224,833 research outputs found
Study of basic physical processes in liquid rocket engines
Inconsistencies between analytical results and measurements for liquid rocket thrust chamber performance, which escape suitable explanations, have motivated the examination of the basic phys ical modeling formulations as to their unlimited application. The publication of Prof. D. Straub's book, 'Thermofluid-dynamics of Optimized Rocket Propulsions,' further stimulated the interest of understanding the gas dynamic relationships in chemically reacting mixtures. A review of other concepts proposed by Falk-Ruppel (Gibbsian Thermodynamics), Straub (Alternative Theory, AT), Prigogine (Non-Equilibrium Thermodynamics), Boltzmann (Kinetic Theory), and Truesdell (Rational Mechanism) has been made to obtain a better understanding of the Navier-Stokes equation, which is now used extensively for chemically reacting flow treatment in combustion chambers. In addition to the study of the different concepts, two workshops were conducted to clarify some of the issues. The first workshop centered on Falk-Ruppel's new 'dynamics' concept, while the second one concentrated on Straub's AT. In this report brief summaries of the reviewed philosophies are presented and compared with the classical Navier-Stokes formulation in a tabular arrangement. Also the highlights of both workshops are addressed
Transonic Shocks In Multidimensional Divergent Nozzles
We establish existence, uniqueness and stability of transonic shocks for
steady compressible non-isentropic potential flow system in a multidimensional
divergent nozzle with an arbitrary smooth cross-section, for a prescribed exit
pressure. The proof is based on solving a free boundary problem for a system of
partial differential equations consisting of an elliptic equation and a
transport equation. In the process, we obtain unique solvability for a class of
transport equations with velocity fields of weak regularity(non-Lipschitz), an
infinite dimensional weak implicit mapping theorem which does not require
continuous Frechet differentiability, and regularity theory for a class of
elliptic partial differential equations with discontinuous oblique boundary
conditions.Comment: 54 page
Global analysis of quadrupole shape invariants based on covariant energy density functionals
Coexistence of different geometric shapes at low energies presents a
universal structure phenomenon that occurs over the entire chart of nuclides.
Studies of the shape coexistence are important for understanding the
microscopic origin of collectivity and modifications of shell structure in
exotic nuclei far from stability. The aim of this work is to provide a
systematic analysis of characteristic signatures of coexisting nuclear shapes
in different mass regions, using a global self-consistent theoretical method
based on universal energy density functionals and the quadrupole collective
model. The low-energy excitation spectrum and quadrupole shape invariants of
the two lowest states of even-even nuclei are obtained as solutions of
a five-dimensional collective Hamiltonian (5DCH) model, with parameters
determined by constrained self-consistent mean-field calculations based on the
relativistic energy density functional PC-PK1, and a finite-range pairing
interaction. The theoretical excitation energies of the states: ,
, , , , as well as the
values, are in very good agreement with the corresponding experimental values
for 621 even-even nuclei. Quadrupole shape invariants have been implemented to
investigate shape coexistence, and the distribution of possible
shape-coexisting nuclei is consistent with results obtained in recent
theoretical studies and available data. The present analysis has shown that,
when based on a universal and consistent microscopic framework of nuclear
density functionals, shape invariants provide distinct indicators and reliable
predictions for the occurrence of low-energy coexisting shapes. This method is
particularly useful for studies of shape coexistence in regions far from
stability where few data are available.Comment: 13 pages, 3 figures, accepted for publication in Phys. Rev.
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Design, characterization, and fabrication of solar-retroreflective cool-wall materials
Raising urban albedo increases the fraction of incident sunlight returned to outer space, cooling cities and their buildings. We evaluated the angular distribution of solar radiation incident on exterior walls in 17 U S. climates to develop performance parameters for solar-retroreflective walls, then applied first-principle physics and ray-tracing simulations to explore designs. Our analysis indicates that retroreflective walls must function at large incidence angles to reflect a substantial portion of summer sunlight, and that this will be difficult to attain with materials that rely on total internal reflection. Gonio-spectrophotometer measurements of the solar spectral bi-directional reflectivity of a bicycle reflector showed little to no retroreflection at large incidence angles. Visual comparisons of retroreflection to specular first-surface reflection for four different retroreflective safety films using violet and green lasers suggest their retroreflection to be no greater than 0.09 at incidence angles up to 45°, and no greater than 0.30 at incidence angles of up to 70°. Attempts to produce a two-surface retroreflector with orthogonal mirror grooves by cutting and polishing an aluminum block indicate that residual surface roughness impedes retroreflection. Ongoing efforts focus on forming orthogonal surfaces with aluminized Mylar film, a material with very high specular reflectance across the solar spectrum. We investigated (1) folding or stamping a free film; (2) adhering the film to a pre-shaped substrate; or (3) attaching the film to a flat ductile substrate, then shaping. The latter two methods were more successful but yielded imperfect right angles
Consensus Formation in Multi-state Majority and Plurality Models
We study consensus formation in interacting systems that evolve by
multi-state majority rule and by plurality rule. In an update event, a group of
G agents (with G odd), each endowed with an s-state spin variable, is
specified. For majority rule, all group members adopt the local majority state;
for plurality rule the group adopts the local plurality state. This update is
repeated until a final consensus state is generally reached. In the mean field
limit, the consensus time for an N-spin system increases as ln N for both
majority and plurality rule, with an amplitude that depends on s and G. For
finite spatial dimensions, domains undergo diffusive coarsening in majority
rule when s or G is small. For larger s and G, opinions spread ballistically
from the few groups with an initial local majority. For plurality rule, there
is always diffusive domain coarsening toward consensus.Comment: 8 pages, 11 figures, 2-column revtex4 format. Updated version: small
changes in response to referee comments. For publication in J Phys
Stability Of contact discontinuity for steady Euler System in infinite duct
In this paper, we prove structural stability of contact discontinuities for
full Euler system
Bending crystals: Emergence of fractal dislocation structures
We provide a minimal continuum model for mesoscale plasticity, explaining the
cellular dislocation structures observed in deformed crystals. Our dislocation
density tensor evolves from random, smooth initial conditions to form
self-similar structures strikingly similar to those seen experimentally -
reproducing both the fractal morphologies and some features of the scaling of
cell sizes and misorientations analyzed experimentally. Our model provides a
framework for understanding emergent dislocation structures on the mesoscale, a
bridge across a computationally demanding mesoscale gap in the multiscale
modeling program, and a new example of self-similar structure formation in
non-equilibrium systems.Comment: 4 pages, 4 figures, 5 movies (They can be found at
http://www.lassp.cornell.edu/sethna/Plasticity/SelfSimilarity.html .) In
press at Phys. Rev. Let
Absolute continuity of symmetric Markov processes
We study Girsanov's theorem in the context of symmetric Markov processes,
extending earlier work of Fukushima-Takeda and Fitzsimmons on Girsanov
transformations of ``gradient type.'' We investigate the most general Girsanov
transformation leading to another symmetric Markov process. This investigation
requires an extension of the forward-backward martingale method of Lyons-Zheng,
to cover the case of processes with jumps.Comment: Published by the Institute of Mathematical Statistics
(http://www.imstat.org) in the Annals of Probability
(http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/00911790400000043
Living on the edge of chaos: minimally nonlinear models of genetic regulatory dynamics
Linearized catalytic reaction equations modeling e.g. the dynamics of genetic
regulatory networks under the constraint that expression levels, i.e. molecular
concentrations of nucleic material are positive, exhibit nontrivial dynamical
properties, which depend on the average connectivity of the reaction network.
In these systems the inflation of the edge of chaos and multi-stability have
been demonstrated to exist. The positivity constraint introduces a nonlinearity
which makes chaotic dynamics possible. Despite the simplicity of such minimally
nonlinear systems, their basic properties allow to understand fundamental
dynamical properties of complex biological reaction networks. We analyze the
Lyapunov spectrum, determine the probability to find stationary oscillating
solutions, demonstrate the effect of the nonlinearity on the effective in- and
out-degree of the active interaction network and study how the frequency
distributions of oscillatory modes of such system depend on the average
connectivity.Comment: 11 pages, 5 figure
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