Implications of causality, time‐translation invariance, linearity, and minimum‐phase behavior for basilar‐membrane response functions

1982 ◽  
Vol 71 (5) ◽  
pp. 1194-1200 ◽  
Author(s):  
Shozo Koshigoe ◽  
Arnold Tubis
Keyword(s):  
Phase Behavior ◽  
Basilar Membrane ◽  
Translation Invariance ◽  
Minimum Phase ◽  
Response Functions ◽  
Time Translation

scholarly journals Charge-current correlation equalities for quantum systems far from equilibrium

2019 ◽  
Vol 6 (6) ◽  
Author(s):  
Dragi Karevski ◽  
Gunter Schütz
Keyword(s):  
Linear Response ◽  
Space Dimension ◽  
Lattice Models ◽  
Quantum Systems ◽  
Translation Invariance ◽  
Response Functions ◽  
Current Correlation ◽  
Far From Equilibrium ◽  
Conserved Currents ◽  
A Current

We prove that a recently derived correlation equality between conserved charges and their associated conserved currents for quantum systems far from equilibrium [O.A. Castro-Alvaredo, B. Doyon, and T. Yoshimura, Phys. Rev. X 6, 041065 (2016)], is valid under more general conditions than assumed so far. Similar correlation identities, which in generalized Gibbs ensembles give rise to a current symmetry somewhat reminiscent of the Onsager relations, turn out to hold also in the absence of translation invariance, for lattice models, and in any space dimension, and to imply a symmetry of the non-equilibrium linear response functions.

scholarly journals Rigorous bounds on dynamical response functions and time-translation symmetry breaking

2020 ◽  
Vol 9 (1) ◽  
Author(s):  
Marko Medenjak ◽  
Tomaz Prosen ◽  
Lenart Zadnik
Keyword(s):  
Dynamical Response ◽  
Response Functions ◽  
Xxz Model ◽  
Dynamical Symmetries ◽  
Time Translation ◽  
Spatially Inhomogeneous ◽  
Translation Symmetry ◽  
Local Operators ◽  
Rigorous Bounds ◽  
Translation Symmetry Breaking

Dynamical response functions are standard tools for probing local physics near the equilibrium. They provide information about relaxation properties after the equilibrium state is weakly perturbed. In this paper we focus on systems which break the assumption of thermalization by exhibiting persistent temporal oscillations. We provide rigorous bounds on the Fourier components of dynamical response functions in terms of extensive or local dynamical symmetries, i.e., extensive or local operators with periodic time dependence. Additionally, we discuss the effects of spatially inhomogeneous dynamical symmetries. The bounds are explicitly implemented on the example of an interacting Floquet system, specifically in the integrable Trotterization of the Heisenberg XXZ model.

The Effects of Membrane Properties and Structural Parameters on the Non-Minimum Phase Behavior of the PEM Fuel Cell Humidification System

2011 ◽  
Vol 9 (1) ◽  
Author(s):  
John F. Hall ◽  
Christine A. Mecklenborg ◽  
Clay S. Hearn ◽  
Dongmei Chen
Keyword(s):  
Fuel Cell ◽  
Phase Behavior ◽  
Material Property ◽  
Coupling Effect ◽  
Structural Parameters ◽  
Pem Fuel Cell ◽  
Membrane Properties ◽  
Minimum Phase ◽  
Vapor Transfer ◽  
Channel Plate

The water vapor transfer across a Nafion® membrane exhibits an undesired non-minimum phase behavior. This paper will show that even in the disturbance-to-output loop, the non-minimum phase zero adversely affects the feedback controller design because of the coupling effect between the disturbance-to-output and the input-to-output loops. The non-minimum phase zero location is influenced by the channel plate structure and the membrane material property. The structural parameters examined in this research include channel plate dimensions and heat transfer coefficients. The membrane properties studied include membrane vapor transfer properties described in the Arrhenius’ equation. A governing equation to link the non-minimum phase zero and the parameters is developed in this paper. This equation shows that the non-minimum phase zero arises from the competing heat and mass transfer dynamics, and is determined by the structural parameters and membrane properties. A sensitivity study is presented and shows that structural and material property optimization can be used with the control system design to mitigate the non-minimum phase behavior in the PEM fuel cell humidification system.

scholarly journals From locality and unitarity to cosmological correlators

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Sadra Jazayeri ◽  
Enrico Pajer ◽  
David Stefanyszyn
Keyword(s):  
Vacuum State ◽  
Tree Level ◽  
Local Theory ◽  
Optical Theorem ◽  
Translation Invariance ◽  
De Sitter ◽  
Integral Theorem ◽  
Vast Number ◽  
Time Translation ◽  
Cauchy’S Integral Theorem

Abstract In the standard approach to deriving inflationary predictions, we evolve a vacuum state in time according to the rules of a given model. Since the only observables are the future values of correlators and not their time evolution, this brings about a large degeneracy: a vast number of different models are mapped to the same minute number of observables. Furthermore, due to the lack of time-translation invariance, even tree-level calculations require an increasing number of nested integrals that quickly become intractable. Here we ask how much of the final observables can be “bootstrapped” directly from locality, unitarity and symmetries.To this end, we introduce two new “boostless” bootstrap tools to efficiently compute tree-level cosmological correlators/wavefunctions without any assumption about de Sitter boosts. The first is a Manifestly Local Test (MLT) that any n-point (wave)function of massless scalars or gravitons must satisfy if it is to arise from a manifestly local theory. When combined with a sub-set of the recently proposed Bootstrap Rules, this allows us to compute explicitly all bispectra to all orders in derivatives for a single scalar. Since we don’t invoke soft theorems, this can also be extended to multi-field inflation. The second is a partial energy recursion relation that allows us to compute exchange correlators. Combining a bespoke complex shift of the partial energies with Cauchy’s integral theorem and the Cosmological Optical Theorem, we fix exchange correlators up to a boundary term. The latter can be determined up to contact interactions using unitarity and manifest locality. As an illustration, we use these tools to bootstrap scalar inflationary trispectra due to graviton exchange and inflaton self-interactions.

High-performance tracking of high-speed supercavitating vehicles with uncertain parameters using novel parameter-optimal iterative learning control

Robotica ◽  
2014 ◽  
Vol 33 (08) ◽  
pp. 1653-1670 ◽  
Author(s):  
Meisam Yahyazadeh ◽  
Abolfazl Ranjbar Noei
Keyword(s):  
Phase Behavior ◽  
Iterative Learning Control ◽  
High Speed ◽  
Learning Control ◽  
Iterative Learning ◽  
Control Input ◽  
Minimum Phase ◽  
Feed Forward ◽  
Feed Forward Control ◽  
Supercavitating Vehicle

SUMMARYThis paper proposes a new technique based on a Parameter-Optimal Iterative Learning Control (POILC) to track a command pitch rate of a high-speed supercavitating vehicle (HSSV). The pitch rate of a supercavitating vehicle has non-minimum phase behavior. Thus, tracking is fundamentally limited to poor performance. To solve this problem, a feed-forward control can be used while using the cavitator as a control input in the feed-forward path to modify the slow response caused by non-minimum phase behavior. The main idea of this paper is to apply the cavitator input with high precision as a feed-forward control to improve tracking performance. The exact value of the feed-forward control is achieved using POILC. However, in the presence of uncertainty, zero convergence of POILC algorithms is threatened. It will be shown that applying adaptive weight in the performance index, the convergence is guaranteed in the presence of uncertainty and also when the system is sign-indefinite. The proposed technique includes an optimal planning to make the error norm monotonically convergent to zero. The convergence and perfect tracking will be guaranteed through a Lyapunov candidate. Performance and significance of the proposed supercavitating vehicle control will be verified by simulation.

GLASSY DYNAMICS AT THE ONSET OF CHAOS WITH ADDITIVE NOISE

2005 ◽  
Vol 05 (02) ◽  
pp. L313-L318 ◽  
Author(s):  
FULVIO BALDOVIN ◽  
ALBERTO ROBLEDO
Keyword(s):  
Glass Transition ◽  
Transition Temperature ◽  
Additive Noise ◽  
Logistic Map ◽  
Supercooled Liquid ◽  
External Noise ◽  
Translation Invariance ◽  
Time Translation ◽  
Onset Of Chaos ◽  
Dynamical Properties

After recalling key phenomenological properties of glass formation, we point out that similar features are exhibited by the dynamical properties of the noise-perturbed iterates of the logistic map at the onset of chaos. The analysis includes two-step relaxation, aging, subdiffusion and arrest, as well as an expression analogous to the Adam–Gibbs relation connecting dynamical and thermodynamic properties of a glass former. The dynamical properties of the logistic map in the presence of external noise are seen to be comparable to those of a supercooled liquid above a glass transition temperature, whereas the noiseless attractor displays typical nonequilibrium aspects like loss of time translation invariance (aging). Reference is made to connections between the noiseless dynamics at the chaos threshold and the nonextensive formalism.

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