area of unsteady simulations with moving boundaries or interfaces, where the motion of the boundary has to be accommodated by deforming the computational grid. Similarly, there exist problems where current mesh needs to be adapted to get more accurate solutions because either the high gradient regions are initially predicted inaccurately or they change location throughout the simulation. To solve these problems, we propose three novel procedures. For this purpose, in the first part of this work, we present an optimization procedure for three-dimensional anisotropic tetrahedral grids based on metric-driven h-adaptation. The desired anisotropy in the grid is dictated by a metric that defines the size, shape, and orientation of the grid elements throughout the computational domain. Through the use of topological and geometrical operators, the mesh is iteratively adapted until the final mesh minimizes a given objective function. In this work, the objective function measures the distance between the metric of each simplex and a target metric, which can be either user-defined (a-priori) or the result of a-posteriori error analysis. During the adaptation process, one tries to decrease the metric-based objective function until the final mesh is compliant with the target within a given tolerance. However, in regions such as corners and complex face intersections, the compliance condition was found to be very difficult or sometimes impossible to satisfy. In order to address this issue, we propose an optimization process based on an ad-hoc application of the simulated annealing technique, which improves the likelihood of removing poor elements from the grid. Moreover, a local implementation of the simulated annealing is proposed to reduce the computational cost. Many challenging multi-physics and multi-field problems that are unsteady in nature are characterized by moving boundaries and/or interfaces. When the boundary displacements are large, which typically occurs when implicit time marching procedures are used, degenerate elements are easily formed in the grid such that frequent remeshing is required. To deal with this problem, in the second part of this work, we propose a new r-adaptation methodology. The new technique is valid for both simplicial (e.g., triangular, tet) and non-simplicial (e.g., quadrilateral, hex) deforming grids that undergo large imposed displacements at their boundaries. A two- or three-dimensional grid is deformed using a network of linear springs composed of edge springs and a set of virtual springs. The virtual springs are constructed in such a way as to oppose element collapsing. This is accomplished by confining each vertex to its ball through springs that are attached to the vertex and its projection on the ball entities. The resulting linear problem is solved using a preconditioned conjugate gradient method. The new method is compared with the classical spring analogy technique in two- and three-dimensional examples, highlighting the performance improvements achieved by the new method. Meshes are an important part of numerical simulations. Depending on the geometry and flow conditions, the most suitable mesh for each particular problem is different. Meshes are usually generated by either using a suitable software package or solving a PDE. In both cases, engineering intuition plays a significant role in deciding where clusterings should take place. In addition, for unsteady problems, the gradients vary for each time step, which requires frequent remeshing during simulations. Therefore, in order to minimize user intervention and prevent frequent remeshings, we conclude this work by defining a novel mesh adaptation technique that integrates metric based target mesh definitions with the ball-vertex mesh deformation method. In this new approach, the entire mesh is deformed based on either an a-priori or an a-posteriori error estimator. In other words, nodal points are repositioned upon application of a force field in order to comply with the target mesh or to get more accurate solutions. The method has been tested for two-dimensional problems of a-priori metric definitions as well as for oblique shock clusterings.

Sound Generation in the Presence of Moving Surfaces with Application to Internally Generated Aircraft Engine Noise

NASA Technical Reports Server (NTRS)

Goldstein, Marvin E.; Envia, E.

2002-01-01

In many cases of technological interest solid boundaries play a direct role in the aerodynamic sound generation process and their presence often results in a large increase in the acoustic radiation. A generalized treatment of the emission of sound from moving boundaries is presented. The approach is similar to that of Ffowcs Williams and Hawkings (1969) but the effect of the surrounding mean flow is explicitly accounted for. The results are used to develop a rational framework for the prediction of internally generated aero-engine noise. The final formulas suggest some new noise sources that may be of practical significance.

Analysis of a turbulent boundary layer over a moving ground plane

NASA Technical Reports Server (NTRS)

Roper, A. T.; Gentry, G. L., Jr.

1972-01-01

Four methods of predicting the integral and friction parameters for a turbulent boundary layer over a moving ground plane were evaluated by using test information obtained in 76.2- by 50.8-centimeter tunnel. The tunnel was operated in the open sidewall configuration. These methods are (1) relative integral parameter method, (2) modified power law method, (3) relative power law method, and (4) modified law of the wall method. The modified law of the wall method predicts a more rapid decrease in skin friction with an increase in the ratio of belt velocity to free steam velocity than do methods (1) and (3).

Forced cubic Schrödinger equation with Robin boundary data: large-time asymptotics

PubMed Central

Kaikina, Elena I.

2013-01-01

We consider the initial-boundary-value problem for the cubic nonlinear Schrödinger equation, formulated on a half-line with inhomogeneous Robin boundary data. We study traditionally important problems of the theory of nonlinear partial differential equations, such as the global-in-time existence of solutions to the initial-boundary-value problem and the asymptotic behaviour of solutions for large time. PMID:24204185

A non-local free boundary problem arising in a theory of financial bubbles

PubMed Central

Berestycki, Henri; Monneau, Regis; Scheinkman, José A.

2014-01-01

We consider an evolution non-local free boundary problem that arises in the modelling of speculative bubbles. The solution of the model is the speculative component in the price of an asset. In the framework of viscosity solutions, we show the existence and uniqueness of the solution. We also show that the solution is convex in space, and establish several monotonicity properties of the solution and of the free boundary with respect to parameters of the problem. To study the free boundary, we use, in particular, the fact that the odd part of the solution solves a more standard obstacle problem. We show that the free boundary is and describe the asymptotics of the free boundary as c, the cost of transacting the asset, goes to zero. PMID:25288815

Unsteady separated stagnation-point flow and heat transfer of a viscous fluid over a moving flat surface

NASA Astrophysics Data System (ADS)

Dholey, S.

2018-04-01

In this paper, we have investigated numerically the laminar unsteady separated stagnation-point flow and heat transfer of a viscous fluid over a moving flat surface in the presence of a time dependent free stream velocity which causes the unsteadiness of this flow problem. The plate is assumed to move in the same or opposite direction of the free stream velocity. The flow is therefore governed by the velocity ratio parameter λ (ratio of the plate velocity to the free stream velocity) and the unsteadiness parameter β. When the plate surface moves in the same direction of the free stream velocity (i.e., when λ > 0), the solution of this flow problem continues for any given value of β. On the other hand, when they move in opposite directions (i.e., when λ < 0), the solution does not exist after a certain value of λ depending upon the values of β. In this case, separation appears inside the layer only for a negative value of β, and for a positive value of β, the boundary layer solution is terminated after a certain distance from the plate surface with an attached flow solution with no point of inflection. The concerning issue of the steady flow (β = 0) case has also been considered and two types of attached flow solutions have been found—one with a point of inflection and the other with no point of inflection, in a definite range of λ (-1.246 58 ≤ λ ≤ -1.07). However, this range decreases with an increase in |β| when β < 0. A novel result which arises from the heat transfer analysis is that for a given value of λ(= 0), first the heat transfer rate increases with the increase of the Prandtl number Pr and after attaining a maximum value, it decreases and finally tends to be zero for large values of Pr depending upon the values of β > 0. On the contrary, for a given value of β(≤ 0), the rate of heat transfer increases consistently with the increase of Pr.

Effects of nanoparticles on melting process with phase-change using the lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Ibrahem, Ahmed M.; El-Amin, Mohamed F.; Sun, Shuyu

In this work, the problem of nanoparticles dispersion effects on coupled heat transfer and solid-liquid phase change has been studied. The lattice Boltzmann method (LBM) enthalpy-based is employed. The collision model of lattice Bhatnagar-Gross-Krook (LBGK) is used to solve the problem of 1D melting by conduction. On the other hand, we use the model of multi-distribution functions (MDF) to calculate the density, the velocity and the temperature for the problem of 2D melting by free convection, associated with different boundary conditions. In these simulations, the volume fractions of copper nanoparticles (0-2%) added to water-base fluid and Rayleigh numbers of 103-105. We use the Chapman-Enskog expansion to derive the governing macroscopic quantities from the mesoscopic lattice Boltzmann equation. The results obtained by these models have been compared to an analytical solution or other numerical methods. The effects of nanoparticles on conduction and natural convection during the melting process have been investigated. Moreover, the influences of nanoparticles on moving of the phase change front, the thermal conductivity and the latent heat of fusion are also studied.

On a numerical method for solving integro-differential equations with variable coefficients with applications in finance

NASA Astrophysics Data System (ADS)

Kudryavtsev, O.; Rodochenko, V.

2018-03-01

We propose a new general numerical method aimed to solve integro-differential equations with variable coefficients. The problem under consideration arises in finance where in the context of pricing barrier options in a wide class of stochastic volatility models with jumps. To handle the effect of the correlation between the price and the variance, we use a suitable substitution for processes. Then we construct a Markov-chain approximation for the variation process on small time intervals and apply a maturity randomization technique. The result is a system of boundary problems for integro-differential equations with constant coefficients on the line in each vertex of the chain. We solve the arising problems using a numerical Wiener-Hopf factorization method. The approximate formulae for the factors are efficiently implemented by means of the Fast Fourier Transform. Finally, we use a recurrent procedure that moves backwards in time on the variance tree. We demonstrate the convergence of the method using Monte-Carlo simulations and compare our results with the results obtained by the Wiener-Hopf method with closed-form expressions of the factors.

A fast direct solver for boundary value problems on locally perturbed geometries

NASA Astrophysics Data System (ADS)

Zhang, Yabin; Gillman, Adrianna

2018-03-01

Many applications including optimal design and adaptive discretization techniques involve solving several boundary value problems on geometries that are local perturbations of an original geometry. This manuscript presents a fast direct solver for boundary value problems that are recast as boundary integral equations. The idea is to write the discretized boundary integral equation on a new geometry as a low rank update to the discretized problem on the original geometry. Using the Sherman-Morrison formula, the inverse can be expressed in terms of the inverse of the original system applied to the low rank factors and the right hand side. Numerical results illustrate for problems where perturbation is localized the fast direct solver is three times faster than building a new solver from scratch.

Distance estimation and collision prediction for on-line robotic motion planning

NASA Technical Reports Server (NTRS)

Kyriakopoulos, K. J.; Saridis, G. N.

1991-01-01

An efficient method for computing the minimum distance and predicting collisions between moving objects is presented. This problem has been incorporated in the framework of an in-line motion planning algorithm to satisfy collision avoidance between a robot and moving objects modeled as convex polyhedra. In the beginning the deterministic problem, where the information about the objects is assumed to be certain is examined. If instead of the Euclidean norm, L(sub 1) or L(sub infinity) norms are used to represent distance, the problem becomes a linear programming problem. The stochastic problem is formulated, where the uncertainty is induced by sensing and the unknown dynamics of the moving obstacles. Two problems are considered: (1) filtering of the minimum distance between the robot and the moving object, at the present time; and (2) prediction of the minimum distance in the future, in order to predict possible collisions with the moving obstacles and estimate the collision time.

Mixed convection boundary layer flow over a moving vertical flat plate in an external fluid flow with viscous dissipation effect.

PubMed

Bachok, Norfifah; Ishak, Anuar; Pop, Ioan

2013-01-01

The steady boundary layer flow of a viscous and incompressible fluid over a moving vertical flat plate in an external moving fluid with viscous dissipation is theoretically investigated. Using appropriate similarity variables, the governing system of partial differential equations is transformed into a system of ordinary (similarity) differential equations, which is then solved numerically using a Maple software. Results for the skin friction or shear stress coefficient, local Nusselt number, velocity and temperature profiles are presented for different values of the governing parameters. It is found that the set of the similarity equations has unique solutions, dual solutions or no solutions, depending on the values of the mixed convection parameter, the velocity ratio parameter and the Eckert number. The Eckert number significantly affects the surface shear stress as well as the heat transfer rate at the surface.

Slip-mediated dewetting of polymer microdroplets

PubMed Central

McGraw, Joshua D.; Chan, Tak Shing; Maurer, Simon; Salez, Thomas; Benzaquen, Michael; Raphaël, Elie; Brinkmann, Martin; Jacobs, Karin

2016-01-01

Classical hydrodynamic models predict that infinite work is required to move a three-phase contact line, defined here as the line where a liquid/vapor interface intersects a solid surface. Assuming a slip boundary condition, in which the liquid slides against the solid, such an unphysical prediction is avoided. In this article, we present the results of experiments in which a contact line moves and where slip is a dominating and controllable factor. Spherical cap-shaped polystyrene microdroplets, with nonequilibrium contact angle, are placed on solid self-assembled monolayer coatings from which they dewet. The relaxation is monitored using in situ atomic force microscopy. We find that slip has a strong influence on the droplet evolutions, both on the transient nonspherical shapes and contact line dynamics. The observations are in agreement with scaling analysis and boundary element numerical integration of the governing Stokes equations, including a Navier slip boundary condition. PMID:26787903

Robust object tacking based on self-adaptive search area

NASA Astrophysics Data System (ADS)

Dong, Taihang; Zhong, Sheng

2018-02-01

Discriminative correlation filter (DCF) based trackers have recently achieved excellent performance with great computational efficiency. However, DCF based trackers suffer boundary effects, which result in the unstable performance in challenging situations exhibiting fast motion. In this paper, we propose a novel method to mitigate this side-effect in DCF based trackers. We change the search area according to the prediction of target motion. When the object moves fast, broad search area could alleviate boundary effects and reserve the probability of locating object. When the object moves slowly, narrow search area could prevent effect of useless background information and improve computational efficiency to attain real-time performance. This strategy can impressively soothe boundary effects in situations exhibiting fast motion and motion blur, and it can be used in almost all DCF based trackers. The experiments on OTB benchmark show that the proposed framework improves the performance compared with the baseline trackers.

Dynamic expression of a Hydra FGF at boundaries and termini.

PubMed

Lange, Ellen; Bertrand, Stephanie; Holz, Oliver; Rebscher, Nicole; Hassel, Monika

2014-12-01

Guidance of cells and tissue sheets is an essential function in developing and differentiating animal tissues. In Hydra, where cells and tissue move dynamically due to constant cell proliferation towards the termini or into lateral, vegetative buds, factors essential for guidance are still unknown. Good candidates to take over this function are fibroblast growth factors (FGFs). We present the phylogeny of several Hydra FGFs and analysis of their expression patterns. One of the FGFs is expressed in all terminal regions targeted by tissue movement and at boundaries crossed by moving tissue and cells with an expression pattern slightly differing in two Hydra strains. A model addressing an involvement of this FGF in cell movement and morphogenesis is proposed: Hydra FGFf-expressing cells might serve as sources to attract tissue and cells towards the termini of the body column and across morphological boundaries. Moreover, a function in morphogenesis and/or differentiation of cells and tissue is suggested.

Integral Method of Boundary Characteristics: Neumann Condition

NASA Astrophysics Data System (ADS)

Kot, V. A.

2018-05-01

A new algorithm, based on systems of identical equalities with integral and differential boundary characteristics, is proposed for solving boundary-value problems on the heat conduction in bodies canonical in shape at a Neumann boundary condition. Results of a numerical analysis of the accuracy of solving heat-conduction problems with variable boundary conditions with the use of this algorithm are presented. The solutions obtained with it can be considered as exact because their errors comprise hundredths and ten-thousandths of a persent for a wide range of change in the parameters of a problem.

Stress-intensity factor calculations using the boundary force method

NASA Technical Reports Server (NTRS)

Tan, P. W.; Raju, I. S.; Newman, J. C., Jr.

1987-01-01

The Boundary Force Method (BFM) was formulated for the three fundamental problems of elasticity: the stress boundary value problem, the displacement boundary value problem, and the mixed boundary value problem. Because the BFM is a form of an indirect boundary element method, only the boundaries of the region of interest are modeled. The elasticity solution for the stress distribution due to concentrated forces and a moment applied at an arbitrary point in a cracked infinite plate is used as the fundamental solution. Thus, unlike other boundary element methods, here the crack face need not be modeled as part of the boundary. The formulation of the BFM is described and the accuracy of the method is established by analyzing a center-cracked specimen subjected to mixed boundary conditions and a three-hole cracked configuration subjected to traction boundary conditions. The results obtained are in good agreement with accepted numerical solutions. The method is then used to generate stress-intensity solutions for two common cracked configurations: an edge crack emanating from a semi-elliptical notch, and an edge crack emanating from a V-notch. The BFM is a versatile technique that can be used to obtain very accurate stress intensity factors for complex crack configurations subjected to stress, displacement, or mixed boundary conditions. The method requires a minimal amount of modeling effort.

Monge-Ampére simulation of fourth order PDEs in two dimensions with application to elastic-electrostatic contact problems

NASA Astrophysics Data System (ADS)

DiPietro, Kelsey L.; Lindsay, Alan E.

2017-11-01

We present an efficient moving mesh method for the simulation of fourth order nonlinear partial differential equations (PDEs) in two dimensions using the Parabolic Monge-Ampére (PMA) equation. PMA methods have been successfully applied to the simulation of second order problems, but not on systems with higher order equations which arise in many topical applications. Our main application is the resolution of fine scale behavior in PDEs describing elastic-electrostatic interactions. The PDE system considered has multiple parameter dependent singular solution modalities, including finite time singularities and sharp interface dynamics. We describe how to construct a dynamic mesh algorithm for such problems which incorporates known self similar or boundary layer scalings of the underlying equation to locate and dynamically resolve fine scale solution features in these singular regimes. We find a key step in using the PMA equation for mesh generation in fourth order problems is the adoption of a high order representation of the transformation from the computational to physical mesh. We demonstrate the efficacy of the new method on a variety of examples and establish several new results and conjectures on the nature of self-similar singularity formation in higher order PDEs.

Method and apparatus for heat extraction by controlled spray cooling

DOEpatents

Edwards, Christopher Francis; Meeks, Ellen; Kee, Robert; McCarty, Kevin

1999-01-01

Two solutions to the problem of cooling a high temperature, high heat flux surface using controlled spray cooling are presented for use on a mandrel. In the first embodiment, spray cooling is used to provide a varying isothermal boundary layer on the side portions of a mandrel by providing that the spray can be moved axially along the mandrel. In the second embodiment, a spray of coolant is directed to the lower temperature surface of the mandrel. By taking advantage of super-Leidenfrost cooling, the temperature of the high temperature surface of the mandrel can be controlled by varying the mass flux rate of coolant droplets. The invention has particular applicability to the field of diamond synthesis using chemical vapor deposition techniques.

Hydrodynamic Contributions to Amoeboid Cell Motility

NASA Astrophysics Data System (ADS)

Lewis, Owen; Guy, Robert

2011-11-01

Understanding the methods by which cells move is a fundamental problem in modern biology. Recent evidence has shown that the fluid dynamics of cytoplasm can play a vital role in cellular motility. The slime mold Physarum polycephalum provides an excellent model organism for the study of amoeboid motion. In this research, we use both analytic and computational models to investigate intracellular fluid flow in a simple model of Physarum. In both models, of we are specifically interested in stresses generated by cytoplasmic flow which act in the direction of cellular motility. In our numerical model, the Immersed Boundary Method is used to account for such stresses. We investigate the relationship between contraction waves, low waves and locomotive forces, and attempt characterize conditions necessary to generate directed motion.

Implicit solution of Navier-Stokes equations on staggered curvilinear grids using a Newton-Krylov method with a novel analytical Jacobian.

NASA Astrophysics Data System (ADS)

Borazjani, Iman; Asgharzadeh, Hafez

2015-11-01

Flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates with explicit and semi-implicit schemes. Implicit schemes can be used to overcome these restrictions. However, implementing implicit solver for nonlinear equations including Navier-Stokes is not straightforward. Newton-Krylov subspace methods (NKMs) are one of the most advanced iterative methods to solve non-linear equations such as implicit descritization of the Navier-Stokes equation. The efficiency of NKMs massively depends on the Jacobian formation method, e.g., automatic differentiation is very expensive, and matrix-free methods slow down as the mesh is refined. Analytical Jacobian is inexpensive method, but derivation of analytical Jacobian for Navier-Stokes equation on staggered grid is challenging. The NKM with a novel analytical Jacobian was developed and validated against Taylor-Green vortex and pulsatile flow in a 90 degree bend. The developed method successfully handled the complex geometries such as an intracranial aneurysm with multiple overset grids, and immersed boundaries. It is shown that the NKM with an analytical Jacobian is 3 to 25 times faster than the fixed-point implicit Runge-Kutta method, and more than 100 times faster than automatic differentiation depending on the grid (size) and the flow problem. The developed methods are fully parallelized with parallel efficiency of 80-90% on the problems tested.

Dynamics of tokamak plasma surface current in 3D ideal MHD model

NASA Astrophysics Data System (ADS)

Galkin, Sergei A.; Svidzinski, V. A.; Zakharov, L. E.

2013-10-01

Interest in the surface current which can arise on perturbed sharp plasma vacuum interface in tokamaks was recently generated by a few papers (see and references therein). In dangerous disruption events with plasma-touching-wall scenarios, the surface current can be shared with the wall leading to the strong, damaging forces acting on the wall A relatively simple analytic definition of δ-function surface current proportional to a jump of tangential component of magnetic field nevertheless leads to a complex computational problem on the moving plasma-vacuum interface, requiring the incorporation of non-linear 3D plasma dynamics even in one-fluid ideal MHD. The Disruption Simulation Code (DSC), which had recently been developed in a fully 3D toroidal geometry with adaptation to the moving plasma boundary, is an appropriate tool for accurate self-consistent δfunction surface current calculation. Progress on the DSC-3D development will be presented. Self-consistent surface current calculation under non-linear dynamics of low m kink mode and VDE will be discussed. Work is supported by the US DOE SBIR grant #DE-SC0004487.

A fast object-oriented Matlab implementation of the Reproducing Kernel Particle Method

NASA Astrophysics Data System (ADS)

Barbieri, Ettore; Meo, Michele

2012-05-01

Novel numerical methods, known as Meshless Methods or Meshfree Methods and, in a wider perspective, Partition of Unity Methods, promise to overcome most of disadvantages of the traditional finite element techniques. The absence of a mesh makes meshfree methods very attractive for those problems involving large deformations, moving boundaries and crack propagation. However, meshfree methods still have significant limitations that prevent their acceptance among researchers and engineers, namely the computational costs. This paper presents an in-depth analysis of computational techniques to speed-up the computation of the shape functions in the Reproducing Kernel Particle Method and Moving Least Squares, with particular focus on their bottlenecks, like the neighbour search, the inversion of the moment matrix and the assembly of the stiffness matrix. The paper presents numerous computational solutions aimed at a considerable reduction of the computational times: the use of kd-trees for the neighbour search, sparse indexing of the nodes-points connectivity and, most importantly, the explicit and vectorized inversion of the moment matrix without using loops and numerical routines.

A review of selected topics in physics based modeling for tunnel field-effect transistors

NASA Astrophysics Data System (ADS)

Esseni, David; Pala, Marco; Palestri, Pierpaolo; Alper, Cem; Rollo, Tommaso

2017-08-01

The research field on tunnel-FETs (TFETs) has been rapidly developing in the last ten years, driven by the quest for a new electronic switch operating at a supply voltage well below 1 V and thus delivering substantial improvements in the energy efficiency of integrated circuits. This paper reviews several aspects related to physics based modeling in TFETs, and shows how the description of these transistors implies a remarkable innovation and poses new challenges compared to conventional MOSFETs. A hierarchy of numerical models exist for TFETs covering a wide range of predictive capabilities and computational complexities. We start by reviewing seminal contributions on direct and indirect band-to-band tunneling (BTBT) modeling in semiconductors, from which most TCAD models have been actually derived. Then we move to the features and limitations of TCAD models themselves and to the discussion of what we define non-self-consistent quantum models, where BTBT is computed with rigorous quantum-mechanical models starting from frozen potential profiles and closed-boundary Schrödinger equation problems. We will then address models that solve the open-boundary Schrödinger equation problem, based either on the non-equilibrium Green’s function NEGF or on the quantum-transmitting-boundary formalism, and show how the computational burden of these models may vary in a wide range depending on the Hamiltonian employed in the calculations. A specific section is devoted to TFETs based on 2D crystals and van der Waals hetero-structures. The main goal of this paper is to provide the reader with an introduction to the most important physics based models for TFETs, and with a possible guidance to the wide and rapidly developing literature in this exciting research field.

Refraction of Sound Emitted Near Solid Boundaries from a Sheared Jet

NASA Technical Reports Server (NTRS)

Dill, Loren H.; Oyedrian, Ayo A.; Krejsa, Eugene A.

1998-01-01

A mathematical model is developed to describe the sound emitted from an arbitrary point within a turbulent flow near solid boundaries. A unidirectional, transversely sheared mean flow is assumed, and the cross-section of the cold jet is of arbitrary shape. The analysis begins with Lilley's formulation of aerodynamic noise and, depending upon the specific model of turbulence used, leads via Fourier analysis to an expression for the spectral density of the intensity of the far-field sound emitted from a unit volume of turbulence. The expressions require solution of a reduced Green's function of Lilley's equation as well as certain moving axis velocity correlations of the turbulence. Integration over the entire flow field is required in order to predict the sound emitted by the complete flow. Calculations are presented for sound emitted from a plugflow jet exiting a semi-infinite flat duct. Polar plots of the far-field directivity show the dependence upon frequency and source position within the duct. Certain model problems are suggested to investigate the effect of duct termination, duct geometry, and mean flow shear upon the far-field sound.

Transient temperature distributions in simple conducting bodies steadily heated through a laminar boundary layer

NASA Technical Reports Server (NTRS)

Parker, Hermon M

1953-01-01

An analysis is made of the transient heat-conduction effects in three simple semi-infinite bodies: the flat insulated plate, the conical shell, and the slender solid cone. The bodies are assumed to have constant initial temperatures and, at zero time, to begin to move at a constant speed and zero angle of attack through a homogeneous atmosphere. The heat input is taken as that through a laminar boundary layer. Radiation heat transfer and transverse temperature gradients are assumed to be zero. The appropriate heat-conduction equations are solved by an iteration method, the zeroeth-order terms describing the situation in the limit of small time. The method is presented and the solutions are calculated to three orders which are sufficient to give reasonably accurate results when the forward edge has attained one-half the total temperature rise (nose half-rise time). Flight Mach number and air properties occur as parameters in the result. Approximate expressions for the extent of the conduction region and nose half-rise times as functions of the parameters of the problem are presented. (author)

Advances in the Application of High-order Techniques in Simulation of Multi-disciplinary Phenomena

NASA Astrophysics Data System (ADS)

Gaitonde, D. V.; Visbal, M. R.

2003-03-01

This paper describes the development of a comprehensive high-fidelity algorithmic framework to simulate the three-dimensional fields associated with multi-disciplinary physics. A wide range of phenomena is considered, from aero-acoustics and turbulence to electromagnetics, non-linear fluid-structure interactions, and magnetogasdynamics. The scheme depends primarily on "spectral-like," up to sixth-order accurate compact-differencing and up to tenth-order filtering techniques. The tightly coupled procedure suppresses numerical instabilities commonly encountered with high-order methods on non-uniform meshes, near computational boundaries or in the simulation of nonlinear dynamics. Particular emphasis is placed on developing the proper metric evaluation procedures for three-dimensional moving and curvilinear meshes so that the advantages of higher-order schemes are retained in practical calculations. A domain-decomposition strategy based on finite-sized overlap regions and interface boundary treatments enables the development of highly scalable solvers. The utility of the method to simulate problems governed by widely disparate governing equations is demonstrated with several examples encompassing vortex dynamics, wave scattering, electro-fluid plasma interactions, and panel flutter.

On safe configurations of a natural-artificial space tether system

NASA Astrophysics Data System (ADS)

Rodnikov, A. V.

2018-05-01

We study the dynamics of a particle moving under gravitation of precessing dynamically symmetric rigid body if the particle motion is restricted by two unilateral (flexible) constraints realized by two weightless unstretchable tethers with ends fixed at body poles, formed as the intersection of the body surface with the axis of its dynamical symmetry. The system under consideration is a simple model of an original natural-artificial space construction consisting of an asteroid and a space station tethered to each other via two cables. We note that the problem is integrable for the system safe configurations, i.e. for motions along the constraints common boundary (both tethers are tensed) if the body gravitational potential is invariant with respect to rotation about the axis of dynamical symmetry. We study these motions depicting phase portraits for possible values of system parameters. We also deduce conditions for the particle coming off the boundary of constraint(s) (if the tether(s) are slackened) and analyze these conditions, eliminating corresponding areas from phase portraits. We also formulate some statements, concerning the particle safety.

27 CFR 9.126 - Santa Clara Valley.

Code of Federal Regulations, 2014 CFR

2014-04-01

...: (1) The beginning point is at the junction of Elephant Head Creek and Pacheco Creek (approx. .75 mile... point the boundary moves in a northerly direction up Elephant Head Creek approx. 1.2 miles until it....G.S. map; (29) Then it moves northeast along Pacheco Creek approx. .5 mile to Elephant Head Creek at...

27 CFR 9.126 - Santa Clara Valley.

Code of Federal Regulations, 2013 CFR

2013-04-01

...: (1) The beginning point is at the junction of Elephant Head Creek and Pacheco Creek (approx. .75 mile... point the boundary moves in a northerly direction up Elephant Head Creek approx. 1.2 miles until it....G.S. map; (29) Then it moves northeast along Pacheco Creek approx. .5 mile to Elephant Head Creek at...

27 CFR 9.126 - Santa Clara Valley.

Code of Federal Regulations, 2010 CFR

2010-04-01

...: (1) The beginning point is at the junction of Elephant Head Creek and Pacheco Creek (approx. .75 mile... point the boundary moves in a northerly direction up Elephant Head Creek approx. 1.2 miles until it....G.S. map; (29) Then it moves northeast along Pacheco Creek approx. .5 mile to Elephant Head Creek at...

27 CFR 9.126 - Santa Clara Valley.

Code of Federal Regulations, 2012 CFR

2012-04-01

...: (1) The beginning point is at the junction of Elephant Head Creek and Pacheco Creek (approx. .75 mile... point the boundary moves in a northerly direction up Elephant Head Creek approx. 1.2 miles until it....G.S. map; (29) Then it moves northeast along Pacheco Creek approx. .5 mile to Elephant Head Creek at...

27 CFR 9.126 - Santa Clara Valley.

Code of Federal Regulations, 2011 CFR

2011-04-01

...: (1) The beginning point is at the junction of Elephant Head Creek and Pacheco Creek (approx. .75 mile... point the boundary moves in a northerly direction up Elephant Head Creek approx. 1.2 miles until it....G.S. map; (29) Then it moves northeast along Pacheco Creek approx. .5 mile to Elephant Head Creek at...

Terrestrial-style slow-moving earthflow kinematics in a submarine landslide complex

Treesearch

Joshu J. Mountjoy; Jim McKean; Philip M. Barnes; Jarg R. Pettinga

2009-01-01

Morphometric analysis of Simrad EM300 multibeam bathymetric DEMs reveals details of deformation patterns in a ~145 km2 submarine landslide complex that are commonly associated with slow-moving earthflows in terrestrial settings. This mode of failure, where existing landslide debris is remobilised repeatedly along discrete shear boundaries and is...

Linear and nonlinear stability of periodic orbits in annular billiards.

PubMed

Dettmann, Carl P; Fain, Vitaly

2017-04-01

An annular billiard is a dynamical system in which a particle moves freely in a disk except for elastic collisions with the boundary and also a circular scatterer in the interior of the disk. We investigate the stability properties of some periodic orbits in annular billiards in which the scatterer is touching or close to the boundary. We analytically show that there exist linearly stable periodic orbits of an arbitrary period for scatterers with decreasing radii that are located near the boundary of the disk. As the position of the scatterer moves away from a symmetry line of a periodic orbit, the stability of periodic orbits changes from elliptic to hyperbolic, corresponding to a saddle-center bifurcation. When the scatterer is tangent to the boundary, the periodic orbit is parabolic. We prove that slightly changing the reflection angle of the orbit in the tangential situation leads to the existence of Kolmogorov-Arnold-Moser islands. Thus, we show that there exists a decreasing to zero sequence of open intervals of scatterer radii, along which the billiard table is not ergodic.

Linear and nonlinear stability of periodic orbits in annular billiards

NASA Astrophysics Data System (ADS)

Dettmann, Carl P.; Fain, Vitaly

2017-04-01

An annular billiard is a dynamical system in which a particle moves freely in a disk except for elastic collisions with the boundary and also a circular scatterer in the interior of the disk. We investigate the stability properties of some periodic orbits in annular billiards in which the scatterer is touching or close to the boundary. We analytically show that there exist linearly stable periodic orbits of an arbitrary period for scatterers with decreasing radii that are located near the boundary of the disk. As the position of the scatterer moves away from a symmetry line of a periodic orbit, the stability of periodic orbits changes from elliptic to hyperbolic, corresponding to a saddle-center bifurcation. When the scatterer is tangent to the boundary, the periodic orbit is parabolic. We prove that slightly changing the reflection angle of the orbit in the tangential situation leads to the existence of Kolmogorov-Arnold-Moser islands. Thus, we show that there exists a decreasing to zero sequence of open intervals of scatterer radii, along which the billiard table is not ergodic.

New Boundary Constraints for Elliptic Systems used in Grid Generation Problems

NASA Technical Reports Server (NTRS)

Kaul, Upender K.; Clancy, Daniel (Technical Monitor)

2002-01-01

This paper discusses new boundary constraints for elliptic partial differential equations as used in grid generation problems in generalized curvilinear coordinate systems. These constraints, based on the principle of local conservation of thermal energy in the vicinity of the boundaries, are derived using the Green's Theorem. They uniquely determine the so called decay parameters in the source terms of these elliptic systems. These constraints' are designed for boundary clustered grids where large gradients in physical quantities need to be resolved adequately. It is observed that the present formulation also works satisfactorily for mild clustering. Therefore, a closure for the decay parameter specification for elliptic grid generation problems has been provided resulting in a fully automated elliptic grid generation technique. Thus, there is no need for a parametric study of these decay parameters since the new constraints fix them uniquely. It is also shown that for Neumann type boundary conditions, these boundary constraints uniquely determine the solution to the internal elliptic problem thus eliminating the non-uniqueness of the solution of an internal Neumann boundary value grid generation problem.

Thermal Stability of Al2O3/Silicone Composites as High-Temperature Encapsulants

NASA Astrophysics Data System (ADS)

Yao, Yiying

Underwater gliders are robust and long endurance ocean sampling platforms that are increasingly being deployed in coastal regions. This new environment is characterized by shallow waters and significant currents that can challenge the mobility of these efficient (but traditionally slow moving) vehicles. This dissertation aims to improve the performance of shallow water underwater gliders through path planning. The path planning problem is formulated for a dynamic particle (or "kinematic car") model. The objective is to identify the path which satisfies specified boundary conditions and minimizes a particular cost. Several cost functions are considered. The problem is addressed using optimal control theory. The length scales of interest for path planning are within a few turn radii. First, an approach is developed for planning minimum-time paths, for a fixed speed glider, that are sub-optimal but are guaranteed to be feasible in the presence of unknown time-varying currents. Next the minimum-time problem for a glider with speed controls, that may vary between the stall speed and the maximum speed, is solved. Last, optimal paths that minimize change in depth (equivalently, maximize range) are investigated. Recognizing that path planning alone cannot overcome all of the challenges associated with significant currents and shallow waters, the design of a novel underwater glider with improved capabilities is explored. A glider with a pneumatic buoyancy engine (allowing large, rapid buoyancy changes) and a cylindrical moving mass mechanism (generating large pitch and roll moments) is designed, manufactured, and tested to demonstrate potential improvements in speed and maneuverability.

Completed Beltrami-Michell formulation for analyzing mixed boundary value problems in elasticity

NASA Technical Reports Server (NTRS)

Patnaik, Surya N.; Kaljevic, Igor; Hopkins, Dale A.; Saigal, Sunil

1995-01-01

In elasticity, the method of forces, wherein stress parameters are considered as the primary unknowns, is known as the Beltrami-Michell formulation (BMF). The existing BMF can only solve stress boundary value problems; it cannot handle the more prevalent displacement of mixed boundary value problems of elasticity. Therefore, this formulation, which has restricted application, could not become a true alternative to the Navier's displacement method, which can solve all three types of boundary value problems. The restrictions in the BMF have been alleviated by augmenting the classical formulation with a novel set of conditions identified as the boundary compatibility conditions. This new method, which completes the classical force formulation, has been termed the completed Beltrami-Michell formulation (CBMF). The CBMF can solve general elasticity problems with stress, displacement, and mixed boundary conditions in terms of stresses as the primary unknowns. The CBMF is derived from the stationary condition of the variational functional of the integrated force method. In the CBMF, stresses for kinematically stable structures can be obtained without any reference to the displacements either in the field or on the boundary. This paper presents the CBMF and its derivation from the variational functional of the integrated force method. Several examples are presented to demonstrate the applicability of the completed formulation for analyzing mixed boundary value problems under thermomechanical loads. Selected example problems include a cylindrical shell wherein membrane and bending responses are coupled, and a composite circular plate.

Experimental investigation of moving surfaces for boundary layer and circulation control of airfoils and wings

NASA Astrophysics Data System (ADS)

Vets, Robert

An experimental study was conducted to assess the application of a moving surface to affect boundary layers and circulation around airfoils for the purpose of altering and enhancing aerodynamic performance of finite wings at moderate Reynolds numbers. The moving surface was established by a wide, lightweight, nylon belt that enveloped a wing's symmetric airfoil profile articulated via a friction drive cylinder such that the direction of the upper surface was in the direction of the free stream. A water tunnel visualization study accompanied wind tunnel testing at the University of Washington, Kirsten Wind Tunnel of finite wings. An experimental study was conducted to assess the application of a moving surface to affect boundary layers and circulation around airfoils for the purpose of altering and enhancing aerodynamic performance of finite wings at moderate Reynolds numbers. The moving surface was established by a wide, lightweight, nylon belt that enveloped a wing's symmetric airfoil profile articulated via a friction drive cylinder such that the direction of the upper surface was in the direction of the free stream. A water tunnel visualization study accompanied wind tunnel testing at the University of Washington, Kirsten Wind Tunnel of finite wings. The defining non-dimensional parameter for the system is the ratio of the surface velocity to the free stream velocity, us/Uo. Results show a general increase in lift with increasing us/Uo. The endurance parameter served as an additional metric for the system's performance. Examining the results of the endurance parameter shows general increase in endurance and lift with the moving surface activated. Peak performance in terms of increased endurance along with increased lift occurs at or slightly above us/Uo = 1. Water tunnel visualization showed a marked difference in the downwash for velocity ratios greater than 1, supporting the measured data. Reynolds numbers for this investigation were 1.9E5 and 4.3E5, relevant to the class of fixed wing, Tier-1, Unmanned Aerial Vehicles (UAV).

A moving control volume approach to computing hydrodynamic forces and torques on immersed bodies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nangia, Nishant; Johansen, Hans; Patankar, Neelesh A.

Here, we present a moving control volume (CV) approach to computing hydrodynamic forces and torques on complex geometries. The method requires surface and volumetric integrals over a simple and regular Cartesian box that moves with an arbitrary velocity to enclose the body at all times. The moving box is aligned with Cartesian grid faces, which makes the integral evaluation straightforward in an immersed boundary (IB) framework. Discontinuous and noisy derivatives of velocity and pressure at the fluid–structure interface are avoided and far-field (smooth) velo city and pressure information is used. We re-visit the approach to compute hydrodynamic forces and torquesmore » through force/torque balance equations in a Lagrangian frame that some of us took in a prior work (Bhalla et al., 2013 [13]). We prove the equivalence of the two approaches for IB methods, thanks to the use of Peskin's delta functions. Both approaches are able to suppress spurious force oscillations and are in excellent agreement, as expected theoretically. Test cases ranging from Stokes to high Reynolds number regimes are considered. We discuss regridding issues for the moving CV method in an adaptive mesh refinement (AMR) context. The proposed moving CV method is not limited to a specific IB method and can also be used, for example, with embedded boundary methods.« less

A moving control volume approach to computing hydrodynamic forces and torques on immersed bodies

DOE PAGES

Nangia, Nishant; Johansen, Hans; Patankar, Neelesh A.; ...

2017-10-01

Here, we present a moving control volume (CV) approach to computing hydrodynamic forces and torques on complex geometries. The method requires surface and volumetric integrals over a simple and regular Cartesian box that moves with an arbitrary velocity to enclose the body at all times. The moving box is aligned with Cartesian grid faces, which makes the integral evaluation straightforward in an immersed boundary (IB) framework. Discontinuous and noisy derivatives of velocity and pressure at the fluid–structure interface are avoided and far-field (smooth) velo city and pressure information is used. We re-visit the approach to compute hydrodynamic forces and torquesmore » through force/torque balance equations in a Lagrangian frame that some of us took in a prior work (Bhalla et al., 2013 [13]). We prove the equivalence of the two approaches for IB methods, thanks to the use of Peskin's delta functions. Both approaches are able to suppress spurious force oscillations and are in excellent agreement, as expected theoretically. Test cases ranging from Stokes to high Reynolds number regimes are considered. We discuss regridding issues for the moving CV method in an adaptive mesh refinement (AMR) context. The proposed moving CV method is not limited to a specific IB method and can also be used, for example, with embedded boundary methods.« less

Nonlinear Conservation Laws and Finite Volume Methods

NASA Astrophysics Data System (ADS)

Leveque, Randall J.

Introduction Software Notation Classification of Differential Equations Derivation of Conservation Laws The Euler Equations of Gas Dynamics Dissipative Fluxes Source Terms Radiative Transfer and Isothermal Equations Multi-dimensional Conservation Laws The Shock Tube Problem Mathematical Theory of Hyperbolic Systems Scalar Equations Linear Hyperbolic Systems Nonlinear Systems The Riemann Problem for the Euler Equations Numerical Methods in One Dimension Finite Difference Theory Finite Volume Methods Importance of Conservation Form - Incorrect Shock Speeds Numerical Flux Functions Godunov's Method Approximate Riemann Solvers High-Resolution Methods Other Approaches Boundary Conditions Source Terms and Fractional Steps Unsplit Methods Fractional Step Methods General Formulation of Fractional Step Methods Stiff Source Terms Quasi-stationary Flow and Gravity Multi-dimensional Problems Dimensional Splitting Multi-dimensional Finite Volume Methods Grids and Adaptive Refinement Computational Difficulties Low-Density Flows Discrete Shocks and Viscous Profiles Start-Up Errors Wall Heating Slow-Moving Shocks Grid Orientation Effects Grid-Aligned Shocks Magnetohydrodynamics The MHD Equations One-Dimensional MHD Solving the Riemann Problem Nonstrict Hyperbolicity Stiffness The Divergence of B Riemann Problems in Multi-dimensional MHD Staggered Grids The 8-Wave Riemann Solver Relativistic Hydrodynamics Conservation Laws in Spacetime The Continuity Equation The 4-Momentum of a Particle The Stress-Energy Tensor Finite Volume Methods Multi-dimensional Relativistic Flow Gravitation and General Relativity References

Accurate boundary conditions for exterior problems in gas dynamics

NASA Technical Reports Server (NTRS)

Hagstrom, Thomas; Hariharan, S. I.

1988-01-01

The numerical solution of exterior problems is typically accomplished by introducing an artificial, far field boundary and solving the equations on a truncated domain. For hyperbolic systems, boundary conditions at this boundary are often derived by imposing a principle of no reflection. However, waves with spherical symmetry in gas dynamics satisfy equations where incoming and outgoing Riemann variables are coupled. This suggests that natural reflections may be important. A reflecting boundary condition is proposed based on an asymptotic solution of the far field equations. Nonlinear energy estimates are obtained for the truncated problem and numerical experiments presented to validate the theory.

Accurate boundary conditions for exterior problems in gas dynamics

NASA Technical Reports Server (NTRS)

Hagstrom, Thomas; Hariharan, S. I.

1988-01-01

The numerical solution of exterior problems is typically accomplished by introducing an artificial, far-field boundary and solving the equations on a truncated domain. For hyperbolic systems, boundary conditions at this boundary are often derived by imposing a principle of no reflection. However, waves with spherical symmetry in gas dynamics satisfy equations where incoming and outgoing Riemann variables are coupled. This suggests that natural reflections may be important. A reflecting boundary condition is proposed based on an asymptotic solution of the far-field equations. Nonlinear energy estimates are obtained for the truncated problem and numerical experiments presented to validate the theory.

Computation of the shock-wave boundary layer interaction with flow separation

NASA Technical Reports Server (NTRS)

Ardonceau, P.; Alziary, T.; Aymer, D.

1980-01-01

The boundary layer concept is used to describe the flow near the wall. The external flow is approximated by a pressure displacement relationship (tangent wedge in linearized supersonic flow). The boundary layer equations are solved in finite difference form and the question of the presence and unicity of the solution is considered for the direct problem (assumed pressure) or converse problem (assumed displacement thickness, friction ratio). The coupling algorithm presented implicitly processes the downstream boundary condition necessary to correctly define the interacting boundary layer problem. The algorithm uses a Newton linearization technique to provide a fast convergence.

Efficient algorithms for analyzing the singularly perturbed boundary value problems of fractional order

NASA Astrophysics Data System (ADS)

Sayevand, K.; Pichaghchi, K.

2018-04-01

In this paper, we were concerned with the description of the singularly perturbed boundary value problems in the scope of fractional calculus. We should mention that, one of the main methods used to solve these problems in classical calculus is the so-called matched asymptotic expansion method. However we shall note that, this was not achievable via the existing classical definitions of fractional derivative, because they do not obey the chain rule which one of the key elements of the matched asymptotic expansion method. In order to accommodate this method to fractional derivative, we employ a relatively new derivative so-called the local fractional derivative. Using the properties of local fractional derivative, we extend the matched asymptotic expansion method to the scope of fractional calculus and introduce a reliable new algorithm to develop approximate solutions of the singularly perturbed boundary value problems of fractional order. In the new method, the original problem is partitioned into inner and outer solution equations. The reduced equation is solved with suitable boundary conditions which provide the terminal boundary conditions for the boundary layer correction. The inner solution problem is next solved as a solvable boundary value problem. The width of the boundary layer is approximated using appropriate resemblance function. Some theoretical results are established and proved. Some illustrating examples are solved and the results are compared with those of matched asymptotic expansion method and homotopy analysis method to demonstrate the accuracy and efficiency of the method. It can be observed that, the proposed method approximates the exact solution very well not only in the boundary layer, but also away from the layer.

Compressible Fluids Interacting with a Linear-Elastic Shell

NASA Astrophysics Data System (ADS)

Breit, Dominic; Schwarzacher, Sebastian

2018-05-01

We study the Navier-Stokes equations governing the motion of an isentropic compressible fluid in three dimensions interacting with a flexible shell of Koiter type. The latter one constitutes a moving part of the boundary of the physical domain. Its deformation is modeled by a linearized version of Koiter's elastic energy. We show the existence of weak solutions to the corresponding system of PDEs provided the adiabatic exponent satisfies {γ > 12/7} ({γ >1 } in two dimensions). The solution exists until the moving boundary approaches a self-intersection. This provides a compressible counterpart of the results in Lengeler and Růžičkaka (Arch Ration Mech Anal 211(1):205-255, 2014) on incompressible Navier-Stokes equations.

On the nonlinear stability of viscous modes within the Rayleigh problem on an infinite flat plate

NASA Technical Reports Server (NTRS)

Webb, J. C.; Otto, S. R.; Lilley, G. M.

1994-01-01

The stability has been investigated of the unsteady flow past an infinite flat plate when it is moved impulsively from rest, in its own plane. For small times the instantaneous stability of the flow depends on the linearized equations of motion which reduce in this problem to the Orr-Sommerfeld equation. It is known that the flow for certain values of Reynolds number, frequency and wave number is unstable to Tollmien-Schlichting waves, as in the case of the Blasius boundary layer flow past a flat plate. With increase in time, the unstable waves only undergo growth for a finite time interval, and this growth rate is itself a function of time. The influence of finite amplitude effects is studied by solving the full Navier-Stokes equations. It is found that the stability characteristics are markedly changed both by the consideration of the time evolution of the flow, and by the introduction of finite amplitude effects.

Modeling local extinction in turbulent combustion using an embedding method

NASA Astrophysics Data System (ADS)

Knaus, Robert; Pantano, Carlos

2012-11-01

Local regions of extinction in diffusion flames, called ``flame holes,'' can reduce the efficiency of combustion and increase the production of certain pollutants. At sufficiently high speeds, a flame may also be lifted from the rim of the burner to a downstream location that may be stable. These two phenomena share a common underlying mechanism of propagation related to edge-flame dynamics where chemistry and fluid mechanics are equally important. We present a formulation that describes the formation, propagation, and growth of flames holes on the stoichiometric surface using edge flame dynamics. The boundary separating the flame from the quenched region is modeled using a progress variable defined on the moving stoichiometric surface that is embedded in the three-dimensional space using an extension algorithm. This Cartesian problem is solved using a high-order finite-volume WENO method extended to this nonconservative problem. This algorithm can track the dynamics of flame holes in a turbulent reacting-shear layer and model flame liftoff without requiring full chemistry calculations.

Snake states and their symmetries in graphene

NASA Astrophysics Data System (ADS)

Tiwari, Rakesh; Liu, Yang; Brada, Matej; Bruder, C.; Kusmartsev, F. V.; Mele, E. J.

Snake states are open trajectories for charged particles moving in two dimensions under the influence of a spatially varying perpendicular magnetic field. They can also occur in a constant perpendicular magnetic field when the particle density is made nonuniform as realized at a pn junction in a semiconductor, or in graphene. We examine the correspondence of such trajectories in monolayer graphene in the quantum limit for two families of domain walls: (a) a uniform doped carrier density in an antisymmetric perpendicular magnetic field and (b) antisymmetric carrier density distribution in a uniform perpendicular magnetic field. Although, these families support different internal symmetries, the pattern of the boundary and interface currents is the same in both cases. We demonstrate that these two physically different situations are gauge equivalent when rewritten in a Nambu doubled formulation of the two limiting problems. Using gauge transformations in particle-hole space to connect these two problems, we map the protected interfacial modes to the Bogoliubov quasiparticles of an interfacial one-dimensional p-wave paired state.

`Relativistic' corrections to the mass of a plucked guitar string

NASA Astrophysics Data System (ADS)

Kolodrubetz, Michael; Polkovnikov, Anatoli

Quantum systems respond non-adiabaticity when parameters controlling them are ramped at a finite rate. If the parameters themselves are dynamical - for instance the position of a box that defines the boundary of a quantum field - the feedback of these excitations gives rise to effective Newtonian equations of motion for the parameter. For the age old problem of photons in a box, this correction gives rise to a mass proportional to the energy of the photons. We show that a similar correction arises for a classical guitar string plucked with energy E; moving clamps at the ends of the string requires inertial mass m = 2 E /cs2 , where cs is the speed of sound. This quasi-relativistic effect should be observable in freshman physics level experiments. We then comment on how these simple methods have been readily extended to treat problems such as ramps and quenches of strongly-interacting superconductors and dynamical trapping near a quantum critical point.

Inter-organisational response to disasters.

PubMed

Paturas, James L; Smith, Stewart R; Albanese, Joseph; Waite, Geraldine

2016-01-01

Inter-organisational communication failures during times of real-world disasters impede the collaborative response of agencies responsible for ensuring the public's health and safety. In the best of circumstances, communications across jurisdictional boundaries are ineffective. In times of crisis, when communities are grappling with the impact of a disaster, communications become critically important and more complex. Important factors for improving inter-organisational communications are critical thinking and problem-solving skills; inter-organisational relationships; as well as strategic, tactical and operational communications. Improving communication, critical thinking, problem-solving and decision-making requires a review of leadership skills. This discussion begins with an analysis of the existing disaster management research and moves to an examination of the importance of inter-organisational working relationships. Before a successful resolution of a disaster by multiple levels of first responders, the group of organisations must have a foundation of trust, collegiality, flexibility, expertise, openness, relational networking and effective communications. Leaders must also be prepared to improve leadership skills through continual development in each of these foundational areas.

COMPLEX VARIABLE BOUNDARY ELEMENT METHOD: APPLICATIONS.

USGS Publications Warehouse

Hromadka, T.V.; Yen, C.C.; Guymon, G.L.

1985-01-01

The complex variable boundary element method (CVBEM) is used to approximate several potential problems where analytical solutions are known. A modeling result produced from the CVBEM is a measure of relative error in matching the known boundary condition values of the problem. A CVBEM error-reduction algorithm is used to reduce the relative error of the approximation by adding nodal points in boundary regions where error is large. From the test problems, overall error is reduced significantly by utilizing the adaptive integration algorithm.

A free-boundary model of a motile cell explains turning behavior.

PubMed

Nickaeen, Masoud; Novak, Igor L; Pulford, Stephanie; Rumack, Aaron; Brandon, Jamie; Slepchenko, Boris M; Mogilner, Alex

2017-11-01

To understand shapes and movements of cells undergoing lamellipodial motility, we systematically explore minimal free-boundary models of actin-myosin contractility consisting of the force-balance and myosin transport equations. The models account for isotropic contraction proportional to myosin density, viscous stresses in the actin network, and constant-strength viscous-like adhesion. The contraction generates a spatially graded centripetal actin flow, which in turn reinforces the contraction via myosin redistribution and causes retraction of the lamellipodial boundary. Actin protrusion at the boundary counters the retraction, and the balance of the protrusion and retraction shapes the lamellipodium. The model analysis shows that initiation of motility critically depends on three dimensionless parameter combinations, which represent myosin-dependent contractility, a characteristic viscosity-adhesion length, and a rate of actin protrusion. When the contractility is sufficiently strong, cells break symmetry and move steadily along either straight or circular trajectories, and the motile behavior is sensitive to conditions at the cell boundary. Scanning of a model parameter space shows that the contractile mechanism of motility supports robust cell turning in conditions where short viscosity-adhesion lengths and fast protrusion cause an accumulation of myosin in a small region at the cell rear, destabilizing the axial symmetry of a moving cell.

Exact solution for a two-phase Stefan problem with variable latent heat and a convective boundary condition at the fixed face

NASA Astrophysics Data System (ADS)

Bollati, Julieta; Tarzia, Domingo A.

2018-04-01

Recently, in Tarzia (Thermal Sci 21A:1-11, 2017) for the classical two-phase Lamé-Clapeyron-Stefan problem an equivalence between the temperature and convective boundary conditions at the fixed face under a certain restriction was obtained. Motivated by this article we study the two-phase Stefan problem for a semi-infinite material with a latent heat defined as a power function of the position and a convective boundary condition at the fixed face. An exact solution is constructed using Kummer functions in case that an inequality for the convective transfer coefficient is satisfied generalizing recent works for the corresponding one-phase free boundary problem. We also consider the limit to our problem when that coefficient goes to infinity obtaining a new free boundary problem, which has been recently studied in Zhou et al. (J Eng Math 2017. https://doi.org/10.1007/s10665-017-9921-y).

2010 and Beyond: Virtual Reality and the Communication Classroom.

ERIC Educational Resources Information Center

Siddens, Paul J., III

The use of virtual reality technology in the Communication discipline is a challenge that educators in the field should investigate thoroughly and begin to embrace as they move into the 21st century. Classrooms with access to the Internet allow students to move outside the physical boundaries of the classroom and suggest a significant change in…

Multi-model stereo restitution

USGS Publications Warehouse

Dueholm, K.S.

1990-01-01

Methods are described that permit simultaneous orientation of many small-frame photogrammetric models in an analytical plotter. The multi-model software program enables the operator to move freely between the oriented models during interpretation and mapping. Models change automatically when the measuring mark is moved from one frame to another, moving to the same ground coordinates in the neighboring model. Thus, data collection and plotting can be performed continuously across model boundaries. The orientation of the models is accomplished by a bundle block adjustment. -from Author

Effect of Surface Waviness on Transition in Three-Dimensional Boundary-Layer Flow

NASA Technical Reports Server (NTRS)

Masad, Jamal A.

1996-01-01

The effect of a surface wave on transition in three-dimensional boundary-layer flow over an infinite swept wing was studied. The mean flow computed using interacting boundary-layer theory, and transition was predicted using linear stability theory coupled with the empirical eN method. It was found that decreasing the wave height, sweep angle, or freestream unit Reynolds number, and increasing the freestream Mach number or suction level all stabilized the flow and moved transition onset to downstream locations.

Continuous protein concentration via free-flow moving reaction boundary electrophoresis.

PubMed

Kong, Fanzhi; Zhang, Min; Chen, Jingjing; Fan, Liuyin; Xiao, Hua; Liu, Shaorong; Cao, Chengxi

2017-07-28

In this work, we developed the model and theory of free-flow moving reaction boundary electrophoresis (FFMRB) for continuous protein concentration for the first time. The theoretical results indicated that (i) the moving reaction boundary (MRB) can be quantitatively designed in free-flow electrophoresis (FFE) system; (ii) charge-to-mass ratio (Z/M) analysis could provide guidance for protein concentration optimization; and (iii) the maximum processing capacity could be predicted. To demonstrate the model and theory, three model proteins of hemoglobin (Hb), cytochrome C (Cyt C) and C-phycocyanin (C-PC) were chosen for the experiments. The experimental results verified that (i) stable MRBs with different velocities could be established in FFE apparatus with weak acid/weak base neutralization reaction system; (ii) proteins of Hb, Cyt C and C-PC were well concentrated with FFMRB; and (iii) a maximum processing capacity and recovery ratio of Cyt C enrichment were 126mL/h and 95.5% respectively, and a maximum enrichment factor was achieved 12.6 times for Hb. All of the experiments demonstrated the protein concentration model and theory. In contrast to other methods, the continuous processing ability enables FFMRB to efficiently enrich diluted protein or peptide in large volume solution. Copyright © 2017 Elsevier B.V. All rights reserved.

Numerical solution of system of boundary value problems using B-spline with free parameter

NASA Astrophysics Data System (ADS)

Gupta, Yogesh

2017-01-01

This paper deals with method of B-spline solution for a system of boundary value problems. The differential equations are useful in various fields of science and engineering. Some interesting real life problems involve more than one unknown function. These result in system of simultaneous differential equations. Such systems have been applied to many problems in mathematics, physics, engineering etc. In present paper, B-spline and B-spline with free parameter methods for the solution of a linear system of second-order boundary value problems are presented. The methods utilize the values of cubic B-spline and its derivatives at nodal points together with the equations of the given system and boundary conditions, ensuing into the linear matrix equation.

State space approach to mixed boundary value problems.

NASA Technical Reports Server (NTRS)

Chen, C. F.; Chen, M. M.

1973-01-01

A state-space procedure for the formulation and solution of mixed boundary value problems is established. This procedure is a natural extension of the method used in initial value problems; however, certain special theorems and rules must be developed. The scope of the applications of the approach includes beam, arch, and axisymmetric shell problems in structural analysis, boundary layer problems in fluid mechanics, and eigenvalue problems for deformable bodies. Many classical methods in these fields developed by Holzer, Prohl, Myklestad, Thomson, Love-Meissner, and others can be either simplified or unified under new light shed by the state-variable approach. A beam problem is included as an illustration.

Visual offline sample stacking via moving neutralization boundary electrophoresis for analysis of heavy metal ion.

PubMed

Fan, Yinping; Li, Shan; Fan, Liuyin; Cao, Chengxi

2012-06-15

In this paper, a moving neutralization boundary (MNB) electrophoresis is developed as a novel model of visual offline sample stacking for the trace analysis of heavy metal ions (HMIs). In the stacking system, the cathodic-direction motion MNB is designed with 1.95-2.8mM HCl+98 mM KCl in phase alfa and 4.0mM NaOH+96 mM KCl in phase beta. If a little of HMI is present in phase alfa, the metal ion electrically migrates towards the MNB and react with hydroxyl ion, producing precipitation and moving precipitation boundary (MPB). The alkaline precipitation is neutralized by hydrogen ion, leading to a moving eluting boundary (MEB), release of HMI from its precipitation, circle of HMI from the MEB to the MPB, and highly efficient visual stacking. As a proof of concept, a set of metal ions (Cu(II), Co(II), Mn(II), Pb(II) and Cr(III)) were chosen as the model HMIs and capillary electrophoresis (CE) was selected as an analytical tool for the experiments demonstrating the feasibility of MNB-based stacking. As shown in this paper, (i) the visual stacking model was manifested by the experiments; (ii) there was a controllable stacking of HMI in the MNB system; (iii) the offline stacking could achieve higher than 123 fold preconcentration; and (iv) the five HMIs were simultaneously stacked via the developed stacking technique for the trace analyses with the limits of detection (LOD): 3.67×10(-3) (Cu(II)), 1.67×10(-3) (Co(II), 4.17×10(-3) (Mn(II)), 4.6×10(-4) (Pb(II)) and 8.40×10(-4)mM (Cr(III)). Even the off-line stacking was demonstrated for the use of CE-based HMI analysis, it has potential applications in atomic absorption spectroscopy (AAS), inductively coupled plasma-mass spectrometry (ICP-MS) and ion chromatography (IC) etc. Copyright © 2012 Elsevier B.V. All rights reserved.

Distance estimation and collision prediction for on-line robotic motion planning

NASA Technical Reports Server (NTRS)

Kyriakopoulos, K. J.; Saridis, G. N.

1992-01-01

An efficient method for computing the minimum distance and predicting collisions between moving objects is presented. This problem is incorporated into the framework of an in-line motion-planning algorithm to satisfy collision avoidance between a robot and moving objects modeled as convex polyhedra. In the beginning, the deterministic problem where the information about the objects is assumed to be certain is examined. L(1) or L(infinity) norms are used to represent distance and the problem becomes a linear programming problem. The stochastic problem is formulated where the uncertainty is induced by sensing and the unknown dynamics of the moving obstacles. Two problems are considered: First, filtering of the distance between the robot and the moving object at the present time. Second, prediction of the minimum distance in the future in order to predict the collision time.

Computation of Transonic Nozzle Sound Transmission and Rotor Problems by the Dispersion-Relation-Preserving Scheme

NASA Technical Reports Server (NTRS)

Tam, Christopher K. W.; Aganin, Alexei

2000-01-01

The transonic nozzle transmission problem and the open rotor noise radiation problem are solved computationally. Both are multiple length scales problems. For efficient and accurate numerical simulation, the multiple-size-mesh multiple-time-step Dispersion-Relation-Preserving scheme is used to calculate the time periodic solution. To ensure an accurate solution, high quality numerical boundary conditions are also needed. For the nozzle problem, a set of nonhomogeneous, outflow boundary conditions are required. The nonhomogeneous boundary conditions not only generate the incoming sound waves but also, at the same time, allow the reflected acoustic waves and entropy waves, if present, to exit the computation domain without reflection. For the open rotor problem, there is an apparent singularity at the axis of rotation. An analytic extension approach is developed to provide a high quality axis boundary treatment.

Computer analysis of multicircuit shells of revolution by the field method

NASA Technical Reports Server (NTRS)

Cohen, G. A.

1975-01-01

The field method, presented previously for the solution of even-order linear boundary value problems defined on one-dimensional open branch domains, is extended to boundary value problems defined on one-dimensional domains containing circuits. This method converts the boundary value problem into two successive numerically stable initial value problems, which may be solved by standard forward integration techniques. In addition, a new method for the treatment of singular boundary conditions is presented. This method, which amounts to a partial interchange of the roles of force and displacement variables, is problem independent with respect to both accuracy and speed of execution. This method was implemented in a computer program to calculate the static response of ring stiffened orthotropic multicircuit shells of revolution to asymmetric loads. Solutions are presented for sample problems which illustrate the accuracy and efficiency of the method.

Collective decision making in cohesive flocks

NASA Astrophysics Data System (ADS)

Bhattacharya, K.; Vicsek, Tamás

2010-09-01

Most of us must have been fascinated by the eye-catching displays of collectively moving animals. Schools of fish can move in a rather orderly fashion and then change direction amazingly abruptly. There are a large number of further examples both from the living and the non-living world for phenomena during which the many interacting, permanently moving units seem to arrive at a common behavioural pattern taking place in a short time. As a paradigm of this type of phenomena we consider the problem of how birds arrive at a decision resulting in their synchronized landing. We introduce a simple model to interpret this process. Collective motion prior to landing is modelled using a simple self-propelled particle (SPP) system with a new kind of boundary condition, while the tendency and the sudden propagation of the intention of landing are introduced through rules analogous to the random field Ising model in an external field. We show that our approach is capable of capturing the most relevant features of collective decision making in a system of units with variance of individual intentions and being under an increasing level of pressure to switch states. We find that as a function of the few parameters of our model the collective switching from the flying to the landing state is indeed much sharper than the distribution of individual landing intentions. The transition is accompanied by a number of interesting features discussed in this paper.

Homogenization of one-dimensional draining through heterogeneous porous media including higher-order approximations

NASA Astrophysics Data System (ADS)

Anderson, Daniel M.; McLaughlin, Richard M.; Miller, Cass T.

2018-02-01

We examine a mathematical model of one-dimensional draining of a fluid through a periodically-layered porous medium. A porous medium, initially saturated with a fluid of a high density is assumed to drain out the bottom of the porous medium with a second lighter fluid replacing the draining fluid. We assume that the draining layer is sufficiently dense that the dynamics of the lighter fluid can be neglected with respect to the dynamics of the heavier draining fluid and that the height of the draining fluid, represented as a free boundary in the model, evolves in time. In this context, we neglect interfacial tension effects at the boundary between the two fluids. We show that this problem admits an exact solution. Our primary objective is to develop a homogenization theory in which we find not only leading-order, or effective, trends but also capture higher-order corrections to these effective draining rates. The approximate solution obtained by this homogenization theory is compared to the exact solution for two cases: (1) the permeability of the porous medium varies smoothly but rapidly and (2) the permeability varies as a piecewise constant function representing discrete layers of alternating high/low permeability. In both cases we are able to show that the corrections in the homogenization theory accurately predict the position of the free boundary moving through the porous medium.

Velocity fields and optical turbulence near the boundary in a strongly convective laboratory flow

NASA Astrophysics Data System (ADS)

Matt, Silvia; Hou, Weilin; Goode, Wesley; Hellman, Samuel

2016-05-01

Boundary layers around moving underwater vehicles or other platforms can be a limiting factor for optical communication. Turbulence in the boundary layer of a body moving through a stratified medium can lead to small variations in the index of refraction, which impede optical signals. As a first step towards investigating this boundary layer effect on underwater optics, we study the flow near the boundary in the Rayleigh-Bénard laboratory tank at the Naval Research Laboratory Stennis Space Center. The tank is set up to generate temperature-driven, i.e., convective turbulence, and allows control of the turbulence intensity. This controlled turbulence environment is complemented by computational fluid dynamics simulations to visualize and quantify multi-scale flow patterns. The boundary layer dynamics in the laboratory tank are quantified using a state-of-the-art Particle Image Velocimetry (PIV) system to examine the boundary layer velocities and turbulence parameters. The velocity fields and flow dynamics from the PIV are compared to the numerical model and show the model to accurately reproduce the velocity range and flow dynamics. The temperature variations and thus optical turbulence effects can then be inferred from the model temperature data. Optical turbulence is also visible in the raw data from the PIV system. The newly collected data are consistent with previously reported measurements from high-resolution Acoustic Doppler Velocimeter profilers (Nortek Vectrino), as well as fast thermistor probes and novel next-generation fiber-optics temperature sensors. This multi-level approach to studying optical turbulence near a boundary, combining in-situ measurements, optical techniques, and numerical simulations, can provide new insight and aid in mitigating turbulence impacts on underwater optical signal transmission.

Explicitly represented polygon wall boundary model for the explicit MPS method

NASA Astrophysics Data System (ADS)

Mitsume, Naoto; Yoshimura, Shinobu; Murotani, Kohei; Yamada, Tomonori

2015-05-01

This study presents an accurate and robust boundary model, the explicitly represented polygon (ERP) wall boundary model, to treat arbitrarily shaped wall boundaries in the explicit moving particle simulation (E-MPS) method, which is a mesh-free particle method for strong form partial differential equations. The ERP model expresses wall boundaries as polygons, which are explicitly represented without using the distance function. These are derived so that for viscous fluids, and with less computational cost, they satisfy the Neumann boundary condition for the pressure and the slip/no-slip condition on the wall surface. The proposed model is verified and validated by comparing computed results with the theoretical solution, results obtained by other models, and experimental results. Two simulations with complex boundary movements are conducted to demonstrate the applicability of the E-MPS method to the ERP model.

A classical Perron method for existence of smooth solutions to boundary value and obstacle problems for degenerate-elliptic operators via holomorphic maps

NASA Astrophysics Data System (ADS)

Feehan, Paul M. N.

2017-09-01

We prove existence of solutions to boundary value problems and obstacle problems for degenerate-elliptic, linear, second-order partial differential operators with partial Dirichlet boundary conditions using a new version of the Perron method. The elliptic operators considered have a degeneracy along a portion of the domain boundary which is similar to the degeneracy of a model linear operator identified by Daskalopoulos and Hamilton [9] in their study of the porous medium equation or the degeneracy of the Heston operator [21] in mathematical finance. Existence of a solution to the partial Dirichlet problem on a half-ball, where the operator becomes degenerate on the flat boundary and a Dirichlet condition is only imposed on the spherical boundary, provides the key additional ingredient required for our Perron method. Surprisingly, proving existence of a solution to this partial Dirichlet problem with ;mixed; boundary conditions on a half-ball is more challenging than one might expect. Due to the difficulty in developing a global Schauder estimate and due to compatibility conditions arising where the ;degenerate; and ;non-degenerate boundaries; touch, one cannot directly apply the continuity or approximate solution methods. However, in dimension two, there is a holomorphic map from the half-disk onto the infinite strip in the complex plane and one can extend this definition to higher dimensions to give a diffeomorphism from the half-ball onto the infinite ;slab;. The solution to the partial Dirichlet problem on the half-ball can thus be converted to a partial Dirichlet problem on the slab, albeit for an operator which now has exponentially growing coefficients. The required Schauder regularity theory and existence of a solution to the partial Dirichlet problem on the slab can nevertheless be obtained using previous work of the author and C. Pop [16]. Our Perron method relies on weak and strong maximum principles for degenerate-elliptic operators, concepts of continuous subsolutions and supersolutions for boundary value and obstacle problems for degenerate-elliptic operators, and maximum and comparison principle estimates previously developed by the author [13].

DOE Office of Scientific and Technical Information (OSTI.GOV)

Luo, Yousong, E-mail: yousong.luo@rmit.edu.au

This paper deals with a class of optimal control problems governed by an initial-boundary value problem of a parabolic equation. The case of semi-linear boundary control is studied where the control is applied to the system via the Wentzell boundary condition. The differentiability of the state variable with respect to the control is established and hence a necessary condition is derived for the optimal solution in the case of both unconstrained and constrained problems. The condition is also sufficient for the unconstrained convex problems. A second order condition is also derived.

The effects of inhomogeneous boundary dilution on the coating flow of an anti-HIV microbicide vehicle

NASA Astrophysics Data System (ADS)

Tasoglu, Savas; Peters, Jennifer J.; Park, Su Chan; Verguet, Stéphane; Katz, David F.; Szeri, Andrew J.

2011-09-01

A recent study in South Africa has confirmed, for the first time, that a vaginal gel formulation of the antiretroviral drug Tenofovir, when topically applied, significantly inhibits sexual HIV transmission to women [Karim et al., Science 329, 1168 (2010)]. However, the gel for this drug and anti-HIV microbicide gels in general have not been designed using an understanding of how gel spreading and retention in the vagina govern successful drug delivery. Elastohydrodynamic lubrication theory can be applied to model spreading of microbicide gels [Szeri et al., Phys. Fluids 20, 083101 (2008)]. This should incorporate the full rheological behavior of a gel, including how rheological properties change due to contact with, and dilution by, ambient vaginal fluids. Here, we extend our initial analysis, incorporating the effects of gel dilution due to contact with vaginal fluid produced at the gel-tissue interface. Our original model is supplemented with a convective-diffusive transport equation to characterize water transport into the gel and, thus, local gel dilution. The problem is solved using a multi-step scheme in a moving domain. The association between local dilution of gel and rheological properties is obtained experimentally, delineating the way constitutive parameters of a shear-thinning gel are modified by dilution. Results show that dilution accelerates the coating flow by creating a slippery region near the vaginal wall akin to a dilution boundary layer, especially if the boundary flux exceeds a certain value. On the other hand, if the diffusion coefficient of boundary fluid is increased, the slippery region diminishes in extent and the overall rate of gel spreading decreases.

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.

2017-10-01

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.

Dynamic analysis of ultrasonically levitated droplet with moving particle semi-implicit and distributed point source method

NASA Astrophysics Data System (ADS)

Wada, Yuji; Yuge, Kohei; Nakamura, Ryohei; Tanaka, Hiroki; Nakamura, Kentaro

2015-07-01

Numerical analysis of an ultrasonically levitated droplet with a free surface boundary is discussed. The droplet is known to change its shape from sphere to spheroid when it is suspended in a standing wave owing to the acoustic radiation force. However, few studies on numerical simulation have been reported in association with this phenomenon including fluid dynamics inside the droplet. In this paper, coupled analysis using the distributed point source method (DPSM) and the moving particle semi-implicit (MPS) method, both of which do not require grids or meshes to handle the moving boundary with ease, is suggested. A droplet levitated in a plane standing wave field between a piston-vibrating ultrasonic transducer and a reflector is simulated with the DPSM-MPS coupled method. The dynamic change in the spheroidal shape of the droplet is successfully reproduced numerically, and the gravitational center and the change in the spheroidal aspect ratio are discussed and compared with the previous literature.

The Agendas of Distance Teaching Universities: Moving from the Margins to the Center Stage of Higher Education.

ERIC Educational Resources Information Center

Guri-Rosenblit, Sarah

1999-01-01

Examined from a comparative perspective the extent to which the agendas of distance teaching universities have moved from the margins to the center stage of higher education. Demonstrates that the boundaries between distance and campus universities are blurring and converging, and that future relations between them will be marked by competition…

Collaboration, Partnerships and Alliances: Perspectives on Erasmus Mundus MA/Magistr in Special Education Needs

ERIC Educational Resources Information Center

Armstrong, Ann Cheryl

2013-01-01

It has been argued that higher education has irreversibly changed over the past 15-20 years. University education has moved from an elite system to a mass system. The frontiers of higher education have expanded more rapidly than they have ever done before by extensively moving across geographical boundaries and accommodating different forms of…

Viscous diffusion of vorticity in unsteady wall layers using the diffusion velocity concept

DOE Office of Scientific and Technical Information (OSTI.GOV)

Strickland, J.H.; Kempka, S.N.; Wolfe, W.P.

1995-03-01

The primary purpose of this paper is to provide a careful evaluation of the diffusion velocity concept with regard to its ability to predict the diffusion of vorticity near a moving wall. A computer code BDIF has been written which simulates the evolution of the vorticity field near a wall of infinite length which is moving in an arbitrary fashion. The simulations generated by this code are found to give excellent results when compared to several exact solutions. We also outline a two-dimensional unsteady viscous boundary layer model which utilizes the diffusion velocity concept and is compatible with vortex methods.more » A primary goal of this boundary layer model is to minimize the number of vortices generated on the surface at each time step while achieving good resolution of the vorticity field near the wall. Preliminary results have been obtained for simulating a simple two-dimensional laminar boundary layer.« less

Measurement of the translation and rotation of a sphere in fluid flow

NASA Astrophysics Data System (ADS)

Barros, Diogo; Hiltbrand, Ben; Longmire, Ellen K.

2018-06-01

The problem of determining the translation and rotation of a spherical particle moving in fluid flow is considered. Lagrangian tracking of markers printed over the surface of a sphere is employed to compute the center motion and the angular velocity of the solid body. The method initially calculates the sphere center from the 3D coordinates of the reconstructed markers, then finds the optimal rotation matrix that aligns a set of markers tracked at sequential time steps. The parameters involved in the experimental implementation of this procedure are discussed, and the associated uncertainty is estimated from numerical analysis. Finally, the proposed methodology is applied to characterize the motion of a large spherical particle released in a turbulent boundary layer developing in a water channel.

Hydrodynamic Contributions to Amoeboid Cell Motility

NASA Astrophysics Data System (ADS)

Lewis, Owen; Guy, Robert

2012-11-01

Understanding the methods by which cells move is a fundamental problem in modern biology. Recent evidence has shown that the fluid dynamics of cytoplasm can play a vital role in cellular motility. The slime mold Physarum polycephalum provides an excellent model organism for the study of amoeboid motion. In this research, we use a simply analytic model in conjuction with computational experiments to investigate intracellular fluid flow in a simple model of Physarum. Of particlar interest are stresses generated by cytoplasmic flow which may be used to aid in cellular motility. In our numerical model, the Immersed Boundary Method is used to account for such stresses. We investigate the relationship between contraction waves, flow waves, adhesion, and locomotive forces in an attempt to characterize conditions necessary to generate directed motion.

Resonance Extraction from the Finite Volume

DOE Office of Scientific and Technical Information (OSTI.GOV)

Doring, Michael; Molina Peralta, Raquel

2016-06-01

The spectrum of excited hadrons becomes accessible in simulations of Quantum Chromodynamics on the lattice. Extensions of Lüscher's method allow to address multi-channel scattering problems using moving frames or modified boundary conditions to obtain more eigenvalues in finite volume. As these are at different energies, interpolations are needed to relate different eigenvalues and to help determine the amplitude. Expanding the T- or the K-matrix locally provides a controlled scheme by removing the known non-analyticities of thresholds. This can be stabilized by using Chiral Perturbation Theory. Different examples to determine resonance pole parameters and to disentangle resonances from thresholds are dis-more » cussed, like the scalar meson f0(980) and the excited baryons N(1535)1/2^- and Lambda(1405)1/2^-.« less

Saltmarsh Boundary Modulates Dispersal of Mangrove Propagules: Implications for Mangrove Migration with Sea-Level Rise

PubMed Central

Peterson, Jennifer M.; Bell, Susan S.

2015-01-01

Few studies have empirically examined the suite of mechanisms that underlie the distributional shifts displayed by organisms in response to changing climatic condition. Mangrove forests are expected to move inland as sea-level rises, encroaching on saltmarsh plants inhabiting higher elevations. Mangrove propagules are transported by tidal waters and propagule dispersal is likely modified upon encountering the mangrove-saltmarsh ecotone, the implications of which are poorly known. Here, using an experimental approach, we record landward and seaward dispersal and subsequent establishment of mangrove propagules that encounter biotic boundaries composed of two types of saltmarsh taxa: succulents and grasses. Our findings revealed that propagules emplaced within saltmarsh vegetation immediately landward of the extant mangrove fringe boundary frequently dispersed in the seaward direction. However, propagules moved seaward less frequently and over shorter distances upon encountering boundaries composed of saltmarsh grasses versus succulents. We uniquely confirmed that the small subset of propagules dispersing landward displayed proportionately higher establishment success than those transported seaward. Although impacts of ecotones on plant dispersal have rarely been investigated in situ, our experimental results indicate that the interplay between tidal transport and physical attributes of saltmarsh vegetation influence boundary permeability to propagules, thereby directing the initial phase of shifting mangrove distributions. The incorporation of tidal inundation information and detailed data on landscape features, such as the structure of saltmarsh vegetation at mangrove boundaries, should improve the accuracy of models that are being developed to forecast mangrove distributional shifts in response to sea-level rise. PMID:25760867

Shear flow of dense granular materials near smooth walls. I. Shear localization and constitutive laws in the boundary region.

PubMed

Shojaaee, Zahra; Roux, Jean-Noël; Chevoir, François; Wolf, Dietrich E

2012-07-01

We report on a numerical study of the shear flow of a simple two-dimensional model of a granular material under controlled normal stress between two parallel smooth frictional walls moving with opposite velocities ± V. Discrete simulations, which are carried out with the contact dynamics method in dense assemblies of disks, reveal that, unlike rough walls made of strands of particles, smooth ones can lead to shear strain localization in the boundary layer. Specifically, we observe, for decreasing V, first a fluidlike regime (A), in which the whole granular layer is sheared, with a homogeneous strain rate except near the walls, then (B) a symmetric velocity profile with a solid block in the middle and strain localized near the walls, and finally (C) a state with broken symmetry in which the shear rate is confined to one boundary layer, while the bulk of the material moves together with the opposite wall. Both transitions are independent of system size and occur for specific values of V. Transient times are discussed. We show that the first transition, between regimes A and B, can be deduced from constitutive laws identified for the bulk material and the boundary layer, while the second one could be associated with an instability in the behavior of the boundary layer. The boundary zone constitutive law, however, is observed to depend on the state of the bulk material nearby.

Saltmarsh boundary modulates dispersal of mangrove propagules: implications for mangrove migration with sea-level rise.

PubMed

Peterson, Jennifer M; Bell, Susan S

2015-01-01

Few studies have empirically examined the suite of mechanisms that underlie the distributional shifts displayed by organisms in response to changing climatic condition. Mangrove forests are expected to move inland as sea-level rises, encroaching on saltmarsh plants inhabiting higher elevations. Mangrove propagules are transported by tidal waters and propagule dispersal is likely modified upon encountering the mangrove-saltmarsh ecotone, the implications of which are poorly known. Here, using an experimental approach, we record landward and seaward dispersal and subsequent establishment of mangrove propagules that encounter biotic boundaries composed of two types of saltmarsh taxa: succulents and grasses. Our findings revealed that propagules emplaced within saltmarsh vegetation immediately landward of the extant mangrove fringe boundary frequently dispersed in the seaward direction. However, propagules moved seaward less frequently and over shorter distances upon encountering boundaries composed of saltmarsh grasses versus succulents. We uniquely confirmed that the small subset of propagules dispersing landward displayed proportionately higher establishment success than those transported seaward. Although impacts of ecotones on plant dispersal have rarely been investigated in situ, our experimental results indicate that the interplay between tidal transport and physical attributes of saltmarsh vegetation influence boundary permeability to propagules, thereby directing the initial phase of shifting mangrove distributions. The incorporation of tidal inundation information and detailed data on landscape features, such as the structure of saltmarsh vegetation at mangrove boundaries, should improve the accuracy of models that are being developed to forecast mangrove distributional shifts in response to sea-level rise.

Vorticity dipoles and a theoretical model of a finite force at the moving contact line singularity

NASA Astrophysics Data System (ADS)

Zhang, Peter; Devoria, Adam; Mohseni, Kamran

2017-11-01

In the well known works of Moffatt (1964) and Huh & Scriven (1971), an infinite force was reported at the moving contact line (MCL) and attributed to a non-integrable stress along the fluid-solid boundary. In our recent investigation of the boundary driven wedge, a model of the MCL, we find that the classical solution theoretically predicts a finite force at the contact line if the forces applied by the two boundaries that make up the corner are taken into consideration. Mathematically, this force can be obtained by the complex contour integral of the holomorphic vorticity-pressure function given by G = μω + ip . Alternatively, this force can also be found using a carefully defined real integral that incorporates the two boundaries. Motivated by this discovery, we have found that the rate of change in circulation, viscous energy dissipation, and viscous energy flux is also finite per unit contact line length. The analysis presented demonstrates that despite a singular stress and a relatively simple geometry, the no-slip semi-infinite wedge is capable of capturing some physical quantities of interest. Furthermore, this result provides a foundation for other challenging topics such as dynamic contact angle.

Thermo-fluid-dynamics of turbulent boundary layer over a moving continuous flat sheet in a parallel free stream

NASA Astrophysics Data System (ADS)

Afzal, Bushra; Noor Afzal Team; Bushra Afzal Team

2014-11-01

The momentum and thermal turbulent boundary layers over a continuous moving sheet subjected to a free stream have been analyzed in two layers (inner wall and outer wake) theory at large Reynolds number. The present work is based on open Reynolds equations of momentum and heat transfer without any closure model say, like eddy viscosity or mixing length etc. The matching of inner and outer layers has been carried out by Izakson-Millikan-Kolmogorov hypothesis. The matching for velocity and temperature profiles yields the logarithmic laws and power laws in overlap region of inner and outer layers, along with friction factor and heat transfer laws. The uniformly valid solution for velocity, Reynolds shear stress, temperature and thermal Reynolds heat flux have been proposed by introducing the outer wake functions due to momentum and thermal boundary layers. The comparison with experimental data for velocity profile, temperature profile, skin friction and heat transfer are presented. In outer non-linear layers, the lowest order momentum and thermal boundary layer equations have also been analyses by using eddy viscosity closure model, and results are compared with experimental data. Retired Professor, Embassy Hotel, Rasal Ganj, Aligarh 202001 India.

NASA Ames three-dimensional potential flow analyses system (POTFAN) boundary condition code (BCDN), version 1

NASA Technical Reports Server (NTRS)

Davis, J. E.; Medan, R. T.

1977-01-01

This segment of the POTFAN system is used to generate right hand sides (boundary conditions) of the system of equations associated with the flow field under consideration. These specified flow boundary conditions are encountered in the oblique derivative boundary value problem (boundary value problem of the third kind) and contain the Neumann boundary condition as a special case. Arbitrary angle of attack and/or sideslip and/or rotation rates may be specified, as well as an arbitrary, nonuniform external flow field and the influence of prescribed singularity distributions.

Guidance and flight control law development for hypersonic vehicles

NASA Technical Reports Server (NTRS)

Calise, A. J.; Markopoulos, N.

1993-01-01

During the third reporting period our efforts were focused on a reformulation of the optimal control problem involving active state-variable inequality constraints. In the reformulated problem the optimization is carried out not with respect to all controllers, but only with respect to asymptotic controllers leading to the state constraint boundary. Intimately connected with the traditional formulation is the fact that when the reduced solution for such problems lies on a state constraint boundary, the corresponding boundary layer transitions are of finite time in the stretched time scale. Thus, it has been impossible so far to apply the classical asymptotic boundary layer theory to such problems. Moreover, the traditional formulation leads to optimal controllers that are one-sided, that is, they break down when a disturbance throws the system on the prohibited side of the state constraint boundary.

Comments on numerical solution of boundary value problems of the Laplace equation and calculation of eigenvalues by the grid method

NASA Technical Reports Server (NTRS)

Lyusternik, L. A.

1980-01-01

The mathematics involved in numerically solving for the plane boundary value of the Laplace equation by the grid method is developed. The approximate solution of a boundary value problem for the domain of the Laplace equation by the grid method consists of finding u at the grid corner which satisfies the equation at the internal corners (u=Du) and certain boundary value conditions at the boundary corners.

Boundary regularized integral equation formulation of the Helmholtz equation in acoustics.

PubMed

Sun, Qiang; Klaseboer, Evert; Khoo, Boo-Cheong; Chan, Derek Y C

2015-01-01

A boundary integral formulation for the solution of the Helmholtz equation is developed in which all traditional singular behaviour in the boundary integrals is removed analytically. The numerical precision of this approach is illustrated with calculation of the pressure field owing to radiating bodies in acoustic wave problems. This method facilitates the use of higher order surface elements to represent boundaries, resulting in a significant reduction in the problem size with improved precision. Problems with extreme geometric aspect ratios can also be handled without diminished precision. When combined with the CHIEF method, uniqueness of the solution of the exterior acoustic problem is assured without the need to solve hypersingular integrals.

Boundary regularized integral equation formulation of the Helmholtz equation in acoustics

PubMed Central

Sun, Qiang; Klaseboer, Evert; Khoo, Boo-Cheong; Chan, Derek Y. C.

2015-01-01

A boundary integral formulation for the solution of the Helmholtz equation is developed in which all traditional singular behaviour in the boundary integrals is removed analytically. The numerical precision of this approach is illustrated with calculation of the pressure field owing to radiating bodies in acoustic wave problems. This method facilitates the use of higher order surface elements to represent boundaries, resulting in a significant reduction in the problem size with improved precision. Problems with extreme geometric aspect ratios can also be handled without diminished precision. When combined with the CHIEF method, uniqueness of the solution of the exterior acoustic problem is assured without the need to solve hypersingular integrals. PMID:26064591

Investigation of Saltwater Intrusion and Recirculation of Seawater for Henry Constant Dispersion and Velocity-Dependent Dispersion Problems and Field-Scale Problem

NASA Astrophysics Data System (ADS)

Motz, L. H.; Kalakan, C.

2013-12-01

Three problems regarding saltwater intrusion, namely the Henry constant dispersion and velocity-dependent dispersion problems and a larger, field-scale velocity-dependent dispersion problem, have been investigated to determine quantitatively how saltwater intrusion and the recirculation of seawater at a coastal boundary are related to the freshwater inflow and the density-driven buoyancy flux. Based on dimensional analysis, saltwater intrusion and the recirculation of seawater are dependent functions of the independent ratio of freshwater advective flux relative to the density-driven vertical buoyancy flux, defined as az (or a for an isotropic aquifer), and the aspect ratio of horizontal and vertical dimensions of the cross-section. For the Henry constant dispersion problem, in which the aquifer is isotropic, saltwater intrusion and recirculation are related to an additional independent dimensionless parameter that is the ratio of the constant dispersion coefficient treated as a scalar quantity, the porosity, and the freshwater advective flux, defined as b. For the Henry velocity-dependent dispersion problem, the ratio b is zero, and saltwater intrusion and recirculation are related to an additional independent dimensionless parameter that is the ratio of the vertical and horizontal dispersivities, or rα = αz/αx. For an anisotropic aquifer, saltwater intrusion and recirculation are also dependent on the ratio of vertical and horizontal hydraulic conductivities, or rK = Kz/Kx. For the field-scale velocity-dependent dispersion problem, saltwater intrusion and recirculation are dependent on the same independent ratios as the Henry velocity-dependent dispersion problem. In the two-dimensional cross-section for all three problems, freshwater inflow occurs at an upgradient boundary, and recirculated seawater outflow occurs at a downgradient coastal boundary. The upgradient boundary is a specified-flux boundary with zero freshwater concentration, and the downgradient boundary is a specified-head boundary with a specified concentration equal to seawater. Equivalent freshwater heads are specified at the downstream boundary to account for density differences between freshwater and saltwater at the downstream boundary. The three problems were solved using the numerical groundwater flow and transport code SEAWAT for two conditions, i.e., first for the uncoupled condition in which the fluid density is constant and thus the flow and transport equations are uncoupled in a constant-density flowfield, and then for the coupled condition in which the fluid density is a function of the total dissolved solids concentration and thus the flow and transport equations are coupled in a variable-density flowfield. A wide range of results for the landward extent of saltwater intrusion and the amount of recirculation of seawater at the coastal boundary was obtained by varying the independent dimensionless ratio az (or a in problem one) in all three problems. The dimensionless dispersion ratio b was also varied in problem one, and the dispersivity ratio rα and the hydraulic conductivity ratio rK were also varied in problems two and three.

Integrable boundary value problems for elliptic type Toda lattice in a disk

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guerses, Metin; Habibullin, Ismagil; Zheltukhin, Kostyantyn

The concept of integrable boundary value problems for soliton equations on R and R{sub +} is extended to regions enclosed by smooth curves. Classes of integrable boundary conditions in a disk for the Toda lattice and its reductions are found.

Cognitive mechanisms of insight: the role of heuristics and representational change in solving the eight-coin problem.

PubMed

Öllinger, Michael; Jones, Gary; Faber, Amory H; Knoblich, Günther

2013-05-01

The 8-coin insight problem requires the problem solver to move 2 coins so that each coin touches exactly 3 others. Ormerod, MacGregor, and Chronicle (2002) explained differences in task performance across different versions of the 8-coin problem using the availability of particular moves in a 2-dimensional search space. We explored 2 further explanations by developing 6 new versions of the 8-coin problem in order to investigate the influence of grouping and self-imposed constraints on solutions. The results identified 2 sources of problem difficulty: first, the necessity to overcome the constraint that a solution can be found in 2-dimensional space and, second, the necessity to decompose perceptual groupings. A detailed move analysis suggested that the selection of moves was driven by the established representation rather than the application of the appropriate heuristics. Both results support the assumptions of representational change theory (Ohlsson, 1992).

Estimates of green tensors for certain boundary value problems

NASA Technical Reports Server (NTRS)

Solonnikov, V.

1988-01-01

Consider the first boundary value problem for a stationary Navier-Stokes system in a bounded three-dimensional region Omega with the boundary S: delta v = grad p+f, div v=0, v/s=0. Odqvist (1930) developed the potential theory and formulated the Green tensor for the above problem. The basic singular solution used by Odqvist to express the Green tensor is given. A theorem generalizing his results is presented along with four associated theorems. A specific problem associated with the study of the differential properties of the solution of stationary problems of magnetohydrodynamics is examined.

Laminar supersonic flow over a backstep - A numerical solution at higher Reynolds numbers

NASA Technical Reports Server (NTRS)

Kronzon, Y.; Rom, J.; Seginer, A.

1976-01-01

The Allen-Cheng solution of the flow over a backward facing step is extended to Reynolds numbers up to 16,000 and to inflow boundary-layer height ratios as low as 0.1 by moving the downstream boundary into the recompression region and by smoothing the resulting errors. The boundary conditions in the supersonic outer flow and the downstream boundary conditions in the wake are determined by an extrapolation procedure. Computational results are compared with relevant experimental data. Fair agreement is found between the calculated base pressures and the experimental values, whereas agreement between heat transfer rates appears to be qualitative only.

Boundary effects in a quasi-two-dimensional driven granular fluid.

PubMed

Smith, N D; Smith, M I

2017-12-01

The effect of a confining boundary on the spatial variations in granular temperature of a driven quasi-two-dimensional layer of particles is investigated experimentally. The radial drop in the relative granular temperature ΔT/T exhibits a maximum at intermediate particle numbers which coincides with a crossover from kinetic to collisional transport of energy. It is also found that at low particle numbers, the distributions of radial velocities are increasingly asymmetric as one approaches the boundary. The radial and tangential granular temperatures split, and in the tails of the radial velocity distribution there is a higher population of fast moving particles traveling away rather than towards the boundary.

New Polyazine-Bridged RuII,RhIII and RuII,RhI Supramolecular Photocatalysts for Water Reduction to Hydrogen Applicable for Solar Energy Conversion and Mechanistic Investigation of the Photocatalytic Cycle

NASA Astrophysics Data System (ADS)

Zhou, Rongwei

Underwater gliders are robust and long endurance ocean sampling platforms that are increasingly being deployed in coastal regions. This new environment is characterized by shallow waters and significant currents that can challenge the mobility of these efficient (but traditionally slow moving) vehicles. This dissertation aims to improve the performance of shallow water underwater gliders through path planning. The path planning problem is formulated for a dynamic particle (or "kinematic car") model. The objective is to identify the path which satisfies specified boundary conditions and minimizes a particular cost. Several cost functions are considered. The problem is addressed using optimal control theory. The length scales of interest for path planning are within a few turn radii. First, an approach is developed for planning minimum-time paths, for a fixed speed glider, that are sub-optimal but are guaranteed to be feasible in the presence of unknown time-varying currents. Next the minimum-time problem for a glider with speed controls, that may vary between the stall speed and the maximum speed, is solved. Last, optimal paths that minimize change in depth (equivalently, maximize range) are investigated. Recognizing that path planning alone cannot overcome all of the challenges associated with significant currents and shallow waters, the design of a novel underwater glider with improved capabilities is explored. A glider with a pneumatic buoyancy engine (allowing large, rapid buoyancy changes) and a cylindrical moving mass mechanism (generating large pitch and roll moments) is designed, manufactured, and tested to demonstrate potential improvements in speed and maneuverability.

Towards and FVE-FAC Method for Determining Thermocapillary Effects on Weld Pool Shape

NASA Technical Reports Server (NTRS)

Canright, David; Henson, Van Emden

1996-01-01

Several practical materials processes, e.g., welding, float-zone purification, and Czochralski crystal growth, involve a pool of molten metal with a free surface, with strong temperature gradients along the surface. In some cases, the resulting thermocapillary flow is vigorous enough to convect heat toward the edges of the pool, increasing the driving force in a sort of positive feedback. In this work we examine this mechanism and its effect on the solid-liquid interface through a model problem: a half space of pure substance with concentrated axisymmetric surface heating, where surface tension is strong enough to keep the liquid free surface flat. The numerical method proposed for this problem utilizes a finite volume element (FVE) discretization in cylindrical coordinates. Because of the axisymmetric nature of the model problem, the control volumes used are torroidal prisms, formed by taking a polygonal cross-section in the (r, z) plane and sweeping it completely around the z-axis. Conservation of energy (in the solid), and conservation of energy, momentum, and mass (in the liquid) are enforced globally by integrating these quantities and enforcing conservation over each control volume. Judicious application of the Divergence Theorem and Stokes' Theorem, combined with a Crank-Nicolson time-stepping scheme leads to an implicit algebraic system to be solved at each time step. It is known that near the boundary of the pool, that is, near the solid-liquid interface, the full conduction-convection solution will require extremely fine length scales to resolve the physical behavior of the system. Furthermore, this boundary moves as a function of time. Accordingly, we develop the foundation of an adaptive refinement scheme based on the principles of Fast Adaptive Composite Grid methods (FAC). Implementation of the method and numerical results will appear in a later report.

Comment on “A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition” by A. Aziz, Comm. Nonlinear Sci. Numer. Simul. 2009;14:1064-8

NASA Astrophysics Data System (ADS)

Magyari, Eugen

2011-01-01

In a recent paper published in this Journal the title problem has been investigated numerically. In the present paper the exact solution for the temperature boundary layer is given in terms of the solution of the flow problem (the Blasius problem) in a compact integral form.

Early time evolution of negative ion clouds and electron density depletions produced during electron attachment chemical release experiments

NASA Technical Reports Server (NTRS)

Scales, W. A.; Bernhardt, P. A.; Ganguli, G.

1994-01-01

Two-dimensional electrostatic particle-in-cell simulations are used to study the early time evolution of electron depletions and negative ion clouds produced during electron attachment chemical releases in the ionosphere. The simulation model considers the evolution in the plane perpendicular to the magnetic field and a three-species plasma that contains electrons, positive ions, and also heavy negative ions that result as a by-product of the electron attachment reaction. The early time evolution (less than the negative ion cyclotron period) of the system shows that a negative charge surplus initially develops outside of the depletion boundary as the heavy negative ions move across the boundary. The electrons are initially restricted from moving into the depletion due to the magnetic field. An inhomogenous electric field develops across the boundary layer due to this charge separation. A highly sheared electron flow velocity develops in the depletion boundary due to E x B and Delta-N x B drifts that result from electron density gradients and this inhomogenous electric field. Structure eventually develops in the depletion boundary layer due to low-frequency electrostatic waves that have growth times shorter than the negative ion cyclotron period. It is proposed that these waves are most likely produced by the electron-ion hybrid instability that results from sufficiently large shears in the electron flow velocity.

SIERRA Multimechanics Module: Aria User Manual Version 4.44

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sierra Thermal /Fluid Team

2017-04-01

Aria is a Galerkin fnite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process fows via the incompressible Navier-Stokes equations specialized to a low Reynolds number ( %3C 1 ) regime. Enhanced modeling support of manufacturing processing is made possible through use of eithermore » arbitrary Lagrangian- Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newton's method with analytic or numerical sensitivities, fully-coupled Newton- Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic h -adaptivity and dynamic load balancing are some of Aria's more advanced capabilities. Aria is based upon the Sierra Framework.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sierra Thermal/Fluid Team

Aria is a Galerkin fnite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process fows via the incompressible Navier-Stokes equations specialized to a low Reynolds number ( %3C 1 ) regime. Enhanced modeling support of manufacturing processing is made possible through use of eithermore » arbitrary Lagrangian- Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newton's method with analytic or numerical sensitivities, fully-coupled Newton- Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic h -adaptivity and dynamic load balancing are some of Aria's more advanced capabilities. Aria is based upon the Sierra Framework.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sierra Thermal /Fluid Team

Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process flows via the incompressible Navier-Stokes equations specialized to a low Reynolds number (Re %3C 1) regime. Enhanced modeling support of manufacturing processing is made possible through use of either arbitrarymore » Lagrangian- Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newton's method with analytic or numerical sensitivities, fully-coupled Newton- Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic h-adaptivity and dynamic load balancing are some of Aria's more advanced capabilities. Aria is based upon the Sierra Framework.« less

A boundary element alternating method for two-dimensional mixed-mode fracture problems

NASA Technical Reports Server (NTRS)

Raju, I. S.; Krishnamurthy, T.

1992-01-01

A boundary element alternating method, denoted herein as BEAM, is presented for two dimensional fracture problems. This is an iterative method which alternates between two solutions. An analytical solution for arbitrary polynomial normal and tangential pressure distributions applied to the crack faces of an embedded crack in an infinite plate is used as the fundamental solution in the alternating method. A boundary element method for an uncracked finite plate is the second solution. For problems of edge cracks a technique of utilizing finite elements with BEAM is presented to overcome the inherent singularity in boundary element stress calculation near the boundaries. Several computational aspects that make the algorithm efficient are presented. Finally, the BEAM is applied to a variety of two dimensional crack problems with different configurations and loadings to assess the validity of the method. The method gives accurate stress intensity factors with minimal computing effort.

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

USGS Publications Warehouse

Konikow, Leonard 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.

Substorm injection boundaries. [magnetospheric electric field model

NASA Technical Reports Server (NTRS)

Mcilwain, C. E.

1974-01-01

An improved magnetospheric electric field model is used to compute the initial locations of particles injected by several substorms. Trajectories are traced from the time of their encounter with the ATS-5 satellite backwards to the onset time given by ground-based magnetometers. A spiral shaped inner boundary of injection is found which is quite similar to that found by a statistical analysis. This injection boundary is shown to move in an energy dependent fashion which can explain the soft energy spectra observed at the inner edge of the electrons plasma sheet.

Dynamics of place, boundary and object encoding in rat anterior claustrum

PubMed Central

Jankowski, Maciej M.; O’Mara, Shane M.

2015-01-01

Discrete populations of brain cells signal differing types of spatial information. These “spatial cells” are largely confined to a closely-connected network of sites. We describe here, for the first time, cells in the anterior claustrum of the freely-moving rat encoding place, boundary and object information. This novel claustral spatial signal potentially directly modulates a wide variety of anterior cortical regions. We hypothesize that one of the functions of the claustrum is to provide information about body position, boundaries and landmark information, enabling dynamic control of behavior. PMID:26557060

A system-approach to the elastohydrodynamic lubrication point-contact problem

NASA Technical Reports Server (NTRS)

Lim, Sang Gyu; Brewe, David E.

1991-01-01

The classical EHL (elastohydrodynamic lubrication) point contact problem is solved using a new system-approach, similar to that introduced by Houpert and Hamrock for the line-contact problem. Introducing a body-fitted coordinate system, the troublesome free-boundary is transformed to a fixed domain. The Newton-Raphson method can then be used to determine the pressure distribution and the cavitation boundary subject to the Reynolds boundary condition. This method provides an efficient and rigorous way of solving the EHL point contact problem with the aid of a supercomputer and a promising method to deal with the transient EHL point contact problem. A typical pressure distribution and film thickness profile are presented and the minimum film thicknesses are compared with the solution of Hamrock and Dowson. The details of the cavitation boundaries for various operating parameters are discussed.

Changes in magnetic domain structure during twin boundary motion in single crystal Ni-Mn-Ga exhibiting magnetic shape memory effect

NASA Astrophysics Data System (ADS)

Kopecký, V.; Fekete, L.; Perevertov, O.; Heczko, O.

2016-05-01

The complexity of Ni-Mn-Ga single crystal originates from the interplay between ferromagnetic domain structure and ferroelastic twinned microstructure. Magnetic domain structure in the vicinity of single twin boundary was studied using magneto-optical indicator film and magnetic force microscopy technique. The single twin boundary of Type I was formed mechanically and an initial magnetization state in both variants were restored by local application of magnetic field (≈40 kA/m). The differently oriented variants exhibited either stripe or labyrinth magnetic domain pattern in agreement with the uniaxial magnetocrystalline anisotropy of the martensite. The twin boundary was then moved by compressive or tensile stress. The passage of the boundary resulted in the formation of granular or rake domains, respectively. Additionally, the specific magnetic domains pattern projected by twin boundary gradually vanished during twin boundary motion.

An inverse problem in thermal imaging

NASA Technical Reports Server (NTRS)

Bryan, Kurt; Caudill, Lester F., Jr.

1994-01-01

This paper examines uniqueness and stability results for an inverse problem in thermal imaging. The goal is to identify an unknown boundary of an object by applying a heat flux and measuring the induced temperature on the boundary of the sample. The problem is studied both in the case in which one has data at every point on the boundary of the region and the case in which only finitely many measurements are available. An inversion procedure is developed and used to study the stability of the inverse problem for various experimental configurations.

Ecological and life-history traits explain recent boundary shifts in elevation and latitude of western North American songbirds

Treesearch

Sonya K. Auer; David I. King

2014-01-01

Species are expected to move uphill or poleward in response to climate change, yet their distributions show idiosyncratic responses; many species are moving in the predicted direction, but others are not shifting at all or are shifting downhill or towards the equator. Fundamental questions remain about the causes of interspecific variation in range responses and...

An accurate boundary element method for the exterior elastic scattering problem in two dimensions

NASA Astrophysics Data System (ADS)

Bao, Gang; Xu, Liwei; Yin, Tao

2017-11-01

This paper is concerned with a Galerkin boundary element method solving the two dimensional exterior elastic wave scattering problem. The original problem is first reduced to the so-called Burton-Miller [1] boundary integral formulation, and essential mathematical features of its variational form are discussed. In numerical implementations, a newly-derived and analytically accurate regularization formula [2] is employed for the numerical evaluation of hyper-singular boundary integral operator. A new computational approach is employed based on the series expansions of Hankel functions for the computation of weakly-singular boundary integral operators during the reduction of corresponding Galerkin equations into a discrete linear system. The effectiveness of proposed numerical methods is demonstrated using several numerical examples.

Moving-Boundary Problems Associated with Lyopreservation

NASA Astrophysics Data System (ADS)

Gruber, Christopher Andrew

The work presented in this Dissertation is motivated by research into the preservation of biological specimens by way of vitrification, a technique known as lyopreservation. The operative principle behind lyopreservation is that a glassy material forms as a solution of sugar and water is desiccated. The microstructure of this glass impedes transport within the material, thereby slowing metabolism and effectively halting the aging processes in a biospecimen. This Dissertation is divided into two segments. The first concerns the nature of diffusive transport within a glassy state. Experimental studies suggest that diffusion within a glass is anomalously slow. Scaled Brownian motion (SBM) is proposed as a mathematical model which captures the qualitative features of anomalously slow diffusion while minimizing computational expense. This model is applied to several moving-boundary problems and the results are compared to a more well-established model, fractional anomalous diffusion (FAD). The virtues of SBM are based on the model's relative mathematical simplicity: the governing equation under FAD dynamics involves a fractional derivative operator, which precludes the use of analytical methods in almost all circumstances and also entails great computational expense. In some geometries, SBM allows similarity solutions, though computational methods are generally required. The use of SBM as an approximation to FAD when a system is "nearly classical'' is also explored. The second portion of this Dissertation concerns spin-drying, which is an experimental approach to biopreservation in a laboratory setting. A biospecimen is adhered to a glass wafer and this substrate is covered with sugar solution and rapidly spun on a turntable while water is evaporated from the film surface. The mathematical model for the spin-drying process includes diffusion, viscous fluid flow, and evaporation, among other contributions to the dynamics. Lubrication theory is applied to the model and an expansion in orthogonal polynomials is applied. The resulting system of equations is solved computationally. The influence of various experimental parameters upon the system dynamics is investigated, particularly the role of the spin rate. A convergence study of the solution verifies that the polynomial expansion method yields accurate results.

10 CFR 626.6 - Acquiring oil by direct purchase.

Code of Federal Regulations, 2014 CFR

2014-01-01

... or refining capability, logistical problems for moving petroleum products, macroeconomic factors, and... capability, logistical problems for moving petroleum products, macroeconomic factors, and any other...

10 CFR 626.6 - Acquiring oil by direct purchase.

Code of Federal Regulations, 2012 CFR

2012-01-01

... or refining capability, logistical problems for moving petroleum products, macroeconomic factors, and... capability, logistical problems for moving petroleum products, macroeconomic factors, and any other...

10 CFR 626.6 - Acquiring oil by direct purchase.

Code of Federal Regulations, 2013 CFR

2013-01-01

... or refining capability, logistical problems for moving petroleum products, macroeconomic factors, and... capability, logistical problems for moving petroleum products, macroeconomic factors, and any other...

Three-dimensional analysis of surface crack-Hertzian stress field interaction

NASA Technical Reports Server (NTRS)

Ballarini, R.; Hsu, Y.

1989-01-01

The results are presented of a stress intensity factor analysis of semicircular surface cracks in the inner raceway of an engine bearing. The loading consists of a moving spherical Hertzian contact load and an axial stress due to rotation and shrink fit. A 3-D linear elastic Boundary Element Method code was developed to perform the stress analysis. The element library includes linear and quadratic isoparametric surface elements. Singular quarter point elements were employed to capture the square root displacement variation and the inverse square root stress singularity along the crack front. The program also possesses the capability to separate the whole domain into two subregions. This procedure enables one to solve nonsymmetric fracture mechanics problems without having to separate the crack surfaces a priori. A wide range of configuration parameters was investigated. The ratio of crack depth to bearing thickness was varied from one-sixtieth to one-fifth for several different locations of the Hertzian load. The stress intensity factors for several crack inclinations were also investigated. The results demonstrate the efficiency and accuracy of the Boundary Element Method. Moreover, the results can provide the basis for crack growth calculations and fatigue life prediction.

Completed Beltrami-Michell Formulation for Analyzing Radially Symmetrical Bodies

NASA Technical Reports Server (NTRS)

Kaljevic, Igor; Saigal, Sunil; Hopkins, Dale A.; Patnaik, Surya N.

1994-01-01

A force method formulation, the completed Beltrami-Michell formulation (CBMF), has been developed for analyzing boundary value problems in elastic continua. The CBMF is obtained by augmenting the classical Beltrami-Michell formulation with novel boundary compatibility conditions. It can analyze general elastic continua with stress, displacement, or mixed boundary conditions. The CBMF alleviates the limitations of the classical formulation, which can solve stress boundary value problems only. In this report, the CBMF is specialized for plates and shells. All equations of the CBMF, including the boundary compatibility conditions, are derived from the variational formulation of the integrated force method (IFM). These equations are defined only in terms of stresses. Their solution for kinematically stable elastic continua provides stress fields without any reference to displacements. In addition, a stress function formulation for plates and shells is developed by augmenting the classical Airy's formulation with boundary compatibility conditions expressed in terms of the stress function. The versatility of the CBMF and the augmented stress function formulation is demonstrated through analytical solutions of several mixed boundary value problems. The example problems include a composite circular plate and a composite circular cylindrical shell under the simultaneous actions of mechanical and thermal loads.

Application of boundary integral equations to elastoplastic problems

NASA Technical Reports Server (NTRS)

Mendelson, A.; Albers, L. U.

1975-01-01

The application of boundary integral equations to elastoplastic problems is reviewed. Details of the analysis as applied to torsion problems and to plane problems is discussed. Results are presented for the elastoplastic torsion of a square cross section bar and for the plane problem of notched beams. A comparison of different formulations as well as comparisons with experimental results are presented.

Teaching And Learning Tectonics With Web-GIS

NASA Astrophysics Data System (ADS)

Anastasio, D. J.; Sahagian, D. L.; Bodzin, A.; Teletzke, A. L.; Rutzmoser, S.; Cirucci, L.; Bressler, D.; Burrows, J. E.

2012-12-01

Tectonics is a new curriculum enhancement consisting of six Web GIS investigations designed to augment a traditional middle school Earth science curriculum. The investigations are aligned to Disciplinary Core Ideas: Earth and Space Science from the National Research Council's (2012) Framework for K-12 Science Education and to tectonics benchmark ideas articulated in the AAAS Project 2061 (2007) Atlas of Science Literacy. The curriculum emphasizes geospatial thinking and scientific inquiry and consists of the following modules: Geohazards, which plate boundary is closest to me? How do we recognize plate boundaries? How does thermal energy move around the Earth? What happens when plates diverge? What happens when plate move sideways past each other? What happens when plates collide? The Web GIS interface uses JavaScript for simplicity, intuition, and convenience for implementation on a variety of platforms making it easier for diverse middle school learners and their teachers to conduct authentic Earth science investigations, including multidisciplinary visualization, analysis, and synthesis of data. Instructional adaptations allow students who are English language learners, have disabilities, or are reluctant readers to perform advanced desktop GIS functions including spatial analysis, map visualization and query. The Web GIS interface integrates graphics, multimedia, and animation in addition to newly developed features, which allow users to explore and discover geospatial patterns that would not be easily visible using typical classroom instructional materials. The Tectonics curriculum uses a spatial learning design model that incorporates a related set of frameworks and design principles. The framework builds on the work of other successful technology-integrated curriculum projects and includes, alignment of materials and assessments with learning goals, casting key ideas in real-world problems, engaging students in scientific practices that foster the use of key ideas, uses geospatial technology, and supports for teachers in adopting and implementing GIS and inquiry-based activities.

Variational data assimilation for limited-area models: solution of the open boundary control problem and its application for the Gulf of Finland

NASA Astrophysics Data System (ADS)

Sheloput, Tatiana; Agoshkov, Valery

2017-04-01

The problem of modeling water areas with `liquid' (open) lateral boundaries is discussed. There are different known methods dealing with open boundaries in limited-area models, and one of the most efficient is data assimilation. Although this method is popular, there are not so many articles concerning its implementation for recovering boundary functions. However, the problem of specifying boundary conditions at the open boundary of a limited area is still actual and important. The mathematical model of the Baltic Sea circulation, developed in INM RAS, is considered. It is based on the system of thermo-hydrodynamic equations in the Boussinesq and hydrostatic approximations. The splitting method that is used for time approximation in the model allows to consider the data assimilation problem as a sequence of linear problems. One of such `simple' temperature (salinity) assimilation problem is investigated in the study. Using well known techniques of study and solution of inverse problems and optimal control problems [1], we propose an iterative solution algorithm and we obtain conditions for existence of the solution, for unique and dense solvability of the problem and for convergence of the iterative algorithm. The investigation shows that if observations satisfy certain conditions, the proposed algorithm converges to the solution of the boundary control problem. Particularly, it converges when observational data are given on the `liquid' boundary [2]. Theoretical results are confirmed by the results of numerical experiments. The numerical algorithm was implemented to water area of the Baltic Sea. Two numerical experiments were carried out in the Gulf of Finland: one with the application of the assimilation procedure and the other without. The analyses have shown that the surface temperature field in the first experiment is close to the observed one, while the result of the second experiment misfits. Number of iterations depends on the regularisation parameter, but generally the algorithm converges after 10 iterations. The results of the numerical experiments show that the usage of the proposed method makes sense. The work was supported by the Russian Science Foundation (project 14-11-00609, the formulation of the iterative process and numerical experiments) and by the Russian Foundation for Basic Research (project 16-01-00548, the formulation of the problem and its study). [1] Agoshkov V. I. Methods of Optimal Control and Adjoint Equations in Problems of Mathematical Physics. INM RAS, Moscow, 2003 (in Russian). [2] Agoshkov V.I., Sheloput T.O. The study and numerical solution of the problem of heat and salinity transfer assuming 'liquid' boundaries // Russ. J. Numer. Anal. Math. Modelling. 2016. Vol. 31, No. 2. P. 71-80.

Numerical solution of the electron transport equation

NASA Astrophysics Data System (ADS)

Woods, Mark

The electron transport equation has been solved many times for a variety of reasons. The main difficulty in its numerical solution is that it is a very stiff boundary value problem. The most common numerical methods for solving boundary value problems are symmetric collocation methods and shooting methods. Both of these types of methods can only be applied to the electron transport equation if the boundary conditions are altered with unrealistic assumptions because they require too many points to be practical. Further, they result in oscillating and negative solutions, which are physically meaningless for the problem at hand. For these reasons, all numerical methods for this problem to date are a bit unusual because they were designed to try and avoid the problem of extreme stiffness. This dissertation shows that there is no need to introduce spurious boundary conditions or invent other numerical methods for the electron transport equation. Rather, there already exists methods for very stiff boundary value problems within the numerical analysis literature. We demonstrate one such method in which the fast and slow modes of the boundary value problem are essentially decoupled. This allows for an upwind finite difference method to be applied to each mode as is appropriate. This greatly reduces the number of points needed in the mesh, and we demonstrate how this eliminates the need to define new boundary conditions. This method is verified by showing that under certain restrictive assumptions, the electron transport equation has an exact solution that can be written as an integral. We show that the solution from the upwind method agrees with the quadrature evaluation of the exact solution. This serves to verify that the upwind method is properly solving the electron transport equation. Further, it is demonstrated that the output of the upwind method can be used to compute auroral light emissions.

Equivalence-point electromigration acid-base titration via moving neutralization boundary electrophoresis.

PubMed

Yang, Qing; Fan, Liu-Yin; Huang, Shan-Sheng; Zhang, Wei; Cao, Cheng-Xi

2011-04-01

In this paper, we developed a novel method of acid-base titration, viz. the electromigration acid-base titration (EABT), via a moving neutralization boundary (MNR). With HCl and NaOH as the model strong acid and base, respectively, we conducted the experiments on the EABT via the method of moving neutralization boundary for the first time. The experiments revealed that (i) the concentration of agarose gel, the voltage used and the content of background electrolyte (KCl) had evident influence on the boundary movement; (ii) the movement length was a function of the running time under the constant acid and base concentrations; and (iii) there was a good linearity between the length and natural logarithmic concentration of HCl under the optimized conditions, and the linearity could be used to detect the concentration of acid. The experiments further manifested that (i) the RSD values of intra-day and inter-day runs were less than 1.59 and 3.76%, respectively, indicating similar precision and stability in capillary electrophoresis or HPLC; (ii) the indicators with different pK(a) values had no obvious effect on EABT, distinguishing strong influence on the judgment of equivalence-point titration in the classic one; and (iii) the constant equivalence-point titration always existed in the EABT, rather than the classic volumetric analysis. Additionally, the EABT could be put to good use for the determination of actual acid concentrations. The experimental results achieved herein showed a new general guidance for the development of classic volumetric analysis and element (e.g. nitrogen) content analysis in protein chemistry. Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Stability of semidiscrete approximations for hyperbolic initial-boundary-value problems: Stationary modes

NASA Technical Reports Server (NTRS)

Warming, Robert F.; Beam, Richard M.

1988-01-01

Spatially discrete difference approximations for hyperbolic initial-boundary-value problems (IBVPs) require numerical boundary conditions in addition to the analytical boundary conditions specified for the differential equations. Improper treatment of a numerical boundary condition can cause instability of the discrete IBVP even though the approximation is stable for the pure initial-value or Cauchy problem. In the discrete IBVP stability literature there exists a small class of discrete approximations called borderline cases. For nondissipative approximations, borderline cases are unstable according to the theory of the Gustafsson, Kreiss, and Sundstrom (GKS) but they may be Lax-Richtmyer stable or unstable in the L sub 2 norm on a finite domain. It is shown that borderline approximation can be characterized by the presence of a stationary mode for the finite-domain problem. A stationary mode has the property that it does not decay with time and a nontrivial stationary mode leads to algebraic growth of the solution norm with mesh refinement. An analytical condition is given which makes it easy to detect a stationary mode; several examples of numerical boundary conditions are investigated corresponding to borderline cases.

Nonsteady Problem for an Elastic Half-Plane with Mixed Boundary Conditions

NASA Astrophysics Data System (ADS)

Kubenko, V. D.

2016-03-01

An approach to studying nonstationary wave processes in an elastic half-plane with mixed boundary conditions of the fourth boundary-value problem of elasticity is proposed. The Laplace and Fourier transforms are used. The sequential inversion of these transforms or the inversion of the joint transform by the Cagniard method allows obtaining the required solution (stresses, displacements) in a closed analytic form. With this approach, the problem can be solved for various types of loads

On the Measure and the Structure of the Free Boundary of the Lower Dimensional Obstacle Problem

NASA Astrophysics Data System (ADS)

Focardi, Matteo; Spadaro, Emanuele

2018-04-01

We provide a thorough description of the free boundary for the lower dimensional obstacle problem in R^{n+1} up to sets of null H^{n-1} measure. In particular, we prove (i) local finiteness of the (n-1)-dimensional Hausdorff measure of the free boundary, (ii) H^{n-1}-rectifiability of the free boundary, (iii) classification of the frequencies up to a set of Hausdorff dimension at most (n-2) and classification of the blow-ups at H^{n-1} almost every free boundary point.

Interaction of moving branes with background massless and tachyon fields in superstring theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rezaei, Z., E-mail: z.rezaei@aut.ac.ir; Kamani, D., E-mail: kamani@aut.ac.ir

2012-02-15

Using the boundary state formalism, we study a moving Dp-brane in a partially compact space-time in the presence of background fields: the Kalb-Ramond field B{sub {mu}{nu}}, a U(1) gauge field A{sub {alpha}}, and the tachyon field. The boundary state enables us to obtain the interaction amplitude of two branes with the above back-ground fields. The branes are parallel or perpendicular to each other. Because of the presence of background fields, compactification of some space-time directions, motion of the branes, and the arbitrariness of the dimensions of the branes, the system is rather general. Due to the tachyon fields and velocitiesmore » of the branes, the behavior of the interaction amplitude reveals obvious differences from the conventional behavior.« less

Cherenkov radiation due to the passage of an oscillatory dipole moving parallel to a conducting barrier

DOE Office of Scientific and Technical Information (OSTI.GOV)

De, P.K.

1973-08-01

The Cherenkov radiation emitted by an oscillating dipole moving in a semi-infinite dielectric with a constant velocity along a straight line parallel to the conducting boundary is calculated by using Maxwell's equations. The wave nature of electromagnetic intensities reveals that waves propagate in two modes, and the radiation takes place in the form of two cones which are semicircular in section, the axes of the cones coinciding wiih the path of the dipole. Conditions for the existence of only one cone are given. The intensity of radiation fluctuates spatially. The conducting boundary acts as a promoter and plays an importantmore » role in the graduation of energy loss which is technically important for concentration of radiation. (RWR)« less

A wideband fast multipole boundary element method for half-space/plane-symmetric acoustic wave problems

NASA Astrophysics Data System (ADS)

Zheng, Chang-Jun; Chen, Hai-Bo; Chen, Lei-Lei

2013-04-01

This paper presents a novel wideband fast multipole boundary element approach to 3D half-space/plane-symmetric acoustic wave problems. The half-space fundamental solution is employed in the boundary integral equations so that the tree structure required in the fast multipole algorithm is constructed for the boundary elements in the real domain only. Moreover, a set of symmetric relations between the multipole expansion coefficients of the real and image domains are derived, and the half-space fundamental solution is modified for the purpose of applying such relations to avoid calculating, translating and saving the multipole/local expansion coefficients of the image domain. The wideband adaptive multilevel fast multipole algorithm associated with the iterative solver GMRES is employed so that the present method is accurate and efficient for both lowand high-frequency acoustic wave problems. As for exterior acoustic problems, the Burton-Miller method is adopted to tackle the fictitious eigenfrequency problem involved in the conventional boundary integral equation method. Details on the implementation of the present method are described, and numerical examples are given to demonstrate its accuracy and efficiency.

A boundary-value problem for a first-order hyperbolic system in a two-dimensional domain

NASA Astrophysics Data System (ADS)

Zhura, N. A.; Soldatov, A. P.

2017-06-01

We consider a strictly hyperbolic first-order system of three equations with constant coefficients in a bounded piecewise-smooth domain. The boundary of the domain is assumed to consist of six smooth non-characteristic arcs. A boundary-value problem in this domain is posed by alternately prescribing one or two linear combinations of the components of the solution on these arcs. We show that this problem has a unique solution under certain additional conditions on the coefficients of these combinations, the boundary of the domain and the behaviour of the solution near the characteristics passing through the corner points of the domain.

High order solution of Poisson problems with piecewise constant coefficients and interface jumps

NASA Astrophysics Data System (ADS)

Marques, Alexandre Noll; Nave, Jean-Christophe; Rosales, Rodolfo Ruben

2017-04-01

We present a fast and accurate algorithm to solve Poisson problems in complex geometries, using regular Cartesian grids. We consider a variety of configurations, including Poisson problems with interfaces across which the solution is discontinuous (of the type arising in multi-fluid flows). The algorithm is based on a combination of the Correction Function Method (CFM) and Boundary Integral Methods (BIM). Interface and boundary conditions can be treated in a fast and accurate manner using boundary integral equations, and the associated BIM. Unfortunately, BIM can be costly when the solution is needed everywhere in a grid, e.g. fluid flow problems. We use the CFM to circumvent this issue. The solution from the BIM is used to rewrite the problem as a series of Poisson problems in rectangular domains-which requires the BIM solution at interfaces/boundaries only. These Poisson problems involve discontinuities at interfaces, of the type that the CFM can handle. Hence we use the CFM to solve them (to high order of accuracy) with finite differences and a Fast Fourier Transform based fast Poisson solver. We present 2-D examples of the algorithm applied to Poisson problems involving complex geometries, including cases in which the solution is discontinuous. We show that the algorithm produces solutions that converge with either 3rd or 4th order of accuracy, depending on the type of boundary condition and solution discontinuity.

Partial differential equations of 3D boundary layer and their numerical solutions in turbomachinery

NASA Astrophysics Data System (ADS)

Zhang, Guoqing; Hua, Yaonan; Wu, Chung-Hua

1991-08-01

This paper studies the 3D boundary layer equations (3DBLE) and their numerical solutions in turbomachinery: (1) the general form of 3DBLE in turbomachines with rotational and curvature effects are derived under the semiorthogonal coordinate system, in which the normal pressure gradient is not equal to zero; (2) the method of solution of the 3DBLE is discussed; (3) the 3D boundary layers on the rotating blade surface, IGV endwall, rotor endwall (with a relatively moving boundary) are numerically solved, and the predicted data correlates well with the measured data; and (4) the comparison is made between the numerical results of 3DBLE with and without normal pressure gradient.

Boundary layer flow of air over water on a flat plate

NASA Technical Reports Server (NTRS)

Nelson, John; Alving, Amy E.; Joseph, Daniel D.

1993-01-01

A non-similar boundary layer theory for air blowing over a water layer on a flat plate is formulated and studied as a two-fluid problem in which the position of the interface is unknown. The problem is considered at large Reynolds number (based on x), away from the leading edge. A simple non-similar analytic solution of the problem is derived for which the interface height is proportional to x(sub 1/4) and the water and air flow satisfy the Blasius boundary layer equations, with a linear profile in the water and a Blasius profile in the air. Numerical studies of the initial value problem suggests that this asymptotic, non-similar air-water boundary layer solution is a global attractor for all initial conditions.

Extraction of a group-pair relation: problem-solving relation from web-board documents.

PubMed

Pechsiri, Chaveevan; Piriyakul, Rapepun

2016-01-01

This paper aims to extract a group-pair relation as a Problem-Solving relation, for example a DiseaseSymptom-Treatment relation and a CarProblem-Repair relation, between two event-explanation groups, a problem-concept group as a symptom/CarProblem-concept group and a solving-concept group as a treatment-concept/repair concept group from hospital-web-board and car-repair-guru-web-board documents. The Problem-Solving relation (particularly Symptom-Treatment relation) including the graphical representation benefits non-professional persons by supporting knowledge of primarily solving problems. The research contains three problems: how to identify an EDU (an Elementary Discourse Unit, which is a simple sentence) with the event concept of either a problem or a solution; how to determine a problem-concept EDU boundary and a solving-concept EDU boundary as two event-explanation groups, and how to determine the Problem-Solving relation between these two event-explanation groups. Therefore, we apply word co-occurrence to identify a problem-concept EDU and a solving-concept EDU, and machine-learning techniques to solve a problem-concept EDU boundary and a solving-concept EDU boundary. We propose using k-mean and Naïve Bayes to determine the Problem-Solving relation between the two event-explanation groups involved with clustering features. In contrast to previous works, the proposed approach enables group-pair relation extraction with high accuracy.

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.

Iberian plate kinematics: A jumping plate boundary between Eurasia and Africa

USGS Publications Warehouse

Srivastava, S.P.; Schouten, Hans; Roest, W.R.; Klitgord, Kim D.; Kovacs, L.C.; Verhoef, J.; Macnab, R.

1990-01-01

THE rotation of Iberia and its relation to the formation of the Pyrenees has been difficult to decipher because of the lack of detailed sea-floor spreading data, although several models have been proposed1-7. Here we use detailed aeromagnetic measurements from the sea floor offshore of the Grand Banks of Newfoundland to show that Iberia moved as part of the African plate from late Cretaceous to mid-Eocene time, with a plate boundary extending westward from the Bay of Biscay. When motion along this boundary ceased, a boundary linking extension in the King's Trough to compression along the Pyrenees came into existence. Finally, since the late Oligocene, Iberia has been part of the Eurasian plate, with the boundary between Eurasia and Africa situated along the Azores-Gibraltar fracture zone.

Experimental measurements of unsteady turbulent boundary layers near separation

NASA Technical Reports Server (NTRS)

Simpson, R. L.

1982-01-01

Investigations conducted to document the behavior of turbulent boundary layers on flat surfaces that separate due to adverse pressure gradients are reported. Laser and hot wire anemometers measured turbulence and flow structure of a steady free stream separating turbulent boundary layer produced on the flow of a wind tunnel section. The effects of sinusoidal and unsteadiness of the free stream velocity on this separating turbulent boundary layer at a reduced frequency were determined. A friction gage and a thermal tuft were developed and used to measure the surface skin friction and the near wall fraction of time the flow moves downstream for several cases. Abstracts are provided of several articles which discuss the effects of the periodic free stream unsteadiness on the structure or separating turbulent boundary layers.

Analysis of the incomplete Galerkin method for modelling of smoothly-irregular transition between planar waveguides

NASA Astrophysics Data System (ADS)

Divakov, D.; Sevastianov, L.; Nikolaev, N.

2017-01-01

The paper deals with a numerical solution of the problem of waveguide propagation of polarized light in smoothly-irregular transition between closed regular waveguides using the incomplete Galerkin method. This method consists in replacement of variables in the problem of reduction of the Helmholtz equation to the system of differential equations by the Kantorovich method and in formulation of the boundary conditions for the resulting system. The formulation of the boundary problem for the ODE system is realized in computer algebra system Maple. The stated boundary problem is solved using Maples libraries of numerical methods.

Application of shifted Jacobi pseudospectral method for solving (in)finite-horizon min-max optimal control problems with uncertainty

NASA Astrophysics Data System (ADS)

Nikooeinejad, Z.; Delavarkhalafi, A.; Heydari, M.

2018-03-01

The difficulty of solving the min-max optimal control problems (M-MOCPs) with uncertainty using generalised Euler-Lagrange equations is caused by the combination of split boundary conditions, nonlinear differential equations and the manner in which the final time is treated. In this investigation, the shifted Jacobi pseudospectral method (SJPM) as a numerical technique for solving two-point boundary value problems (TPBVPs) in M-MOCPs for several boundary states is proposed. At first, a novel framework of approximate solutions which satisfied the split boundary conditions automatically for various boundary states is presented. Then, by applying the generalised Euler-Lagrange equations and expanding the required approximate solutions as elements of shifted Jacobi polynomials, finding a solution of TPBVPs in nonlinear M-MOCPs with uncertainty is reduced to the solution of a system of algebraic equations. Moreover, the Jacobi polynomials are particularly useful for boundary value problems in unbounded domain, which allow us to solve infinite- as well as finite and free final time problems by domain truncation method. Some numerical examples are given to demonstrate the accuracy and efficiency of the proposed method. A comparative study between the proposed method and other existing methods shows that the SJPM is simple and accurate.

Impacts of climate change on growth period and planting boundaries of winter wheat in China under RCP4.5 scenario

NASA Astrophysics Data System (ADS)

Sun, Z.; Jia, S. F.; Lv, A. F.; Yang, K. J.; Svensson, J.; Gao, Y. C.

2015-10-01

This paper advances understanding of the impacts of climate change on crops in China by moving from ex-post analysis to forecasting, and by demonstrating how the effects of climate change will affect the growth period and the planting boundaries of winter wheat. Using a multiple regression model based on agricultural meteorological observations and the IPCC AR5 GCMs simulations, we find that the sowing date of winter wheat in the base period, 2040s and 2070s, shows a gradually delayed trend from north to south and the growth period of winter wheat in China will be shortened under climate change. The simulation results also show that (i) the north planting boundaries of winter wheat in China will likely move northward and expand westward in the future, while the south planting boundary will rise and spread in south Hainan and Taiwan; and (ii) the Xinjiang Uygur Autonomous Region and the Inner Mongolia Autonomous Region will have the largest increases in planting areas in 2040s and 2070s. Our simulation implies that Xinjiang and Inner Mongolia are more sensitive to climate change than other regions in China and priority should be given to design adaptation strategies for winter wheat planting for these provinces.

Construction Method of Analytical Solutions to the Mathematical Physics Boundary Problems for Non-Canonical Domains

NASA Astrophysics Data System (ADS)

Mobarakeh, Pouyan Shakeri; Grinchenko, Victor T.

2015-06-01

The majority of practical cases of acoustics problems requires solving the boundary problems in non-canonical domains. Therefore construction of analytical solutions of mathematical physics boundary problems for non-canonical domains is both lucrative from the academic viewpoint, and very instrumental for elaboration of efficient algorithms of quantitative estimation of the field characteristics under study. One of the main solving ideologies for such problems is based on the superposition method that allows one to analyze a wide class of specific problems with domains which can be constructed as the union of canonically-shaped subdomains. It is also assumed that an analytical solution (or quasi-solution) can be constructed for each subdomain in one form or another. However, this case implies some difficulties in the construction of calculation algorithms, insofar as the boundary conditions are incompletely defined in the intervals, where the functions appearing in the general solution are orthogonal to each other. We discuss several typical examples of problems with such difficulties, we study their nature and identify the optimal methods to overcome them.

Gas evolution from spheres

NASA Astrophysics Data System (ADS)

Longhurst, G. R.

1991-04-01

Gas evolution from spherical solids or liquids where no convective processes are active is analyzed. Three problem classes are considered: (1) constant concentration boundary, (2) Henry's law (first order) boundary, and (3) Sieverts' law (second order) boundary. General expressions are derived for dimensionless times and transport parameters appropriate to each of the classes considered. However, in the second order case, the non-linearities of the problem require the presence of explicit dimensional variables in the solution. Sample problems are solved to illustrate the method.

Mathematics and Statistics Research Department progress report, period ending June 30, 1982

DOE Office of Scientific and Technical Information (OSTI.GOV)

Denson, M.V.; Funderlic, R.E.; Gosslee, D.G.

1982-08-01

This report is the twenty-fifth in the series of progress reports of the Mathematics and Statistics Research Department of the Computer Sciences Division, Union Carbide Corporation Nuclear Division (UCC-ND). Part A records research progress in analysis of large data sets, biometrics research, computational statistics, materials science applications, moving boundary problems, numerical linear algebra, and risk analysis. Collaboration and consulting with others throughout the UCC-ND complex are recorded in Part B. Included are sections on biology, chemistry, energy, engineering, environmental sciences, health and safety, materials science, safeguards, surveys, and the waste storage program. Part C summarizes the various educational activities inmore » which the staff was engaged. Part D lists the presentations of research results, and Part E records the staff's other professional activities during the report period.« less

Mathematics and statistics research department. Progress report, period ending June 30, 1981

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lever, W.E.; Kane, V.E.; Scott, D.S.

1981-09-01

This report is the twenty-fourth in the series of progress reports of the Mathematics and Statistics Research Department of the Computer Sciences Division, Union Carbide Corporation - Nuclear Division (UCC-ND). Part A records research progress in biometrics research, materials science applications, model evaluation, moving boundary problems, multivariate analysis, numerical linear algebra, risk analysis, and complementary areas. Collaboration and consulting with others throughout the UCC-ND complex are recorded in Part B. Included are sections on biology and health sciences, chemistry, energy, engineering, environmental sciences, health and safety research, materials sciences, safeguards, surveys, and uranium resource evaluation. Part C summarizes the variousmore » educational activities in which the staff was engaged. Part D lists the presentations of research results, and Part E records the staff's other professional activities during the report period.« less

A problem of collision avoidance

NASA Technical Reports Server (NTRS)

Vincent, T. L.; Cliff, E. M.; Grantham, W. J.; Peng, W. Y.

1972-01-01

Collision avoidance between two vehicles of constant speed with limited turning radii, moving in a horizontal plane is investigated. Collision avoidance is viewed as a game by assuming that the operator of one vehicle has perfect knowledge of the state of the other, whereas the operator of the second vehicle is unaware of any impending danger. The situation envisioned is that of an encounter between a commercial aircraft and a small light aircraft. This worse case situation is examined to determine the conditions under which the commercial aircraft should execute a collision avoidance maneuver. Three different zones of vulnerability are defined and the boundaries, or barriers, between these zones are determined for a typical aircraft encounter. A discussion of the methods used to obtain the results as well as some of the salient features associated with the resultant barriers is included.

A spatially nonlocal model for polymer-penetrant diffusion

NASA Astrophysics Data System (ADS)

Edwards, D. A.

Diffusion of a penetrant in a polymer entanglement network cannot be described by Fick's Law alone; rather, one must incorporate other nonlocal effects. In contrast to previous viscoelastic models which have modeled these effects through hereditary integrals in time, a new model is presented exploiting the disparate lengths of the polymer in the glassy (dry) and rubbery (saturated) states. This model leads to a partial integrodifferential equation which is nonlocal in space. The system is recast as a moving boundary-value problem between sets of coupled partial differential equations. Using singular perturbation techniques, sorption in a semi-infinite polymer is studied on several time scales with varying exposed interface conditions. Though some of the results match with those from viscoelastic models, new physically relevant behaviors also appear. These include the formation of stopping fronts and overshoot in the pseudostress.

Nonlinear gas oscillations in pipes. I - Theory.

NASA Technical Reports Server (NTRS)

Jimenez, J.

1973-01-01

The problem of forced acoustic oscillations in a pipe is studied theoretically. The oscillations are produced by a moving piston in one end of the pipe, while a variety of boundary conditions ranging from a completely closed to a completely open mouth at the other end are considered. The linear theory predicts large amplitudes near resonance and that nonlinear effects become crucially important. By expanding the equations of motion in a series in the Mach number, both the amplitude and waveform of the oscillation are predicted there. In both the open- and closed-end cases the need for shock waves in some range of parameters is found. The amplitude of the oscillation is different for the two cases, however, being proportional to the square root of the piston amplitude in the closed-end case and to the cube root for the open end.

Primer vector theory applied to the linear relative-motion equations. [for N-impulse space trajectory optimization

NASA Technical Reports Server (NTRS)

Jezewski, D.

1980-01-01

Prime vector theory is used in analyzing a set of linear relative-motion equations - the Clohessy-Wiltshire (C/W) equations - to determine the criteria and necessary conditions for an optimal N-impulse trajectory. The analysis develops the analytical criteria for improving a solution by: (1) moving any dependent or independent variable in the initial and/or final orbit, and (2) adding intermediate impulses. If these criteria are violated, the theory establishes a sufficient number of analytical equations. The subsequent satisfaction of these equations will result in the optimal position vectors and times of an N-impulse trajectory. The solution is examined for the specific boundary conditions of: (1) fixed-end conditions, two impulse, and time-open transfer; (2) an orbit-to-orbit transfer; and (3) a generalized renezvous problem.

[Contemporary family systems--developments, problems, and possibilities].

PubMed

Reich, Günter

2005-12-01

Contemporary forms of family life and their development are described. The thesis of the pluralism of family types as a historical new phenomenon is critically reviewed, with special consideration of the relationship between family life and working world. An increasing move away from the "fordistic model" of family life took place during the last two decades towards the "multilocal multigenerational family". This development is, among others, due to the increased life expectancy and the change in the population structure. Simultaneous to this the boundaries between family and working world become more permeable. If the stability of employments decreases and the mobility of employees increases in a large scale, is discussed controversely. For an increasing number of families it becomes more and more difficult to make flexibility at work compatible with security for the children or to cope with the consequences of unemployment.

Heat and mass transfer enhancement of nanofluids flow in the presence of metallic/metallic-oxides spherical nanoparticles

NASA Astrophysics Data System (ADS)

Qureshi, M. Zubair Akbar; Ali, Kashif; Iqbal, M. Farooq; Ashraf, Muhammad; Ahmad, Shazad

2017-01-01

The numerical study of heat and mass transfer for an incompressible magnetohydrodynamics (MHD) nanofluid flow containing spherical shaped nanoparticles through a channel with moving porous walls is presented. Further, another endeavour is to study the effect of two types of fluids, namely the metallic nanofluid (Au + water) and metallic-oxides nanofluid (TiO2 + water) are studied. The phenomena of spherical metallic and metallic-oxides nanoparticles have been also mathematically modelled by using the Hamilton-Crosser model. The influence of the governing parameters on the flow, heat and mass transfer aspects of the problem is discussed. The outcome of the investigation may be beneficial to the application of biotechnology and industrial purposes. Numerical solutions for the velocity, heat and mass transfer rate at the boundary are obtained and analysed.

An adjoint view on flux consistency and strong wall boundary conditions to the Navier–Stokes equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stück, Arthur, E-mail: arthur.stueck@dlr.de

2015-11-15

Inconsistent discrete expressions in the boundary treatment of Navier–Stokes solvers and in the definition of force objective functionals can lead to discrete-adjoint boundary treatments that are not a valid representation of the boundary conditions to the corresponding adjoint partial differential equations. The underlying problem is studied for an elementary 1D advection–diffusion problem first using a node-centred finite-volume discretisation. The defect of the boundary operators in the inconsistently defined discrete-adjoint problem leads to oscillations and becomes evident with the additional insight of the continuous-adjoint approach. A homogenisation of the discretisations for the primal boundary treatment and the force objective functional yieldsmore » second-order functional accuracy and eliminates the defect in the discrete-adjoint boundary treatment. Subsequently, the issue is studied for aerodynamic Reynolds-averaged Navier–Stokes problems in conjunction with a standard finite-volume discretisation on median-dual grids and a strong implementation of noslip walls, found in many unstructured general-purpose flow solvers. Going out from a base-line discretisation of force objective functionals which is independent of the boundary treatment in the flow solver, two improved flux-consistent schemes are presented; based on either body wall-defined or farfield-defined control-volumes they resolve the dual inconsistency. The behaviour of the schemes is investigated on a sequence of grids in 2D and 3D.« less

A Method of Computing Electric Field Parameters on Boundaries between Two Media

ERIC Educational Resources Information Center

Rizhov, Alexander

2010-01-01

Many problems of electric field strength on a boundary between two media require college-level mathematical analysis. However, when the boundary between media is represented by a sphere or a flat plane, these types of problems can be solved algebraically, placing them within reach of high school students. This article presents a solution analysis…

[Boundaries and integrity in the "Social Contract for Spanish Science", 1907-1939].

PubMed

Gómez, Amparo

2014-01-01

This article analyzes the relationship between science and politics in Spain in the early 20th century from the perspective of the Social Contract for Science. The article shows that a genuine social contract for science was instituted in Spain during this period, although some boundary and integrity problems emerged. These problems are analyzed, showing that the boundary problems were a product of the conservative viewpoint on the relationship between science and politics, while the integrity problems involved the activation of networks of influence in the awarding of scholarships to study abroad. Finally, the analysis reveals that these problems did not invalidate the Spanish social contract for science.

Kinematic Modeling of Central Nepal: Thermochronometer Cooling Ages as a Constraint for Balanced Cross Sections

NASA Astrophysics Data System (ADS)

Olree, E.; Robinson, D. M.; McQuarrie, N.; Ghoshal, S.; Olsen, J.

2016-12-01

Using balanced cross sections, one can visualize a valid and admissible interpretation of the surface and subsurface data. Khanal (2014) and Cross (2014) produced two valid and admissible cross sections along the Marsyandi River in central Nepal. However, thermochronologic data adds another dimension that must be adhered to when producing valid and admissible balanced cross sections. Since the previous cross sections were produced, additional zircon-helium (ZHe) cooling ages along the Marsyandi River show ages of 1 Ma near the Main Central thrust in the hinterland to 4 Ma near the Main Boundary thrust closer to the foreland. This distribution of cooling ages requires recent uplift in the hinterland, which is not present in the cross sections. Although a restored version of the Khanal (2014) cross section is sequentially deformed using 2D Move, the kinematic sequence implied in the cross section is inconsistent with the ZHe age distribution. The hinterland dipping duplex proposed by Khanal would require cooling ages that are oldest near the Main Central thrust and young southwards toward the active ramp located 80 km north of the Main Frontal thrust. Instead, the 4 Ma age near the Main Boundary thrust and the increasingly younger ages to the north could be produced by either a foreland-dipping Lesser Himalayan duplex, which would keep active uplift in the north, or by translation of the hinterland dipping duplex southward over the ramp, moving the active thrust ramp northward. To address this problem, a new balanced cross section was produced using both new mapping through the region and the ZHe age distribution as additional constraints. The section was then restored and sequentially deformed in 2D Move. This study illustrates that multiple cross sections can be viable and admissible; however, they can still be incorrect. Thermochronology places additional constraints on the permissible geometries, and thus increases our ability to predict subsurface geometries. The next step of this project is to link the uplift and erosion implied by the kinematic sequence of the new cross section to the measured cooling history by importing the cross section kinematics into advection diffusion modeling software that predicts cooling ages.

Perceptual organization reconsidered in the light of the watercolor illusion: The problem of perception of holes and the object-hole effect.

PubMed

Pinna, Baingio; Tanca, Maria

2008-05-23

The watercolor illusion is a long-range color assimilation (coloration effect) imparting a figure-ground segregation (figural effect) across large enclosed areas (B. Pinna, 1987; B. Pinna, G. Brelstaff, & L. Spillmann, 2001; B. Pinna, L. Spillmann, & J. S. Werner, 2003; B. Pinna, J. S. Werner, & L. Spillmann, 2003). The watercolored figure has a very poorly reversible or univocal figure-ground segregation and strongly enhances the unilateral belongingness of the boundaries (E. Rubin, 1915), a principle stating that the boundaries belong only to the figure and not to the background. The figural effect determines grouping and figure-ground segregation more strongly than the well-known Gestalt principles. Under watercolor conditions both the figure and the background assume new properties becoming respectively bulging object and hole both with a 3-D volumetric appearance (object-hole effect). Our purposes were: (i) to demonstrate that the hole induced by the watercolor illusion has unique figural properties comparable to those of the object and not present in the background induced by the known figure-ground principles; (ii) to demonstrate a dissociation of the object-hole effect from the coloration one; (iii) to demonstrate that the object-hole effect depends on a new principle. This was psychophysically tested by weakening (ungrouping) the whole figural organization of the watercolor illusion, i.e. by imparting motion to only some components of a stimulus, while other components remain stationary. The results showed that (i) subjects perceived moving holes more strongly than moving figures or objects enlarging and shrinking. (ii) Paradoxically, moving holes appear more as figures than the bulging surfaces. (iii) When motion was imparted to components that while stationary were perceived as objects, their figurality is further enhanced (summation effect). (iv) When object-hole and coloration effects were dissociated no significant difference compared to illusory colored conditions was reported. Coloration can be considered independent from the object-hole effect of the watercolor illusion. The object-hole effect may depend on the "asymmetric luminance contrast principle" (B. Pinna, 2005).

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hintermueller, M., E-mail: hint@math.hu-berlin.de; Kao, C.-Y., E-mail: Ckao@claremontmckenna.edu; Laurain, A., E-mail: laurain@math.hu-berlin.de

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 thresholdmore » 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.« less

A method of boundary equations for unsteady hyperbolic problems in 3D

NASA Astrophysics Data System (ADS)

Petropavlovsky, S.; Tsynkov, S.; Turkel, E.

2018-07-01

We consider interior and exterior initial boundary value problems for the three-dimensional wave (d'Alembert) equation. First, we reduce a given problem to an equivalent operator equation with respect to unknown sources defined only at the boundary of the original domain. In doing so, the Huygens' principle enables us to obtain the operator equation in a form that involves only finite and non-increasing pre-history of the solution in time. Next, we discretize the resulting boundary equation and solve it efficiently by the method of difference potentials (MDP). The overall numerical algorithm handles boundaries of general shape using regular structured grids with no deterioration of accuracy. For long simulation times it offers sub-linear complexity with respect to the grid dimension, i.e., is asymptotically cheaper than the cost of a typical explicit scheme. In addition, our algorithm allows one to share the computational cost between multiple similar problems. On multi-processor (multi-core) platforms, it benefits from what can be considered an effective parallelization in time.

On some problems in a theory of thermally and mechanically interacting continuous media. Ph.D. Thesis; [linearized theory of interacting mixture of elastic solid and viscous fluid

NASA Technical Reports Server (NTRS)

Lee, Y. M.

1971-01-01

Using a linearized theory of thermally and mechanically interacting mixture of linear elastic solid and viscous fluid, we derive a fundamental relation in an integral form called a reciprocity relation. This reciprocity relation relates the solution of one initial-boundary value problem with a given set of initial and boundary data to the solution of a second initial-boundary value problem corresponding to a different initial and boundary data for a given interacting mixture. From this general integral relation, reciprocity relations are derived for a heat-conducting linear elastic solid, and for a heat-conducting viscous fluid. An initial-boundary value problem is posed and solved for the mixture of linear elastic solid and viscous fluid. With the aid of the Laplace transform and the contour integration, a real integral representation for the displacement of the solid constituent is obtained as one of the principal results of the analysis.

A direct force model for Galilean invariant lattice Boltzmann simulation of fluid-particle flows

NASA Astrophysics Data System (ADS)

Tao, Shi; He, Qing; Chen, Baiman; Yang, Xiaoping; Huang, Simin

The lattice Boltzmann method (LBM) has been widely used in the simulation of particulate flows involving complex moving boundaries. Due to the kinetic background of LBM, the bounce-back (BB) rule and the momentum exchange (ME) method can be easily applied to the solid boundary treatment and the evaluation of fluid-solid interaction force, respectively. However, recently it has been found that both the BB and ME schemes may violate the principle of Galilean invariance (GI). Some modified BB and ME methods have been proposed to reduce the GI error. But these remedies have been recognized subsequently to be inconsistent with Newton’s Third Law. Therefore, contrary to those corrections based on the BB and ME methods, a unified iterative approach is adopted to handle the solid boundary in the present study. Furthermore, a direct force (DF) scheme is proposed to evaluate the fluid-particle interaction force. The methods preserve the efficiency of the BB and ME schemes, and the performance on the accuracy and GI is verified and validated in the test cases of particulate flows with freely moving particles.

Numerical Solution of Moving Phase Boundary and Diffusion-Induced Stress of Sn Anode in the Lithium-Ion Battery

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Chun-Hao; Chason, Eric; Guduru, Pradeep R.

Here, we have previously observed a large transient stress in Sn film anodes at the beginning of the Sn-Li 2Sn 5 phase transformation. To understand this behavior, we use numerical modeling to simulate the kinetics of the 1-D moving boundary and Li diffusion in the Sn anodes. A mixture of diffusion-controlled and interface-controlled kinetics is found. The Li concentration in the Li 2Sn 5 phase remains near a steady-state profile as the phase boundary propagates, whereas the Li diffusion in Sn is more complicated. Li continuously diffuses into the Sn layer and produces a supersaturation; the Li can then diffusemore » toward the Sn/Li 2Sn 5 interface and contribute to further phase transformation. Finally, the evolution of Li concentration in the Sn induces strain which involves rate-dependent plasticity and elastic unloading, resulting in the complex stress evolution that is observed. In the long term, the measured stress is dominated by the stress in the growing Li 2Sn 5 phase.« less

Effect of wakes from moving upstream rods on boundary layer separation from a high lift airfoil

NASA Astrophysics Data System (ADS)

Volino, Ralph J.

2011-11-01

Highly loaded airfoils in turbines allow power generation using fewer airfoils. High loading, however, can cause boundary layer separation, resulting in reduced lift and increased aerodynamic loss. Separation is affected by the interaction between rotating blades and stationary vanes. Wakes from upstream vanes periodically impinge on downstream blades, and can reduce separation. The wakes include elevated turbulence, which can induce transition, and a velocity deficit, which results in an impinging flow on the blade surface known as a ``negative jet.'' In the present study, flow through a linear cascade of very high lift airfoils is studied experimentally. Wakes are produced with moving rods which cut through the flow upstream of the airfoils, simulating the effect of upstream vanes. Pressure and velocity fields are documented. Wake spacing and velocity are varied. At low Reynolds numbers without wakes, the boundary layer separates and does not reattach. At high wake passing frequencies separation is largely suppressed. At lower frequencies, ensemble averaged velocity results show intermittent separation and reattachment during the wake passing cycle. Supported by NASA.

Numerical Solution of Moving Phase Boundary and Diffusion-Induced Stress of Sn Anode in the Lithium-Ion Battery

DOE PAGES

Chen, Chun-Hao; Chason, Eric; Guduru, Pradeep R.

2017-08-02

Here, we have previously observed a large transient stress in Sn film anodes at the beginning of the Sn-Li 2Sn 5 phase transformation. To understand this behavior, we use numerical modeling to simulate the kinetics of the 1-D moving boundary and Li diffusion in the Sn anodes. A mixture of diffusion-controlled and interface-controlled kinetics is found. The Li concentration in the Li 2Sn 5 phase remains near a steady-state profile as the phase boundary propagates, whereas the Li diffusion in Sn is more complicated. Li continuously diffuses into the Sn layer and produces a supersaturation; the Li can then diffusemore » toward the Sn/Li 2Sn 5 interface and contribute to further phase transformation. Finally, the evolution of Li concentration in the Sn induces strain which involves rate-dependent plasticity and elastic unloading, resulting in the complex stress evolution that is observed. In the long term, the measured stress is dominated by the stress in the growing Li 2Sn 5 phase.« less

Implementation of a boundary element method to solve for the near field effects of an array of WECs

NASA Astrophysics Data System (ADS)

Oskamp, J. A.; Ozkan-Haller, H. T.

2010-12-01

When Wave Energy Converters (WECs) are installed, they affect the shoreline wave climate by removing some of the wave energy which would have reached the shore. Before large WEC projects are launched, it is important to understand the potential coastal impacts of these installations. The high cost associated with ocean scale testing invites the use of hydrodynamic models to play a major role in estimating these effects. In this study, a wave structure interaction program (WAMIT) is used to model an array of WECs. The program predicts the wave field throughout the array using a boundary element method to solve the potential flow fluid problem, taking into account the incident waves, the power dissipated, and the way each WEC moves and interacts with the others. This model is appropriate for a small domain near the WEC array in order to resolve the details in the interactions, but not extending to the coastline (where the far-field effects must be assessed). To propagate these effects to the coastline, the waves leaving this small domain will be used as boundary conditions for a larger model domain which will assess the shoreline effects caused by the array. The immediate work is concerned with setting up the WAMIT model for a small array of point absorbers. A 1:33 scale lab test is planned and will provide data to validate the WAMIT model on this small domain before it is nested with the larger domain to estimate shoreline effects.

Modeling of oxidation of aluminum nanoparticles by using Cabrera Mott Model

NASA Astrophysics Data System (ADS)

Ramazanova, Zamart; Zyskin, Maxim; Martirosyan, Karen

2012-10-01

Our research focuses on modeling new Nanoenergetic Gas-Generator (NGG) formulations that rapidly release a large amount of gaseous products and generates shock and pressure waves. Nanoenergetic thermite reagents include mixtures of Al and metal oxides such as bismuth trioxide and iodine pentoxide. The research problem is considered a spherically symmetric case and used the Cabrera Mott oxidation model to describe the kinetics of oxide growth on spherical Al nanoparticles for evaluating reaction time which a process of the reaction with oxidizer happens on the outer part of oxide layer of aluminum ions are getting in contact with an oxidizing agent and react. We assumed that a ball of Al of radius 20 to 50 nm is covered by a thin oxide layer 2-4 nm and is surrounded by abundant amount of oxygen stored by oxidizers. The ball is rapidly heated up to ignition temperature to initiate self-sustaining oxidation reaction. As a result highly exothermic reaction is generated. In the oxide layer of excess concentrations of electrons and ions are dependent on the electric field potential with the corresponding of the Gibbs factors and that it conducts to the solution of a nonlinear Poisson equation for the electric field potential in a moving boundary domain. Motion of the boundary is determined by the gradient of a solution on the boundary. We investigated oxidation model numerically, using the COMSOL software utilizing finite element analysis. The computing results demonstrate that oxidation rate increases with the decreasing particle radius.

Lane detection using Randomized Hough Transform

NASA Astrophysics Data System (ADS)

Mongkonyong, Peerawat; Nuthong, Chaiwat; Siddhichai, Supakorn; Yamakita, Masaki

2018-01-01

According to the report of the Royal Thai Police between 2006 and 2015, lane changing without consciousness is one of the most accident causes. To solve this problem, many methods are considered. Lane Departure Warning System (LDWS) is considered to be one of the potential solutions. LDWS is a mechanism designed to warn the driver when the vehicle begins to move out of its current lane. LDWS contains many parts including lane boundary detection, driver warning and lane marker tracking. This article focuses on the lane boundary detection part. The proposed lane boundary detection detects the lines of the image from the input video and selects the lane marker of the road surface from those lines. Standard Hough Transform (SHT) and Randomized Hough Transform (RHT) are considered in this article. They are used to extract lines of an image. SHT extracts the lines from all of the edge pixels. RHT extracts only the lines randomly picked by the point pairs from edge pixels. RHT algorithm reduces the time and memory usage when compared with SHT. The increase of the threshold value in RHT will increase the voted limit of the line that has a high possibility to be the lane marker, but it also consumes the time and memory. By comparison between SHT and RHT with the different threshold values, 500 frames of input video from the front car camera will be processed. The accuracy and the computational time of RHT are similar to those of SHT in the result of the comparison.

The primer vector in linear, relative-motion equations. [spacecraft trajectory optimization

NASA Technical Reports Server (NTRS)

1980-01-01

Primer vector theory is used in analyzing a set of linear, relative-motion equations - the Clohessy-Wiltshire equations - to determine the criteria and necessary conditions for an optimal, N-impulse trajectory. Since the state vector for these equations is defined in terms of a linear system of ordinary differential equations, all fundamental relations defining the solution of the state and costate equations, and the necessary conditions for optimality, can be expressed in terms of elementary functions. The analysis develops the analytical criteria for improving a solution by (1) moving any dependent or independent variable in the initial and/or final orbit, and (2) adding intermediate impulses. If these criteria are violated, the theory establishes a sufficient number of analytical equations. The subsequent satisfaction of these equations will result in the optimal position vectors and times of an N-impulse trajectory. The solution is examined for the specific boundary conditions of (1) fixed-end conditions, two-impulse, and time-open transfer; (2) an orbit-to-orbit transfer; and (3) a generalized rendezvous problem. A sequence of rendezvous problems is solved to illustrate the analysis and the computational procedure.

A Finite Element Method for Simulation of Compressible Cavitating Flows

NASA Astrophysics Data System (ADS)

Shams, Ehsan; Yang, Fan; Zhang, Yu; Sahni, Onkar; Shephard, Mark; Oberai, Assad

2016-11-01

This work focuses on a novel approach for finite element simulations of multi-phase flows which involve evolving interface with phase change. Modeling problems, such as cavitation, requires addressing multiple challenges, including compressibility of the vapor phase, interface physics caused by mass, momentum and energy fluxes. We have developed a mathematically consistent and robust computational approach to address these problems. We use stabilized finite element methods on unstructured meshes to solve for the compressible Navier-Stokes equations. Arbitrary Lagrangian-Eulerian formulation is used to handle the interface motions. Our method uses a mesh adaptation strategy to preserve the quality of the volumetric mesh, while the interface mesh moves along with the interface. The interface jump conditions are accurately represented using a discontinuous Galerkin method on the conservation laws. Condensation and evaporation rates at the interface are thermodynamically modeled to determine the interface velocity. We will present initial results on bubble cavitation the behavior of an attached cavitation zone in a separated boundary layer. We acknowledge the support from Army Research Office (ARO) under ARO Grant W911NF-14-1-0301.

An analytical study of reduced-gravity liquid reorientation using a simplified marker and cell technique

NASA Technical Reports Server (NTRS)

Betts, W. S., Jr.

1972-01-01

A computer program called HOPI was developed to predict reorientation flow dynamics, wherein liquids move from one end of a closed, partially filled, rigid container to the other end under the influence of container acceleration. The program uses the simplified marker and cell numerical technique and, using explicit finite-differencing, solves the Navier-Stokes equations for an incompressible viscous fluid. The effects of turbulence are also simulated in the program. HOPI can consider curved as well as straight walled boundaries. Both free-surface and confined flows can be calculated. The program was used to simulate five liquid reorientation cases. Three of these cases simulated actual NASA LeRC drop tower test conditions while two cases simulated full-scale Centaur tank conditions. It was concluded that while HOPI can be used to analytically determine the fluid motion in a typical settling problem, there is a current need to optimize HOPI. This includes both reducing the computer usage time and also reducing the core storage required for a given size problem.

Correlation of ERTS MSS data and earth coordinate systems

NASA Technical Reports Server (NTRS)

Malila, W. A. (Principal Investigator); Hieber, R. H.; Mccleer, A. P.

1973-01-01

The author has identified the following significant results. Experience has revealed a problem in the analysis and interpretation of ERTS-1 multispectral scanner (MSS) data. The problem is one of accurately correlating ERTS-1 MSS pixels with analysis areas specified on aerial photographs or topographic maps for training recognition computers and/or evaluating recognition results. It is difficult for an analyst to accurately identify which ERTS-1 pixels on a digital image display belong to specific areas and test plots, especially when they are small. A computer-aided procedure to correlate coordinates from topographic maps and/or aerial photographs with ERTS-1 data coordinates has been developed. In the procedure, a map transformation from earth coordinates to ERTS-1 scan line and point numbers is calculated using selected ground control points nad the method of least squares. The map transformation is then applied to the earth coordinates of selected areas to obtain the corresponding ERTS-1 point and line numbers. An optional provision allows moving the boundaries of the plots inward by variable distances so the selected pixels will not overlap adjacent features.

Optimal control, optimization and asymptotic analysis of Purcell's microswimmer model

NASA Astrophysics Data System (ADS)

Wiezel, Oren; Or, Yizhar

2016-11-01

Purcell's swimmer (1977) is a classic model of a three-link microswimmer that moves by performing periodic shape changes. Becker et al. (2003) showed that the swimmer's direction of net motion is reversed upon increasing the stroke amplitude of joint angles. Tam and Hosoi (2007) used numerical optimization in order to find optimal gaits for maximizing either net displacement or Lighthill's energetic efficiency. In our work, we analytically derive leading-order expressions as well as next-order corrections for both net displacement and energetic efficiency of Purcell's microswimmer. Using these expressions enables us to explicitly show the reversal in direction of motion, as well as obtaining an estimate for the optimal stroke amplitude. We also find the optimal swimmer's geometry for maximizing either displacement or energetic efficiency. Additionally, the gait optimization problem is revisited and analytically formulated as an optimal control system with only two state variables, which can be solved using Pontryagin's maximum principle. It can be shown that the optimal solution must follow a "singular arc". Numerical solution of the boundary value problem is obtained, which exactly reproduces Tam and Hosoi's optimal gait.

Can phoretic particles swim in two dimensions?

NASA Astrophysics Data System (ADS)

Sondak, David; Hawley, Cory; Heng, Siyu; Vinsonhaler, Rebecca; Lauga, Eric; Thiffeault, Jean-Luc

2016-12-01

Artificial phoretic particles swim using self-generated gradients in chemical species (self-diffusiophoresis) or charges and currents (self-electrophoresis). These particles can be used to study the physics of collective motion in active matter and might have promising applications in bioengineering. In the case of self-diffusiophoresis, the classical physical model relies on a steady solution of the diffusion equation, from which chemical gradients, phoretic flows, and ultimately the swimming velocity may be derived. Motivated by disk-shaped particles in thin films and under confinement, we examine the extension to two dimensions. Because the two-dimensional diffusion equation lacks a steady state with the correct boundary conditions, Laplace transforms must be used to study the long-time behavior of the problem and determine the swimming velocity. For fixed chemical fluxes on the particle surface, we find that the swimming velocity ultimately always decays logarithmically in time. In the case of finite Péclet numbers, we solve the full advection-diffusion equation numerically and show that this decay can be avoided by the particle moving to regions of unconsumed reactant. Finite advection thus regularizes the two-dimensional phoretic problem.

F-16XL ship #1 - CAWAP boundary layer rakes and hot film on left wing

NASA Technical Reports Server (NTRS)

1996-01-01

This photo shows the boundary layer hot film and the boundary layer rakes on the left wing of NASA's single-seat F-16XL (ship #1) used for the Cranked-Arrow Wing Aerodynamic Project (CAWAP) at Dryden Flight Research Center, Edwards, California. The modified airplane features a delta 'cranked-arrow' wing with strips of tubing along the leading edge to the trailing edge to sense static on the wing and obtain pressure distribution data. The right wing receives data on pressure distribution and the left wing has three types of instrumentation - preston tubes to measure local skin friction, boundary layer rakes to measure boundary layer profiles (the layer where the air interacts with the surfaces of a moving aircraft), and hot films to determine boundary layer transition locations. The first flight of CAWAP occurred on November 21, 1995, and the test program ended in April 1996.

An iterative truncation method for unbounded electromagnetic problems using varying order finite elements

NASA Astrophysics Data System (ADS)

Paul, Prakash

2009-12-01

The finite element method (FEM) is used to solve three-dimensional electromagnetic scattering and radiation problems. Finite element (FE) solutions of this kind contain two main types of error: discretization error and boundary error. Discretization error depends on the number of free parameters used to model the problem, and on how effectively these parameters are distributed throughout the problem space. To reduce the discretization error, the polynomial order of the finite elements is increased, either uniformly over the problem domain or selectively in those areas with the poorest solution quality. Boundary error arises from the condition applied to the boundary that is used to truncate the computational domain. To reduce the boundary error, an iterative absorbing boundary condition (IABC) is implemented. The IABC starts with an inexpensive boundary condition and gradually improves the quality of the boundary condition as the iteration continues. An automatic error control (AEC) is implemented to balance the two types of error. With the AEC, the boundary condition is improved when the discretization error has fallen to a low enough level to make this worth doing. The AEC has these characteristics: (i) it uses a very inexpensive truncation method initially; (ii) it allows the truncation boundary to be very close to the scatterer/radiator; (iii) it puts more computational effort on the parts of the problem domain where it is most needed; and (iv) it can provide as accurate a solution as needed depending on the computational price one is willing to pay. To further reduce the computational cost, disjoint scatterers and radiators that are relatively far from each other are bounded separately and solved using a multi-region method (MRM), which leads to savings in computational cost. A simple analytical way to decide whether the MRM or the single region method will be computationally cheaper is also described. To validate the accuracy and savings in computation time, different shaped metallic and dielectric obstacles (spheres, ogives, cube, flat plate, multi-layer slab etc.) are used for the scattering problems. For the radiation problems, waveguide excited antennas (horn antenna, waveguide with flange, microstrip patch antenna) are used. Using the AEC the peak reduction in computation time during the iteration is typically a factor of 2, compared to the IABC using the same element orders throughout. In some cases, it can be as high as a factor of 4.

The Relation Between Alloy Chemistry and Hot-Cracking

NASA Technical Reports Server (NTRS)

Nunes, A. C., Jr.; Talia, J. E.

2000-01-01

Hot cracking is a problem in welding 2195 aluminum-lithium alloy. Weld wire additives seem to reduce the problem. This study proposes a model intended to clarify the way alloying elements affect hot-cracking. The brittle temperature range of an alloy extends wherever the tensile stress required to move the meniscus of the liquid film at the grain/dendrite boundaries is less than the bulks flow stress Sigma(sub B) of the grains: 2gamma/delta <= sigma(sub B) + P where gamma is boundary film surface tension delta= boundary film thickness P = gas pressure (Some alloys outgas.) If the above condition is not met, the grains deform under stress and the liquid film remains in place. Curves of 2gamma/delta and sigma(sub B) vs. temperature in the range just below the melting temperature determine the hot cracking susceptibility of an alloy. Both are zero at onset of solidification. sigma(sub B) rises as the thermal activation of the slip mechanism is reduced. 2gamma/delta rises as the film thickness delta which can be estimated from the Scheil equation, drops. But, given an embrittled alloy, whether the alloy actually cracks is determined by the strain imposed upon it in the embrittled condition. A critical strain is estimated, Epsilon(sub C) on the order of Epsilon(sub C) is approximately delta/l where L = grain size and where the the volume increment due to the strain, concentrated at the liquid film, is on the order of the liquid film volume. In the early 80's an empirical critical strain cracking envelope Epsilon(sub C)(T) was incorporated into a damage criterion to estimate the effect of welding parameters on the formation of microfissures in a superalloy with good results. These concepts, liquid film decoherence vs. grain bulk deformation and critical strain, form the key elements of a quantitative theory of hot-cracking applicable for assessing the effect of alloying elements on hot-cracking during welding.

Introducing Differential Equations Students to the Fredholm Alternative--In Staggered Doses

ERIC Educational Resources Information Center

Savoye, Philippe

2011-01-01

The development, in an introductory differential equations course, of boundary value problems in parallel with initial value problems and the Fredholm Alternative. Examples are provided of pairs of homogeneous and nonhomogeneous boundary value problems for which existence and uniqueness issues are considered jointly. How this heightens students'…

Digital structural interpretation of mountain-scale photogrammetric 3D models (Kamnik Alps, Slovenia)

NASA Astrophysics Data System (ADS)

Dolžan, Erazem; Vrabec, Marko

2015-04-01

From the earliest days of geological science, mountainous terrains with their extreme topographic relief and sparse to non-existent vegetation were utilized to a great advantage for gaining 3D insight into geological structure. But whereas Alpine vistas may offer perfect panoramic views of geology, the steep mountain slopes and vertical cliffs make it very time-consuming and difficult (if not impossible) to acquire quantitative mapping data such as precisely georeferenced traces of geological boundaries and attitudes of structural planes. We faced this problem in mapping the central Kamnik Alps of northern Slovenia, which are built up from Mid to Late Triassic succession of carbonate rocks. Polyphase brittle tectonic evolution, monotonous lithology and the presence of temporally and spatially irregular facies boundary between bedded platform carbonates and massive reef limestones considerably complicate the structural interpretation of otherwise perfectly exposed, but hardly accessible massif. We used Agisoft Photoscan Structure-from-Motion photogrammetric software to process a series of overlapping high-resolution (~0.25 m ground resolution) vertical aerial photographs originally acquired by the Geodetic Authority of the Republic of Slovenia for surveying purposes, to derive very detailed 3D triangular mesh models of terrain and associated photographic textures. Phototextures are crucial for geological interpretation of the models as they provide additional levels of detail and lithological information which is not resolvable from geometrical mesh models alone. We then exported the models to Paradigm Gocad software to refine and optimize the meshing. Structural interpretation of the models, including mapping of traces and surfaces of faults and stratigraphic boundaries and determining dips of structural planes, was performed in MVE Move suite which offers a range of useful tools for digital mapping and interpretation. Photogrammetric model was complemented by georeferenced geological field data acquired along mountain trail transects, mainly using the MVE Field Move software application. In our experience, vertical aerophotos were sufficient to generate precise surface models in all but the steepest mountain cliffs. Therefore, using existing vertical photoimagery (where available) is a very cost-effective alternative to organizing shooting campaigns with rented aircraft. For handling reasonably large models (cca 3 x 3 km, up to 10 million triangles), a low-end computer workstation with mid-range professional 3D graphic card is sufficient. The biggest bottleneck is the photogrammetric processing step which is time-consuming (10s of hrs) and has large RAM requirements, although those can be offset by dividing models into smaller parts. The major problem with geological modeling software like Gocad or Move is that it at present does not handle well projecting of phototextures. Whereas Photoscan-generated orthophotos can be vertically projected onto mesh models, this results in unacceptable distortions and gaps in subvertical or overhanging parts of the mountain cliff models. A real 3D UV texture mapping method, such as implemented in Photoscan, would be required to realistically model such areas. This limitations notwithstanding, digital geological mapping of photogrammetric models of mountains is a very promising, cost- and time-effective method for rapid structural interpretation and mapping of barren mountainous terrains, particularly when it is complemented by field measurements and observations.

A family of position- and orientation-independent embedded boundary methods for viscous flow and fluid-structure interaction problems

NASA Astrophysics Data System (ADS)

Huang, Daniel Z.; De Santis, Dante; Farhat, Charbel

2018-07-01

The Finite Volume method with Exact two-material Riemann Problems (FIVER) is both a computational framework for multi-material flows characterized by large density jumps, and an Embedded Boundary Method (EBM) for computational fluid dynamics and highly nonlinear Fluid-Structure Interaction (FSI) problems. This paper deals with the EBM aspect of FIVER. For FSI problems, this EBM has already demonstrated the ability to address viscous effects along wall boundaries, and large deformations and topological changes of such boundaries. However, like for most EBMs - also known as immersed boundary methods - the performance of FIVER in the vicinity of a wall boundary can be sensitive with respect to the position and orientation of this boundary relative to the embedding mesh. This is mainly due to ill-conditioning issues that arise when an embedded interface becomes too close to a node of the embedding mesh, which may lead to spurious oscillations in the computed solution gradients at the wall boundary. This paper resolves these issues by introducing an alternative definition of the active/inactive status of a mesh node that leads to the removal of all sources of potential ill-conditioning from all spatial approximations performed by FIVER in the vicinity of a fluid-structure interface. It also makes two additional contributions. The first one is a new procedure for constructing the fluid-structure half Riemann problem underlying the semi-discretization by FIVER of the convective fluxes. This procedure eliminates one extrapolation from the conventional treatment of the wall boundary conditions and replaces it by an interpolation, which improves robustness. The second contribution is a post-processing algorithm for computing quantities of interest at the wall that achieves smoothness in the computed solution and its gradients. Lessons learned from these enhancements and contributions that are triggered by the new definition of the status of a mesh node are then generalized and exploited to eliminate from the original version of the FIVER method its sensitivities with respect to both of the position and orientation of the wall boundary relative to the embedding mesh, while maintaining the original definition of the status of a mesh node. This leads to a family of second-generation FIVER methods whose performance is illustrated in this paper for several flow and FSI problems. These include a challenging flow problem over a bird wing characterized by a feather-induced surface roughness, and a complex flexible flapping wing problem for which experimental data is available.

Locating CVBEM collocation points for steady state heat transfer problems

USGS Publications Warehouse

Hromadka, T.V.

1985-01-01

The Complex Variable Boundary Element Method or CVBEM provides a highly accurate means of developing numerical solutions to steady state two-dimensional heat transfer problems. The numerical approach exactly solves the Laplace equation and satisfies the boundary conditions at specified points on the boundary by means of collocation. The accuracy of the approximation depends upon the nodal point distribution specified by the numerical analyst. In order to develop subsequent, refined approximation functions, four techniques for selecting additional collocation points are presented. The techniques are compared as to the governing theory, representation of the error of approximation on the problem boundary, the computational costs, and the ease of use by the numerical analyst. ?? 1985.

Automatic Control via Thermostats of a Hyperbolic Stefan Problem with Memory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Colli, P.; Grasselli, M.; Sprekels, J.

1999-03-15

A hyperbolic Stefan problem based on the linearized Gurtin-Pipkin heat conduction law is considered. The temperature and free boundary are controlled by a thermostat acting on the boundary. This feedback control is based on temperature measurements performed by real thermal sensors located within the domain containing the two-phase system and/or at its boundary. Three different types of thermostats are analyzed: simple switch, relay switch, and a Preisach hysteresis operator. The resulting models lead to integrodifferential hyperbolic Stefan problems with nonlinear and nonlocal boundary conditions. Existence results are proved in all the cases. Uniqueness is also shown, except in the situationmore » corresponding to the ideal switch.« less

Solutions of the benchmark problems by the dispersion-relation-preserving scheme

NASA Technical Reports Server (NTRS)

Tam, Christopher K. W.; Shen, H.; Kurbatskii, K. A.; Auriault, L.

1995-01-01

The 7-point stencil Dispersion-Relation-Preserving scheme of Tam and Webb is used to solve all the six categories of the CAA benchmark problems. The purpose is to show that the scheme is capable of solving linear, as well as nonlinear aeroacoustics problems accurately. Nonlinearities, inevitably, lead to the generation of spurious short wave length numerical waves. Often, these spurious waves would overwhelm the entire numerical solution. In this work, the spurious waves are removed by the addition of artificial selective damping terms to the discretized equations. Category 3 problems are for testing radiation and outflow boundary conditions. In solving these problems, the radiation and outflow boundary conditions of Tam and Webb are used. These conditions are derived from the asymptotic solutions of the linearized Euler equations. Category 4 problems involved solid walls. Here, the wall boundary conditions for high-order schemes of Tam and Dong are employed. These conditions require the use of one ghost value per boundary point per physical boundary condition. In the second problem of this category, the governing equations, when written in cylindrical coordinates, are singular along the axis of the radial coordinate. The proper boundary conditions at the axis are derived by applying the limiting process of r approaches 0 to the governing equations. The Category 5 problem deals with the numerical noise issue. In the present approach, the time-independent mean flow solution is computed first. Once the residual drops to the machine noise level, the incident sound wave is turned on gradually. The solution is marched in time until a time-periodic state is reached. No exact solution is known for the Category 6 problem. Because of this, the problem is formulated in two totally different ways, first as a scattering problem then as a direct simulation problem. There is good agreement between the two numerical solutions. This offers confidence in the computed results. Both formulations are solved as initial value problems. As such, no Kutta condition is required at the trailing edge of the airfoil.

Revisiting Boundary Perturbation Theory for Inhomogeneous Transport Problems

DOE PAGES

Favorite, Jeffrey A.; Gonzalez, Esteban

2017-03-10

Adjoint-based first-order perturbation theory is applied again to boundary perturbation problems. Rahnema developed a perturbation estimate that gives an accurate first-order approximation of a flux or reaction rate within a radioactive system when the boundary is perturbed. When the response of interest is the flux or leakage current on the boundary, the Roussopoulos perturbation estimate has long been used. The Rahnema and Roussopoulos estimates differ in one term. Our paper shows that the Rahnema and Roussopoulos estimates can be derived consistently, using different responses, from a single variational functional (due to Gheorghiu and Rahnema), resolving any apparent contradiction. In analyticmore » test problems, Rahnema’s estimate and the Roussopoulos estimate produce exact first derivatives of the response of interest when appropriately applied. We also present a realistic, nonanalytic test problem.« less

Non-local sub-characteristic zones of influence in unsteady interactive boundary-layers

NASA Technical Reports Server (NTRS)

Rothmayer, A. P.

1992-01-01

The properties of incompressible, unsteady, interactive, boundary layers are examined for a model hypersonic boundary layer and internal flow past humps or, equivalently, external flow past short-scaled humps. Using a linear high frequency analysis, it is shown that the domains of dependence within the viscous sublayer may be a strong function of position within the sublayer and may be strongly influenced by the pressure displacement interaction, or the prescribed displacement condition. Detailed calculations are presented for the hypersonic boundary layer. This effect is found to carry over directly to the fully viscous problem as well as the nonlinear problem. In the fully viscous problem, the non-local character of the domains of dependence manifests itself in the sub-characteristics. Potential implications of the domain of dependence structure on finite difference computations of unsteady boundary layers are briefly discussed.

Solving free-plasma-boundary problems with the SIESTA MHD code

NASA Astrophysics Data System (ADS)

Sanchez, R.; Peraza-Rodriguez, H.; Reynolds-Barredo, J. M.; Tribaldos, V.; Geiger, J.; Hirshman, S. P.; Cianciosa, M.

2017-10-01

SIESTA is a recently developed MHD equilibrium code designed to perform fast and accurate calculations of ideal MHD equilibria for 3D magnetic configurations. It is an iterative code that uses the solution obtained by the VMEC code to provide a background coordinate system and an initial guess of the solution. The final solution that SIESTA finds can exhibit magnetic islands and stochastic regions. In its original implementation, SIESTA addressed only fixed-boundary problems. This fixed boundary condition somewhat restricts its possible applications. In this contribution we describe a recent extension of SIESTA that enables it to address free-plasma-boundary situations, opening up the possibility of investigating problems with SIESTA in which the plasma boundary is perturbed either externally or internally. As an illustration, the extended version of SIESTA is applied to a configuration of the W7-X stellarator.

Applying the method of fundamental solutions to harmonic problems with singular boundary conditions

NASA Astrophysics Data System (ADS)

Valtchev, Svilen S.; Alves, Carlos J. S.

2017-07-01

The method of fundamental solutions (MFS) is known to produce highly accurate numerical results for elliptic boundary value problems (BVP) with smooth boundary conditions, posed in analytic domains. However, due to the analyticity of the shape functions in its approximation basis, the MFS is usually disregarded when the boundary functions possess singularities. In this work we present a modification of the classical MFS which can be applied for the numerical solution of the Laplace BVP with Dirichlet boundary conditions exhibiting jump discontinuities. In particular, a set of harmonic functions with discontinuous boundary traces is added to the MFS basis. The accuracy of the proposed method is compared with the results form the classical MFS.

Rhetorical Moves in Problem Statement Section of Iranian EFL Postgraduate Students' Theses

ERIC Educational Resources Information Center

Nimehchisalem, Vahid; Tarvirdizadeh, Zahra; Paidary, Sara Sayed; Binti Mat Hussin, Nur Izyan Syamimi

2016-01-01

The Problem Statement (PS) section of a thesis, usually a subsection of the first chapter, is supposed to justify the objectives of the study. Postgraduate students are often ignorant of the rhetorical moves that they are expected to make in their PS. This descriptive study aimed to explore the rhetorical moves of the PS in Iranian master's (MA)…

Bifurcation and stability analysis of rotating chemical spirals in circular domains: Boundary-induced meandering and stabilization

NASA Astrophysics Data System (ADS)

Bär, Markus; Bangia, Anil K.; Kevrekidis, Ioannis G.

2003-05-01

Recent experimental and model studies have revealed that the domain size may strongly influence the dynamics of rotating spirals in two-dimensional pattern forming chemical reactions. Hartmann et al. [Phys. Rev. Lett. 76, 1384 (1996)], report a frequency increase of spirals in circular domains with diameters substantially smaller than the spiral wavelength in a large domain for the catalytic NO+CO reaction on a microstructured platinum surface. Accompanying simulations with a simple reaction-diffusion system reproduced the behavior. Here, we supplement these studies by a numerical bifurcation and stability analysis of rotating spirals in a simple activator-inhibitor model. The problem is solved in a corotating frame of reference. No-flux conditions are imposed at the boundary of the circular domain. At large domain sizes, eigenvalues and eigenvectors very close to those corresponding to infinite medium translational invariance are observed. Upon decrease of domain size, we observe a simultaneous change in the rotation frequency and a deviation of these eigenvalues from being neutrally stable (zero real part). The latter phenomenon indicates that the translation symmetry of the spiral solution is appreciably broken due to the interaction with the (now nearby) wall. Various dynamical regimes are found: first, the spiral simply tries to avoid the boundary and its tip moves towards the center of the circular domain corresponding to a negative real part of the “translational” eigenvalues. This effect is noticeable at a domain radius of R

Dielectric boundary force and its crucial role in gramicidin

NASA Astrophysics Data System (ADS)

Nadler, Boaz; Hollerbach, Uwe; Eisenberg, R. S.

2003-08-01

In an electrostatic problem with nonuniform geometry, a charge Q in one region induces surface charges [called dielectric boundary charges (DBC)] at boundaries between different dielectrics. These induced surface charges, in return, exert a force [called dielectric boundary force (DBF)] on the charge Q that induced them. The DBF is often overlooked. It is not present in standard continuum theories of (point) ions in or near membranes and proteins, such as Gouy-Chapman, Debye-Huckel, Poisson-Boltzmann or Poisson-Nernst- Planck. The DBF is important when a charge Q is near dielectric interfaces, for example, when ions permeate through protein channels embedded in biological membranes. In this paper, we define the DBF and calculate it explicitly for a planar dielectric wall and for a tunnel geometry resembling the ionic channel gramicidin. In general, we formulate the DBF in a form useful for continuum theories, namely, as a solution of a partial differential equation with boundary conditions. The DBF plays a crucial role in the permeation of ions through the gramicidin channel. A positive ion in the channel produces a DBF of opposite sign to that of the fixed charge force (FCF) produced by the permanent charge of the gramicidin polypeptide, and so the net force on the positive ion is reduced. A negative ion creates a DBF of the same sign as the FCF and so the net (repulsive) force on the negative ion is increased. Thus, a positive ion can permeate the channel, while a negative ion is excluded from it. In gramicidin, it is this balance between the FCF and DBF that allows only singly charged positive ions to move into and through the channel. The DBF is not directly responsible, however, for selectivity between the alkali metal ions (e.g., Li+, Na+, K+): we prove that the DBF on a mobile spherical ion is independent of the ion’s radius.

Application of the perturbation iteration method to boundary layer type problems.

PubMed

Pakdemirli, Mehmet

2016-01-01

The recently developed perturbation iteration method is applied to boundary layer type singular problems for the first time. As a preliminary work on the topic, the simplest algorithm of PIA(1,1) is employed in the calculations. Linear and nonlinear problems are solved to outline the basic ideas of the new solution technique. The inner and outer solutions are determined with the iteration algorithm and matched to construct a composite expansion valid within all parts of the domain. The solutions are contrasted with the available exact or numerical solutions. It is shown that the perturbation-iteration algorithm can be effectively used for solving boundary layer type problems.

Re-Innovating Recycling for Turbulent Boundary Layer Simulations

NASA Astrophysics Data System (ADS)

Ruan, Joseph; Blanquart, Guillaume

2017-11-01

Historically, turbulent boundary layers along a flat plate have been expensive to simulate numerically, in part due to the difficulty of initializing the inflow with ``realistic'' turbulence, but also due to boundary layer growth. The former has been resolved in several ways, primarily dedicating a region of at least 10 boundary layer thicknesses in width to rescale and recycle flow or by extending the region far enough downstream to allow a laminar flow to develop into turbulence. Both of these methods are relatively costly. We propose a new method to remove the need for an inflow region, thus reducing computational costs significantly. Leveraging the scale similarity of the mean flow profiles, we introduce a coordinate transformation so that the boundary layer problem can be solved as a parallel flow problem with additional source terms. The solutions in the new coordinate system are statistically homogeneous in the downstream direction and so the problem can be solved with periodic boundary conditions. The present study shows the stability of this method, its implementation and its validation for a few laminar and turbulent boundary layer cases.

Investigations of Compression Shocks and Boundary Layers in Gases Moving at High Speed

NASA Technical Reports Server (NTRS)

Ackeret, J.; Feldmann, F.; Rott, N.

1947-01-01

The mutual influences of compression shocks and friction boundary layers were investigated by means of high speed wind tunnels.Schlieren optics provided a clear picture of the flow phenomena and were used for determining the location of the compression shocks, measurement of shock angles, and also for Mach angles. Pressure measurement and humidity measurements were also taken into consideration.Results along with a mathematical model are described.

A Realistic Framework for Delay-Tolerant Network Routing in Open Terrains with Continuous Churn

NASA Astrophysics Data System (ADS)

Mahendran, Veeramani; Anirudh, Sivaraman K.; Murthy, C. Siva Ram

The conventional analysis of Delay-Tolerant Network (DTN) routing assumes that the terrain over which nodes move is closed implying that when the nodes hit a boundary, they either wrap around or get reflected. In this work, we study the effect of relaxing this closed terrain assumption on the routing performance, where a continuous stream of nodes enter the terrain and get absorbed upon hitting the boundary.

Immersed boundary method for Boltzmann model kinetic equations

NASA Astrophysics Data System (ADS)

Pekardan, Cem; Chigullapalli, Sruti; Sun, Lin; Alexeenko, Alina

2012-11-01

Three different immersed boundary method formulations are presented for Boltzmann model kinetic equations such as Bhatnagar-Gross-Krook (BGK) and Ellipsoidal statistical Bhatnagar-Gross-Krook (ESBGK) model equations. 1D unsteady IBM solution for a moving piston is compared with the DSMC results and 2D quasi-steady microscale gas damping solutions are verified by a conformal finite volume method solver. Transient analysis for a sinusoidally moving beam is also carried out for the different pressure conditions (1 atm, 0.1 atm and 0.01 atm) corresponding to Kn=0.05,0.5 and 5. Interrelaxation method (Method 2) is shown to provide a faster convergence as compared to the traditional interpolation scheme used in continuum IBM formulations. Unsteady damping in rarefied regime is characterized by a significant phase-lag which is not captured by quasi-steady approximations.

Boundary elements; Proceedings of the Fifth International Conference, Hiroshima, Japan, November 8-11, 1983

NASA Astrophysics Data System (ADS)

Brebbia, C. A.; Futagami, T.; Tanaka, M.

The boundary-element method (BEM) in computational fluid and solid mechanics is examined in reviews and reports of theoretical studies and practical applications. Topics presented include the fundamental mathematical principles of BEMs, potential problems, EM-field problems, heat transfer, potential-wave problems, fluid flow, elasticity problems, fracture mechanics, plates and shells, inelastic problems, geomechanics, dynamics, industrial applications of BEMs, optimization methods based on the BEM, numerical techniques, and coupling.

Falling, flapping, flying, swimming,...: High-Re fluid-solid interactions with vortex shedding

NASA Astrophysics Data System (ADS)

Michelin, Sebastien Honore Roland

The coupling between the motion of a solid body and the dynamics of the surrounding flow is essential to the understanding of a large number of engineering and physical problems, from the stability of a slender structure exposed to the wind to the locomotion of insects, birds and fishes. Because of the strong coupling on a moving boundary of the equations for the solid and fluid, the simulation of such problems is computationally challenging and expensive. This justifies the development of simplified models for the fluid-solid interactions to study their physical properties and behavior. This dissertation proposes a reduced-order model for the interaction of a sharp-edged solid body with a strongly unsteady high Reynolds number flow. In such a case, viscous forces in the fluid are often negligible compared to the fluid inertia or the pressure forces, and the thin boundary layers separate from the solid at the edges, leading to the shedding of large and persistent vortices in the solid's wake. A general two-dimensional framework is presented based on complex potential flow theory. The formation of the solid's vortical wake is accounted for by the shedding of point vortices with unsteady intensity from the solid's sharp edges, and the fluid-solid problem is reformulated exclusively as a solid-vortex interaction problem. In the case of a rigid solid body, the coupled problem is shown to reduce to a set of non-linear ordinary differential equations. This model is used to study the effect of vortex shedding on the stability of falling objects. The solid-vortex model is then generalized to study the fluttering instability and non-linear flapping dynamics of flexible plates or flags. The uttering instability and resulting flapping motion result from the competing effects of the fluid forcing and of the solid's flexural rigidity and inertia. Finally, the solid-vortex model is applied to the study of the fundamental effect of bending rigidity on the flapping performance of flapping appendages such as insect wings or fish fins.

On solving wave equations on fixed bounded intervals involving Robin boundary conditions with time-dependent coefficients

NASA Astrophysics Data System (ADS)

van Horssen, Wim T.; Wang, Yandong; Cao, Guohua

2018-06-01

In this paper, it is shown how characteristic coordinates, or equivalently how the well-known formula of d'Alembert, can be used to solve initial-boundary value problems for wave equations on fixed, bounded intervals involving Robin type of boundary conditions with time-dependent coefficients. A Robin boundary condition is a condition that specifies a linear combination of the dependent variable and its first order space-derivative on a boundary of the interval. Analytical methods, such as the method of separation of variables (SOV) or the Laplace transform method, are not applicable to those types of problems. The obtained analytical results by applying the proposed method, are in complete agreement with those obtained by using the numerical, finite difference method. For problems with time-independent coefficients in the Robin boundary condition(s), the results of the proposed method also completely agree with those as for instance obtained by the method of separation of variables, or by the finite difference method.

Cognitive Mechanisms of Insight: The Role of Heuristics and Representational Change in Solving the Eight-Coin Problem

ERIC Educational Resources Information Center

Öllinger, Michael; Jones, Gary; Faber, Amory H.; Knoblich, Günther

2013-01-01

The 8-coin insight problem requires the problem solver to move 2 coins so that each coin touches exactly 3 others. Ormerod, MacGregor, and Chronicle (2002) explained differences in task performance across different versions of the 8-coin problem using the availability of particular moves in a 2-dimensional search space. We explored 2 further…

Boundary-layer development and transition due to free-stream exothermic reactions in shock-induced flows

NASA Technical Reports Server (NTRS)

Hall, J. L.

1974-01-01

A study of the effect of free-stream thermal-energy release from shock-induced exothermic reactions on boundary-layer development and transition is presented. The flow model is that of a boundary layer developing behind a moving shock wave in two-dimensional unsteady flow over a shock-tube wall. Matched sets of combustible hydrogen-oxygen-nitrogen mixtures and inert hydrogen-nitrogen mixtures were used to obtain transition data over a range of transition Reynolds numbers from 1,100,000 to 21,300,000. The heat-energy is shown to significantly stabilize the boundary layer without changing its development character. A method for application of this data to flat-plate steady flows is included.

The behavior of plasma with an arbitrary degree of degeneracy of electron gas in the conductive layer

NASA Astrophysics Data System (ADS)

Latyshev, A. V.; Gordeeva, N. M.

2017-09-01

We obtain an analytic solution of the boundary problem for the behavior (fluctuations) of an electron plasma with an arbitrary degree of degeneracy of the electron gas in the conductive layer in an external electric field. We use the kinetic Vlasov-Boltzmann equation with the Bhatnagar-Gross-Krook collision integral and the Maxwell equation for the electric field. We use the mirror boundary conditions for the reflections of electrons from the layer boundary. The boundary problem reduces to a one-dimensional problem with a single velocity. For this, we use the method of consecutive approximations, linearization of the equations with respect to the absolute distribution of the Fermi-Dirac electrons, and the conservation law for the number of particles. Separation of variables then helps reduce the problem equations to a characteristic system of equations. In the space of generalized functions, we find the eigensolutions of the initial system, which correspond to the continuous spectrum (Van Kampen mode). Solving the dispersion equation, we then find the eigensolutions corresponding to the adjoint and discrete spectra (Drude and Debye modes). We then construct the general solution of the boundary problem by decomposing it into the eigensolutions. The coefficients of the decomposition are given by the boundary conditions. This allows obtaining the decompositions of the distribution function and the electric field in explicit form.

Weak stability of the plasma-vacuum interface problem

NASA Astrophysics Data System (ADS)

Catania, Davide; D'Abbicco, Marcello; Secchi, Paolo

2016-09-01

We consider the free boundary problem for the two-dimensional plasma-vacuum interface in ideal compressible magnetohydrodynamics (MHD). In the plasma region, the flow is governed by the usual compressible MHD equations, while in the vacuum region we consider the Maxwell system for the electric and the magnetic fields. At the free interface, driven by the plasma velocity, the total pressure is continuous and the magnetic field on both sides is tangent to the boundary. We study the linear stability of rectilinear plasma-vacuum interfaces by computing the Kreiss-Lopatinskiĭ determinant of an associated linearized boundary value problem. Apart from possible resonances, we obtain that the piecewise constant plasma-vacuum interfaces are always weakly linearly stable, independently of the size of tangential velocity, magnetic and electric fields on both sides of the characteristic discontinuity. We also prove that solutions to the linearized problem obey an energy estimate with a loss of regularity with respect to the source terms, both in the interior domain and on the boundary, due to the failure of the uniform Kreiss-Lopatinskiĭ condition, as the Kreiss-Lopatinskiĭ determinant associated with this linearized boundary value problem has roots on the boundary of the frequency space. In the proof of the a priori estimates, a crucial part is played by the construction of symmetrizers for a reduced differential system, which has poles at which the Kreiss-Lopatinskiĭ condition may fail simultaneously.

Interweaving Knowledge Resources to Address Complex Environmental Health Challenges.

PubMed

Anderson, Beth Ellen; Naujokas, Marisa F; Suk, William A

2015-11-01

Complex problems do not respect academic disciplinary boundaries. Environmental health research is complex and often moves beyond these boundaries, integrating diverse knowledge resources to solve such challenges. Here we describe an evolving paradigm for interweaving approaches that integrates widely diverse resources outside of traditional academic environments in full partnerships of mutual respect and understanding. We demonstrate that scientists, social scientists, and engineers can work with government agencies, industry, and communities to interweave their expertise into metaphorical knowledge fabrics to share understanding, resources, and enthusiasm. Our goal is to acknowledge and validate how interweaving research approaches can contribute to research-driven, solution-oriented problem solving in environmental health, and to inspire more members of the environmental health community to consider this approach. The National Institutes of Health's National Institute of Environmental Health Sciences Superfund Research Program (SRP), as mandated by Congress, has evolved to become a program that reaches across a wide range of knowledge resources. SRP fosters interweaving multiple knowledge resources to develop innovative multidirectional partnerships for research and training. Here we describe examples of how motivation, ideas, knowledge, and expertise from different people, institutions, and agencies can integrate to tackle challenges that can be as complex as the resources they bring to bear on it. By providing structure for interweaving science with its stakeholders, we are better able to leverage resources, increase potential for innovation, and proactively ensure a more fully developed spectrum of beneficial outcomes of research investments. Anderson BE, Naujokas MF, Suk WA. 2015. Interweaving knowledge resources to address complex environmental health challenges. Environ Health Perspect 123:1095-1099; http://dx.doi.org/10.1289/ehp.1409525.

Initial-boundary value problems associated with the Ablowitz-Ladik system

NASA Astrophysics Data System (ADS)

Xia, Baoqiang; Fokas, A. S.

2018-02-01

We employ the Ablowitz-Ladik system as an illustrative example in order to demonstrate how to analyze initial-boundary value problems for integrable nonlinear differential-difference equations via the unified transform (Fokas method). In particular, we express the solutions of the integrable discrete nonlinear Schrödinger and integrable discrete modified Korteweg-de Vries equations in terms of the solutions of appropriate matrix Riemann-Hilbert problems. We also discuss in detail, for both the above discrete integrable equations, the associated global relations and the process of eliminating of the unknown boundary values.

On Compressible Vortex Sheets

NASA Astrophysics Data System (ADS)

Secchi, Paolo

2005-05-01

We introduce the main known results of the theory of incompressible and compressible vortex sheets. Moreover, we present recent results obtained by the author with J. F. Coulombel about supersonic compressible vortex sheets in two space dimensions. The problem is a nonlinear free boundary hyperbolic problem with two difficulties: the free boundary is characteristic and the Lopatinski condition holds only in a weak sense, yielding losses of derivatives. Under a supersonic condition that precludes violent instabilities, we prove an energy estimate for the boundary value problem obtained by linearization around an unsteady piecewise solution.

Global and blowup solutions of a mixed problem with nonlinear boundary conditions for a one-dimensional semilinear wave equation

NASA Astrophysics Data System (ADS)

Kharibegashvili, S. S.; Jokhadze, O. M.

2014-04-01

A mixed problem for a one-dimensional semilinear wave equation with nonlinear boundary conditions is considered. Conditions of this type occur, for example, in the description of the longitudinal oscillations of a spring fastened elastically at one end, but not in accordance with Hooke's linear law. Uniqueness and existence questions are investigated for global and blowup solutions to this problem, in particular how they depend on the nature of the nonlinearities involved in the equation and the boundary conditions. Bibliography: 14 titles.

Boundary Approximation Methods for Sloving Elliptic Problems on Unbounded Domains

NASA Astrophysics Data System (ADS)

Li, Zi-Cai; Mathon, Rudolf

1990-08-01

Boundary approximation methods with partial solutions are presented for solving a complicated problem on an unbounded domain, with both a crack singularity and a corner singularity. Also an analysis of partial solutions near the singular points is provided. These methods are easy to apply, have good stability properties, and lead to highly accurate solutions. Hence, boundary approximation methods with partial solutions are recommended for the treatment of elliptic problems on unbounded domains provided that piecewise solution expansions, in particular, asymptotic solutions near the singularities and infinity, can be found.

A Transition in the Cumulative Reaction Rate of Two Species Diffusion with Bimolecular Reaction

NASA Astrophysics Data System (ADS)

Rajaram, Harihar; Arshadi, Masoud

2015-04-01

Diffusion and bimolecular reaction between two initially separated reacting species is a prototypical small-scale description of reaction induced by transverse mixing. It is also relevant to diffusion controlled transport regimes as encountered in low-permeability matrix blocks in fractured media. In previous work, the reaction-diffusion problem has been analyzed as a Stefan problem involving a distinct moving boundary (reaction front), which predicts that front motion scales as √t, and the cumulative reaction rate scales as 1/√t-. We present a general non-dimensionalization of the problem and a perturbation analysis to show that there is an early time regime where the cumulative reaction rate scales as √t- rather than 1/√t. The duration of this early time regime (where the cumulative rate is kinetically rather than diffusion controlled) depends on the rate parameter, in a manner that is consistently predicted by our non-dimensionalization. We also present results on the scaling of the reaction front width. We present numerical simulations in homogeneous and heterogeneous porous media to demonstrate the limited influence of heterogeneity on the behavior of the reaction-diffusion system. We illustrate applications to the practical problem of in-situ chemical oxidation of TCE and PCE by permanganate, which is employed to remediate contaminated sites where the DNAPLs are largely dissolved in the rock matrix.

Towards Understanding the Mechanism of Receptivity and Bypass Dynamics in Laminar Boundary Layers

NASA Technical Reports Server (NTRS)

Lasseigne, D. G.; Criminale, W. O.; Joslin, R. D.; Jackson, T. L.

1999-01-01

Three problems concerning laminar-turbulent transition are addressed by solving a series of initial value problems. The first problem is the calculation of resonance within the continuous spectrum of the Blasius boundary layer. The second is calculation of the growth of Tollmien-Schlichting waves that are a direct result of disturbances that only lie outside of the boundary layer. And, the third problem is the calculation of non-parallel effects. Together, these problems represent a unified approach to the study of freestream disturbance effects that could lead to transition. Solutions to the temporal, initial-value problem with an inhomogeneous forcing term imposed upon the flow is sought. By solving a series of problems, it is shown that: A transient disturbance lying completely outside of the boundary layer can lead to the growth of an unstable Tollmien-Schlichting wave. A resonance with the continuous spectrum leads to strong amplification that may provide a mechanism for bypass transition once nonlinear effects are considered. A disturbance with a very weak unstable Tollmien-Schlichting wave can lead to a much stronger Tollmien-Schlichting wave downstream, if the original disturbance has a significant portion of its energy in the continuum modes.

Heading off boundary problems: clinical supervision as risk management.

PubMed

Walker, R; Clark, J J

1999-11-01

The effective management of risk in clinical practice includes steps to limit harm to clients resulting from ethical violations or professional misconduct. Boundary problems constitute some of the most damaging ethical violations. The authors propose an active use of clinical supervision to anticipate and head off possible ethical violations by intervening when signs of boundary problems appear. The authors encourage a facilitative, Socratic method, rather than directive approaches, to help supervisees maximize their learning about ethical complexities. Building on the idea of a slippery slope, in which seemingly insignificant acts can lead to unethical patterns of behavior, the authors discuss ten cues to potential boundary problems, including strong feelings about a client; extended sessions with clients; gift giving between clinician and client; loans, barter, and sale of goods; clinician self-disclosures; and touching and sex. The authors outline supervisory interventions to be made when the cues are detected.

Boundary value problem for the solution of magnetic cutoff rigidities and some special applications

NASA Technical Reports Server (NTRS)

Edmonds, Larry

1987-01-01

Since a planet's magnetic field can sometimes provide a spacecraft with some protection against cosmic ray and solar flare particles, it is important to be able to quantify this protection. This is done by calculating cutoff rigidities. An alternate to the conventional method (particle trajectory tracing) is introduced, which is to treat the problem as a boundary value problem. In this approach trajectory tracing is only needed to supply boundary conditions. In some special cases, trajectory tracing is not needed at all because the problem can be solved analytically. A differential equation governing cutoff rigidities is derived for static magnetic fields. The presense of solid objects, which can block a trajectory and other force fields are not included. A few qualititative comments, on existence and uniqueness of solutions, are made which may be useful when deciding how the boundary conditions should be set up. Also included are topics on axially symmetric fields.

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.

Techniques for determining physical zones of influence

DOEpatents

Hamann, Hendrik F; Lopez-Marrero, Vanessa

2013-11-26

Techniques for analyzing flow of a quantity in a given domain are provided. In one aspect, a method for modeling regions in a domain affected by a flow of a quantity is provided which includes the following steps. A physical representation of the domain is provided. A grid that contains a plurality of grid-points in the domain is created. Sources are identified in the domain. Given a vector field that defines a direction of flow of the quantity within the domain, a boundary value problem is defined for each of one or more of the sources identified in the domain. Each of the boundary value problems is solved numerically to obtain a solution for the boundary value problems at each of the grid-points. The boundary problem solutions are post-processed to model the regions affected by the flow of the quantity on the physical representation of the domain.

Extension of the SIESTA MHD equilibrium code to free-plasma-boundary problems

DOE PAGES

Peraza-Rodriguez, Hugo; Reynolds-Barredo, J. M.; Sanchez, Raul; ...

2017-08-28

Here, SIESTA is a recently developed MHD equilibrium code designed to perform fast and accurate calculations of ideal MHD equilibria for three-dimensional magnetic configurations. Since SIESTA does not assume closed magnetic surfaces, the solution can exhibit magnetic islands and stochastic regions. In its original implementation SIESTA addressed only fixed-boundary problems. That is, the shape of the plasma edge, assumed to be a magnetic surface, was kept fixed as the solution iteratively converges to equilibrium. This condition somewhat restricts the possible applications of SIESTA. In this paper we discuss an extension that will enable SIESTA to address free-plasma-boundary problems, opening upmore » the possibility of investigating problems in which the plasma boundary is perturbed either externally or internally. As an illustration, SIESTA is applied to a configuration of the W7-X stellarator.« less

Extension of the SIESTA MHD equilibrium code to free-plasma-boundary problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Peraza-Rodriguez, Hugo; Reynolds-Barredo, J. M.; Sanchez, Raul

Here, SIESTA is a recently developed MHD equilibrium code designed to perform fast and accurate calculations of ideal MHD equilibria for three-dimensional magnetic configurations. Since SIESTA does not assume closed magnetic surfaces, the solution can exhibit magnetic islands and stochastic regions. In its original implementation SIESTA addressed only fixed-boundary problems. That is, the shape of the plasma edge, assumed to be a magnetic surface, was kept fixed as the solution iteratively converges to equilibrium. This condition somewhat restricts the possible applications of SIESTA. In this paper we discuss an extension that will enable SIESTA to address free-plasma-boundary problems, opening upmore » the possibility of investigating problems in which the plasma boundary is perturbed either externally or internally. As an illustration, SIESTA is applied to a configuration of the W7-X stellarator.« less

Bifurcation approach to a logistic elliptic equation with a homogeneous incoming flux boundary condition

NASA Astrophysics Data System (ADS)

Umezu, Kenichiro

In this paper, we consider a semilinear elliptic boundary value problem in a smooth bounded domain, having the so-called logistic nonlinearity that originates from population dynamics, with a nonlinear boundary condition. Although the logistic nonlinearity has an absorption effect in the problem, the nonlinear boundary condition is induced by the homogeneous incoming flux on the boundary. The objective of our study is to analyze the existence of a bifurcation component of positive solutions from trivial solutions and its asymptotic behavior and stability. We perform this analysis using the method developed by Lyapunov and Schmidt, based on a scaling argument.

Some boundary-value problems for anisotropic quarter plane

NASA Astrophysics Data System (ADS)

Arkhypenko, K. M.; Kryvyi, O. F.

2018-04-01

To solve the mixed boundary-value problems of the anisotropic elasticity for the anisotropic quarter plane, a method based on the use of the space of generalized functions {\\Im }{\\prime }({\\text{R}}+2) with slow growth properties was developed. The two-dimensional integral Fourier transform was used to construct the system of fundamental solutions for the anisotropic quarter plane in this space and a system of eight boundary integral relations was obtained, which allows one to reduce the mixed boundary-value problems for the anisotropic quarter plane directly to systems of singular integral equations with fixed singularities. The exact solutions of these systems were found by using the integral Mellin transform. The asymptotic behavior of solutions was investigated at the vertex of the quarter plane.

Multispectral processing based on groups of resolution elements

NASA Technical Reports Server (NTRS)

Richardson, W.; Gleason, J. M.

1975-01-01

Several nine-point rules are defined and compared with previously studied rules. One of the rules performed well in boundary areas, but with reduced efficiency in field interiors; another combined best performance on field interiors with good sensitivity to boundary detail. The basic threshold gradient and some modifications were investigated as a means of boundary point detection. The hypothesis testing methods of closed-boundary formation were also tested and evaluated. An analysis of the boundary detection problem was initiated, employing statistical signal detection and parameter estimation techniques to analyze various formulations of the problem. These formulations permit the atmospheric and sensor system effects on the data to be thoroughly analyzed. Various boundary features and necessary assumptions can also be investigated in this manner.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jo, J.C.; Shin, W.K.; Choi, C.Y.

Transient heat transfer problems with phase changes (Stefan problems) occur in many engineering situations, including potential core melting and solidification during pressurized-water-reactor severe accidents, ablation of thermal shields, melting and solidification of alloys, and many others. This article addresses the numerical analysis of nonlinear transient heat transfer with melting or solidification. An effective and simple procedure is presented for the simulation of the motion of the boundary and the transient temperature field during the phase change process. To accomplish this purpose, an iterative implicit solution algorithm has been developed by employing the dual-reciprocity boundary-element method. The dual-reciprocity boundary-element approach providedmore » in this article is much simpler than the usual boundary-element method in applying a reciprocity principle and an available technique for dealing with the domain integral of the boundary element formulation simultaneously. In this article, attention is focused on two-dimensional melting (ablation)/solidification problems for simplicity. The accuracy and effectiveness of the present analysis method have been illustrated through comparisons of the calculation results of some examples of one-phase ablation/solidification problems with their known semianalytical or numerical solutions where available.« less

Two-phase flows in the formed tornado funnel

NASA Astrophysics Data System (ADS)

Sinkevich, O. A.; Bortsova, A. A.

2017-10-01

At present, it is obvious that the problem of the tornado is important not only for our planetЮ to determine the conditions for the formation of a tornado, it is required to take into account a number of hydrodynamic and plasma processes [1 - 6]. Along to prediction of a tornado generation conditions [1 - 3] it is necessary to evaluate the characteristics of its quasi-stationary motion in a formed funnel: the mass of the moving moist air involved in the funnel and the size and form of the funnel. For a complete description of the phenomena, it is necessary to involve numerical calculations. We note that even for numerical calculations using powerful computers, the problem is very difficult because of the need to calculate multiphase turbulent flows with free, self-organizing boundaries [1, 6]. However, “strict” numerical calculations, it is impossible to do without the use of many, often mutually exclusive, models. For example, how to choice an adequate model of turbulence (algebraic, k-ε model, etc.) or the use of additional, often not accepted, hypotheses about certain processes used in calculations (mechanisms on the nature of moisture condensation, etc.). Therefore, along with numerical calculations of such flows, modeling problems that allow an exact solution and allow to determine the most important and observed characteristics of a tornado.

Two-dimensional CFD modeling of wave rotor flow dynamics

NASA Technical Reports Server (NTRS)

Welch, Gerard E.; Chima, Rodrick V.

1994-01-01

A two-dimensional Navier-Stokes solver developed for detailed study of wave rotor flow dynamics is described. The CFD model is helping characterize important loss mechanisms within the wave rotor. The wave rotor stationary ports and the moving rotor passages are resolved on multiple computational grid blocks. The finite-volume form of the thin-layer Navier-Stokes equations with laminar viscosity are integrated in time using a four-stage Runge-Kutta scheme. Roe's approximate Riemann solution scheme or the computationally less expensive advection upstream splitting method (AUSM) flux-splitting scheme is used to effect upwind-differencing of the inviscid flux terms, using cell interface primitive variables set by MUSCL-type interpolation. The diffusion terms are central-differenced. The solver is validated using a steady shock/laminar boundary layer interaction problem and an unsteady, inviscid wave rotor passage gradual opening problem. A model inlet port/passage charging problem is simulated and key features of the unsteady wave rotor flow field are identified. Lastly, the medium pressure inlet port and high pressure outlet port portion of the NASA Lewis Research Center experimental divider cycle is simulated and computed results are compared with experimental measurements. The model accurately predicts the wave timing within the rotor passages and the distribution of flow variables in the stationary inlet port region.

Two-dimensional CFD modeling of wave rotor flow dynamics

NASA Technical Reports Server (NTRS)

Welch, Gerard E.; Chima, Rodrick V.

1993-01-01

A two-dimensional Navier-Stokes solver developed for detailed study of wave rotor flow dynamics is described. The CFD model is helping characterize important loss mechanisms within the wave rotor. The wave rotor stationary ports and the moving rotor passages are resolved on multiple computational grid blocks. The finite-volume form of the thin-layer Navier-Stokes equations with laminar viscosity are integrated in time using a four-stage Runge-Kutta scheme. The Roe approximate Riemann solution scheme or the computationally less expensive Advection Upstream Splitting Method (AUSM) flux-splitting scheme are used to effect upwind-differencing of the inviscid flux terms, using cell interface primitive variables set by MUSCL-type interpolation. The diffusion terms are central-differenced. The solver is validated using a steady shock/laminar boundary layer interaction problem and an unsteady, inviscid wave rotor passage gradual opening problem. A model inlet port/passage charging problem is simulated and key features of the unsteady wave rotor flow field are identified. Lastly, the medium pressure inlet port and high pressure outlet port portion of the NASA Lewis Research Center experimental divider cycle is simulated and computed results are compared with experimental measurements. The model accurately predicts the wave timing within the rotor passage and the distribution of flow variables in the stationary inlet port region.

Recursive recovery of Markov transition probabilities from boundary value data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Patch, Sarah Kathyrn

1994-04-01

In an effort to mathematically describe the anisotropic diffusion of infrared radiation in biological tissue Gruenbaum posed an anisotropic diffusion boundary value problem in 1989. In order to accommodate anisotropy, he discretized the temporal as well as the spatial domain. The probabilistic interpretation of the diffusion equation is retained; radiation is assumed to travel according to a random walk (of sorts). In this random walk the probabilities with which photons change direction depend upon their previous as well as present location. The forward problem gives boundary value data as a function of the Markov transition probabilities. The inverse problem requiresmore » finding the transition probabilities from boundary value data. Problems in the plane are studied carefully in this thesis. Consistency conditions amongst the data are derived. These conditions have two effects: they prohibit inversion of the forward map but permit smoothing of noisy data. Next, a recursive algorithm which yields a family of solutions to the inverse problem is detailed. This algorithm takes advantage of all independent data and generates a system of highly nonlinear algebraic equations. Pluecker-Grassmann relations are instrumental in simplifying the equations. The algorithm is used to solve the 4 x 4 problem. Finally, the smallest nontrivial problem in three dimensions, the 2 x 2 x 2 problem, is solved.« less

Analytical methods for solving boundary value heat conduction problems with heterogeneous boundary conditions on lines. I - Review

NASA Astrophysics Data System (ADS)

Kartashov, E. M.

1986-10-01

Analytical methods for solving boundary value problems for the heat conduction equation with heterogeneous boundary conditions on lines, on a plane, and in space are briefly reviewed. In particular, the method of dual integral equations and summator series is examined with reference to stationary processes. A table of principal solutions to dual integral equations and pair summator series is proposed which presents the known results in a systematic manner. Newly obtained results are presented in addition to the known ones.