1,925 research outputs found
GRID2D/3D: A computer program for generating grid systems in complex-shaped two- and three-dimensional spatial domains. Part 1: Theory and method
An efficient computer program, called GRID2D/3D was developed to generate single and composite grid systems within geometrically complex two- and three-dimensional (2- and 3-D) spatial domains that can deform with time. GRID2D/3D generates single grid systems by using algebraic grid generation methods based on transfinite interpolation in which the distribution of grid points within the spatial domain is controlled by stretching functions. All single grid systems generated by GRID2D/3D can have grid lines that are continuous and differentiable everywhere up to the second-order. Also, grid lines can intersect boundaries of the spatial domain orthogonally. GRID2D/3D generates composite grid systems by patching together two or more single grid systems. The patching can be discontinuous or continuous. For continuous composite grid systems, the grid lines are continuous and differentiable everywhere up to the second-order except at interfaces where different single grid systems meet. At interfaces where different single grid systems meet, the grid lines are only differentiable up to the first-order. For 2-D spatial domains, the boundary curves are described by using either cubic or tension spline interpolation. For 3-D spatial domains, the boundary surfaces are described by using either linear Coon's interpolation, bi-hyperbolic spline interpolation, or a new technique referred to as 3-D bi-directional Hermite interpolation. Since grid systems generated by algebraic methods can have grid lines that overlap one another, GRID2D/3D contains a graphics package for evaluating the grid systems generated. With the graphics package, the user can generate grid systems in an interactive manner with the grid generation part of GRID2D/3D. GRID2D/3D is written in FORTRAN 77 and can be run on any IBM PC, XT, or AT compatible computer. In order to use GRID2D/3D on workstations or mainframe computers, some minor modifications must be made in the graphics part of the program; no modifications are needed in the grid generation part of the program. This technical memorandum describes the theory and method used in GRID2D/3D
Measuring information-transfer delays
In complex networks such as gene networks, traffic systems or brain circuits it is important to understand how long it takes for the different parts of the network to effectively influence one another. In the brain, for example, axonal delays between brain areas can amount to several tens of milliseconds, adding an intrinsic component to any timing-based processing of information. Inferring neural interaction delays is thus needed to interpret the information transfer revealed by any analysis of directed interactions across brain structures. However, a robust estimation of interaction delays from neural activity faces several challenges if modeling assumptions on interaction mechanisms are wrong or cannot be made. Here, we propose a robust estimator for neuronal interaction delays rooted in an information-theoretic framework, which allows a model-free exploration of interactions. In particular, we extend transfer entropy to account for delayed source-target interactions, while crucially retaining the conditioning on the embedded target state at the immediately previous time step. We prove that this particular extension is indeed guaranteed to identify interaction delays between two coupled systems and is the only relevant option in keeping with Wiener’s principle of causality. We demonstrate the performance of our approach in detecting interaction delays on finite data by numerical simulations of stochastic and deterministic processes, as well as on local field potential recordings. We also show the ability of the extended transfer entropy to detect the presence of multiple delays, as well as feedback loops. While evaluated on neuroscience data, we expect the estimator to be useful in other fields dealing with network dynamics
Numerical investigation of the aerodynamic performance for a Wells-type turbine in a wave energy converter
Ocean waves constitute an extensive energy resource, whose extraction
has been the subject of intense research activity in the last three decades. Among the
different variants of Wave Energy Converters, the principle of the Oscillating Water Col- umn (OWC)
is one of the most promising ones. An OWC comprises two key elements: a collector chamber, which
transfers the wave oscillations’ energy to the air within the chamber by back and forth
displacement, and a power take off system, which converts the pneumatic power into electricity or
some other usable form. The Wells turbine is a self-rectifying air turbine, a suitable solution
for energy extraction from reciprocating air flow in an OWC. In the present work, the steady state,
inviscid flow in the Wells turbine is investigated by numerical simulations. The relatively novel
Virtual Multiple Reference Frame (VMRF) technique is used to account for the rotary motion of the
turbine, and
the overall performance is compared with results in the literature
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Improving Performance of M-to-N Processing and Data Redistribution in In Transit Analysis and Visualization
In an in transit setting, a parallel data producer, such as a numerical simulation, runs on one set of ranks M, while a data consumer, such as a parallel visualization application, runs on a different set of ranks N. One of the central challenges in this in transit setting is to determine the mapping of data from the set of M producer ranks to the set of N consumer ranks. This is a challenging problem for several reasons, such as the producer and consumer codes potentially having different scaling characteristics and different data models. The resulting mapping from M to N ranks can have a significant impact on aggregate application performance. In this work, we present an approach for performing this M-to-N mapping in a way that has broad applicability across a diversity of data producer and consumer applications. We evaluate its design and performance with
a study that runs at high concurrency on a modern HPC platform. By leveraging design characteristics, which facilitate an “intelligent” mapping from M-to-N, we observe significant performance gains are possible in terms of several different metrics, including time-to-solution and amount of data moved
Numerical investigation of the aerodynamic performance for a wells-type turbine in a wave energy converter
Ocean waves constitute an extensive energy resource, whose extraction has been the subject of intense research activity in the last three decades. Among the different variants of Wave Energy Converters, the principle of the Oscillating Water Column (OWC) is one of the most promising ones. An OWC comprises two key elements: A collector chamber, which transfers the wave oscillations' energy to the air within the chamber by back and forth displacement, and a power take off system, which converts the pneumatic power into electricity or some other usable form. The Wells turbine is a self-rectifying air turbine, a suitable solution for energy extraction from reciprocating air flow in an OWC. In the present work, the steady state, inviscid flow in the Wells turbine is investigated by numerical simulations. The relatively novel Virtual Multiple Reference Frame (VMRF) technique is used to account for the rotary motion of the turbine, and the overall performance is compared with results in the literature
Dispersive and diffusive-dispersive shock waves for nonconvex conservation laws
We consider two physically and mathematically distinct regularization
mechanisms of scalar hyperbolic conservation laws. When the flux is convex, the
combination of diffusion and dispersion are known to give rise to monotonic and
oscillatory traveling waves that approximate shock waves. The zero-diffusion
limits of these traveling waves are dynamically expanding dispersive shock
waves (DSWs). A richer set of wave solutions can be found when the flux is
non-convex. This review compares the structure of solutions of Riemann problems
for a conservation law with non-convex, cubic flux regularized by two different
mechanisms: 1) dispersion in the modified Korteweg--de Vries (mKdV) equation;
and 2) a combination of diffusion and dispersion in the mKdV-Burgers equation.
In the first case, the possible dynamics involve two qualitatively different
types of DSWs, rarefaction waves (RWs) and kinks (monotonic fronts). In the
second case, in addition to RWs, there are traveling wave solutions
approximating both classical (Lax) and non-classical (undercompressive) shock
waves. Despite the singular nature of the zero-diffusion limit and rather
differing analytical approaches employed in the descriptions of dispersive and
diffusive-dispersive regularization, the resulting comparison of the two cases
reveals a number of striking parallels. In contrast to the case of convex flux,
the mKdVB to mKdV mapping is not one-to-one. The mKdV kink solution is
identified as an undercompressive DSW. Other prominent features, such as
shock-rarefactions, also find their purely dispersive counterparts involving
special contact DSWs, which exhibit features analogous to contact
discontinuities. This review describes an important link between two major
areas of applied mathematics, hyperbolic conservation laws and nonlinear
dispersive waves.Comment: Revision from v2; 57 pages, 19 figure
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