scholarly journals Non-Standard Analysis for Regularization of Geometric-Zeno Behaviour in Hybrid Systems

Systems ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 15
Author(s):  
Ayman Aljarbouh ◽  
Muhammad Fayaz ◽  
Muhammad Shuaib Qureshi
Keyword(s):  
Hybrid Systems ◽  
Infinite Number ◽  
Time Interval ◽  
Finite Time Interval ◽  
Discrete Events ◽  
Time Step ◽  
Standard Analysis ◽  
Non Standard Analysis ◽  
Simulation Time

Geometric-Zeno behaviour is a highly challenging problem in the analysis (including simulation) of hybrid systems. Geometric-Zeno can be defined as an infinite number of discrete mode switches in a finite time interval. Typically, for hybrid models exhibiting geometric-Zeno, the numerical simulation either halts or produces false results, because an infinite number of discrete events occur in a given simulation time-step. In this paper, we provide formal methods for regularization of geometric-Zeno behaviour by using a non-standard analysis. In particular, we provide formal conditions for the existence of geometric-Zeno in hybrid systems, and we propose methods to allow geometric-Zeno executions to be continued beyond geometric-Zeno limit points. The concepts are illustrated with a case study throughout the paper.

ENTRAINMENT OF MODULATION FREQUENCY: A CASE STUDY

2005 ◽  
Vol 15 (11) ◽  
pp. 3579-3588 ◽  
Author(s):  
KLAUS R. SCHNEIDER
Keyword(s):  
Finite Time ◽  
Modulation Frequency ◽  
Approximation Error ◽  
Wave Frequency ◽  
Time Interval ◽  
Asymptotically Stable ◽  
Finite Time Interval ◽  
Perturbed System ◽  
Wave Solutions

We consider a system of autonomous ODE's which is S1-equivariant and has a family of asymptotically stable modulated wave solutions with wave frequency α0 and modulation frequency β0. This system will be perturbed, where the applied nonautonomous force also represents a modulated wave, but with wave frequency α and modulations frequency β. The strength of this perturbation is not necessarily small. Our goal is to look for conditions such that the perturbed system exhibits an approximate entrainment of the modulation frequency β on any given finite time interval, where the approximation error can be controlled by the wave frequency.

scholarly journals Qualitative Reasoning for Quantitative Simulation

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Mehmet Fatih Hocaoğlu
Keyword(s):  
Quantitative Information ◽  
Qualitative Reasoning ◽  
Time Interval ◽  
Time Step ◽  
Qualitative Variable ◽  
Qualitative Simulation ◽  
Qualitative Variables ◽  
System Variables ◽  
Simulation Time ◽  
Time Point

Qualitative simulation is a well-known reasoning technique that involves the use of simulation technologies. Reasoning is made to determine qualitative values and change directions of system variables, and it is done for each time point and time interval following the time point. Qualitative variables possess continuous qualitative value sets that are discretized by landmark points. Qualitative simulation uses qualitative time representation and its quantitative value is of no interest. The main purpose of this study was to develop a technique to determine time steps for a quantitative simulation under guidance of qualitative information. The proposed technique determined time advances using qualitative and quantitative information together to obtain a robust time step as wide as possible for simulation time advances. For this purpose, sign algebraic properties and derivation roots of quantitative equations and qualitative variable values with their change directions were used to compute time advances. In the approach, qualitative simulation determined landmark points to be advanced, and quantitative simulation calculated the duration required. Using the proposed algorithm, the simulation is advanced instead of iterating simulation time for a predefined time step and checking whether or not there is any activity in the interval, directly to the time points that are qualitatively different.

scholarly journals On the Numerical Simulation of HPDEs Using θ-Weighted Scheme and the Galerkin Method

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 78
Author(s):  
Haifa Bin Jebreen ◽  
Fairouz Tchier
Keyword(s):  
Differential Equation ◽  
Galerkin Method ◽  
Linear Ordinary Differential Equation ◽  
Time Interval ◽  
Hyperbolic Partial Differential Equation ◽  
Time Step ◽  
Numerical Examples ◽  
One Dimensional ◽  
The Stability ◽  
The Galerkin Method

Herein, an efficient algorithm is proposed to solve a one-dimensional hyperbolic partial differential equation. To reach an approximate solution, we employ the θ-weighted scheme to discretize the time interval into a finite number of time steps. In each step, we have a linear ordinary differential equation. Applying the Galerkin method based on interpolating scaling functions, we can solve this ODE. Therefore, in each time step, the solution can be found as a continuous function. Stability, consistency, and convergence of the proposed method are investigated. Several numerical examples are devoted to show the accuracy and efficiency of the method and guarantee the validity of the stability, consistency, and convergence analysis.

scholarly journals A Review on Combination of Ab Initio Molecular Dynamics and NMR Parameters Calculations

2021 ◽  
Vol 22 (9) ◽  
pp. 4378
Author(s):  
Anna Helena Mazurek ◽  
Łukasz Szeleszczuk ◽  
Dariusz Maciej Pisklak
Keyword(s):  
Molecular Dynamics ◽  
Ab Initio ◽  
Small Amplitude ◽  
Ab Initio Molecular Dynamics ◽  
Quantum Mechanical ◽  
Time Step ◽  
Noticeable Effect ◽  
Nmr Parameters ◽  
Mechanical Methods ◽  
Simulation Time

This review focuses on a combination of ab initio molecular dynamics (aiMD) and NMR parameters calculations using quantum mechanical methods. The advantages of such an approach in comparison to the commonly applied computations for the structures optimized at 0 K are presented. This article was designed as a convenient overview of the applied parameters such as the aiMD type, DFT functional, time step, or total simulation time, as well as examples of previously studied systems. From the analysis of the published works describing the applications of such combinations, it was concluded that including fast, small-amplitude motions through aiMD has a noticeable effect on the accuracy of NMR parameters calculations.

Temporal dynamics of encrusting communities during the Late Devonian: a case study from the Central Devonian Field, Russia

Paleobiology ◽  
2017 ◽  
Vol 43 (4) ◽  
pp. 550-568 ◽  
Author(s):  
Michał Zatoń ◽  
Tomasz Borszcz ◽  
Michał Rakociński
Keyword(s):  
Temporal Dynamics ◽  
Small Sample ◽  
Time Interval ◽  
Faunal Turnover ◽  
Central Devonian Field ◽  
Before And After ◽  
Substrate Size ◽  
Mass Extinction Event ◽  
Diversity Dynamics

AbstractIn this study we focused on the dynamics of encrusting assemblages preserved on brachiopod hosts collected from upper Frasnian and lower Famennian deposits of the Central Devonian Field, Russia. Because the encrusted brachiopods come from deposits bracketing the Frasnian/Famennian (F/F) boundary, the results also shed some light on ecological differences in encrusting communities before and after the Frasnian–Famennian (F-F) event. To explore the diversity dynamics of encrusting assemblages, we analyzed more than 1300 brachiopod valves (substrates) from two localities. Taxon accumulation plots and shareholder quorum subsampling (SQS) routines indicated that a reasonably small sample of brachiopod host valves (n=50) is sufficient to capture the majority of the encrusting genera recorded at a given site. The richness of encrusters per substrate declined simultaneously with the number of encrusting taxa in the lower Famennian, accompanied by a decrease in epibiont abundance, with a comparable decrease in mean encrustation intensity (percentage of bioclasts encrusted by one or more epibionts). Epibiont abundance and occupancy roughly mirror each other. Strikingly, few ecological characteristics are correlated with substrate size, possibly reflecting random settlement of larvae. Evenness, which is negatively correlated with substrate size, shows greater within-stage variability among samples than between Frasnian and Famennian intervals and may indicate the instability of early Famennian biocenoses following the faunal turnover. The occurrence distribution of encrusters points to nonrandom associations and exclusions among several encrusting taxa. However, abundance and occupancy of microconchids remained relatively stable throughout the sampled time interval. The notable decline in abundance (~60%) and relatively minor decline in diversity (~30%) suggest jointly that encrusting communities experienced ecological collapse rather than a major mass extinction event. The differences between the upper Frasnian and lower Famennian encrusting assemblages may thus record a turnover associated with the F-F event.

scholarly journals Transient and Stationary Losses in a Finite-Buffer Queue with Batch Arrivals

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Andrzej Chydzinski ◽  
Blazej Adamczyk
Keyword(s):  
Batch Size ◽  
Buffer Size ◽  
Arrival Process ◽  
Time Interval ◽  
Finite Buffer ◽  
Finite Time Interval ◽  
Batch Arrivals ◽  
Batch Markovian Arrival Process ◽  
Buffer Overflows ◽  
Finite Buffer Queue

We present an analysis of the number of losses, caused by the buffer overflows, in a finite-buffer queue with batch arrivals and autocorrelated interarrival times. Using the batch Markovian arrival process, the formulas for the average number of losses in a finite time interval and the stationary loss ratio are shown. In addition, several numerical examples are presented, including illustrations of the dependence of the number of losses on the average batch size, buffer size, system load, autocorrelation structure, and time.

Time suboptimal control of industrial manipulators along specified paths while keeping an end-effector orientation unchanged

Robotica ◽  
2003 ◽  
Vol 21 (2) ◽  
pp. 153-161 ◽  
Author(s):  
S. Kilicaslan ◽  
Y. Ercan
Keyword(s):  
Suboptimal Control ◽  
Time Step ◽  
End Effector ◽  
Industrial Manipulator ◽  
Industrial Manipulators ◽  
Angular Velocities ◽  
System Equations ◽  
Six Degree Of Freedom ◽  
Time Suboptimal Control

A method for the time suboptimal control of an industrial manipulator that moves along a specified path while keeping its end-effector orientation unchanged is proposed. Nonlinear system equations that describe the manipulator motion are linearized at each time step along the path. A method which gives control inputs (joint angular velocities) for time suboptimal control of the manipulator is developed. In the formulation, joint angular velocity and acceleration limitations are also taken into consideration. A six degree of freedom elbow type manipulator is used in a case study to verify the method developed.

A finite-time ruin probability formula for continuous claim severities

2004 ◽  
Vol 41 (2) ◽  
pp. 570-578 ◽  
Author(s):  
Zvetan G. Ignatov ◽  
Vladimir K. Kaishev
Keyword(s):  
Real Function ◽  
Finite Time ◽  
Ruin Probability ◽  
Joint Distribution ◽  
Time Interval ◽  
Insurance Company ◽  
Finite Time Interval ◽  
Appell Polynomials ◽  
Premium Income ◽  
Inverted Dirichlet

An explicit formula for the probability of nonruin of an insurance company in a finite time interval is derived, assuming Poisson claim arrivals, any continuous joint distribution of the claim amounts and any nonnegative, increasing real function representing its premium income. The formula is compact and expresses the nonruin probability in terms of Appell polynomials. An example, illustrating its numerical convenience, is also given in the case of inverted Dirichlet-distributed claims and a linearly increasing premium-income function.

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