27,442 research outputs found
GRID2D/3D: A computer program for generating grid systems in complex-shaped two- and three-dimensional spatial domains. Part 2: User's manual and program listing
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. The theory and method used in GRID2D/3D is described
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
A generalization of Clausen's identity
The paper aims to generalize Clausen's identity to the square of any Gauss
hypergeometric function. Accordingly, solutions of the related 3rd order linear
differential equation are found in terms of certain bivariate series that can
reduce to 3F2 series similar to those in Clausen's identity. The general
contiguous variation of Clausen's identity is found. The related Chaundy's
identity is generalized without any restriction on the parameters of Gauss
hypergeometric function. The special case of dihedral Gauss hypergeometric
functions is underscored
Recommended from our members
Strain amplitude response and the microstructure of PA/clay nanocomposites
Polyamide 6/clay nanocomposites (PAn, where n is the mass fraction of clay) with various clay loading were prepared by melt compounding in a twin screw extruder. Exfoliation of clay in a PA matrix was confirmed by X-ray diffraction. Strain amplitude response of PAn in both melt and solution states has been investigated. In the melt state, critical strain amplitude of PAn is sensitive to strain amplitude response and decrease logarithmically with increasing clay loading. The elastic moduli (G′) of PAn are reversible under frequency loop sweeps. Comparisons of strain amplitude response in both melt and solution states have been conducted. Two different responses have been observed: strain thinning in the melt state and weak strain overshoot in the solution state. FTIR studies show that amide II band of PAn shifts toward high wavenumbers, but amide I band and N–H stretching vibration are independent of clay loading. We suggest that two types of strain amplitude response of PAn can be explained: strain thinning which is dominant in PAn caused by physical adsorption and entanglement of PA chains on nanoclays and weak strain overshoot caused by weak bonds between PA chains and nanoclays
Solution of an infection model near threshold
We study the Susceptible-Infected-Recovered model of epidemics in the
vicinity of the threshold infectivity. We derive the distribution of total
outbreak size in the limit of large population size . This is accomplished
by mapping the problem to the first passage time of a random walker subject to
a drift that increases linearly with time. We recover the scaling results of
Ben-Naim and Krapivsky that the effective maximal size of the outbreak scales
as , with the average scaling as , with an explicit form for
the scaling function
Invasion threshold in heterogeneous metapopulation networks
We study the dynamics of epidemic and reaction-diffusion processes in
metapopulation models with heterogeneous connectivity pattern. In SIR-like
processes, along with the standard local epidemic threshold, the system
exhibits a global invasion threshold. We provide an explicit expression of the
threshold that sets a critical value of the diffusion/mobility rate below which
the epidemic is not able to spread to a macroscopic fraction of subpopulations.
The invasion threshold is found to be affected by the topological fluctuations
of the metapopulation network. The presented results provide a general
framework for the understanding of the effect of travel restrictions in
epidemic containment.Comment: 4 pages, 2 figure
A Mesolithic settlement site at Howick, Northumberland: a preliminary report
Excavations at a coastal site at Howick during 2000 and 2002 have revealed evidence for a substantial Mesolithic settlement and a Bronze Age cist cemetery. Twenty one radiocarbon determinations of the earlier eighth millennium BP (Cal.) indicate that the Mesolithic site is one of the earliest known in northern Britain. An 8m core of sediment was recovered from stream deposits adjacent to the archaeological site which provides information on local environmental conditions. Howick offers a unique opportunity to understand aspects of hunter-gatherer colonisation and settlement during a period of rapid palaeogeographical change around the margins of the North Sea basin, at a time when it was being progressively inundated by the final stages of the postglacial marine transgression. The cist cemetery will add to the picture of Bronze Age occupation of the coastal strip and again reveals a correlation between the location of Bronze Age and Mesolithic sites which has been observed elsewhere in the region
Effect of Cluster Formation on Isospin Asymmetry in the Liquid-Gas Phase Transition Region
Nuclear matter within the liquid-gas phase transition region is investigated
in a mean-field two-component Fermi-gas model. Following largely analytic
considerations, it is shown that: (1) Due to density dependence of asymmetry
energy, some of the neutron excess from the high-density phase could be
expelled into the low-density region. (2) Formation of clusters in the gas
phase tends to counteract this trend, making the gas phase more liquid-like and
reducing the asymmetry in the gas phase. Flow of asymmetry between the
spectator and midrapidity region in reactions is discussed and a possible
inversion of the flow direction is indicated.Comment: 9 pages,3 figures, RevTe
Development of optical diaphragm deflection sensors
The objective of this project was to develop high-temperature pressure sensors using non-metallic components and optical sensing methods. The sensors are to operate over a temperature range from room temperature approx. 20C to 540C, to respond to internal pressure up to 690 kPa, to respond to external pressure up to 690 kPa, and to withstand external overpressure of 2070 kPa. Project tasks include evaluating sensing techniques and sensor systems. These efforts include materials and sensing method selection, sensor design, sensor fabrication, and sensor testing. Sensors are tested as a function of temperature, pressure, overpressure, and vibration. The project results show that high-temperature pressure sensors based on glass components and optical sensing methods are feasible. The microbend optical diaphragm deflection sensor exhibits the required sensitivity and stability for use as a pressure sensor with temperature compensation. for the microbend sensor, the 95% confidence level deviation of input pressure from the pressure calculated from the overall temperature-compensated calibration equation is 3.7% of full scale. The limitations of the sensors evaluated are primarily due to the restricted temperature range of suitable commercially available optical fibers and the problems associated with glass-to-metal pressure sealing over the entire testing temperature range
- …