15,626 research outputs found
Analysis of the velocity field of granular hopper flow
We report the analysis of radial characteristics of the flow of granular
material through a conical hopper. The discharge is simulated for various
orifice sizes and hopper opening angles. Velocity profiles are measured along
two radial lines from the hopper cone vertex: along the main axis of the cone
and along its wall. An approximate power law dependence on the distance from
the orifice is observed for both profiles, although differences between them
can be noted. In order to quantify these differences, we propose a Local Mass
Flow index that is a promising tool in the direction of a more reliable
classification of the flow regimes in hoppers
On the Shape of the Tail of a Two Dimensional Sand Pile
We study the shape of the tail of a heap of granular material. A simple
theoretical argument shows that the tail adds a logarithmic correction to the
slope given by the angle of repose. This expression is in good agreement with
experiments. We present a cellular automaton that contains gravity, dissipation
and surface roughness and its simulation also gives the predicted shape.Comment: LaTeX file 4 pages, 4 PS figures, also available at
http://pmmh.espci.fr
Riemann solvers and undercompressive shocks of convex FPU chains
We consider FPU-type atomic chains with general convex potentials. The naive
continuum limit in the hyperbolic space-time scaling is the p-system of mass
and momentum conservation. We systematically compare Riemann solutions to the
p-system with numerical solutions to discrete Riemann problems in FPU chains,
and argue that the latter can be described by modified p-system Riemann
solvers. We allow the flux to have a turning point, and observe a third type of
elementary wave (conservative shocks) in the atomistic simulations. These waves
are heteroclinic travelling waves and correspond to non-classical,
undercompressive shocks of the p-system. We analyse such shocks for fluxes with
one or more turning points.
Depending on the convexity properties of the flux we propose FPU-Riemann
solvers. Our numerical simulations confirm that Lax-shocks are replaced by so
called dispersive shocks. For convex-concave flux we provide numerical evidence
that convex FPU chains follow the p-system in generating conservative shocks
that are supersonic. For concave-convex flux, however, the conservative shocks
of the p-system are subsonic and do not appear in FPU-Riemann solutions
Risk and Business Goal Based Security Requirement and Countermeasure Prioritization
Companies are under pressure to be in control of their assets but at the same time they must operate as efficiently as possible. This means that they aim to implement “good-enough security” but need to be able to justify their security investment plans. Currently companies achieve this by means of checklist-based security assessments, but these methods are a way to achieve consensus without being able to provide justifications of countermeasures in terms of business goals. But such justifications are needed to operate securely and effectively in networked businesses. In this paper, we first compare a Risk-Based Requirements Prioritization method (RiskREP) with some requirements engineering and risk assessment methods based on their requirements elicitation and prioritization properties. RiskREP extends misuse case-based requirements engineering methods with IT architecture-based risk assessment and countermeasure definition and prioritization. Then, we present how RiskREP prioritizes countermeasures by linking business goals to countermeasure specification. Prioritizing countermeasures based on business goals is especially important to provide the stakeholders with structured arguments for choosing a set of countermeasures to implement. We illustrate RiskREP and how it prioritizes the countermeasures it elicits by an application to an action case
Discrete concavity and the half-plane property
Murota et al. have recently developed a theory of discrete convex analysis
which concerns M-convex functions on jump systems. We introduce here a family
of M-concave functions arising naturally from polynomials (over a field of
generalized Puiseux series) with prescribed non-vanishing properties. This
family contains several of the most studied M-concave functions in the
literature. In the language of tropical geometry we study the tropicalization
of the space of polynomials with the half-plane property, and show that it is
strictly contained in the space of M-concave functions. We also provide a short
proof of Speyer's hive theorem which he used to give a new proof of Horn's
conjecture on eigenvalues of sums of Hermitian matrices.Comment: 14 pages. The proof of Theorem 4 is corrected
Action minimizing fronts in general FPU-type chains
We study atomic chains with nonlinear nearest neighbour interactions and
prove the existence of fronts (heteroclinic travelling waves with constant
asymptotic states). Generalizing recent results of Herrmann and Rademacher we
allow for non-convex interaction potentials and find fronts with non-monotone
profile. These fronts minimize an action integral and can only exists if the
asymptotic states fulfil the macroscopic constraints and if the interaction
potential satisfies a geometric graph condition. Finally, we illustrate our
findings by numerical simulations.Comment: 19 pages, several figure
Infrared spectroscopy of diatomic molecules - a fractional calculus approach
The eigenvalue spectrum of the fractional quantum harmonic oscillator is
calculated numerically solving the fractional Schr\"odinger equation based on
the Riemann and Caputo definition of a fractional derivative. The fractional
approach allows a smooth transition between vibrational and rotational type
spectra, which is shown to be an appropriate tool to analyze IR spectra of
diatomic molecules.Comment: revised + extended version, 9 pages, 6 figure
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