Computing of Existence and Uniqueness Solutions for Differential Equations in Metric Spaces by Using MATLAB

A metric space is a set along with a measurement on the set, A metric actuates topological properties like open and shut sets, which lead to the investigation of more theoretical topological spaces. It also has many applications in functional analysis. The aim of this work is design and develop highly efficient algorithms that provide the existence of unique solutions to the differential equation in metric spaces using MATLAB. The quality algorithm was used and developed to solve the differential equation in metric spaces. For accurate results. The proposed model contributed to providing an integrated computer solution for all stages of the solution starting from the stage of solving differential equations in metric space and the stage of displaying and representing the results graphically in the MATLAB program

SIMULATION MODELING OF MOVEMENT OF INDUSTRIAL ROBOT MANIPULATOR IN THE MATLAB PROGRAM

In the work the information support for carrying out of simulation modeling of the industrial robot manipulator in the Matlab program is developed. The structure of the program for research of kinematics of industrial robot is developed. A graphical interface using the Matlab GUI has been developed for simulation of an industrial robot. The Denova-Hartenberg parameters for modeling the motion of an industrial robot are derived from the 3D model of the ABB IRB 2400 robot manipulator.

Variation in isocentre location of an Elekta Unity MR-linac through full gantry rotation

Objective: The objective of this study was to separately quantify the stability of the megavoltage imager (MVI) and radiation head of an Elekta Unity MRL, throughout full gantry rotation. Approach: A ball-bearing (BB) phantom was attached to the radiation head of the Unity, while a single BB was placed at isocentre. Images were acquired during rotation, using the MVI. These images were processed using an in-house developed MATLAB program to reduce the errors resulted by noise, and the positions of the BBs in the images were analysed to extract MVI and radiation head sag data. Main results: The results returned by this method showed reproducibility, with a mean standard deviation of 7 µm for the position of BBs across all gantry angles. The radiation head was found to sag throughout rotation, with a maximum course of movement of 0.59 mm. The sag pattern was stable over a period greater than a year but showed some dependence on gantry rotation direction. Significance: As MRL is a relatively new system, it is promising to have data supporting the high level of precision on one Elekta Unity machine. Isolating and quantifying the sources of uncertainty in radiation delivery may allow more sophisticated analysis of how the system performance may be improved.

Verification and comparison of MIT-BIH arrhythmia database based on number of beats

<span lang="EN-US">The ECG signal processing methods are tested and evaluated based on many databases. The most ECG database used for many researchers is the MIT-BIH arrhythmia database. The QRS-detection algorithms are essential for ECG analyses to detect the beats for the ECG signal. There is no standard number of beats for this database that are used from numerous researches. Different beat numbers are calculated for the researchers depending on the difference in understanding the annotation file. In this paper, the beat numbers for existing methods are studied and compared to find the correct beat number that should be used. We propose a simple function to standardize the beats number for any ECG PhysioNet database to improve the waveform database toolbox (WFDB) for the MATLAB program. This function is based on the annotation's description from the databases and can be added to the Toolbox. The function is removed the non-beats annotation without any errors. The results show a high percentage of 71% from the reviewed methods used an incorrect number of beats for this database.</span>

Obtaining the sensitivity of a calibrator for interferometric gravitational wave

Interferometric gravitational wave detectors (IGWD) are a very complex detector, the need to lock the detector in a dark fringe condition besides the vibrations that affect the mirrors, creates the necessity of using active suspension systems. These active systems make the system reach the desired sensitivity but make the calibration of such detectors much more difficult. To solve this problem a calibrator is proposed, a resonant mass gravitational wave detector could be used to detect the same signal in a narrower band and use the measured amplitude to calibrate the IGWD, as resonant mass gravitational wave detectors are easily calibrated. This work aims to obtain the expected sensitivity of such a calibrator by using lumped modelling in such mechanical detectors. The calibrator is modelled as a spring mass system and the sensitivity curve is presented calculated in by a matlab program. The curve shows that using state of art parameters for the detector the final sensitivity is close to the quantum limit and can be used to calibrate the IGWDs.

Theoretical Study for the Calculation of Proton Range in Human Body Tissues

The main rationale for using charged particles in radiation therapy is the strong rise of energy loss (deposited dose) with maximum penetration depth ( Bragg peak) and rapid dose deposited behind the peak. Thus, a large dose can be applied to a deep seated tumor, with saving the surrounding normal tissues . Proton radiotherapy is nowadays an established method in the management of cancer diseases, although its availability is still limited to a few specialized centers. In this study, the range and the stopping power for proton interaction in the skeleton and intestine tissues, for an energy range from 0.01 to 300 MeV, was studied. The numerical calculations and analyses of Bethe Ziegler, along with CASP and SRIM software programs, were applied using Matlab program. The absorbed dose and the Bragg peak were calculated and presented as tables and figures .

A Method to Resolve Simulation of Discontinuous Flow Field: a Valve Example From Full Closing to Re-Closure

In transient computational fluid dynamics (CFD) simulations, the continuity of the flow field is an essential prerequisite. However, continuous flows can be separated under certain conditions, such as the process from valve opening to re-closure. The current method often leaves a narrow gap to estimate the full closing status, which will introduce a deviation. To address this issue, a full closing numerical simulation method (FCNSM) is developed to solve the problem of simulation between discontinuous flow field (DFF) and continuous flow field (CFF). The matrix laboratory (MATLAB) program has been used to communicate Fluent as a server session to call the files Fluent and automatically execute text-based user interface (TUI) commands. The radial basis function (RBF) is used to construct the relationship between the variables of the flow field and the coordinates of mesh nodes, which can achieve the data transmission from a DFF to a CFF. Automatic stopping of transient calculations is achieved by passing variables among MATLAB program, scheme language, and user-defined functions (UDF) when a physical quantity reaches a set value. Based on this method, a transient simulation with a dynamic mesh of a 2-D model regarding a pressure relief valve (PRV) is performed to simulate the process of the valve from full closing to re-closure, the flow characteristics through the PRV are obtained using this method. This study makes it possible to use FCNSM for understanding dynamic characteristics from DFF to CFF.

KINEMATICS OF TWO LINK MANIPULATOR IN MATLAB/SIMULINK AND MSC ADAMS/VIEW SOFTWARE

The paper deals with the kinematic analysis of a manipulator mechanism. The matrix method of kinematic analysis is used for the solution. The robot's mechanism is an open kinematic chain. The vector of position, velocity and acceleration is determined. The problem is solved using Matlab and MSC Adams / View. The Matlab program is used to solve kinematics equations in symbolic form. Computer software reduces the design time and also brings economic benefits. Conditions are being created for faster research and the creation of new mechanical systems gradually appearing in the production area. Computer simulation can also serve an educational purpose and giving additional information about the mechanical systems through simulation and kinematic analysis.

LAPS v1.0.0: Lagrangian Advection of Particles at Sea, a Matlab program to simulate the displacement of particles in the ocean

We develop a Matlab program named LAPS (Lagrangian Advection of Particles at Sea) to simulate the advection of suspended particles in the global ocean with a minimal user effort to install, set and run the simulations. LAPS uses the 3D sea current velocity fields provided by ECCO2 to track the fate of suspended particles injected in the ocean, at specific places and times, during a period of time. LAPS runs with a short configuration file set by the user and returns the distribution of the particles at the end of the advection. A continuous tracking option is also available to record the complete trajectory of the particles throughout the entire period of advection. The effect of water waves, or Stokes drift, which alter sea surface current velocities, can also be taken into account. The principle and usage of the program is detailed and then applied to three case studies. The first two cases studies are applied to suspended sediment transport. We show how LAPS simulations can be used to investigate the spatio-temporal distribution of fine particles observed by satellites in the upper ocean. We also estimated sediment deposit areas on the seafloor as a function of sediment grain sizes. The third case study simulates the dispersion of microplastic particles during a tropical cyclone, and shows how the Stokes drift, which is significant during storm events, alters the particles trajectories compared to the case where the Stokes drift is neglected.