( 26 ) On the theorem of Riemann-Roch for adjoint systems on Kiihlerian varieties

2015 ◽  
pp. 475-480
Author(s):  
Kunihiko Kodaira
Keyword(s):  
Adjoint Systems

Inverse sensitivity method to self-adjoint systems with repeated eigenvalues

AIAA Journal ◽  
1999 ◽  
Vol 37 ◽  
pp. 933-938
Author(s):  
H. W. Song ◽  
L. F. Chen ◽  
W. L. Wang
Keyword(s):  
Adjoint Systems ◽  
Repeated Eigenvalues ◽  
Sensitivity Method

A System Identification Method for Excitation-Frequency Dependent Rotordynamic Coefficients

2012 ◽  
Author(s):  
Timothy W. Dimond ◽  
Amir A. Younan ◽  
Paul Allaire
Keyword(s):  
System Identification ◽  
Measurement Uncertainty ◽  
Excitation Frequency ◽  
Frequency Dependent ◽  
Rotordynamic Coefficients ◽  
Adjoint Systems ◽  
Dynamic Coefficients ◽  
Backward Whirl ◽  
Identification Technique ◽  
Damped Systems

Experimental identification of rotordynamic systems presents unique challenges. Gyroscopics, generally damped systems, and non-self-adjoint systems due to fluid structure interaction forces mean that symmetry cannot be used to reduce the number of parameters to be identified. Rotordynamic system experimental measurements are often noisy, which complicates comparisons with theory. When linearized, the resulting dynamic coefficients are also often a function of excitation frequency, as distinct from operating speed. In this paper, a frequency domain system identification technique is presented that addresses these issues for rigid-rotor test rigs. The method employs power spectral density functions and forward and backward whirl orbits to obtain the excitation frequency dependent effective stiffness and damping. The method is highly suited for use with experiments that employ active magnetic exciters that can perturb the rotor in the forward and backward whirl directions. Simulation examples are provided for excitation-frequency reduced tilting pad bearing dynamic coefficients. In the simulations, 20 and 50 percent Gaussian output noise was considered. Based on ensemble averages of the coefficient estimates, the 95 percent confidence intervals due to noise effects were within 1.2% of the identified value. The method is suitable for identification of linear dynamic coefficients for rotordynamic system components referenced to shaft motion. The method can be used to reduce the effect of noise on measurement uncertainty. The statistical framework can also be used to make decisions about experimental run times and acceptable levels of measurement uncertainty. The data obtained from such an experimental design can be used to verify component models and give rotordynamicists greater confidence in the design of turbomachinery.

Adjoint systems in nonconservative problems of elastic stability.

AIAA Journal ◽  
1966 ◽  
Vol 4 (12) ◽  
pp. 2221-2222 ◽  
Author(s):  
S. NEMAT-NASSER ◽  
G. HERRMANN
Keyword(s):  
Elastic Stability ◽  
Adjoint Systems

scholarly journals On Fitting Of Mathematical Models Of Cell Signaling Pathways Using Adjoint Systems

2005 ◽  
Vol 2 (3) ◽  
pp. 527-534 ◽  
Author(s):  
Krzysztof Fujarewicz ◽  
◽  
Marek Kimmel ◽  
Andrzej Swierniak ◽  
Keyword(s):  
Cell Signaling ◽  
Mathematical Models ◽  
Signaling Pathways ◽  
Adjoint Systems ◽  
Cell Signaling Pathways

Transfer Function Modeling of Distributed Piezoelectric Vibration Energy Harvesters

2009 ◽  
Author(s):  
Chin An Tan ◽  
Heather L. Lai
Keyword(s):  
Transfer Function ◽  
Transfer Functions ◽  
Vibration Energy ◽  
System Response ◽  
Distributed Parameter ◽  
Domain Modeling ◽  
Vibration Energy Harvesting ◽  
Energy Harvesters ◽  
Adjoint Systems ◽  
The Stability

Extensive research has been conducted on vibration energy harvesting utilizing a distributed piezoelectric beam structure. A fundamental issue in the design of these harvesters is the understanding of the response of the beam to arbitrary external excitations (boundary excitations in most models). The modal analysis method has been the primary tool for evaluating the system response. However, a change in the model boundary conditions requires a reevaluation of the eigenfunctions in the series and information of higher-order dynamics may be lost in the truncation. In this paper, a frequency domain modeling approach based in the system transfer functions is proposed. The transfer function of a distributed parameter system contains all of the information required to predict the system spectrum, the system response under any initial and external disturbances, and the stability of the system response. The methodology proposed in this paper is valid for both self-adjoint and non-self-adjoint systems, and is useful for numerical computer coding and energy harvester design investigations. Examples will be discussed to demonstrate the effectiveness of this approach for designs of vibration energy harvesters.

scholarly journals Sensitivity Analysis for Hybrid Systems and Systems With Memory

2019 ◽  
Vol 14 (9) ◽  
Author(s):  
Radu Serban ◽  
Antonio Recuero
Keyword(s):  
Hybrid Systems ◽  
Exponential Model ◽  
Differential Algebraic Equations ◽  
Mode Switching ◽  
Continuous Systems ◽  
Algebraic Equations ◽  
Adjoint Sensitivity ◽  
Adjoint Systems ◽  
Systems With Memory ◽  
With Memory

We present an adjoint sensitivity method for hybrid discrete—continuous systems, extending previously published forward sensitivity methods (FSA). We treat ordinary differential equations (ODEs) and differential-algebraic equations (DAEs) of index up to two (Hessenberg) and provide sufficient solvability conditions for consistent initialization and state transfer at mode switching points, for both the sensitivity and adjoint systems. Furthermore, we extend the analysis to so-called hybrid systems with memory where the dynamics of any given mode depend explicitly on the states at the last mode transition point. We present and discuss several numerical examples, including a computational mechanics problem based on the so-called exponential model (EM) constitutive material law for steel reinforcement under cyclic loading.

Borg's Periodicity Theorems for First-Order Self-Adjoint Systems with Complex Potentials

2016 ◽  
Vol 60 (3) ◽  
pp. 615-633 ◽  
Author(s):  
Sonja Currie ◽  
Thomas T. Roth ◽  
Bruce A. Watson
Keyword(s):  
Periodic Potential ◽  
Adjoint System ◽  
Complex Potentials ◽  
Order System ◽  
Compact Sets ◽  
Periodic Functions ◽  
First Order ◽  
Adjoint Systems ◽  
Pauli Matrices

AbstractA self-adjoint first-order system with Hermitian π-periodic potential Q(z), integrable on compact sets, is considered. It is shown that all zeros of are double zeros if and only if this self-adjoint system is unitarily equivalent to one in which Q(z) is π/2-periodic. Furthermore, the zeros of are all double zeros if and only if the associated self-adjoint system is unitarily equivalent to one in which Q(z) = σ2Q(z)σ2. Here, Δ denotes the discriminant of the system and σ0, σ2 are Pauli matrices. Finally, it is shown that all instability intervals vanish if and only if Q = rσ0 + qσ2, for some real-valued π-periodic functions r and q integrable on compact sets.

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