scholarly journals On the constructive approximation of non-linear operators in the modelling of dynamical systems

1997 ◽  
Vol 39 (1) ◽  
pp. 1-27 ◽  
Author(s):  
A. P. Torokhti ◽  
P. G. Howlett
Keyword(s):  
Dynamical Systems ◽  
Real Number ◽  
Input Signal ◽  
Linear Operators ◽  
Non Linear ◽  
Constructive Approximation ◽  
Modelling Process ◽  
Theoretical Procedure ◽  
Small Disturbances

AbstractIn this paper we propose a systematic theoretical procedure for the constructive approximation of non-linear operators and show how this procedure can be applied to the modelling of dynamical systems. We extend previous work to show that the model is stable to small disturbances in the input signal and we pay special attention to the role of real number parameters in the modelling process. The implications of computability are also discussed. A number of specific examples are presented for the particular purpose of illustrating the theoretical procedure.

Regularität in der nichtlinearen Spektraltheorie

1979 ◽  
Vol 83 (1-2) ◽  
pp. 81-91 ◽  
Author(s):  
Jürgen Weyer
Keyword(s):  
Spectral Theory ◽  
Nonlinear Theory ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Linear Operators ◽  
Non Linear

SynopsisA non-linear spectral theory is developed which includes the spectral theory of linear operators and the theory of (maximal) monotone operators. In this nonlinear theory certain polytone operators will play the role of the linear or monotone operators. The concept of λ-polytonicity allows the characterization of regular points in terms of maximality. Furthermore, properties of the spectrum of non-linear operators are discussed in terms of the corresponding properties of their linearizations and vice versa.

The Non-Causal Character of Renormalization Group Explanations

2018 ◽  
Author(s):  
Margaret Morrison
Keyword(s):  
Probability Theory ◽  
Renormalization Group ◽  
Dynamical Systems ◽  
Recent Literature ◽  
Mathematical Explanation ◽  
Causal Status ◽  
Physical Information ◽  
The Relationship ◽  
Structural Aspects

After reviewing some of the recent literature on non-causal and mathematical explanation, this chapter develops an argument as to why renormalization group (RG) methods should be seen as providing non-causal, yet physical, information about certain kinds of systems/phenomena. The argument centres on the structural character of RG explanations and the relationship between RG and probability theory. These features are crucial for the claim that the non-causal status of RG explanations involves something different from simply ignoring or “averaging over” microphysical details—the kind of explanations common to statistical mechanics. The chapter concludes with a discussion of the role of RG in treating dynamical systems and how that role exemplifies the structural aspects of RG explanations which in turn exemplifies the non-causal features.

scholarly journals Sensitivity of wavepackets in jets to non-linear effects: the role of the critical layer

2015 ◽  
Author(s):  
Gilles Tissot ◽  
Mengqi Zhang ◽  
Francisco C. Lajús ◽  
André V. Cavalieri ◽  
Peter Jordan ◽  
...  
Keyword(s):  
Critical Layer ◽  
Non Linear ◽  
Linear Effects

scholarly journals A Unified Mathematical Formalism for First to Third Order Dielectric Response of Matter: Application to Surface-Specific Two-Colour Vibrational Optical Spectroscopy

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 153 ◽  
Author(s):  
Christophe Humbert ◽  
Thomas Noblet
Keyword(s):  
Dielectric Response ◽  
Structure And Properties ◽  
Linear Optics ◽  
Third Order ◽  
Mathematical Functions ◽  
Sum Frequency ◽  
Non Linear Optics ◽  
Non Linear ◽  
Light Excitation

To take advantage of the singular properties of matter, as well as to characterize it, we need to interact with it. The role of optical spectroscopies is to enable us to demonstrate the existence of physical objects by observing their response to light excitation. The ability of spectroscopy to reveal the structure and properties of matter then relies on mathematical functions called optical (or dielectric) response functions. Technically, these are tensor Green’s functions, and not scalar functions. The complexity of this tensor formalism sometimes leads to confusion within some articles and books. Here, we do clarify this formalism by introducing the physical foundations of linear and non-linear spectroscopies as simple and rigorous as possible. We dwell on both the mathematical and experimental aspects, examining extinction, infrared, Raman and sum-frequency generation spectroscopies. In this review, we thus give a personal presentation with the aim of offering the reader a coherent vision of linear and non-linear optics, and to remove the ambiguities that we have encountered in reference books and articles.

Numerical characterization of nonlinear dynamical systems using parallel computing: The role of GPUs approach

2016 ◽  
Vol 37 ◽  
pp. 143-162 ◽  
Author(s):  
Filipe I. Fazanaro ◽  
Diogo C. Soriano ◽  
Ricardo Suyama ◽  
Marconi K. Madrid ◽  
José Raimundo de Oliveira ◽  
...  
Keyword(s):  
Parallel Computing ◽  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical ◽  
Numerical Characterization

In search of lost space: The process of space planning through remembering and history

Organization ◽  
2015 ◽  
Vol 23 (1) ◽  
pp. 71-89 ◽  
Author(s):  
Fabio James Petani ◽  
Jeanne Mengis
Keyword(s):  
Production Of Space ◽  
Space Planning ◽  
The Past ◽  
Time Space ◽  
Non Linear ◽  
Over Time ◽  
Contested Narratives

This article explores the role of remembering and history in the process of planning new spaces. We trace how the organizational remembering of past spaces enters the conception (i.e. planning) of a large culture center. By drawing on Henri Lefebvre’s reflections on history, time and memory, we analyze the processual interconnections of his spatial triad, namely between the planned, practiced, and lived moments of the production of space. We find that over time space planning involves recurrent, changing, and contested narratives on ‘lost spaces’, remembering happy spaces of the past that articulate a desire to regain them. The notion of lost space adds to our understanding of how space planning involves, through organizational remembering, a sociomaterial and spatiotemporal work of relating together different spaces and times in non-linear narratives of repetition.

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