The Reference Problem for Small Disturbances

1999 ◽  
pp. 1-7
Author(s):  
Pierre Ladevèze
Keyword(s):  
Reference Problem ◽  
Small Disturbances

On Mackworth's "problem finder": And a reference problem.

1966 ◽  
Vol 21 (2) ◽  
pp. 165-166 ◽  
Author(s):  
Anne Roe
Keyword(s):  
Reference Problem

scholarly journals Aircraft Maintenance Check Scheduling Using Reinforcement Learning

Aerospace ◽  
2021 ◽  
Vol 8 (4) ◽  
pp. 113
Author(s):  
Pedro Andrade ◽  
Catarina Silva ◽  
Bernardete Ribeiro ◽  
Bruno F. Santos
Keyword(s):  
Reinforcement Learning ◽  
Time Horizon ◽  
Learning Algorithm ◽  
Initial Conditions ◽  
Q Learning ◽  
Scheduling Policy ◽  
Real Scenario ◽  
Maintenance Plan ◽  
Small Disturbances

This paper presents a Reinforcement Learning (RL) approach to optimize the long-term scheduling of maintenance for an aircraft fleet. The problem considers fleet status, maintenance capacity, and other maintenance constraints to schedule hangar checks for a specified time horizon. The checks are scheduled within an interval, and the goal is to, schedule them as close as possible to their due date. In doing so, the number of checks is reduced, and the fleet availability increases. A Deep Q-learning algorithm is used to optimize the scheduling policy. The model is validated in a real scenario using maintenance data from 45 aircraft. The maintenance plan that is generated with our approach is compared with a previous study, which presented a Dynamic Programming (DP) based approach and airline estimations for the same period. The results show a reduction in the number of checks scheduled, which indicates the potential of RL in solving this problem. The adaptability of RL is also tested by introducing small disturbances in the initial conditions. After training the model with these simulated scenarios, the results show the robustness of the RL approach and its ability to generate efficient maintenance plans in only a few seconds.

The entrainment interface

1972 ◽  
Vol 51 (1) ◽  
pp. 97-118 ◽  
Author(s):  
O. M. Phillips
Keyword(s):  
Velocity Field ◽  
Turbulent Flow ◽  
Surface Area ◽  
Large Scale ◽  
Positive Curvature ◽  
Lagrangian Description ◽  
Eulerian Description ◽  
Entrainment Process ◽  
Necessary And Sufficient ◽  
Small Disturbances

A theory is developed to describe the evolution of the entrainment interface in turbulent flow, in which the surface is convoluted by the large-scale eddies of the motion and at the same time advances relative to the fluid as a result of the micro-scale entrainment process. A pseudo-Lagrangian description of the process indicates that the interface is characterized by the appearance of ‘billows’ of negative curvature, over which surface area is, on average, being generated, separated by re-entrant wedges (lines of very large positive curvature) where surface area is consumed. An alternative Eulerian description allows calculation of the development of the interfacial configuration when the velocity field is prescribed. Several examples are considered in which the prescribed velocity field in the z direction is of the general form w = Wf(x – Ut), where the maximum value of the function f is unity. These indicate the importance of leading points on the surface which are such that small disturbances in the vicinity will move away from the point in all directions. The necessary and sufficient condition for the existence of one or more leading points on the surface is that U [les ] V, the speed of advance of an element of the surface relative to the fluid element at the same point. The existence of leading points is accompanied by the appearance of line discontinuities in the surface slope re-entrant wedges, In these circumstances, the overall speed of advance of the convoluted surface is found to be W + (V2 – U2)½, where W is the maximum outwards velocity in the region; this result is independent of the distribution f.When the speed U with which an ‘eddy’ moves relative to the outside fluid is greater than the speed of advance V of an element of the front, the interface develops neither leading points nor discontinuities in slope; the amplitude of the surface convolutions and the overall entrainment speed are both reduced greatly. In a turbulent flow, therefore, the large-scale motions influencing entrainment are primarily those that move slowly relative to the outside fluid (with relative speed less than V). The experimental results of Kovasznay, Kibens & Blackwelder (1970) are reviewed in the light of these conclusions. It appears that in their experiments the entrainment speed V is of the order fifteen times the Kolmogorov velocity, the large constant of proportionality being apparently the result of augmentation by micro-convolutions of the interface associated with small and meso-scale eddies of the turbulence.

NATIONAL SECURITY AND SOLAR-TERRESTRIAL COUPLING

2021 ◽  
Vol 4 (1) ◽  
pp. 24-34
Author(s):  
A.V. Volkov ◽  
◽  
A.A. Khadartsev ◽  
L.V. Kashintseva ◽  
O.A. Sedova ◽  
...  
Keyword(s):  
Public Health ◽  
Magnetic Field ◽  
National Security ◽  
Economic Security ◽  
The State ◽  
Complex Dynamic ◽  
Scientific Publications ◽  
Annual Variations ◽  
Biological Environment ◽  
Small Disturbances

The paper presents the results of the analysis of scientific publications in order to identify heliogeophysical interactions and their impact on the state of biospheric processes. It is demonstrated that small disturbances in the biological environment lead to global process-es with little predictable consequences that radically change politics, economics and public health. These processes pose a serious threat to national and economic security. The studies have shown that the Earth's ionosphere is a complex dynamic system, the state of which is de-termined not only by the parameters of the atmosphere itself, but also by variations in helium and geomagnetic factors. Investigation of interrelated processes in the lower and upper lay-ers of the atmosphere is one of the priority geophysical and meteorological tasks. Key words: solar activity, heliogeophysical interactions; the Earth's magnetic field; interplanetary field; annual variations; cosmic rays.

scholarly journals Structure and dynamical behavior of non-normal networks

2018 ◽  
Vol 4 (12) ◽  
pp. eaau9403 ◽  
Author(s):  
Malbor Asllani ◽  
Renaud Lambiotte ◽  
Timoteo Carletti
Keyword(s):  
Network Science ◽  
Wide Spectrum ◽  
Dynamical Behavior ◽  
Transient Phase ◽  
The Stability ◽  
Normal Networks ◽  
Empirical Networks ◽  
Peculiar Behavior ◽  
Potential Use ◽  
Small Disturbances

We analyze a collection of empirical networks in a wide spectrum of disciplines and show that strong non-normality is ubiquitous in network science. Dynamical processes evolving on non-normal networks exhibit a peculiar behavior, as initial small disturbances may undergo a transient phase and be strongly amplified in linearly stable systems. In addition, eigenvalues may become extremely sensible to noise and have a diminished physical meaning. We identify structural properties of networks that are associated with non-normality and propose simple models to generate networks with a tunable level of non-normality. We also show the potential use of a variety of metrics capturing different aspects of non-normality and propose their potential use in the context of the stability of complex ecosystems.

On the Use of the Automatic Differentiation for Developing a Linear Harmonic Solver

2018 ◽  
Author(s):  
Wei Zhang ◽  
Dingxi Wang ◽  
Xiuquan Huang ◽  
Tianxiao Yang ◽  
Hong Yan ◽  
...  
Keyword(s):  
Harmonic Balance ◽  
Automatic Differentiation ◽  
Harmonic Balance Method ◽  
Source Codes ◽  
Reverse Mode ◽  
Frequency Domain Methods ◽  
The Cost ◽  
Time Periodic ◽  
Small Disturbances

The linear and nonlinear harmonic methods are efficient frequency domain methods for analyzing time periodic unsteady flow fields. They have been widely used in both academia and industry. But the cost and complexity of developing a linear harmonic solver has been limiting its wider applications. On the other hand, the automatic differentiation (AD) has long been used in the CFD community with a focus on generating adjoint codes in a reverse mode. All those AD tools can do a much better job in generating linearized codes in a tangent mode, but so far very little, if any, attention is paid to using AD for developing linear harmonic solvers. The linear harmonic method, in comparison with the harmonic balance method, has its own advantages. For example, it can capture small disturbances very effectively, and avoids aliasing errors which can lead to solution instability since each wave component is solved for separately. This paper presents the effort of using an AD tool to generate major source codes for the development of a linear harmonic solver for analyzing time periodic unsteady flows. It includes the procedures and advice of using AD for such a purpose. A case study is also presented to validate the developed linear harmonic solver.

scholarly journals On the position-dependent mass Schrödinger equation for Mie-type potentials

2021 ◽  
Vol 2090 (1) ◽  
pp. 012165
Author(s):  
G Ovando ◽  
J J Peña ◽  
J Morales ◽  
J López-Bonilla
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Energy Operator ◽  
Constant Mass ◽  
Point Canonical Transformation ◽  
Mass Distributions ◽  
Exactly Solvable ◽  
Reference Problem ◽  
Dependent Mass ◽  
Position Dependent Mass

Abstract The exactly solvable Position Dependent Mass Schrödinger Equation (PDMSE) for Mie-type potentials is presented. To that, by means of a point canonical transformation the exactly solvable constant mass Schrödinger equation is transformed into a PDMSE. The mapping between both Schrödinger equations lets obtain the energy spectra and wave functions for the potential under study. This happens for any selection of the O von Roos ambiguity parameters involved in the kinetic energy operator. The exactly solvable multiparameter exponential-type potential for the constant mass Schrödinger equation constitutes the reference problem allowing to solve the PDMSE for Mie potentials and mass functions of the form given by m(x) = skx s-1/(xs + 1))2. Thereby, as a useful application of our proposal, the particular Lennard-Jones potential is presented as an example of Mie potential by considering the mass distribution m(x) = 6kx 5/(x 6 + 1))2. The proposed method is general and can be straightforwardly applied to the solution of the PDMSE for other potential models and/or with different position-dependent mass distributions.

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