scholarly journals ITERATIONS OF THE SAWTOOTH MAP AS A DYNAMICAL MODEL FOR CVD/CVI SiC POLYTYPE GROWTH

1993 ◽  
Vol 03 (05) ◽  
pp. 1177-1194 ◽  
Author(s):  
GÉRARD L. VIGNOLES
Keyword(s):  
Mathematical Model ◽  
Point Of View ◽  
Dynamical Model ◽  
Reported Data ◽  
Combinatorial Point ◽  
Simple Logistic ◽  
Kneading Theory ◽  
Two Parameter ◽  
Silicon Carbide Polytype ◽  
Parameter Bifurcation

In order to describe silicon carbide polytype growth under CVD/CVI conditions, a dynamical model based on iterations of the sawtooth map has been studied. A two-parameter bifurcation diagram has been computed for a simple logistic-like family, and its structure has been studied in more detail by means of kneading theory and study of the skeleton. All the routes to chaos are shown to derive from the application of a central theorem involved in the construction of the skeleton. A comparison, under a combinatorial point of view, between this mathematical model and the reported data on known SiC polytypes is carried out and discussed. Indeed, the model is able to generate any periodic or chaotic polytypic sequence.

scholarly journals Computational Analysis of Ca2+ Oscillatory Bio-Signals: Two-Parameter Bifurcation Diagrams

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 876
Author(s):  
Wieslaw Marszalek ◽  
Jan Sadecki ◽  
Maciej Walczak
Keyword(s):  
Equilibrium Points ◽  
Autonomous Systems ◽  
Cytosolic Calcium ◽  
Calcium Oscillations ◽  
Dynamical Model ◽  
Bifurcation Diagrams ◽  
Step Size ◽  
Oscillatory Systems ◽  
Two Parameter ◽  
Parameter Bifurcation

Two types of bifurcation diagrams of cytosolic calcium nonlinear oscillatory systems are presented in rectangular areas determined by two slowly varying parameters. Verification of the periodic dynamics in the two-parameter areas requires solving the underlying model a few hundred thousand or a few million times, depending on the assumed resolution of the desired diagrams (color bifurcation figures). One type of diagram shows period-n oscillations, that is, periodic oscillations having n maximum values in one period. The second type of diagram shows frequency distributions in the rectangular areas. Each of those types of diagrams gives different information regarding the analyzed autonomous systems and they complement each other. In some parts of the considered rectangular areas, the analyzed systems may exhibit non-periodic steady-state solutions, i.e., constant (equilibrium points), oscillatory chaotic or unstable solutions. The identification process distinguishes the later types from the former one (periodic). Our bifurcation diagrams complement other possible two-parameter diagrams one may create for the same autonomous systems, for example, the diagrams of Lyapunov exponents, Ls diagrams for mixed-mode oscillations or the 0–1 test for chaos and sample entropy diagrams. Computing our two-parameter bifurcation diagrams in practice and determining the areas of periodicity is based on using an appropriate numerical solver of the underlying mathematical model (system of differential equations) with an adaptive (or constant) step-size of integration, using parallel computations. The case presented in this paper is illustrated by the diagrams for an autonomous dynamical model for cytosolic calcium oscillations, an interesting nonlinear model with three dynamical variables, sixteen parameters and various nonlinear terms of polynomial and rational types. The identified frequency of oscillations may increase or decrease a few hundred times within the assumed range of parameters, which is a rather unusual property. Such a dynamical model of cytosolic calcium oscillations, with mitochondria included, is an important model in which control of the basic functions of cells is achieved through the Ca2+ signal regulation.

scholarly journals A mathematical model to investigate the transmission of COVID-19 in the Kingdom of Saudi Arabia

2020 ◽  
Author(s):  
Fehaid Salem Alshammari
Keyword(s):  
Mathematical Model ◽  
Saudi Arabia ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
European Countries ◽  
Dynamical Model ◽  
Kingdom Of Saudi Arabia ◽  
Ministry Of Health ◽  
Reported Data ◽  
The Basic Reproduction Number

AbstractSince the first confirmed case of SARS-CoV-2 coronavirus (COVID-19) in the 2nd day of March, Saudi Arabia has not report a quite rapid COVD-19 spread compared to America and many European countries. Possible causes include the spread of asymptomatic cases. To characterize the transmission of COVID-19 in Saudi Arabia, this paper applies a susceptible, exposed, symptomatic, asymptomatic, hospitalized, and recovered dynamical model, along with the official COVID-19 reported data by the Ministry of Health in Saudi Arabia. The basic reproduction number R0 is estimated to range from 2.87 to 4.9.

Oscillation Reconstruction and Bifurcation Analysis of a Drillbit–Rock Vibro-Impact System

2017 ◽  
Vol 27 (01) ◽  
pp. 1750013 ◽  
Author(s):  
Maolin Liao ◽  
Yinao Su ◽  
Yingcao Zhou
Keyword(s):  
Mathematical Model ◽  
Numerical Continuation ◽  
Simplified Model ◽  
Percussive Drilling ◽  
Impact System ◽  
Codimension One ◽  
Drilling System ◽  
Parameter Continuation ◽  
Two Parameter ◽  
Parameter Bifurcation

A drillbit–rock vibro-impact system with a linear rock contact law is considered in this paper. This system is a simplified model to study the drillbit oscillation in a percussive drilling system. The main purpose of this work is to explore the optimized vibration condition of the drillbit to improve the drilling efficiency in practical drilling applications. In order to eliminate the influences of drilling progression on the dynamic analysis of drillbit oscillation, the drillbit oscillation is separated from its drift via oscillation reconstruction. The obtained bounded mathematical model is analyzed by numerical integration and numerical continuation. Based on the codimension-one bifurcations detected by TC-HAT during one-parameter continuation, the two-parameter bifurcation curves are traced by two-parameter continuation. These explored two-parameter bifurcation curves constitute the parameter boundaries for the period-one one-impact oscillation of drillbit, which is verified as the optimal oscillation with the highest drilling efficiency.

On the displacements of the contours of the optic-electronic space images. Mathematical modeling of displacement

2017 ◽  
Vol 992 (4) ◽  
pp. 32-38 ◽  
Author(s):  
E.G. Voronin
Keyword(s):  
Mathematical Modeling ◽  
Remote Sensing ◽  
Mathematical Model ◽  
Point Of View ◽  
Design Features ◽  
Space Images ◽  
Electronic Imaging ◽  
Measuring Accuracy ◽  
Physical Laws

The article opens a cycle of three consecutive publications dedicated to the phenomenon of the displacement of the same points in overlapping scans obtained adjacent CCD matrices with opto-electronic imagery. This phenomenon was noticed by other authors, but the proposed explanation for the origin of displacements and the resulting estimates are insufficient, and developed their solutions seem controversial from the point of view of recovery of the measuring accuracy of opticalelectronic space images, determined by the physical laws of their formation. In the first article the mathematical modeling of the expected displacements based on the design features of a scanning opto-electronic imaging equipment. It is shown that actual bias cannot be forecast, because they include additional terms, which may be gross, systematic and random values. The proposed algorithm for computing the most probable values of the additional displacement and ways to address some of the systematic components of these displacements in a mathematical model of optical-electronic remote sensing.

Two-parameter bifurcation analysis of longitudinal flight dynamics

2003 ◽  
Vol 39 (3) ◽  
pp. 1103-1112 ◽  
Author(s):  
Der-Cherng Liaw ◽  
Chau-Chung Song ◽  
Yew-Wen Liang ◽  
Wen-Ching Chung
Keyword(s):  
Bifurcation Analysis ◽  
Flight Dynamics ◽  
Two Parameter ◽  
Parameter Bifurcation

scholarly journals Characterization and Evaluation of Salvia hispanica L. and Salvia columbariae Benth. Varieties for Their Cultivation in Southwestern Germany

Agronomy ◽  
2020 ◽  
Vol 10 (12) ◽  
pp. 2012
Author(s):  
Samantha Jo Grimes ◽  
Filippo Capezzone ◽  
Peteh Mehdi Nkebiwe ◽  
Simone Graeff-Hönninger
Keyword(s):  
Seed Mass ◽  
Point Of View ◽  
Raw Material ◽  
Salvia Hispanica ◽  
Environmentally Sustainable ◽  
Chia Seed ◽  
Increasing Demand ◽  
Salvia Hispanica L ◽  
Reported Data ◽  
Seed Yields

Rising consumer attraction towards superfoods and the steadily increasing demand for healthy, environmentally sustainable, and regionally produced food products has sharpened the demand for chia. Over the course of 4 years, two early flowering chia varieties belonging to Salvia hispanica L., and Salvia columbariae Benth. Species were identified to complete their phenological development and, therefore, able to reach maturity under a photoperiod >12 h, thus enabling the cultivation of chia in central Europe—more specifically, in southwestern Germany—consistently for the first time. Results obtained by the conducted field trial in 2018 showed that chia seed yields and thousand-seed mass ranged from 284.13 to 643.99 kg ha−1 and 0.92 to 1.36 g, respectively. Further, the statistical analyses showed that the protein content of the cultivated chia varieties ranged from 22.14 to 27.78%, the mucilage content varied from 10.35 to 20.66%, and the crude oil content amounted up to 28.00 and 31.73%. Fatty acid profiles were similar to previously reported data with α-Linolenic acid being the most prominent one, ranging from 60.40 to 65.87%, and we obtained ω6:ω3 ratios between 0.2 and 0.3. In conclusion, chia could represent a promising raw material from a nutritional point of view, while being able to diversify the local food basis of southwestern Germany.

scholarly journals Asymmetric and chaotic responses of dry friction oscillators with different static and kinetic coefficients of friction

Meccanica ◽  
2021 ◽  
Author(s):  
Gábor Csernák ◽  
Gábor Licskó
Keyword(s):  
Dry Friction ◽  
Continuation Method ◽  
Friction Model ◽  
Lugre Friction Model ◽  
Kinetic Coefficients ◽  
Friction Oscillator ◽  
Lugre Friction ◽  
Friction Parameters ◽  
Two Parameter ◽  
Parameter Bifurcation

AbstractThe responses of a simple harmonically excited dry friction oscillator are analysed in the case when the coefficients of static and kinetic coefficients of friction are different. One- and two-parameter bifurcation curves are determined at suitable parameters by continuation method and the largest Lyapunov exponents of the obtained solutions are estimated. It is shown that chaotic solutions can occur in broad parameter domains—even at realistic friction parameters—that are tightly enclosed by well-defined two-parameter bifurcation curves. The performed analysis also reveals that chaotic trajectories are bifurcating from special asymmetric solutions. To check the robustness of the qualitative results, characteristic bifurcation branches of two slightly modified oscillators are also determined: one with a higher harmonic in the excitation, and another one where Coulomb friction is exchanged by a corresponding LuGre friction model. The qualitative agreement of the diagrams supports the validity of the results.

A note on design-based versus model-based variance estimation in stereology

2002 ◽  
Vol 34 (03) ◽  
pp. 484-490 ◽  
Author(s):  
Asger Hobolth ◽  
Eva B. Vedel Jensen
Keyword(s):  
Mathematical Model ◽  
Original Problem ◽  
Variance Estimation ◽  
Point Of View ◽  
Systematic Sampling ◽  
Variance Estimator ◽  
Shape Model ◽  
Model Based ◽  
Versus Model ◽  
Special Case

Recently, systematic sampling on the circle and the sphere has been studied by Gual-Arnau and Cruz-Orive (2000) from a design-based point of view. In this note, it is shown that their mathematical model for the covariogram is, in a model-based statistical setting, a special case of the p-order shape model suggested by Hobolth, Pedersen and Jensen (2000) and Hobolth, Kent and Dryden (2002) for planar objects without landmarks. Benefits of this observation include an alternative variance estimator, applicable in the original problem of systematic sampling. In a wider perspective, the paper contributes to the discussion concerning design-based versus model-based stereology.

Effective Properties of Superconducting and Superfluid Composites

1998 ◽  
Vol 12 (29n31) ◽  
pp. 3063-3073 ◽  
Author(s):  
Leonid Berlyand
Keyword(s):  
Mathematical Model ◽  
Linear Problem ◽  
Effective Properties ◽  
Point Of View ◽  
Periodicity Cell ◽  
Unit Size ◽  
Composite Media ◽  
Homogenization Procedure

We consider a mathematical model which describes an ideal superfluid with a large number of thin insulating rods and an ideal superconductor reinforced by such rods. We suggest a homogenization procedure for calculating effective properties of both composite media. From the numerical point of view the procedure amounts to solving a linear problem in a periodicity cell of unit size.

Sign in / Sign up

Export Citation Format

Share Document