Asymptotic determination of single-frequency vibrations in a quasi-linear autonomous system with time-lag

1969 ◽  
Vol 20 (6) ◽  
pp. 703-712 ◽  
Author(s):  
S. N. Shimanov
Keyword(s):  
Autonomous System ◽  
Time Lag ◽  
Single Frequency ◽  
Linear Autonomous System ◽  
Asymptotic Determination

GENERATING 3-D SCROLL GRID ATTRACTORS OF FRACTIONAL DIFFERENTIAL SYSTEMS VIA STAIR FUNCTION

2007 ◽  
Vol 17 (11) ◽  
pp. 3965-3983 ◽  
Author(s):  
WEIHUA DENG
Keyword(s):  
Differential System ◽  
Autonomous System ◽  
Function Approach ◽  
Differential Systems ◽  
Fractional Differential Systems ◽  
Fractional Differential System ◽  
Linear Autonomous System ◽  
Fractional Differential ◽  
The One ◽  
Number Of Equilibria

This paper discusses the stair function approach for the generation of scroll grid attractors of fractional differential systems. The one-directional (1-D) n-grid scroll, two-directional (2-D) (n × m)-grid scroll and three-directional (3-D) (n × m × l)-grid scroll attractors are created from a fractional linear autonomous system with a simple stair function controller. Being similar to the scroll grid attractors of classical differential systems, the scrolls of 1-D n-grid scroll, 2-D (n × m)-grid scroll and 3-D (n × m × l)-grid scroll attractors are located around the equilibria of fractional differential system on a line, on a plane or in 3D, respectively and the number of scrolls is equal to the corresponding number of equilibria.

Modeling the Vibratory Drilling Process

1999 ◽  
Author(s):  
Stephen A. Batzer ◽  
Alexander M. Gouskov ◽  
Sergey A. Voronov
Keyword(s):  
Rotational Velocity ◽  
Time Lag ◽  
Chip Thickness ◽  
Cutting Conditions ◽  
Model Parameters ◽  
Drilling Process ◽  
Workpiece Material ◽  
Velocity Amplitude ◽  
The Stability

Abstract The dynamic behavior of deep-hole vibratory drilling is analyzed. The mathematical model presented allows the determination of axial tool and workpiece displacements and cutting forces for significant dynamic system behavior such as the entrance of the cutting tool into workpiece material and exit. Model parameters include the actual rigidity of the tool and workpiece, time-varying chip thickness, time lag for chip formation due to tool rotation and possible disengagement of drill cutting edges from the workpiece due to tool and/or workpiece axial vibrations. The main features of this model are its nonlinearity and inclusion of time lag differential equations which require numeric solutions. The specific cutting conditions (feed, tool rotational velocity, amplitude and frequency of forced vibrations) necessary to obtain discontinuous chips and reliable removal are determined. The stability conditions of excited vibrations are also investigated. Calculated bifurcation diagrams make it possible to derive the domain of system parameters along with the determination of optimal cutting conditions.

Weak duality and the asymptotic determination of mass spectra

1970 ◽  
Vol 65 (4) ◽  
pp. 683-688
Author(s):  
D. Atkinson ◽  
K. Dietz
Keyword(s):  
Mass Spectra ◽  
Weak Duality ◽  
Asymptotic Determination

A study on first citations of patents through a combination of Bradford’s distribution, Cox regression and life tables method

2019 ◽  
Vol 46 (4) ◽  
pp. 496-507
Author(s):  
Mohammad Tavakolizadeh-Ravari ◽  
Faramarz Soheili ◽  
Fatemeh Makkizadeh ◽  
Fatemeh Akrami
Keyword(s):  
Survival Analysis ◽  
Cox Regression ◽  
Time Lag ◽  
The United States ◽  
Life Tables ◽  
Analysis Methods ◽  
Life Table Data ◽  
Table Data ◽  
States Patent

The current research employs two survival analysis methods: Cox regression and life tables. The first determines the effect of inventor, assignee and country for receiving the first citation by patents. Life tables concern the time-lag between the dates of granting and receiving the first citation by patents. Bradford’s method is also established as a technique for categorization of patents, inventors, assignees and countries as a prerequisite for survival analysis. The research materials consist of 2837 patents in the area of ‘purification, separation, or recovery of hydrocarbon components’ which were classified under the classes 585/800 and 585/868 by the United States Patent and Trademark Office (USPTO). The findings showed that Bradford’s method complies with the distribution of citations of patents, first inventors and assignees. It means that Bradford’s distribution is well suited for determination of key patents, inventors and assignees in an area too. Cox regression revealed that only the inventors’ variable decides for receiving the first citation in terms of frequency, degrees of their inventions and citations. Life table data revealed that one half of the first citations were received in the first 10 years. As a conclusion, survival analysis methods provide the possibility for deciding technology lifetime and for predicting the determinants for the flow of knowledge through citation analysis.

scholarly journals Quantification of drainable water storage volumes on landmasses and in river networks based on GRACE and river runoff using a cascaded storage approach – first application on the Amazon

2020 ◽  
Vol 24 (3) ◽  
pp. 1447-1465 ◽  
Author(s):  
Johannes Riegger
Keyword(s):  
Phase Shift ◽  
River Runoff ◽  
River Discharge ◽  
Time Lag ◽  
Water Storage ◽  
River Network ◽  
River Networks ◽  
Time Constants ◽  
Tropical Conditions

Abstract. The knowledge of water storage volumes in catchments and in river networks leading to river discharge is essential for the description of river ecology, the prediction of floods and specifically for a sustainable management of water resources in the context of climate change. Measurements of mass variations by the GRACE gravity satellite or by ground-based observations of river or groundwater level variations do not permit the determination of the respective storage volumes, which could be considerably bigger than the mass variations themselves. For fully humid tropical conditions like the Amazon the relationship between GRACE and river discharge is linear with a phase shift. This permits the hydraulic time constant to be determined and thus the total drainable storage directly from observed runoff can be quantified, if the phase shift can be interpreted as the river time lag. As a time lag can be described by a storage cascade, a lumped conceptual model with cascaded storages for the catchment and river network is set up here with individual hydraulic time constants and mathematically solved by piecewise analytical solutions. Tests of the scheme with synthetic recharge time series show that a parameter optimization either versus mass anomalies or runoff reproduces the time constants for both the catchment and the river network τC and τR in a unique way, and this then permits an individual quantification of the respective storage volumes. The application to the full Amazon basin leads to a very good fitting performance for total mass, river runoff and their phasing (Nash–Sutcliffe for signals 0.96, for monthly residuals 0.72). The calculated river network mass highly correlates (0.96 for signals, 0.76 for monthly residuals) with the observed flood area from GIEMS and corresponds to observed flood volumes. The fitting performance versus GRACE permits river runoff and drainable storage volumes to be determined from recharge and GRACE exclusively, i.e. even for ungauged catchments. An adjustment of the hydraulic time constants (τC, τR) on a training period facilitates a simple determination of drainable storage volumes for other times directly from measured river discharge and/or GRACE and thus a closure of data gaps without the necessity of further model runs.

GENERATING CHAOS VIA A DYNAMICAL CONTROLLER

2001 ◽  
Vol 11 (03) ◽  
pp. 865-869 ◽  
Author(s):  
GUO-QUN ZHONG ◽  
KIM F. MAN ◽  
GUANRONG CHEN
Keyword(s):  
Computer Simulation ◽  
Autonomous System ◽  
Quadratic Function ◽  
Feedback Controller ◽  
Nonlinear Feedback ◽  
Circuit Implementation ◽  
Linear Autonomous System

This Letter studies the generation of chaos from a linear autonomous system by employing a dynamical nonlinear feedback controller. The system setup is quite simple, and the only nonlinearity is a piecewise-quadratic function in the form of x|x|. Both computer simulation and circuit implementation are given to verify the chaos generated by this mechanism.

Sign in / Sign up

Export Citation Format

Share Document