scholarly journals Energy Minimization Scheme for Split Potential Systems Using Exponential Variational Integrators

2021 ◽  
Vol 2 (3) ◽  
pp. 431-441
Author(s):  
Odysseas Kosmas
Keyword(s):  
Numerical Solutions ◽  
Oscillatory Behavior ◽  
Lagrangian Function ◽  
Computational Time ◽  
Variational Integrators ◽  
Weighted Sum ◽  
Lagrange Equations ◽  
Exponential Functions ◽  
Intermediate Time ◽  
Definition Of

In previous works we developed a methodology of deriving variational integrators to provide numerical solutions of systems having oscillatory behavior. These schemes use exponential functions to approximate the intermediate configurations and velocities, which are then placed into the discrete Lagrangian function characterizing the physical system. We afterwards proved that, higher order schemes can be obtained through the corresponding discrete Euler–Lagrange equations and the definition of a weighted sum of “continuous intermediate Lagrangians” each of them evaluated at an intermediate time node. In the present article, we extend these methods so as to include Lagrangians of split potential systems, namely, to address cases when the potential function can be decomposed into several components. Rather than using many intermediate points for the complete Lagrangian, in this work we introduce different numbers of intermediate points, resulting within the context of various reliable quadrature rules, for the various potentials. Finally, we assess the accuracy, convergence and computational time of the proposed technique by testing and comparing them with well known standards.

Normal form method in search for periodic solutions of ordinary differential equations. Case of the fourth order

2018 ◽  
pp. 24-34
Author(s):  
V. F. Edneral ◽  
O. D. Timofeevskaya
Keyword(s):  
Normal Form ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Periodic Solutions ◽  
Fourth Order ◽  
Numerical Solutions ◽  
Numerical Calculations ◽  
Computational Time ◽  
Resonant Normal Form ◽  
Normal Form Method

Introduction:The method of resonant normal form is based on reducing a system of nonlinear ordinary differential equations to a simpler form, easier to explore. Moreover, for a number of autonomous nonlinear problems, it is possible to obtain explicit formulas which approximate numerical calculations of families of their periodic solutions. Replacing numerical calculations with their precalculated formulas leads to significant savings in computational time. Similar calculations were made earlier, but their accuracy was insufficient, and their complexity was very high.Purpose:Application of the resonant normal form method and a software package developed for these purposes to fourth-order systems in order to increase the calculation speed.Results:It has been shown that with the help of a single algorithm it is possible to study equations of high orders (4th and higher). Comparing the tabulation of the obtained formulas with the numerical solutions of the corresponding equations shows good quantitative agreement. Moreover, the speed of calculation by prepared approximating formulas is orders of magnitude greater than the numerical calculation speed. The obtained approximations can also be successfully applied to unstable solutions. For example, in the Henon — Heyles system, periodic solutions are surrounded by chaotic solutions and, when numerically integrated, the algorithms are often unstable on them.Practical relevance:The developed approach can be used in the simulation of physical and biological systems.

scholarly journals The contribution of resident physicians to hospital productivity

2021 ◽  
Author(s):  
Maria J. Perez-Villadóniga ◽  
Ana Rodriguez-Alvarez ◽  
David Roibas
Keyword(s):  
Production Functions ◽  
Weighted Sum ◽  
Main Hypothesis ◽  
Resident Physicians ◽  
Suitable Parameter ◽  
Functional Forms ◽  
The One ◽  
Definition Of ◽  
Hospital Productivity ◽  
Natural Hypothesis

AbstractResident physicians play a double role in hospital activity. They participate in medical practices and thus, on the one hand, they should be considered as an input. Also, they are medical staff in training and, on the other hand, must be considered as an output. The net effect on hospital activities should therefore be empirically determined. Additionally, when considering their role as active physicians, a natural hypothesis is that resident physicians are not more productive than senior ones. This is a property that standard logarithmic production functions (including Cobb–Douglas and Translog functional forms) cannot verify for the whole technology set. Our main contribution is the development of a Translog modification, which implies the definition of the input “doctors” as a weighted sum of senior and resident physicians, where the weights are estimated from the empirical application. This modification of the standard Translog is able, under suitable parameter restrictions, to verify our main hypothesis across the whole technology set while determining if the net effect of resident physicians in hospitals’ production should be associated to an output or to an input. We estimate the resulting output distance function frontier with a sample of Spanish hospitals. Our findings show that the overall contribution of resident physicians to hospitals’ production allows considering them as an input in most cases. In particular, their average productivity is around 37% of that corresponding to senior physicians.

An Improved Assembling Algorithm in Boundary Elements With Galerkin Weighting Applied to Three-Dimensional Stokes Flows

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
Sofia Sarraf ◽  
Ezequiel López ◽  
Laura Battaglia ◽  
Gustavo Ríos Rodríguez ◽  
Jorge D'Elía
Keyword(s):  
Boundary Element Method ◽  
Linear System ◽  
Boundary Element ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Computational Time ◽  
Creeping Flows ◽  
Order Of Magnitude ◽  
Element Method

In the boundary element method (BEM), the Galerkin weighting technique allows to obtain numerical solutions of a boundary integral equation (BIE), giving the Galerkin boundary element method (GBEM). In three-dimensional (3D) spatial domains, the nested double surface integration of GBEM leads to a significantly larger computational time for assembling the linear system than with the standard collocation method. In practice, the computational time is roughly an order of magnitude larger, thus limiting the use of GBEM in 3D engineering problems. The standard approach for reducing the computational time of the linear system assembling is to skip integrations whenever possible. In this work, a modified assembling algorithm for the element matrices in GBEM is proposed for solving integral kernels that depend on the exterior unit normal. This algorithm is based on kernels symmetries at the element level and not on the flow nor in the mesh. It is applied to a BIE that models external creeping flows around 3D closed bodies using second-order kernels, and it is implemented using OpenMP. For these BIEs, the modified algorithm is on average 32% faster than the original one.

scholarly journals A Novel Autonomous Perceptron Model for Pattern Classification Applications

Entropy ◽  
2019 ◽  
Vol 21 (8) ◽  
pp. 763 ◽  
Author(s):  
Alaa Sagheer ◽  
Mohammed Zidan ◽  
Mohammed M. Abdelsamea
Keyword(s):  
Pattern Classification ◽  
Data Science ◽  
Science Research ◽  
Efficient Solutions ◽  
Classification Model ◽  
Computational Time ◽  
Quantum Bit ◽  
Training Samples ◽  
Artificial Neural Network Ann ◽  
Definition Of

Pattern classification represents a challenging problem in machine learning and data science research domains, especially when there is a limited availability of training samples. In recent years, artificial neural network (ANN) algorithms have demonstrated astonishing performance when compared to traditional generative and discriminative classification algorithms. However, due to the complexity of classical ANN architectures, ANNs are sometimes incapable of providing efficient solutions when addressing complex distribution problems. Motivated by the mathematical definition of a quantum bit (qubit), we propose a novel autonomous perceptron model (APM) that can solve the problem of the architecture complexity of traditional ANNs. APM is a nonlinear classification model that has a simple and fixed architecture inspired by the computational superposition power of the qubit. The proposed perceptron is able to construct the activation operators autonomously after a limited number of iterations. Several experiments using various datasets are conducted, where all the empirical results show the superiority of the proposed model as a classifier in terms of accuracy and computational time when it is compared with baseline classification models.

scholarly journals Revision of the convective transport module CVTRANS 2.4 in the EMAC atmospheric chemistry–climate model

2015 ◽  
Vol 8 (8) ◽  
pp. 2435-2445 ◽  
Author(s):  
H. G. Ouwersloot ◽  
A. Pozzer ◽  
B. Steil ◽  
H. Tost ◽  
J. Lelieveld
Keyword(s):  
Atmospheric Chemistry ◽  
Climate Model ◽  
Convective Transport ◽  
Computational Time ◽  
Cloud Base ◽  
Mixing Ratio ◽  
Time Step ◽  
Mixing Ratios ◽  
Time Stepping ◽  
Intermediate Time

Abstract. The convective transport module, CVTRANS, of the ECHAM/MESSy Atmospheric Chemistry (EMAC) model has been revised to better represent the physical flows and incorporate recent findings on the properties of the convective plumes. The modifications involve (i) applying intermediate time stepping based on a settable criterion, (ii) using an analytic expression to account for the intra-time-step mixing ratio evolution below cloud base, and (iii) implementing a novel expression for the mixing ratios of atmospheric compounds at the base of an updraft. Even when averaged over a year, the predicted mixing ratios of atmospheric compounds are affected considerably by the intermediate time stepping. For example, for an exponentially decaying atmospheric tracer with a lifetime of 1 day, the zonal averages can locally differ by more than a factor of 6 and the induced root mean square deviation from the original code is, weighted by the air mass, higher than 40 % of the average mixing ratio. The other modifications result in smaller differences. However, since they do not require additional computational time, their application is also recommended.

scholarly journals NUMERICAL SOLUTION OF TUMOR-IMMUNE INTERACTION USING 2-POINT BLOCK BACKWARD DIFFERENTIATION METHOD

2012 ◽  
Vol 09 ◽  
pp. 278-284 ◽  
Author(s):  
NOR AIN AZEANY MOHD NASIR ◽  
ZARINA BIBI IBRAHIM ◽  
MOHAMED SULEIMAN ◽  
K. I. OTHMAN ◽  
YONG FAEZAH RAHIM
Keyword(s):  
Numerical Solution ◽  
Numerical Solutions ◽  
Interaction Model ◽  
Numerical Results ◽  
Model Systems ◽  
Computational Time ◽  
Differentiation Formula ◽  
Backward Differentiation Formula ◽  
Differentiation Method ◽  
Interaction System

In this paper, we consider tumor-immune interaction model systems. The numerical solutions for the tumor-immune interaction system are obtained by using the 2-point Block Backward Differentiation Formula (BBDF) methods developed by Zarina et al. in 2007. The numerical results are presented in terms of computational time and accuracy of the solutions.

Lie Symmetry and Approximate Hojman Conserved Quantity of Lagrange Equations for a Weakly Nonholonomic System

2013 ◽  
Vol 30 (1) ◽  
pp. 21-27 ◽  
Author(s):  
Y.-L. Han ◽  
X.-X. Wang ◽  
M.-L. Zhang ◽  
L.-Q. Jia
Keyword(s):  
Nonholonomic System ◽  
Equations Of Motion ◽  
Lie Symmetry ◽  
Conserved Quantity ◽  
Holonomic System ◽  
Lagrange Equations ◽  
Definition Of ◽  
Weakly Nonholonomic System ◽  
Infinitesimal Transformations ◽  
Hojman Conserved Quantity

ABSTRACTThe Lie symmetry and Hojman conserved quantity of Lagrange equations for a weakly nonholonomic system and its first-degree approximate holonomic system are studied. The differential equations of motion for the system are established. Under the special infinitesimal transformations of group in which the time is invariable, the definition of the Lie symmetry for the weakly nonholonomic system and its first-degree approximate holonomic system are given, and the exact and approximate Hojman conserved quantities deduced directly from the Lie symmetry are obtained. Finally, an example is given to study the exact and approximate Hojman conserved quantity for the system.

Effects of Linear Hysteric Material Damping and Shock Pulse Shapes for Uniform Board Response

2016 ◽  
Author(s):  
Sharan Kallolimath ◽  
Jiang Zhou
Keyword(s):  
Test Performance ◽  
Strain Distribution ◽  
Computational Models ◽  
Numerical Solutions ◽  
Flexural Rigidity ◽  
Interpolation Method ◽  
Computational Time ◽  
Stress Concentrations ◽  
Stress Strain ◽  
Test Board

Validation of surface mounted electronic devices for drop test performance is considered as one of the most challenging tasks for researchers to search for key dynamic parameters either by experimentation or by numerical simulation. It has not only become challenging task to capture some of the important parameters that affect board flexural rigidity, stiffness, dynamic stresses and strains, but also avoid stress concentrations near undesired locations resulting in non-uniform strain distribution throughout the test board. There is a requirement to simulate exact drop condition that quantifies high impact energy on the board and also control drop to improve the board surface stress/strain distribution measured should be independent from standoff stress region. In this paper, an effort to find the importance of viscous and linear hysteric damping characteristics on uniform board response has been made. The influence of damped responses during no ring impact has been analyzed. Two different types of computational models are developed and an approximate FEA numerical solutions are obtained to compare current JEDEC test board and alternative hexagonal boards at reduced computational time and challenging experimental cost. The effect of board responses with two types of linear damping models are considered to study the effect. An approach towards finding key parameters that affect stress/strain distribution under both free as well as constrained model has been made, with including different pulse shapes parameters into effect. Maximum board strains are validated and compared using Global FEA model and maximum stresses on the components are evaluated using cut boundary interpolation method. Comparative to empirical results data, an effort to improve uniform stress strain distribution of package solder joints has been made and results are correlated.

Numerical Solutions of Nano/Microphenomena Coupled With Macroscopic Process of Heat Transfer and Fluid Flow: A Brief Review

2015 ◽  
Vol 137 (9) ◽  
Author(s):  
Ya-Ling He ◽  
Wen-Quan Tao
Keyword(s):  
Heat Transfer ◽  
Fluid Flow ◽  
Numerical Solutions ◽  
Dynamics Simulation ◽  
Computational Time ◽  
Computational Domain ◽  
Flow Problems ◽  
Coupling Algorithms ◽  
Volume Method ◽  
Boltzmann Method

In this paper, numerical simulation approaches for multiscale process of heat transfer and fluid flow are briefly reviewed, and the existing coupling algorithms are summarized. These molecular dynamics simulation (MDS)–finite volume method (FVM), MD–lattice Boltzmann method (LBM), and direct simulation of Monte Carlo method (DSMC)–FVM. The available reconstruction operators for LBM–FVM coupling are introduced. Four multiscale examples for fluid flow and heat transfer are presented by using these coupled methods. It is shown that by coupled method different resolution requirements in the computational domain can be satisfied successfully while computational time can be significantly saved. Further research needs for the study of multiscale heat transfer and fluid flow problems are proposed.

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