scholarly journals Simple model for an upper bound on density fluctuations in a turbulent pinch

1980 ◽  
Author(s):  
A.R. Jacobson
Keyword(s):  
Simple Model ◽  
Upper Bound ◽  
Density Fluctuations

scholarly journals Asymptotic spectral gap and Weyl law for Ruelle resonances of open partially expanding maps

2015 ◽  
Vol 37 (1) ◽  
pp. 1-58 ◽  
Author(s):  
JEAN FRANCOIS ARNOLDI ◽  
FRÉDÉRIC FAURE ◽  
TOBIAS WEICH
Keyword(s):  
Phase Space ◽  
Simple Model ◽  
Upper Bound ◽  
Large Time ◽  
Spectral Gap ◽  
Semiclassical Limit ◽  
Gauss Map ◽  
Fourier Component ◽  
Expanding Map ◽  
Weyl Law

We consider a simple model of an open partially expanding map. Its trapped set ${\mathcal{K}}$ in phase space is a fractal set. We first show that there is a well-defined discrete spectrum of Ruelle resonances which describes the asymptotic of correlation functions for large time and which is parametrized by the Fourier component $\unicode[STIX]{x1D708}$ in the neutral direction of the dynamics. We introduce a specific hypothesis on the dynamics that we call ‘minimal captivity’. This hypothesis is stable under perturbations and means that the dynamics is univalued in a neighborhood of ${\mathcal{K}}$. Under this hypothesis we show the existence of an asymptotic spectral gap and a fractal Weyl law for the upper bound of density of Ruelle resonances in the semiclassical limit $\unicode[STIX]{x1D708}\rightarrow \infty$. Some numerical computations with the truncated Gauss map and Bowen–Series maps illustrate these results.

scholarly journals Dispersal-induced instability in complex ecosystems

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
Joseph W. Baron ◽  
Tobias Galla
Keyword(s):  
Simple Model ◽  
Pattern Formation ◽  
Upper Bound ◽  
Trophic Structure ◽  
Stable Equilibrium ◽  
Ecosystem Stability ◽  
Matrix Approach ◽  
Natural Ecosystems ◽  
Upper Limit ◽  
Complex Ecosystem

AbstractIn his seminal work in the 1970s, Robert May suggested that there is an upper limit to the number of species that can be sustained in stable equilibrium by an ecosystem. This deduction was at odds with both intuition and the observed complexity of many natural ecosystems. The so-called stability-diversity debate ensued, and the discussion about the factors contributing to ecosystem stability or instability continues to this day. We show in this work that dispersal can be a destabilising influence. To do this, we combine ideas from Alan Turing’s work on pattern formation with May’s random-matrix approach. We demonstrate how a stable equilibrium in a complex ecosystem with trophic structure can become unstable with the introduction of dispersal in space, and we discuss the factors which contribute to this effect. Our work highlights that adding more details to the model of May can give rise to more ways for an ecosystem to become unstable. Making May’s simple model more realistic is therefore unlikely to entirely remove the upper bound on complexity.

Chaos and secular cycles in a structurally simple model society

2012 ◽  
Author(s):  
Alexander Medvinsky ◽  
Alexey Rusakov
Keyword(s):  
Simple Model

A Simple Model of Changes in Lumbar Intervertebral Angles During Sagittal Torso Flexion

2011 ◽  
Author(s):  
Riley E. Splittstoesser ◽  
Greg G. Knapik ◽  
William S. Marras
Keyword(s):  
Simple Model

Discussion of the band structure effects on thermoemission as deduced from a simple model

1976 ◽  
Vol 37 (2) ◽  
pp. 149-158 ◽  
Author(s):  
A.K. Bhattacharjee ◽  
B. Caroli ◽  
D. Saint-James
Keyword(s):  
Simple Model ◽  
Band Structure

Description of a Simple Model for the Study of Bone Calcium Metabolism

1980 ◽  
Vol 19 (01) ◽  
pp. 11-15
Author(s):  
G. Roncari ◽  
L. Rapisardi ◽  
L. Conte ◽  
G. Pedroli
Keyword(s):  
Simple Model ◽  
Calcium Metabolism ◽  
Good Description ◽  
Radioactive Tracer ◽  
Normal Subjects ◽  
Bone Diseases ◽  
Compartment System ◽  
Bone Calcium ◽  
Finite Period ◽  
Kinetics Of

A simple model for the study of bone calcium metabolism is proposed. It describes the kinetics of a radioactive tracer in terms of an open single compartment system with an expanding volume for a finite period of time. In addition to the simplicity of the hypotheses introduced, the model is able to give a good description of the biological processes which regulate calcium kinetics. Moreover the functional parameters can be easily calculated, even just graphically. 15 normal subjects and 22 patients affected by various bone diseases were studied. The results were compared with those obtained by using the model proposed by Burkinshaw et al. and the method described by Reeve et al.

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