scholarly journals Diffusion–Advection Equations on a Comb: Resetting and Random Search

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 221
Author(s):  
Trifce Sandev ◽  
Viktor Domazetoski ◽  
Alexander Iomin ◽  
Ljupco Kocarev
Keyword(s):  
Numerical Simulations ◽  
Random Search ◽  
Langevin Equations ◽  
Brownian Diffusion ◽  
Drift Diffusion ◽  
Search Problems ◽  
Comb Structure ◽  
Analytical Results

This review addresses issues of various drift–diffusion and inhomogeneous advection problems with and without resetting on comblike structures. Both a Brownian diffusion search with drift and an inhomogeneous advection search on the comb structures are analyzed. The analytical results are verified by numerical simulations in terms of coupled Langevin equations for the comb structure. The subordination approach is one of the main technical methods used here, and we demonstrated how it can be effective in the study of various random search problems with and without resetting.

Impact noise radiated by collision of two spheres: Comparison between numerical simulations, experiments and analytical results

2011 ◽  
Vol 25 (7) ◽  
pp. 1675-1685 ◽  
Author(s):  
K. Mehraby ◽  
H. Khademhosseini Beheshti ◽  
M. Poursina
Keyword(s):  
Numerical Simulations ◽  
Impact Noise ◽  
Analytical Results

scholarly journals Metode Iterasi Tiga Langkah untuk Menyelesaikan Persamaan NonLinear dengan Menggunakan Matlab

2019 ◽  
Vol 4 (2) ◽  
pp. 34
Author(s):  
Deasy Wahyuni ◽  
Elisawati Elisawati
Keyword(s):  
Numerical Simulations ◽  
Nonlinear Equations ◽  
Newton Method ◽  
Iteration Method ◽  
Newton's Method ◽  
Order Of Convergence ◽  
Higher Order ◽  
Convergence Order ◽  
Matlab Program ◽  
Analytical Results

Newton method is one of the most frequently used methods to find solutions to the roots of nonlinear equations. Along with the development of science, Newton's method has undergone various modifications. One of them is the hasanov method and the newton method variant (vmn), with a higher order of convergence. In this journal focuses on the three-step iteration method in which the order of convergence is higher than the three methods. To find the convergence order of the three-step iteration method requires a program that can support the analytical results of both methods. One of them using the help of the matlab program. Which will then be compared with numerical simulations also using the matlab program.  Keywords : newton method, newton method variant, Hasanov Method and order of convergence

A stochastic threshold of a delayed epidemic model incorporating Lévy processes with harmonic mean and vaccination

2020 ◽  
Vol 13 (07) ◽  
pp. 2050069 ◽  
Author(s):  
Mohamed El Fatini ◽  
Idriss Sekkak ◽  
Aziz Laaribi ◽  
Roger Pettersson ◽  
Kai Wang
Keyword(s):  
Numerical Simulations ◽  
Epidemic Model ◽  
Harmonic Mean ◽  
Lévy Noise ◽  
Model Parameters ◽  
Well Posedness ◽  
Nonlinear Incidence ◽  
Model Driven ◽  
Analytical Results ◽  
Tuberculosis Disease

The aim of this paper is to investigate a stochastic threshold for a delayed epidemic model driven by Lévy noise with a nonlinear incidence and vaccination. Mainly, we derive a stochastic threshold [Formula: see text] which depends on model parameters and stochastic coefficients for a better understanding of the dynamical spreading of the disease. First, we prove the well posedness of the model. Then, we study the extinction and the persistence of the disease according to the values of [Formula: see text]. Furthermore, using different scenarios of Tuberculosis disease in Morocco, we perform some numerical simulations to support the analytical results.

scholarly journals Permanence and Global Stability of Positive Periodic Solutions of a Discrete Competitive System

2009 ◽  
Vol 2009 ◽  
pp. 1-13 ◽  
Author(s):  
Wenjie Qin ◽  
Zhijun Liu ◽  
Yiping Chen
Keyword(s):  
Global Stability ◽  
Numerical Simulations ◽  
Periodic Solutions ◽  
Positive Periodic Solutions ◽  
Competitive System ◽  
Dynamic Behaviors ◽  
System A ◽  
Analytical Results

We consider the dynamic behaviors of a discrete competitive system. A good understanding of the permanence, existence, and global stability of positive periodic solutions is gained. Numerical simulations are also presented to substantiate the analytical results.

MODELING THE SPREADING OF HIV IN HOMOSEXUAL POPULATIONS WITH HETEROGENEOUS PREVENTIVE ATTITUDE

2004 ◽  
Vol 12 (04) ◽  
pp. 439-456 ◽  
Author(s):  
JOSÉ ROBERTO C. PIQUEIRA ◽  
MARCOS CASADO CASTAÑO ◽  
LUIZ HENRIQUE ALVES MONTEIRO
Keyword(s):  
Social Networks ◽  
Numerical Simulations ◽  
Hiv Transmission ◽  
Equilibrium Points ◽  
Analytical Results ◽  
Blood Screening

A model for HIV transmission in homosexual populations is proposed taking into consideration different preventive attitudes, blood screening and effects of social networks. The equilibrium points of the system are calculated with and without blood screening and their stabilities are analyzed. By using these analytical results and numerical simulations, some evolving aspects of the epidemic are discussed.

scholarly journals A Prey-Predator Model with Michael Mentence Type of Predator Harvesting and Infectious Disease in Prey

2020 ◽  
pp. 1146-1163
Author(s):  
Hiba Abdullah Ibrahim ◽  
Raid Kamel Naji
Keyword(s):  
Infectious Disease ◽  
Numerical Simulations ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Local Bifurcation ◽  
Persistence Conditions ◽  
Analytical Results ◽  
Predator Model ◽  
Disease In Prey

A prey-predator model with Michael Mentence type of predator harvesting and infectious disease in prey is studied. The existence, uniqueness and boundedness of the solution of the model are investigated. The dynamical behavior of the system is studied locally as well as globally. The persistence conditions of the system are established. Local bifurcation near each of the equilibrium points is investigated. Finally, numerical simulations are given to show our obtained analytical results.

scholarly journals The Dynamics of Sokol-Howell Prey-Predator Model Involving Strong Allee Effect

2021 ◽  
pp. 3114-3127
Author(s):  
Saad M. A. Al-Momen ◽  
Raid Kamil Naji
Keyword(s):  
Numerical Simulations ◽  
Local Stability ◽  
Allee Effect ◽  
Pitchfork Bifurcation ◽  
Stability Conditions ◽  
Analytical Results ◽  
Saddle Node ◽  
Strong Allee Effect ◽  
Predator Model

In this paper,  a Sokol-Howell prey-predator model involving strong Allee effect is proposed and analyzed. The existence, uniqueness, and boundedness are studied. All the five possible equilibria have been are obtained and their local stability conditions are established. Using Sotomayor's theorem, the conditions of local saddle-node and transcritical and pitchfork bifurcation are derived and drawn. Numerical simulations are performed to clarify the analytical results

scholarly journals Viruses such as SARS-CoV-2 can be partially shielded from UV radiation when in particles generated by sneezing or coughing: Numerical simulations

2020 ◽  
Author(s):  
David C. Doughty ◽  
Steven C. Hill ◽  
Daniel W. Mackowski
Keyword(s):  
Numerical Modeling ◽  
Optical Properties ◽  
Numerical Simulations ◽  
Uv Radiation ◽  
Uv Light ◽  
Spherical Particles ◽  
Brownian Diffusion ◽  
Uv Illumination ◽  
Light Intensities ◽  
Respiratory Droplets

AbstractUV radiation can inactivate viruses such as SARS-CoV-2. However, designing effective UV germicidal irradiation (UVGI) systems can be difficult because the effects of dried respiratory droplets and other fomites on UV light intensities are poorly understood. Numerical modeling of UV intensities inside virus-containing particles on surfaces can increase understanding of these possible reductions in UV intensity. We model UV intensities within spherical approximations of virions randomly positioned within spherical particles. The model virions and dried particles have sizes and optical properties to approximate SARS-CoV-2 and dried particles formed from respiratory droplets, respectively. Wavelengths used are 260 nm (germicidal UVC) and 302 nm (solar UVB). In 5- and 9-μm diameter particles on a surface, illuminated by 260-nm UV light from a direction perpendicular to the surface, 10% and 18% (respectively) of simulated virions are exposed to intensities less than 1/100th of intensities in individually exposed virions (i.e., they are partially shielded). Even for 302-nm light, where the absorption is small, 11% of virions in 9-µm particles have exposures 1/100th those of individually exposed virions. Calculated results show that shielding of virions in a particle can be strongly reduced by illuminating a particle either from multiple widely separated incident directions, or by illuminating a particle rotating in air (because of turbulence, Brownian diffusion, etc.) for a time sufficient to rotate through all orientations with respect to the UV illumination. Because highly UV-reflective paints and surfaces can increase the angular ranges of illumination, they appear likely to be useful for reducing shielding of virions.

Programmable Constant-Force Multistable Mechanisms

2018 ◽  
Author(s):  
Mohamed Zanaty ◽  
Simon Henein
Keyword(s):  
Numerical Simulations ◽  
Reaction Force ◽  
Experimental Measurements ◽  
Constant Force ◽  
Stable States ◽  
Zero Force ◽  
Stability Behavior ◽  
Analytical Results ◽  
Potential Applications ◽  
Axially Loaded

Programmable multistable mechanisms exhibit stability behavior whereby the stiffness and the number of stable states can be controlled via programming inputs. In this paper, we report the zero stiffness behavior of a 2-degree of programming (DOP) T-combined, axially loaded double parallelogram multistable mechanism. We demonstrate zero force monostability, constant force monostability, zero force bistability, constant force bistability and zero force tristability behaviors by tuning the programming input. We derive analytically the reaction force of the mechanism for each configuration and verify our analytical results using numerical simulations and experimental measurements, showing less than 10% discrepancy. The concept of constant-force programming can be extended to N-DOP T-combined, serial combined and parallel combined programmable multistable mechanisms. Finally, we present potential applications of stability programming.

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.

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