scholarly journals White noise perturbation of locally stable dynamical systems

2016 ◽  
Vol 17 (01) ◽  
pp. 1750002 ◽  
Author(s):  
Oskar Sultanov
Keyword(s):  
White Noise ◽  
Stable Equilibrium ◽  
Perturbation Parameter ◽  
Time Interval ◽  
Random Perturbations ◽  
Perturbed System ◽  
Noise Perturbation ◽  
Long Time ◽  
Small Random Perturbations ◽  
Deterministic Dynamical System

The influence of small random perturbations on a deterministic dynamical system with a locally stable equilibrium is considered. The perturbed system is described by the Itô stochastic differential equation. It is assumed that the noise does not vanish at the equilibrium. In this case the trajectories of the stochastic system may leave any bounded domain with probability one. We analyze the stochastic stability of the equilibrium under a persistent perturbation by white noise on an asymptotically long time interval [Formula: see text], where [Formula: see text] is a perturbation parameter.

An Adaptive and Learning System for Feedback-Controlled Evoked Response Studies

1981 ◽  
Vol 20 (03) ◽  
pp. 169-173
Author(s):  
J. Wagner ◽  
G. Pfurtscheixer
Keyword(s):  
Brain Activity ◽  
Evoked Response ◽  
Learning System ◽  
Time Interval ◽  
Electrical Brain Activity ◽  
Long Time ◽  
The Subject ◽  
Eeg Power ◽  
Stimulation System ◽  
Background Eeg

The shape, latency and amplitude of changes in electrical brain activity related to a stimulus (Evoked Potential) depend both on the stimulus parameters and on the background EEG at the time of stimulation. An adaptive, learnable stimulation system is introduced, whereby the subject is stimulated (e.g. with light), whenever the EEG power is subthreshold and minimal. Additionally, the system is conceived in such a way that a certain number of stimuli could be given within a particular time interval. Related to this time criterion, the threshold specific for each subject is calculated at the beginning of the experiment (preprocessing) and adapted to the EEG power during the processing mode because of long-time fluctuations and trends in the EEG. The process of adaptation is directed by a table which contains the necessary correction numbers for the threshold. Experiences of the stimulation system are reflected in an automatic correction of this table. Because the corrected and improved table is stored after each experiment and is used as the starting table for the next experiment, the system >learns<. The system introduced here can be used both for evoked response studies and for alpha-feedback experiments.

scholarly journals Optimal Perturbations of an Oceanic Vortex Lens

Fluids ◽  
2018 ◽  
Vol 3 (3) ◽  
pp. 63 ◽  
Author(s):  
Thomas Meunier ◽  
Claire Ménesguen ◽  
Xavier Carton ◽  
Sylvie Le Gentil ◽  
Richard Schopp
Keyword(s):  
Normal Mode ◽  
Growth Rates ◽  
Time Interval ◽  
Time Intervals ◽  
Horizontal Structure ◽  
Azimuthal Wave ◽  
Wave Numbers ◽  
Non Linear ◽  
Long Time ◽  
Short Time

The stability properties of a vortex lens are studied in the quasi geostrophic (QG) framework using the generalized stability theory. Optimal perturbations are obtained using a tangent linear QG model and its adjoint. Their fine-scale spatial structures are studied in details. Growth rates of optimal perturbations are shown to be extremely sensitive to the time interval of optimization: The most unstable perturbations are found for time intervals of about 3 days, while the growth rates continuously decrease towards the most unstable normal mode, which is reached after about 170 days. The horizontal structure of the optimal perturbations consists of an intense counter-shear spiralling. It is also extremely sensitive to time interval: for short time intervals, the optimal perturbations are made of a broad spectrum of high azimuthal wave numbers. As the time interval increases, only low azimuthal wave numbers are found. The vertical structures of optimal perturbations exhibit strong layering associated with high vertical wave numbers whatever the time interval. However, the latter parameter plays an important role in the width of the vertical spectrum of the perturbation: short time interval perturbations have a narrow vertical spectrum while long time interval perturbations show a broad range of vertical scales. Optimal perturbations were set as initial perturbations of the vortex lens in a fully non linear QG model. It appears that for short time intervals, the perturbations decay after an initial transient growth, while for longer time intervals, the optimal perturbation keeps on growing, quickly leading to a non-linear regime or exciting lower azimuthal modes, consistent with normal mode instability. Very long time intervals simply behave like the most unstable normal mode. The possible impact of optimal perturbations on layering is also discussed.

scholarly journals Radiomorphology of the Habib Sealer-Induced Resection Plane during Long-Time Followup:A Longitudinal Single Center Experience after 64 Radiofrequency-AssistedLiver Resections

HPB Surgery ◽  
2010 ◽  
Vol 2010 ◽  
pp. 1-7 ◽  
Author(s):  
Robert Kleinert ◽  
Roger Wahba ◽  
Christoph Bangard ◽  
Klaus Prenzel ◽  
Arnulf H. Hölscher ◽  
...  
Keyword(s):  
Liver Resection ◽  
Morphological Characteristics ◽  
Postoperative Mortality ◽  
Coagulation Necrosis ◽  
Time Interval ◽  
Safe Alternative ◽  
Time Points ◽  
Single Center Experience ◽  
Long Time

Background. Radiofrequency (RF-) assisted liver resection devices like the Habib sealer induce a necrotic resection plane from which a small margin of necrotic liver tissue remains in situ. The aim of the present paper was to report our long-time experience with the new resection method and the morphological characteristics of the remaining necrotic resection plane. Methods. 64 RF-assisted liver resections were performed using the Habib sealer. Followup was assessed at defined time points. Results. The postoperative mortality was 3,6% and morbidity was 18%. The followup revealed that the necrotic zone was detectable in all analyzed CT and MRI images as a hypodense structure without any contrast enhancement at all time points, irrespectively of the time interval between resection and examination. Conclusion. Liver resection utilizing radiofrequency-induced resection plane coagulation is a safe alternative to the established resection techniques. The residual zone of coagulation necrosis remains basically unchanged during a followup of three years. This has to be kept in mind when evaluating the follow up imaging of these patients.

LONG‐TIME RESPONSE PREDICTED BY EXACT ELASTIC RAY THEORY

Geophysics ◽  
1965 ◽  
Vol 30 (3) ◽  
pp. 363-368 ◽  
Author(s):  
T. W. Spencer
Keyword(s):  
Formal Solution ◽  
Intermediate Stage ◽  
Time Limit ◽  
Time Interval ◽  
Individual Response ◽  
Axially Symmetric ◽  
Long Time ◽  
The Difference ◽  
The Individual ◽  
Significant Figures

The formal solution for an axially symmetric radiation field in a multilayered, elastic system can be expanded in an infinite series. Each term in the series is associated with a particular raypath. It is shown that in the long‐time limit the individual response functions produced by a step input in particle velocity are given by polynomials in odd powers of the time. For rays which suffer m reflections, the degree of the polynomials is 2m+1. The total response is obtained by summing all rays which contribute in a specified time interval. When the rays are selected indiscriminately, the difference between the magnitude of the partial sum at an intermediate stage of computation and the magnitude of the correct total sum may be greater than the number of significant figures carried by the computer. A prescription is stated for arranging the rays into groups. Each group response function varies linearly in the long‐time limit and goes to zero when convolved with a physically realizable source function.

scholarly journals Dynamics of transposable elements under the selection model

1999 ◽  
Vol 74 (2) ◽  
pp. 159-164 ◽  
Author(s):  
A. TSITRONE ◽  
S. CHARLES ◽  
C. BIÉMONT
Keyword(s):  
Equilibrium Point ◽  
Dynamic Characteristics ◽  
Time Scale ◽  
Copy Number ◽  
Stable Equilibrium ◽  
Stable Equilibrium Point ◽  
Asymptotically Stable ◽  
Weak Selection ◽  
Strong Selection ◽  
Long Time

We examine an analytical model of selection against the deleterious effects of transposable element (TE) insertions in Drosophila, focusing attention on the asymptotic and dynamic characteristics. With strong selection the only asymptotically stable equilibrium point corresponds to extinction of the TEs. With very weak selection a stable and realistic equilibrium point can be obtained. The dynamics of the system is fast for strong selection and slow, on the human time scale, for weak selection. Hence weak selection acts as a force that contributes to the stabilization of mean TE copy number. The consequence is that under weak selection, and ‘out-of-equilibrium’ situation can be maintained for a long time in populations, with mean TE copy number appearing stabilized.

scholarly journals On Jensen-type Inequalities for Nonsmooth Radial Scattering Solutions of a Loglog Energy-Supercritical Schrödinger Equation

2018 ◽  
Vol 2020 (8) ◽  
pp. 2501-2541
Author(s):  
Tristan Roy
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
A Priori ◽  
Time Interval ◽  
Type Estimate ◽  
A Priori Bound ◽  
Long Time ◽  
Supercritical Nonlinearity ◽  
Gamma S ◽  
Radial Scattering

Abstract We prove scattering of solutions of the loglog energy-supercritical Schrödinger equation $i \partial _{t} u + \triangle u = |u|^{\frac{4}{n-2}} u g(|u|)$ with $g(|u|) := \log ^{\gamma } {( \log{(10+|u|^{2})} )}$, $0 &lt; \gamma &lt; \gamma _{n}$, n ∈ {3, 4, 5}, and with radial data $u(0) := u_{0} \in \tilde{H}^{k}:= \dot{H}^{k} (\mathbb{R}^{n})\,\cap\,\dot{H}^{1} (\mathbb{R}^{n})$, where $\frac{n}{2} \geq k&gt; 1 \left(\text{resp.}\,\frac{4}{3}&gt; k &gt; 1\right)$ if n ∈ {3, 4} (resp. n = 5). The proof uses concentration techniques (see e.g., [ 2, 12]) to prove a long-time Strichartz-type estimate on an arbitrarily long time interval J depending on an a priori bound of some norms of the solution, combined with an induction on time of the Strichartz estimates in order to bound these norms a posteriori (see e.g., [ 8, 10]). We also revisit the scattering theory of solutions with radial data in $\tilde{H}^{k}$, $k&gt; \frac{n}{2}$, and n ∈ {3, 4}; more precisely, we prove scattering for a larger range of $\gamma$ s than in [ 10]. In order to control the barely supercritical nonlinearity for nonsmooth solutions, that is, solutions with data in $\tilde{H}^{k}$, $k \leq \frac{n}{2}$, we prove some Jensen-type inequalities.

scholarly journals ANALYSIS OF THE TIME‐DEPENDENT BEHAVIOUR OF COMPOSITE CROSS‐SECTIONS BY LAPLACE‐TRANSFORM

2005 ◽  
Vol 11 (3) ◽  
pp. 203-209
Author(s):  
Erich Raue ◽  
Thorsten Heidolf
Keyword(s):  
Laplace Transform ◽  
Cross Sections ◽  
Composite Structures ◽  
Time Dependent ◽  
Time Interval ◽  
Final State ◽  
Long Time ◽  
Time Dependent Behaviour ◽  
Linear Differential ◽  
Dependent Behaviour

Composite structures consisting of precast and cast in‐situ concrete elements are increasingly common. These combinations demand a mechanical model which takes into account the time‐dependent behaviour and analysis of the different ages of the connected concrete components. The effect of creep and shrinkage of the different concrete components can be of relevance for the state of serviceability, as well as for the final state. The long‐time behaviour of concrete can be described by the rate‐of‐creep method, combined with a discretisation of time. The internal forces are described for each time interval using a system of linear differential equations, which can be solved by Laplace‐transform.

Sign in / Sign up

Export Citation Format

Share Document