17,365 research outputs found
The Response of Normal Shocks in Diffusers
The frequency response of a normal shock in a diverging channel is calculated for application to problems of
pressure oscillations in ramjet engines. Two limits of a linearized analysis arc discussed: one represents isentropic
flow on both sides of a shock wave; the other may be a crude appr'l'I;imation to the influence of flow separation
induced hy the wave. Numerical results arc given, and the influences of the shock wave on oscillations in the
engine are discus,ed
Modeling pressure oscillations in Ramjets
Pressure oscillations in ramjet engines are approximated as one-dimensional motions and treated within linear acoustics. The exhaust nozzle is represented by the admittance function for a short choked nozzle. New results have been obtained for the quasi-steady response of a
normal shock wave in the diffuser. Acoustic fields in the inlet region and in the combustion chamber are matched to provide an analytical expression of the criterion for linear stability. Combustion processes are accommodated but not treated in detail. As examples, data are discussed
for two liquid-fueled engines, one having axial dump and one having side dumps
TMDlib and TMDplotter: library and plotting tools for transverse-momentum-dependent parton distributions
Transverse-momentum-dependent distributions (TMDs) are central in high-energy
physics from both theoretical and phenomenological points of view. In this
manual we introduce the library, TMDlib, of fits and parameterisations for
transverse-momentum-dependent parton distribution functions (TMD PDFs) and
fragmentation functions (TMD FFs) together with an online plotting tool,
TMDplotter. We provide a description of the program components and of the
different physical frameworks the user can access via the available
parameterisations.Comment: version 2, referring to TMDlib 1.0.2 - comments and references adde
Optimizing spread dynamics on graphs by message passing
Cascade processes are responsible for many important phenomena in natural and
social sciences. Simple models of irreversible dynamics on graphs, in which
nodes activate depending on the state of their neighbors, have been
successfully applied to describe cascades in a large variety of contexts. Over
the last decades, many efforts have been devoted to understand the typical
behaviour of the cascades arising from initial conditions extracted at random
from some given ensemble. However, the problem of optimizing the trajectory of
the system, i.e. of identifying appropriate initial conditions to maximize (or
minimize) the final number of active nodes, is still considered to be
practically intractable, with the only exception of models that satisfy a sort
of diminishing returns property called submodularity. Submodular models can be
approximately solved by means of greedy strategies, but by definition they lack
cooperative characteristics which are fundamental in many real systems. Here we
introduce an efficient algorithm based on statistical physics for the
optimization of trajectories in cascade processes on graphs. We show that for a
wide class of irreversible dynamics, even in the absence of submodularity, the
spread optimization problem can be solved efficiently on large networks.
Analytic and algorithmic results on random graphs are complemented by the
solution of the spread maximization problem on a real-world network (the
Epinions consumer reviews network).Comment: Replacement for "The Spread Optimization Problem
Implementation of the Backlund transformations for the Ablowitz-Ladik hierarchy
The derivation of the Backlund transformations (BTs) is a standard problem of
the theory of the integrable systems. Here, I discuss the equations describing
the BTs for the Ablowitz-Ladik hierarchy (ALH), which have been already
obtained by several authors. The main aim of this work is to solve these
equations. This can be done in the framework of the so-called functional
representation of the ALH, when an infinite number of the evolutionary
equations are replaced, using the Miwa's shifts, with a few equations linking
tau-functions with different arguments. It is shown that starting from these
equations it is possible to obtain explicit solutions of the BT equations. In
other words, the main result of this work is a presentation of the discrete BTs
as a superposition of an infinite number of evolutionary flows of the
hierarchy. These results are used to derive the superposition formulae for the
BTs as well as pure soliton solutions.Comment: 20 page
Spectral Theory of Sparse Non-Hermitian Random Matrices
Sparse non-Hermitian random matrices arise in the study of disordered
physical systems with asymmetric local interactions, and have applications
ranging from neural networks to ecosystem dynamics. The spectral
characteristics of these matrices provide crucial information on system
stability and susceptibility, however, their study is greatly complicated by
the twin challenges of a lack of symmetry and a sparse interaction structure.
In this review we provide a concise and systematic introduction to the main
tools and results in this field. We show how the spectra of sparse
non-Hermitian matrices can be computed via an analogy with infinite dimensional
operators obeying certain recursion relations. With reference to three
illustrative examples --- adjacency matrices of regular oriented graphs,
adjacency matrices of oriented Erd\H{o}s-R\'{e}nyi graphs, and adjacency
matrices of weighted oriented Erd\H{o}s-R\'{e}nyi graphs --- we demonstrate the
use of these methods to obtain both analytic and numerical results for the
spectrum, the spectral distribution, the location of outlier eigenvalues, and
the statistical properties of eigenvectors.Comment: 60 pages, 10 figure
The Euler-Maruyama approximation for the absorption time of the CEV diffusion
A standard convergence analysis of the simulation schemes for the hitting
times of diffusions typically requires non-degeneracy of their coefficients on
the boundary, which excludes the possibility of absorption. In this paper we
consider the CEV diffusion from the mathematical finance and show how a weakly
consistent approximation for the absorption time can be constructed, using the
Euler-Maruyama scheme
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