2,395 research outputs found
Hydraulic flow through a channel contraction: multiple steady states
We have investigated shallow water flows through a channel with a contraction by experimental and theoretical means. The horizontal channel consists of a sluice gate and an upstream channel of constant width ending in a linear contraction of minimum width . Experimentally, we observe upstream steady and moving bores/shocks, and oblique waves in the contraction, as single and multiple steady states, as well as a steady reservoir with a complex hydraulic jump in the contraction occurring in a small section of the and Froude number parameter plane. One-dimensional hydraulic theory provides a comprehensive leading-order approximation, in which a turbulent frictional parametrization is used to achieve quantitative agreement. An analytical and numerical analysis is given for two-dimensional supercritical shallow water flows. It shows that the one-dimensional hydraulic analysis for inviscid flows away from hydraulic jumps holds surprisingly well, even though the two-dimensional oblique hydraulic jump patterns can show large variations across the contraction channel
The development and technology transfer of software engineering technology at NASA. Johnson Space Center
The United State's big space projects of the next decades, such as Space Station and the Human Exploration Initiative, will need the development of many millions of lines of mission critical software. NASA-Johnson (JSC) is identifying and developing some of the Computer Aided Software Engineering (CASE) technology that NASA will need to build these future software systems. The goal is to improve the quality and the productivity of large software development projects. New trends are outlined in CASE technology and how the Software Technology Branch (STB) at JSC is endeavoring to provide some of these CASE solutions for NASA is described. Key software technology components include knowledge-based systems, software reusability, user interface technology, reengineering environments, management systems for the software development process, software cost models, repository technology, and open, integrated CASE environment frameworks. The paper presents the status and long-term expectations for CASE products. The STB's Reengineering Application Project (REAP), Advanced Software Development Workstation (ASDW) project, and software development cost model (COSTMODL) project are then discussed. Some of the general difficulties of technology transfer are introduced, and a process developed by STB for CASE technology insertion is described
Discrete Feynman-Kac formulas for branching random walks
Branching random walks are key to the description of several physical and
biological systems, such as neutron multiplication, genetics and population
dynamics. For a broad class of such processes, in this Letter we derive the
discrete Feynman-Kac equations for the probability and the moments of the
number of visits of the walker to a given region in the phase space.
Feynman-Kac formulas for the residence times of Markovian processes are
recovered in the diffusion limit.Comment: 4 pages, 3 figure
Boundary driven zero-range processes in random media
The stationary states of boundary driven zero-range processes in random media
with quenched disorder are examined, and the motion of a tagged particle is
analyzed. For symmetric transition rates, also known as the random barrier
model, the stationary state is found to be trivial in absence of boundary
drive. Out of equilibrium, two further cases are distinguished according to the
tail of the disorder distribution. For strong disorder, the fugacity profiles
are found to be governed by the paths of normalized -stable
subordinators. The expectations of integrated functions of the tagged particle
position are calculated for three types of routes.Comment: 23 page
Solution of the Fokker-Planck equation with a logarithmic potential and mixed eigenvalue spectrum
Motivated by a problem in climate dynamics, we investigate the solution of a
Bessel-like process with negative constant drift, described by a Fokker-Planck
equation with a potential V(x) = - [b \ln(x) + a\, x], for b>0 and a<0. The
problem belongs to a family of Fokker-Planck equations with logarithmic
potentials closely related to the Bessel process, that has been extensively
studied for its applications in physics, biology and finance. The Bessel-like
process we consider can be solved by seeking solutions through an expansion
into a complete set of eigenfunctions. The associated imaginary-time
Schroedinger equation exhibits a mix of discrete and continuous eigenvalue
spectra, corresponding to the quantum Coulomb potential describing the bound
states of the hydrogen atom. We present a technique to evaluate the
normalization factor of the continuous spectrum of eigenfunctions that relies
solely upon their asymptotic behavior. We demonstrate the technique by solving
the Brownian motion problem and the Bessel process both with a negative
constant drift. We conclude with a comparison with other analytical methods and
with numerical solutions.Comment: 21 pages, 8 figure
Reengineering legacy software to object-oriented systems
NASA has a legacy of complex software systems that are becoming increasingly expensive to maintain. Reengineering is one approach to modemizing these systems. Object-oriented technology, other modem software engineering principles, and automated tools can be used to reengineer the systems and will help to keep maintenance costs of the modemized systems down. The Software Technology Branch at the NASA/Johnson Space Center has been developing and testing reengineering methods and tools for several years. The Software Technology Branch is currently providing training and consulting support to several large reengineering projects at JSC, including the Reusable Objects Software Environment (ROSE) project, which is reengineering the flight analysis and design system (over 2 million lines of FORTRAN code) into object-oriented C++. Many important lessons have been learned during the past years; one of these is that the design must never be allowed to diverge from the code during maintenance and enhancement. Future work on open, integrated environments to support reengineering is being actively planned
Levy-Student Distributions for Halos in Accelerator Beams
We describe the transverse beam distribution in particle accelerators within
the controlled, stochastic dynamical scheme of the Stochastic Mechanics (SM)
which produces time reversal invariant diffusion processes. This leads to a
linearized theory summarized in a Shchr\"odinger--like (\Sl) equation. The
space charge effects have been introduced in a recent paper~\cite{prstab} by
coupling this \Sl equation with the Maxwell equations. We analyze the space
charge effects to understand how the dynamics produces the actual beam
distributions, and in particular we show how the stationary, self--consistent
solutions are related to the (external, and space--charge) potentials both when
we suppose that the external field is harmonic (\emph{constant focusing}), and
when we \emph{a priori} prescribe the shape of the stationary solution. We then
proceed to discuss a few new ideas~\cite{epac04} by introducing the generalized
Student distributions, namely non--Gaussian, L\'evy \emph{infinitely divisible}
(but not \emph{stable}) distributions. We will discuss this idea from two
different standpoints: (a) first by supposing that the stationary distribution
of our (Wiener powered) SM model is a Student distribution; (b) by supposing
that our model is based on a (non--Gaussian) L\'evy process whose increments
are Student distributed. We show that in the case (a) the longer tails of the
power decay of the Student laws, and in the case (b) the discontinuities of the
L\'evy--Student process can well account for the rare escape of particles from
the beam core, and hence for the formation of a halo in intense beams.Comment: revtex4, 18 pages, 12 figure
Windings of the 2D free Rouse chain
We study long time dynamical properties of a chain of harmonically bound
Brownian particles. This chain is allowed to wander everywhere in the plane. We
show that the scaling variables for the occupation times T_j, areas A_j and
winding angles \theta_j (j=1,...,n labels the particles) take the same general
form as in the usual Brownian motion. We also compute the asymptotic joint laws
P({T_j}), P({A_j}), P({\theta_j}) and discuss the correlations occuring in
those distributions.Comment: Latex, 17 pages, submitted to J. Phys.
Random tree growth by vertex splitting
We study a model of growing planar tree graphs where in each time step we
separate the tree into two components by splitting a vertex and then connect
the two pieces by inserting a new link between the daughter vertices. This
model generalises the preferential attachment model and Ford's -model
for phylogenetic trees. We develop a mean field theory for the vertex degree
distribution, prove that the mean field theory is exact in some special cases
and check that it agrees with numerical simulations in general. We calculate
various correlation functions and show that the intrinsic Hausdorff dimension
can vary from one to infinity, depending on the parameters of the model.Comment: 47 page
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