scholarly journals Resonance frequency control using the rank-one perturbation of the self-compliance matrix at interface degrees of freedom

2020 ◽  
Vol 86 (881) ◽  
pp. 19-00163-19-00163 ◽  
Author(s):  
Yuichi MATSUMURA ◽  
Masashi KOMADA ◽  
Masami MATSUBARA ◽  
Ichiro KIDO
Keyword(s):  
Resonance Frequency ◽  
Degrees Of Freedom ◽  
Frequency Control ◽  
The Self ◽  
Compliance Matrix ◽  
Rank One Perturbation ◽  
Rank One

scholarly journals Dimension of the Exceptional Set in the Aronszajn–Donoghue Theorem for Finite Rank Perturbations

2020 ◽  
Author(s):  
Constanze Liaw ◽  
Sergei Treil ◽  
Alexander Volberg
Keyword(s):  
Finite Rank ◽  
Measure Zero ◽  
Adjoint Operator ◽  
Cyclic Vector ◽  
Spectral Measures ◽  
Hermitian Matrices ◽  
Exceptional Set ◽  
Direct Sum ◽  
Rank One Perturbation ◽  
Rank One

Abstract The classical Aronszajn–Donoghue theorem states that for a rank-one perturbation of a self-adjoint operator (by a cyclic vector) the singular parts of the spectral measures of the original and perturbed operators are mutually singular. As simple direct sum type examples show, this result does not hold for finite rank perturbations. However, the set of exceptional perturbations is pretty small. Namely, for a family of rank $d$ perturbations $A_{\boldsymbol{\alpha }}:= A + {\textbf{B}} {\boldsymbol{\alpha }} {\textbf{B}}^*$, ${\textbf{B}}:{\mathbb C}^d\to{{\mathcal{H}}}$, with ${\operatorname{Ran}}{\textbf{B}}$ being cyclic for $A$, parametrized by $d\times d$ Hermitian matrices ${\boldsymbol{\alpha }}$, the singular parts of the spectral measures of $A$ and $A_{\boldsymbol{\alpha }}$ are mutually singular for all ${\boldsymbol{\alpha }}$ except for a small exceptional set $E$. It was shown earlier by the 1st two authors, see [4], that $E$ is a subset of measure zero of the space $\textbf{H}(d)$ of $d\times d$ Hermitian matrices. In this paper, we show that the set $E$ has small Hausdorff dimension, $\dim E \le \dim \textbf{H}(d)-1 = d^2-1$.

Study on Evaluation of Sound Speed in Duct With Tube Banks

2010 ◽  
Author(s):  
Kunihiko Ishihara
Keyword(s):  
Heat Exchanger ◽  
Resonance Frequency ◽  
Vortex Shedding ◽  
Sound Speed ◽  
Flow Direction ◽  
Fem Analysis ◽  
The Self ◽  
Resonance Phenomenon ◽  
Acoustic Characteristics ◽  
Tube Banks

As tube banks are set in a duct in a boiler and a heat exchanger, the resonance phenomenon or the self sustained tone are generated due to the interference between vortex shedding and the acoustic characteristics of the duct. It is necessary to know the resonance frequency of the duct, namely sound speed, for avoiding any trouble that may arise. In general, it is said that the sound speed decreases in the duct with tube banks and an evaluation formula is given. However, this formula is often used for the perpendicular direction of the flow. We wanted to know whether this formula would be able to be used for the flow direction and for various arrays of patterns or not. In this paper, the applicability of this expression is discussed by using FEM analysis and experiments.

Quantum genetic algorithm to evolve controllers for self-reconfigurable modular robots

2020 ◽  
Vol 17 (3) ◽  
pp. 427-435
Author(s):  
Mohamed Khalil Mezghiche ◽  
Noureddine Djedi
Keyword(s):  
Genetic Algorithms ◽  
Degrees Of Freedom ◽  
Optimization Problems ◽  
The Self ◽  
Modular Robots ◽  
Modular Robot ◽  
Adaptive Locomotion ◽  
Content Type ◽  
Quantum Genetic Algorithm ◽  
Neural Controllers

Purpose The purpose of this study is to explore using real-observation quantum genetic algorithms (RQGAs) to evolve neural controllers that are capable of controlling a self-reconfigurable modular robot in an adaptive locomotion task. Design/methodology/approach Quantum-inspired genetic algorithms (QGAs) have shown their superiority against conventional genetic algorithms in numerous challenging applications in recent years. The authors have experimented with several QGAs variants and real-observation QGA achieved the best results in solving numerical optimization problems. The modular robot used in this study is a hybrid simulated robot; each module has two degrees of freedom and four connecting faces. The modular robot also possesses self-reconfiguration and self-mobile capabilities. Findings The authors have conducted several experiments using different robot configurations ranging from a single module configuration to test the self-mobile property to several disconnected modules configuration to examine self-reconfiguration, as well as snake, quadruped and rolling track configurations. The results demonstrate that the robot was able to perform self-reconfiguration and produce stable gaits in all test scenarios. Originality/value The artificial neural controllers evolved using the real-observation QGA were able to control the self-reconfigurable modular robot in the adaptive locomotion task efficiently.

scholarly journals Phase mixing importance for both Landau instability and damping

2017 ◽  
Vol 83 (1) ◽  
Author(s):  
D. D. A. Santos ◽  
Yves Elskens
Keyword(s):  
Numerical Calculation ◽  
Degrees Of Freedom ◽  
Hamiltonian Formalism ◽  
Langmuir Wave ◽  
The Self ◽  
Phase Mixing ◽  
Mixing Effect ◽  
Self Consistent ◽  
Landau Instability

We discuss the self-consistent dynamics of plasmas by means of a Hamiltonian formalism for a system of $N$ near-resonant electrons interacting with a single Langmuir wave. The connection with the Vlasov description is revisited through the numerical calculation of the van Kampen-like eigenfrequencies of the linearized dynamics for many degrees of freedom. Both the exponential-like growth as well as damping of the Langmuir wave are shown to emerge from a phase mixing effect among beam modes, revealing unexpected similarities between the stable and unstable regimes.

Spin radiation effects in the BMT model of spinning charge

2014 ◽  
Vol 29 (31) ◽  
pp. 1450186 ◽  
Author(s):  
S. L. Lebedev
Keyword(s):  
Imaginary Part ◽  
Radiation Effects ◽  
Degrees Of Freedom ◽  
The Self ◽  
Spin Magnetic Moment ◽  
Self Energy ◽  
Radiation Processes ◽  
Nonzero Spin ◽  
Derivatives Of ◽  
Spin Contribution

The radiation processes emerging as a result of interaction between spin and orbit degrees of freedom of spinning charge are investigated with the use of the Bargmann–Michel–Telegdi (BMT) model. The spin contribution to the self-energy of the ultrarelativistic particle is imaginary and proportional to invariant constructed from the derivatives of the worldline and from the spin. This invariant determines up to negative numerical factor of the QED spin contribution to the imaginary part of the mass shift (MS). Particular cases of crossed, electric and magnetic external fields are considered in detail. The influence of an ideal boundary upon the self-energy of the particle is analyzed for the crossed field case. In the presence of the "mirror" the imaginary part of the MS gets an addition and the nonzero spin dependent real part appears, both however giving the small corrections to no-boundary MS. An alternative method to obtain the spin magnetic moment correction to the power of synchrotron radiation entails in generalization of the result known for the planar motion. Special attention is given to disagreement between classical and quantum pictures of spin radiation.

scholarly journals Application of a Rank-One Perturbation to Pendulum Systems

2020 ◽  
Vol 12 (5) ◽  
pp. 47
Author(s):  
Traor´e. G. Y. Arouna ◽  
M. Dosso ◽  
J.-C. Koua Brou
Keyword(s):  
Perturbation Theory ◽  
Strong Stability ◽  
Double Pendulum ◽  
Simple Pendulum ◽  
Rank One Perturbation ◽  
Stability And Instability ◽  
Rank One

From a perturbation theory proposed by Mehl, et al., a study of the rank-one perturbation of the problems governed by pendulum systems is presented. Thus, a study of motion of the simple pendulum, double and triple pendulums with oscillating support, not coupled as coupled by a spring and double pendulum with fixed support is proposed. Finally (strong) stability and instability zones are calculated for each studied system.

scholarly journals Halo Properties in Helium Nuclei from the Perspective of Geometrical Thermodynamics

2021 ◽  
Author(s):  
M. C. Parker ◽  
C. Jeynes ◽  
W. N. Catford
Keyword(s):  
Ground State ◽  
Degrees Of Freedom ◽  
Characteristic Length ◽  
The Self ◽  
Neutron Halo ◽  
Helium Isotopes ◽  
Centre Of Mass ◽  
Characteristic Length Scale ◽  
Charge Radii ◽  
Weak Binding

Abstract The nuclear matter and charge radii of the helium isotopes (A = 4,6,8) are calculated by quantitative geometrical thermodynamics (QGT) taking as input the symmetry of the alpha-particle, the very weak binding (and hence halo nature) of the heavier helium isotopes, and a characteristic length scale given by the proton size. The results follow by considering each isotope in its ground state, with QGT representing each system as a maximum entropy configuration that conforms to the Holographic Principle. This allows key geometric parameters to be determined from the number of degrees of freedom available. QGT treats 6He as a 4He core plus a concentric neutron shell comprising a holomorphic pair of neutrons, and the 8He neutron halo is treated as a holomorphic pair of holomorphic pairs. Considering the information content of each system allows a correlation angle of 2pi/3 between the holomorphic entities to be inferred, and then the charge radii of the three isotopes can be calculated from the displacement of the 4He core from the centre of mass. The calculations for the charge and matter radii of 4,6,8He agree closely with observed values. Similar QGT calculation of the sizes of the self-conjugate A = 4n nuclei {4He,8Be,12C,16O,20Ne,24Mg,28Si,32S,36Ar,40Ca} also agree well with experiment.

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