An Analytical Solution to Dujmovic’s Iterative OWA

2016 ◽  
Vol 24 (Suppl. 2) ◽  
pp. 165-179 ◽  
Author(s):  
Luigi Troiano ◽  
Irene Díaz
Keyword(s):  
Analytical Solution ◽  
Theoretical Result ◽  
Numerical Simulations ◽  
Owa Operator ◽  
Two Stage ◽  
Nested Iteration ◽  
Weighting Vector ◽  
Matrix Power ◽  
Computational Solution

Iterative OWA (ItOWA) as proposed by Dujmovic, is a two-stage procedure for computing the weighting vector by a double nested iteration: (i) weights at step h are computed as limit to infinity of a matrix power, (ii) the result is used to start the computation at step h + 1, until the OWA operator arity n is reached. Thereafter Dujmovic suggested a computational solution based on the conjecture that the limit exists, and numerical simulations have being supported the hypothesis that the conjecture is correct. In this paper, we prove that the limit actually exists and we provide an analytical solution to the procedure, so the weighting vector can be computed directly instead of an iterative time-consuming procedure. This theoretical result enables a faster computation of the weighting vector and characterization in terms of weights values, attitudinal character and entropy.

Analysis of Motion of the Impact-Dry-Friction Pair of Bodies and its Application to the Investigation of the Impact Dampers Dynamics

1999 ◽  
Author(s):  
František Peterka
Keyword(s):  
Analytical Solution ◽  
Numerical Simulations ◽  
Mechanical System ◽  
Relative Motion ◽  
Dry Friction ◽  
Friction Pair ◽  
Strong Nonlinearity ◽  
Friction Forces ◽  
The Impact ◽  
Analysis Of Motion

Abstract The motion with impacts and dry friction forces appears in some mechanical systems as mechanisms with clearances, (e.g., in gearings, pins, slots, guides, valve gears etc.), impact dampers, relays, forming and mailing machines, power pics etc. Such mechanisms include one or more pairs of impacting bodies, which introduce the strong nonlinearity into the system motion. The motion of the general pair of bodies with the both-sides impacts and dry friction forces is assumed (Fig.1). It can be the part of a more complex chain of masses in the mechanical system. Dead zones in the relative motion of bodies can be caused by assumed nonlinearities. The mathematical conditions controlling the numerical simulations or analytical solution of the motion are introduced. The application of this method is explained by the study of the influence of dry friction force on amplitude-frequency characteristics of four types of dynamical and impact dampers with optimised parameters.

Boubaker Polynomials Expansion Scheme Solution to the Heat Transfer Equation Inside Laser Heated Biological Tissues

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
M. A. Aweda ◽  
M. Agida ◽  
M. Dada ◽  
O. B. Awojoyogbe ◽  
K. Isah ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Analytical Solution ◽  
Numerical Simulations ◽  
Laser Heating ◽  
Transfer Equation ◽  
Biological Tissues ◽  
Heat Transfer Equation ◽  
Boubaker Polynomials ◽  
Laser Heated ◽  
Expansion Scheme

In this study, an analytical solution to the heat transfer equation in biological tissues during laser heating is presented. The results were compared to recently published numerical simulations.

scholarly journals Innovation and product market concentration: Schumpeter, arrow, and the inverted U-shape curve

2020 ◽  
Author(s):  
Flavio Delbono ◽  
Luca Lambertini
Keyword(s):  
Numerical Simulations ◽  
Empirical Research ◽  
Product Market ◽  
Market Concentration ◽  
Relative Strength ◽  
Stage Model ◽  
Two Stage ◽  
Shape Curve ◽  
The Relationship ◽  
Theoretical Results

Abstract We investigate the relationship between market concentration and industry innovative effort within a familiar two-stage model of R&D race in which firms compete à la Cournot in the product market. With the help of numerical simulations, we show that such a setting is rich enough to generate Arrovian, Schumpeterian, and inverted U curves. We interpret these different patterns on the basis of the relative strength of the technological incentive and the strategic incentive. We then bridge our theoretical results and some recent empirical research.

scholarly journals NUMERICAL AND EXPERIMENTAL STUDY OF A TWO-STAGE SAVONIUS WIND TURBINE

2019 ◽  
Vol 18 (2) ◽  
pp. 52
Author(s):  
L. B. Kothe ◽  
A. P. Petry
Keyword(s):  
Experimental Study ◽  
Numerical Simulations ◽  
Wind Turbine ◽  
Vertical Axis ◽  
Relative Difference ◽  
Performance Comparison ◽  
Speed Ratio ◽  
Vertical Axis Wind Turbine ◽  
Two Stage ◽  
Index Method

This article presents a numerical and experimental study of vertical axis wind turbine performance comparison involving a two-stage Savonius rotor with similar parameters. The experimental study is conducted in the aerodynamic tunnel at the Fluid Mechanics Laboratory of the Federal University of Rio Grande do Sul. The aerodynamics rotors are manufactured by 3D prototyping technique. Numerical simulations are performed using the Finite Volumes Method performed by the solution of the Reynolds Averaged Navier-Stokes (RANS) and continuity equations using the SST k-ω turbulence model. The numerical domain is modeled in order to maintain the same characteristics of the experimental model. The mesh quality is evaluated through the GCI (Grid Convergence Index) method. The static and dynamic torque coefficients and the power coefficients are compared. The tests are made without blockage corrections due to the small blockage ratio from 7.5%. Results show that the turbine has a positive static torque coefficient for any rotor angles. The dynamic torque reaches the maximum value for a tip speed ratio (λ) of 0.2 for the experimental and numerical cases. The relative difference between the numerical simulations and the experimental results are between 3.8% and 13.4%.

scholarly journals Coda-wave decorrelation sensitivity kernels in 2-D elastic media: a numerical approach

2020 ◽  
Vol 223 (2) ◽  
pp. 934-943
Author(s):  
Alejandro Duran ◽  
Thomas Planès ◽  
Anne Obermann
Keyword(s):  
Analytical Solution ◽  
Numerical Simulations ◽  
Heterogeneous Media ◽  
Synthetic Data ◽  
Numerical Approach ◽  
Coda Waves ◽  
Coda Wave ◽  
Elastic Media ◽  
S Wave ◽  
Velocity Changes

SUMMARY Probabilistic sensitivity kernels based on the analytical solution of the diffusion and radiative transfer equations have been used to locate tiny changes detected in late arriving coda waves. These analytical kernels accurately describe the sensitivity of coda waves towards velocity changes located at a large distance from the sensors in the acoustic diffusive regime. They are also valid to describe the acoustic waveform distortions (decorrelations) induced by isotropically scattering perturbations. However, in elastic media, there is no analytical solution that describes the complex propagation of wave energy, including mode conversions, polarizations, etc. Here, we derive sensitivity kernels using numerical simulations of wave propagation in heterogeneous media in the acoustic and elastic regimes. We decompose the wavefield into P- and S-wave components at the perturbation location in order to construct separate P to P, S to S, P to S and S to P scattering sensitivity kernels. This allows us to describe the influence of P- and S-wave scattering perturbations separately. We test our approach using acoustic and elastic numerical simulations where localized scattering perturbations are introduced. We validate the numerical sensitivity kernels by comparing them with analytical kernel predictions and with measurements of coda decorrelations on the synthetic data.

scholarly journals Analytical solution for magnetized thin accretion disk in comparison with numerical simulations

2018 ◽  
Vol 14 (S346) ◽  
pp. 264-267
Author(s):  
Miljenko Čemeljić ◽  
Varadarajan Parthasarathy ◽  
Włodek Kluźniak
Keyword(s):  
Magnetic Field ◽  
Analytical Solution ◽  
Numerical Simulations ◽  
Accretion Disk ◽  
Asymptotic Approximation ◽  
Numerical Solutions ◽  
Analytical Results ◽  
Physical Quantities ◽  
General Conditions

AbstractWe obtained equations for a thin magnetic accretion disk, using the method of asymptotic approximation. They cannot be solved analytically-without solutions for a magnetic field in the magnetosphere between the star and the disk, only a set of general conditions on the solutions can be derived. To compare the analytical results with numerical solutions, we find expressions for physical quantities in the disk, using our results from resistive and viscous star-disk magnetospheric interaction simulations.

scholarly journals A Biological Model of Acupuncture and its Derived Mathematical Modeling and Simulations

2015 ◽  
Vol 18 (4) ◽  
pp. 831-849 ◽  
Author(s):  
Marc Thiriet ◽  
Yannick Deleuze ◽  
Tony Wen-Hann Sheu
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Numerical Simulations ◽  
Blow Up ◽  
Biological Model ◽  
Mesh Adaptivity ◽  
Simple Mathematical Model ◽  
Global Knowledge ◽  
Small Width ◽  
The Brain

Abstract(Aims) Acupuncture was employed since 2 millenaries, but the underlying mechanisms are not globally handled. The present study is aimed at proposing an explanation by pointing out involved processes and a convincing modeling to demonstrate its efficiency when carried out by trained practitioners.(Method) In the absence of global knowledge of any mechanism explaining the acupuncture process, a biological model is first developed, based on stimulation in a given domain around the needle tip of a proper mastocyte population by a mechanical stress, electrical, electromagnetic, or heat field. Whatever the type of mechanical or physical stimuli, mastocytes degranulate. Released messengers either facilitate the transfer of main mediators, or target their cognate receptors of local nerve terminals or after being conveyed by blood their receptors on cerebral cells. Signaling to the brain is fast by nervous impulses and delayed by circulating messengers that nevertheless distribute preferentially in the brain region of interest due to hyperemia. The process is self-sustained due to mastocyte chemotaxis from the nearby dense microcirculatory circuit and surrounding mastocyte pools, which are inadequate for acupuncture, but serve as a signal relay. A simple mathematical model is solved analytically. Numerical simulations are also carried out using the finite element method with mesh adaptivity.(Results) The analytical solution of the simple mathematical model demonstrates the conditions filled by a mastocyte population to operate efficiently. A theorem gives the blow-up condition. This analytical solution serves for validation of numerical experiments. Numerical simulations show that when the needle is positioned in the periphery of the acupoint or outside it, the response is too weak. This explains why a long training is necessary as the needle implantation requires a precision with a magnitude of the order of 1mm.(Conclusion) The acupoint must contain a highly concentrated population of mastocytes (e.g., very-high–amplitude, small-width Gaussian distribution) to get an initial proper response. Permanent signaling is provided by chemotaxis and continuous recruitment of mastocytes. Therefore, the density and distribution of mastocytes are crucial factors for efficient acupuncture as well as availability of circulating and neighboring pools of mastocytes.

scholarly journals The Positive Role of Multiplicative Noise in Complete Synchronization of Unidirectionally Coupled Ring with Three Nodes

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Yuzhu Xiao ◽  
Sufang Tang ◽  
Zhongkui Sun
Keyword(s):  
Differential Equations ◽  
Theoretical Result ◽  
Numerical Simulations ◽  
Neuron Model ◽  
Multiplicative Noise ◽  
Lorenz System ◽  
Complete Synchronization ◽  
Positive Role ◽  
The Lorenz System

The role of multiplicative noise in the synchronization of unidirectionally coupled ring with three nodes is studied. Based on the theory of stochastic differential equations, we demonstrate that noise plays a positive role in complete synchronization. In numerical simulations, the Lorenz system, Rössler like system, and Hindmarsh-Rose neuron model are employed to demonstrate the correctness of our theoretical result.

scholarly journals MODELING AND NUMERICAL SIMULATION OF SPACE CHARGE DOMINATED BEAMS IN THE PARAXIAL APPROXIMATION

2006 ◽  
Vol 16 (05) ◽  
pp. 763-791 ◽  
Author(s):  
FRANCIS FILBET ◽  
ERIC SONNENDRÜCKER
Keyword(s):  
Numerical Simulation ◽  
Analytical Solution ◽  
Space Charge ◽  
Numerical Simulations ◽  
Paraxial Approximation ◽  
Particle Beams ◽  
Mathematical Background ◽  
Code Validation

This work is devoted to the modeling of space charge dominated particle beams in the paraxial approximation with several types of external focusing fields (uniform, periodic and alternating gradient). A solid mathematical background for numerical beam simulation is established. The Kapchinsky–Vladimirsky (KV) distribution which can be matched exactly or numerically to the focusing channel is first studied. Then the matched KV beam is used to approximately match arbitrary beams. Moreover, Waterbag and Maxwell–Boltzmann beams are studied to give analytical solution for code validation. Finally, numerical simulations are presented in different configurations.

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