Treatment of the Time Derivative (Parabolic and Hyperbolic PDEs)

2016 ◽  
pp. 219-275
Author(s):  
Sandip Mazumder
Keyword(s):  
Time Derivative ◽  
Hyperbolic Pdes

Optimized control over modes of hydraulic percussion cutting heads of mining machines

2020 ◽  
pp. 95-104
Author(s):  
Yu. M. Smirnov ◽  
B. M. Kenzhin ◽  
N. S. Smakova ◽  
M. A. Zhurunova
Keyword(s):  
Time Derivative ◽  
Operating Conditions ◽  
Control Action ◽  
Main Function ◽  
Output Data ◽  
Working Cycle ◽  
Control Units ◽  
Action Change ◽  
Function Element ◽  
Service Factors

The main cause of the disagreement between the actual and calculated output data of hydraulic percussion mining machines is the erroneous feed of manipulation signals by the control units. For the maximal fitting of the calculated and actual figures, the continuous method of control action using the third time derivative of the law of motion of the main function element is accepted, namely, the accuracy. The mathematical models of control using displacement, velocity and acceleration are developed. The service factors of mining machines are found. Based on the theory of control and the mathematical logic theory, the logical circuits of formation of manipulation signals in each phase of the working cycle are developed. The main elements are converters, integrators and accumulators ensuring decomposition of elements of the logical circuits and further generation of appropriate control action. It is found that the simplest way is to generate the control action for acceleration of the key function element. For the developed circuits, it is recommended to use general charts of the control action change, implementable for a certain design of hydraulic percussion cutting heads in certain operating conditions.

scholarly journals Multiresolution based adaptive schemes for second order hyperbolic PDEs in elastodynamic problems

2013 ◽  
Vol 37 (12-13) ◽  
pp. 7095-7127 ◽  
Author(s):  
Hassan Yousefi ◽  
Asadollah Noorzad ◽  
Jamshid Farjoodi
Keyword(s):  
Second Order ◽  
Hyperbolic Pdes ◽  
Adaptive Schemes

scholarly journals Assessing Stability of Crutch Users by Non-Contact Methods

2021 ◽  
Vol 18 (6) ◽  
pp. 3001
Author(s):  
Achilles Vairis ◽  
Suzana Brown ◽  
Maurice Bess ◽  
Kyu Hyun Bae ◽  
Jonathan Boyack
Keyword(s):  
Signal To Noise Ratio ◽  
Time Derivative ◽  
Assistive Devices ◽  
Signal To Noise ◽  
Physically Disabled ◽  
Significant Difference ◽  
Novice Users ◽  
Noise Ratio ◽  
Physically Disabled People

Enhancing gait stability in people who use crutches is paramount for their health. With the significant difference in gait compared to users who do not require an assistive device, the use of standard gait analysis tools to measure movement for temporary crush users and physically disabled people proves to be more challenging. In this paper, a novel approach based on video analysis is proposed as non-contact low-cost solution to the more expensive alternative with the data collected from processed videos, two values are calculated: the Signal to Noise Ratio (SNR) of acceleration, and the Signal to Noise Ratio of the jerk (time derivative of acceleration), to assess the user’s stability while they walk with crutches. The adopted methodology has been tested on a total of 10 participants. Five are temporary users of assistive devices with one being a long-term user and the other four novice users, and five are disabled participants who use those assistive devices permanently. Preliminary results show differences between novice users, long-term users, and physically disabled users. The approach is promising and could improve the assessment of crutch user stability, allowing for the correction of gait for individuals while using an inexpensive non-contact setup and preventing unnecessary falls.

scholarly journals Next-Point Prediction for Direct Touch Using Finite-Time Derivative Estimation

2018 ◽  
Author(s):  
Mathieu Nancel ◽  
Stanislav Aranovskiy ◽  
Rosane Ushirobira ◽  
Denis Efimov ◽  
Sebastien Poulmane ◽  
...  
Keyword(s):  
Finite Time ◽  
Time Derivative ◽  
Derivative Estimation

scholarly journals Diagnostics and Prognostics of Energy Conversion Processes via Knowledge-Based Systems

Proceedings ◽  
2020 ◽  
Vol 58 (1) ◽  
pp. 1
Author(s):  
Roberto Melli ◽  
Enrico Sciubba
Keyword(s):  
Expert System ◽  
Knowledge Base ◽  
Real Time ◽  
System Analysis ◽  
Intelligent System ◽  
Time Derivative ◽  
Time History ◽  
Control Procedure ◽  
Time Data ◽  
Ongoing Research

This paper presents a critical and analytical description of an ongoing research program aimed at the implementation of an expert system capable of monitoring, through an Intelligent Health Control procedure, the instantaneous performance of a cogeneration plant. The expert system is implemented in the CLIPS environment and is denominated PROMISA as the acronym for Prognostic Module for Intelligent System Analysis. It generates, in real time and in a form directly useful to the plant manager, information on the existence and severity of faults, forecasts on the future time history of both detected and likely faults, and suggestions on how to control the problem. The expert procedure, working where and if necessary with the support of a process simulator, derives from the available real-time data a list of selected performance indicators for each plant component. For a set of faults, pre-defined with the help of the plant operator (Domain Expert), proper rules are defined in order to establish whether the component is working correctly; in several instances, since one single failure (symptom) can originate from more than one fault (cause), complex sets of rules expressing the combination of multiple indices have been introduced in the knowledge base as well. Creeping faults are detected by analyzing the trend of the variation of an indicator over a pre-assigned interval of time. Whenever the value of this ‘‘discrete time derivative’’ becomes ‘‘high’’ with respect to a specified limit value, a ‘‘latent creeping fault’’ condition is prognosticated. The expert system architecture is based on an object-oriented paradigm. The knowledge base (facts and rules) is clustered—the chunks of knowledge pertain to individual components. A graphic user interface (GUI) allows the user to interrogate PROMISA about its rules, procedures, classes and objects, and about its inference path. The paper also presents the results of some simulation tests.

scholarly journals Caputo Fractional Derivative and Quantum-Like Coherence

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 211
Author(s):  
Garland Culbreth ◽  
Mauro Bologna ◽  
Bruce J. West ◽  
Paolo Grigolini
Keyword(s):  
Diffusion Equation ◽  
Fractional Derivative ◽  
Anomalous Diffusion ◽  
Caputo Fractional Derivative ◽  
Quantum Coherence ◽  
Time Derivative ◽  
The Other ◽  
Diffusion Equations ◽  
Self Organization ◽  
Ordinary Time

We study two forms of anomalous diffusion, one equivalent to replacing the ordinary time derivative of the standard diffusion equation with the Caputo fractional derivative, and the other equivalent to replacing the time independent diffusion coefficient of the standard diffusion equation with a monotonic time dependence. We discuss the joint use of these prescriptions, with a phenomenological method and a theoretical projection method, leading to two apparently different diffusion equations. We prove that the two diffusion equations are equivalent and design a time series that corresponds to the anomalous diffusion equation proposed. We discuss these results in the framework of the growing interest in fractional derivatives and the emergence of cognition in nature. We conclude that the Caputo fractional derivative is a signature of the connection between cognition and self-organization, a form of cognition emergence different from the other source of anomalous diffusion, which is closely related to quantum coherence. We propose a criterion to detect the action of self-organization even in the presence of significant quantum coherence. We argue that statistical analysis of data using diffusion entropy should help the analysis of physiological processes hosting both forms of deviation from ordinary scaling.

Fractional abstract Cauchy problem on complex interpolation scales

2020 ◽  
Vol 23 (4) ◽  
pp. 1125-1140
Author(s):  
Andriy Lopushansky ◽  
Oleh Lopushansky ◽  
Anna Szpila
Keyword(s):  
Cauchy Problem ◽  
Time Derivative ◽  
Abstract Cauchy Problem ◽  
Initial Boundary ◽  
Sectorial Operator ◽  
Complex Interpolation ◽  
Bounded Domains ◽  
Initial Boundary Value Problems ◽  
Fractional Time Derivative ◽  
Initial Boundary Value

AbstractAn fractional abstract Cauchy problem generated by a sectorial operator is investigated. An inequality of coercivity type for its solution with respect to a complex interpolation scale generated by a sectorial operator with the same parameters is established. An application to differential parabolic initial-boundary value problems in bounded domains with a fractional time derivative is shown.

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