A new approach in the analysis of linear systems with periodic coefficients for applications in rotorcraft dynamics

1994 ◽  
Vol 98 (971) ◽  
pp. 9-16 ◽  
Author(s):  
D.-H. Wu ◽  
S.C. Sinha
Keyword(s):  
Numerical Technique ◽  
Numerical Accuracy ◽  
Solution Vector ◽  
Suggested Approach ◽  
New Approach ◽  
Stiffness Matrices ◽  
Bladed Rotor ◽  
The Stability ◽  
Varying Mass ◽  
Second Order Equations

Abstract A numerical technique for the stability analysis of linear mechanical dynamic systems with periodically varying parameters is proposed. The technique is based on representation of the solution vector in terms of Chebyshev polynomials defined over the principal period. Two formulations have been presented. The first formulation is suitable for systems described by state space equations, while the second can be applied directly to a set of second order equations with periodically varying mass, damping and stiffness matrices. As an illustrative example, the flap-lag stability of a multi-bladed rotor is examined. The numerical accuracy and efficiency of the proposed technique is compared with standard numerical codes based on Runge-Kutta, Adams-Moulton and Gear algorithms. The results indicate that the suggested approach is by far the most efficient one, particularly for systems with larger dimensions.

Host-Guest Interactions on Electrode Surfaces for Immobilization of Molecular Catalysts

2020 ◽  
Author(s):  
Laurent Sévery ◽  
Jacek Szczerbiński ◽  
Mert Taskin ◽  
Isik Tuncay ◽  
Fernanda Brandalise Nunes ◽  
...  
Keyword(s):  
Aqueous Media ◽  
Heterogeneous Systems ◽  
Catalytic Systems ◽  
New Approach ◽  
Molecular Systems ◽  
Electrode Surfaces ◽  
Catalytic Surfaces ◽  
Oxide Electrodes ◽  
The Stability ◽  
Molecular Catalysts

The strategy of anchoring molecular catalysts on electrode surfaces combines the high selectivity and activity of molecular systems with the practicality of heterogeneous systems. The stability of molecular catalysts is, however, far less than that of traditional heterogeneous electrocatalysts, and therefore a method to easily replace anchored molecular catalysts that have degraded could make such electrosynthetic systems more attractive. Here, we apply a non-covalent “click” chemistry approach to reversibly bind molecular electrocatalysts to electrode surfaces via host-guest complexation with surface-anchored cyclodextrins. The host-guest interaction is remarkably strong and allows the flow of electrons between the electrode and the guest catalyst. Electrosynthesis in both organic and aqueous media was demonstrated on metal oxide electrodes, with stability on the order of hours. The catalytic surfaces can be recycled by controlled release of the guest from the host cavities and readsorption of fresh guest. This strategy represents a new approach to practical molecular-based catalytic systems.

scholarly journals Methodology and Models for Individuals’ Creditworthiness Management Using Digital Footprint Data and Machine Learning Methods

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1820
Author(s):  
Ekaterina V. Orlova
Keyword(s):  
Interest Rates ◽  
Additional Data ◽  
Risk Level ◽  
Gradient Boosting ◽  
Cluster Number ◽  
New Approach ◽  
Credit Risks ◽  
Stochastic Gradient Boosting ◽  
The Stability ◽  
Digital Footprints

This research deals with the challenge of reducing banks’ credit risks associated with the insolvency of borrowing individuals. To solve this challenge, we propose a new approach, methodology and models for assessing individual creditworthiness, with additional data about borrowers’ digital footprints to implement comprehensive analysis and prediction of a borrower’s credit profile. We suggest a model for borrowers’ clustering based on the method of hierarchical clustering and the k-means method, which groups actual borrowers having similar creditworthiness and similar credit risks into homogeneous clusters. We also design the model for borrowers’ classification based on the stochastic gradient boosting (SGB) method, which reliably determines the cluster number and therefore the risk level for a new borrower. The developed models are the basis for decision making regarding the decision about lending value, interest rates and lending terms for each risk-homogeneous borrower’s group. The modified version of the methodology for assessing individual creditworthiness is presented, which is to reduce the credit risks and to increase the stability and profitability of financial organizations.

A new approach to the stability analysis of thawing slopes

1980 ◽  
Vol 17 (4) ◽  
pp. 607-612 ◽  
Author(s):  
Luis E. Vallejo
Keyword(s):  
Stability Analysis ◽  
Water Content ◽  
Pore Water ◽  
Active Layer ◽  
Necessary Conditions ◽  
Mass Movements ◽  
New Approach ◽  
Pore Water Pressures ◽  
The Stability ◽  
Excess Pore

A new approach to the stability analysis of thawing slopes at shallow depths, taking into consideration their structure (this being a mixture of hard crumbs of soil and a fluid matrix), is presented. The new approach explains shallow mass movements such as skin flows and tongues of bimodal flows, which usually take place on very low slope inclinations independently of excess pore water pressures or increased water content in the active layer, which are necessary conditions in the methods available to date to explain these movements.

Bifurcation analysis of steady natural convection in a tilted cubical cavity with adiabatic sidewalls

2014 ◽  
Vol 756 ◽  
pp. 650-688 ◽  
Author(s):  
J. F. Torres ◽  
D. Henry ◽  
A. Komiya ◽  
S. Maruyama
Keyword(s):  
Natural Convection ◽  
Rotation Axis ◽  
Numerical Technique ◽  
Continuation Method ◽  
Rotation Vector ◽  
Saddle Node Bifurcation ◽  
Saddle Node ◽  
Stable Solutions ◽  
The Stability ◽  
Cubical Cavity

AbstractNatural convection in an inclined cubical cavity heated from two opposite walls maintained at different temperatures and with adiabatic sidewalls is investigated numerically. The cavity is inclined by an angle $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\theta $ around a lower horizontal edge and the isothermal wall set at the higher temperature is the lower wall in the horizontal situation ($\theta = 0^\circ $). A continuation method developed from a three-dimensional spectral finite-element code is applied to determine the bifurcation diagrams for steady flow solutions. The numerical technique is used to study the influence of ${\theta }$ on the stability of the flow for moderate Rayleigh numbers in the range $\mathit{Ra} \leq 150\, 000$, focusing on the Prandtl number $\mathit{Pr} = 5.9$. The results show that the inclination breaks the degeneracy of the stable solutions obtained at the first bifurcation point in the horizontal cubic cavity: (i) the transverse stable rolls, whose rotation vector is in the same direction as the inclination vector ${\boldsymbol{\Theta}}$, start from $\mathit{Ra} \to 0$ forming a leading branch and becoming more predominant with increasing $\theta $; (ii) a disconnected branch consisting of transverse rolls, whose rotation vector is opposite to ${\boldsymbol{\Theta}}$, develops from a saddle-node bifurcation, is stabilized at a pitchfork bifurcation, but globally disappears at a critical inclination angle; (iii) the semi-transverse stable rolls, whose rotation axis is perpendicular to ${\boldsymbol{\Theta}}$ at $\theta \to 0^\circ $, develop from another saddle-node bifurcation, but the branch also disappears at a critical angle. We also found the stability thresholds for the stable diagonal-roll and four-roll solutions, which increase with $\theta $ until they disappear at other critical angles. Finally, the families of stable solutions are presented in the $\mathit{Ra}-\theta $ parameter space by determining the locus of the primary, secondary, saddle-node, and Hopf bifurcation points as a function of $\mathit{Ra}$ and $\theta $.

On the Stability Properties of a Periodically Forced, Time-Varying Mass System

2009 ◽  
Author(s):  
W. T. van Horssen ◽  
O. V. Pischanskyy ◽  
J. L. A. Dubbeldam
Keyword(s):  
Periodic Solutions ◽  
Forced Vibrations ◽  
Time Varying ◽  
Mass System ◽  
Single Degree Of Freedom ◽  
Stability Properties ◽  
Single Degree ◽  
Existence Of Periodic Solutions ◽  
The Stability ◽  
Varying Mass

In this paper the forced vibrations of a linear, single degree of freedom oscillator (sdofo) with a time-varying mass will be studied. The forced vibrations are due to small masses which are periodically hitting and leaving the oscillator with different velocities. Since these small masses stay for some time on the oscillator surface the effective mass of the oscillator will periodically vary in time. Not only solutions of the oscillator equation will be constructed, but also the stability properties, and the existence of periodic solutions will be discussed.

scholarly journals INTEGRAL TRANSFORM TECHNIQUE FOR MESON WAVE FUNCTIONS

1996 ◽  
Vol 11 (20) ◽  
pp. 1611-1626 ◽  
Author(s):  
A.P. BAKULEV ◽  
S.V. MIKHAILOV
Keyword(s):  
Wave Function ◽  
Sum Rules ◽  
Integral Transform ◽  
Wave Functions ◽  
Sum Rule ◽  
New Approach ◽  
Exactly Solvable ◽  
The Stability ◽  
The Masses ◽  
Integral Transform Technique

In a recent paper1 we have proposed a new approach for extracting the wave function of the π-meson φπ(x) and the masses and wave functions of its first resonances from the new QCD sum rules for nondiagonal correlators obtained in Ref. 2. Here, we test our approach using an exactly solvable toy model as illustration. We demonstrate the validity of the method and suggest a pure algebraic procedure for extracting the masses and wave functions relating to the case under investigation. We also explore the stability of the procedure under perturbations of the theoretical part of the sum rule. In application to the pion case, this results not only in the mass and wave function of the first resonance (π′), but also in the estimation of π″-mass.

scholarly journals A sieve algorithm based on overlattices

2014 ◽  
Vol 17 (A) ◽  
pp. 49-70 ◽  
Author(s):  
Anja Becker ◽  
Nicolas Gama ◽  
Antoine Joux
Keyword(s):  
Heuristic Algorithm ◽  
Orthonormal Basis ◽  
Complexity Analysis ◽  
Computer Architectures ◽  
High Dimensions ◽  
Average Case ◽  
Solution Vector ◽  
New Approach ◽  
Bounded Norm

AbstractIn this paper, we present a heuristic algorithm for solving exact, as well as approximate, shortest vector and closest vector problems on lattices. The algorithm can be seen as a modified sieving algorithm for which the vectors of the intermediate sets lie in overlattices or translated cosets of overlattices. The key idea is hence no longer to work with a single lattice but to move the problems around in a tower of related lattices. We initiate the algorithm by sampling very short vectors in an overlattice of the original lattice that admits a quasi-orthonormal basis and hence an efficient enumeration of vectors of bounded norm. Taking sums of vectors in the sample, we construct short vectors in the next lattice. Finally, we obtain solution vector(s) in the initial lattice as a sum of vectors of an overlattice. The complexity analysis relies on the Gaussian heuristic. This heuristic is backed by experiments in low and high dimensions that closely reflect these estimates when solving hard lattice problems in the average case.This new approach allows us to solve not only shortest vector problems, but also closest vector problems, in lattices of dimension$\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}n$in time$2^{0.3774\, n}$using memory$2^{0.2925\, n}$. Moreover, the algorithm is straightforward to parallelize on most computer architectures.

scholarly journals INVESTIGATION OF THE GEOMECHANICAL STATE OF SOFT ADJOINING ROCKS UNDER PROTECTIVE CONSTRUCTIONS

2021 ◽  
Vol 36 (4) ◽  
pp. 61-71
Author(s):  
Serhii Nehrii ◽  
Tetiana Nehrii ◽  
Oksana Zolotarova ◽  
Serhii Volkov
Keyword(s):  
Physical And Mechanical Properties ◽  
New Approach ◽  
Soft Rocks ◽  
The Face ◽  
Geomechanical State ◽  
Rock Mass Failure ◽  
The Stability ◽  
Seam Mining ◽  
Mine Roadways

The conditions of coal seam mining in the mines of Ukraine have been considered. The problem of conducting coal mining by longwalls in the conditions of soft adjoining rocks, which concerns the protection of mine roadways located near the face, has been revealed. In such conditions, the existing protective constructions are ineffective due to the fact that they yield and get pressed into the soft rocks of the footwall. This indicated the need for research into the geomechanical state of soft rocks of the footwall. According to the results of known studies on the mechanism of rock mass failure around roadways and the data of physical and mechanical properties of the coal mass, which is represented by soft rocks, the correlation dependence has been obtained, the use of which allowed for the determination of the parameters of the rock deformation diagram and the establishment of the stability criterion of footwall rocks under the protection means and stability conditions of the geotechnical system “protective construction – adjoining rocks.” They are the basis of a new approach to ensure the stability of the roadways, which are supported behind the faces, by controlling the stress state in the system “protective construction – adjoining rocks.” This may be the basis for the development of new methods of protecting roadways in conditions of soft adjoining rocks.

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