Abstract: An envy behavioral game theoretical model with two
types of homogeneous players is considered in this paper. The
strategy space of each type of players is a discrete set with only
two alternatives. The preferences of each type of players is given
by a discrete utility function. All envy strategies that form Nash
equilibria and the corresponding envy Nash domains for each type
of players have been characterized. We use geometry to construct
two dimensional envy tilings where the horizontal axis reflects the
preference for players of type one, while the vertical axis reflects
the preference for the players of type two. The influence of the envy
behavior parameters on the Cartesian position of the equilibria has
been studied, and in each envy tiling we determine the envy Nash
equilibria. We observe that there are 1024 combinatorial classes of
envy tilings generated from envy chromosomes: 256 of them are
being structurally stable while 768 are with bifurcation. Finally, some
conditions for the disparate envy Nash equilibria are stated.
Abstract: Cardiovascular diseases (CVDs) are the main cause of death globally. Most CVDs can be prevented by avoiding habitual risk factors. Separate from the habitual risk factors, there are some inherent factors in each individual that can increase the risk potential of CVDs. Vessel shapes and geometry are influential factors, having great impact on the blood flow and the hemodynamic behavior of the vessels. In the present study, the influence of bifurcation angle on blood flow characteristics is studied. In order to approach this topic, by simplifying the details of the bifurcation, three models with angles 30°, 45°, and 60° were created, then by using CFD analysis, the response of these models for stable flow and pulsatile flow was studied. In the conducted simulation in order to eliminate the influence of other geometrical factors, only the angle of the bifurcation was changed and other parameters remained constant during the research. Simulations are conducted under dynamic and stable condition. In the stable flow simulation, a steady velocity of 0.17 m/s at the inlet plug was maintained and in dynamic simulations, a typical LAD flow waveform is implemented. The results show that the bifurcation angle has an influence on the maximum speed of the flow. In the stable flow condition, increasing the angle lead to decrease the maximum flow velocity. In the dynamic flow simulations, increasing the bifurcation angle lead to an increase in the maximum velocity. Since blood flow has pulsatile characteristics, using a uniform velocity during the simulations can lead to a discrepancy between the actual results and the calculated results.
Abstract: The variations in the arteries have been drawing attention of anatomists for a long time because of their clinical significance. The brachial artery is the principal artery of the arm which is the continuation of the axillary artery from the lower border of the Teres Major. It terminates into the radial and ulnar arteries below the elbow joint at the neck radius. The present study aims at exploring the clinical significance of the high termination of the brachial artery. During the routine cadaveric dissection of the arm, for the undergraduate students of medicine at our university, we observed a high bifurcation of the radial and the ulnar artery at the midshaft of the humerus. The median nerve was seen passing between these two junctions. Further, the course and the relations of this artery were studied. The accurate knowledge regarding these kinds of variation in the blood vessels is mandatory for planning of designing. General physicians, surgeons and radiologists should keep in mind the variations in the branching pattern of the arteries in their daily medical, diagnostic and therapeutic procedures to avoid complications in diagnostic and surgical procedures.
Abstract: Propagation of nonlinear acoustic wave in dense electron-positron (e-p) plasmas in the presence of an external magnetic field and stationary ions (to neutralize the plasma background) is studied. By means of the quantum hydrodynamics model and applying the reductive perturbation method, the Zakharov-Kuznetsov equation is derived. Using the bifurcation theory of planar dynamical systems, the compressive structure of electrostatic solitary wave and periodic travelling waves is found. The numerical results show how the ion density ratio, the ion cyclotron frequency, and the direction cosines of the wave vector affect the nonlinear electrostatic travelling waves. The obtained results may be useful to better understand the obliquely nonlinear electrostatic travelling wave of small amplitude localized structures in dense magnetized quantum e-p plasmas and may be applicable to study the particle and energy transport mechanism in compact stars such as the interior of massive white dwarfs etc.
Abstract: In this paper, the dynamic modeling of a single-link flexible beam with a tip mass is given by using Hamilton's principle. The link has been rotational and translational motion and it was assumed that the beam is moving with a harmonic velocity about a constant mean velocity. Non-linearity has been introduced by including the non-linear strain to the analysis. Dynamic model is obtained by Euler-Bernoulli beam assumption and modal expansion method. Also, the effects of rotary inertia, axial force, and associated boundary conditions of the dynamic model were analyzed. Since the complex boundary value problem cannot be solved analytically, the multiple scale method is utilized to obtain an approximate solution. Finally, the effects of several conditions on the differences among the behavior of the non-linear term, mean velocity on natural frequencies and the system stability are discussed.
Abstract: This work aims to provide a comprehensive study on the heat transfer and entropy generation rates of a horizontal channel partially filled with a porous medium which experiences internal heat generation or consumption due to exothermic or endothermic chemical reaction. The focus has been given to the local thermal non-equilibrium (LTNE) model. The LTNE approach helps us to deliver more accurate data regarding temperature distribution within the system and accordingly to provide more accurate Nusselt number and entropy generation rates. Darcy-Brinkman model is used for the momentum equations, and constant heat flux is assumed for boundary conditions for both upper and lower surfaces. Analytical solutions have been provided for both velocity and temperature fields. By incorporating the investigated velocity and temperature formulas into the provided fundamental equations for the entropy generation, both local and total entropy generation rates are plotted for a number of cases. Bifurcation phenomena regarding temperature distribution and interface heat flux ratio are observed. It has been found that the exothermicity or endothermicity characteristic of the channel does have a considerable impact on the temperature fields and entropy generation rates.
Abstract: In this paper, a magnetron memristor model based on hyperbolic sine function is presented and the correctness proved by studying the trajectory of its voltage and current phase, and then a memristor chaotic system with the memristor model is presented. The phase trajectories and the bifurcation diagrams and Lyapunov exponent spectrum of the magnetron memristor system are plotted by numerical simulation, and the chaotic evolution with changing the parameters of the system is also given. The paper includes numerical simulations and mathematical model, which confirming that the system, has a wealth of dynamic behavior.
Abstract: Numerical simulations of vortex-induced vibration of a three-dimensional flexible tube under uniform turbulent flow are calculated when Reynolds number is 1.35×104. In order to achieve the vortex-induced vibration, the three-dimensional unsteady, viscous, incompressible Navier-Stokes equation and LES turbulence model are solved with the finite volume approach, the tube is discretized according to the finite element theory, and its dynamic equilibrium equations are solved by the Newmark method. The fluid-tube interaction is realized by utilizing the diffusion-based smooth dynamic mesh method. Considering the vortex-induced vibration system, the variety trends of lift coefficient, drag coefficient, displacement, vertex shedding frequency, phase difference angle of tube are analyzed under different frequency ratios. The nonlinear phenomena of locked-in, phase-switch are captured successfully. Meanwhile, the limit cycle and bifurcation of lift coefficient and displacement are analyzed by using trajectory, phase portrait, and Poincaré sections. The results reveal that: when drag coefficient reaches its minimum value, the transverse amplitude reaches its maximum, and the “lock-in” begins simultaneously. In the range of lock-in, amplitude decreases gradually with increasing of frequency ratio. When lift coefficient reaches its minimum value, the phase difference undergoes a suddenly change from the “out-of-phase” to the “in-phase” mode.
Abstract: In population dynamics the study of both, the
abundance and the spatial distribution of the populations in a
given habitat, is a fundamental issue a From ecological point of
view, the determination of the factors influencing such changes
involves important problems. In this paper a mathematical model to
describe the temporal dynamic and the spatiotemporal dynamic of the
interaction of three populations (pollinators, plants and herbivores) is
presented. The study we present is carried out by stages: 1. The
temporal dynamics and 2. The spatio-temporal dynamics. In turn,
each of these stages is developed by considering three cases which
correspond to the dynamics of each type of interaction. For instance,
for stage 1, we consider three ODE nonlinear systems describing
the pollinator-plant, plant-herbivore and plant-pollinator-herbivore,
interactions, respectively. In each of these systems different types of
dynamical behaviors are reported. Namely, transcritical and pitchfork
bifurcations, existence of a limit cycle, existence of a heteroclinic
orbit, etc. For the spatiotemporal dynamics of the two mathematical
models a novel factor are introduced. This consists in considering
that both, the pollinators and the herbivores, move towards those
places of the habitat where the plant population density is high.
In mathematical terms, this means that the diffusive part of the
pollinators and herbivores equations depend on the plant population
density. The analysis of this part is presented by considering pairs of
populations, i. e., the pollinator-plant and plant-herbivore interactions
and at the end the two mathematical model is presented, these models
consist of two coupled nonlinear partial differential equations of
reaction-diffusion type. These are defined on a rectangular domain
with the homogeneous Neumann boundary conditions. We focused
in the role played by the density dependent diffusion term into
the coexistence of the populations. For both, the temporal and
spatio-temporal dynamics, a several of numerical simulations are
included.
Abstract: Aerobatic and military pilots are subjected to high gravitational forces that could cause blackout, physical injuries or death. A CFD simulation using fluid-solid interactions scheme has been conducted to investigate the gravitational effects and hazards inside cerebral aneurysms. Medical data have been used to derive the size and geometry of a simple aneurysm on a T-shaped bifurcation. The results show that gravitational force has no effect on maximum Wall Shear Stress (WSS); hence, it will not cause aneurysm initiation/formation. However, gravitational force cause causes hypertension which could contribute to aneurysm rupture.
Abstract: In this paper, applying frequency domain approach, a
delayed competitive web-site system is investigated. By choosing
the parameter α as a bifurcation parameter, it is found that Hopf
bifurcation occurs as the bifurcation parameter α passes a critical
values. That is, a family of periodic solutions bifurcate from the
equilibrium when the bifurcation parameter exceeds a critical value.
Some numerical simulations are included to justify the theoretical
analysis results. Finally, main conclusions are given.
Abstract: In this work we make a bifurcation analysis for a
single compartment representation of Traub model, one of the most
important conductance-based models. The analysis focus in two
principal parameters: current and leakage conductance. Study of
stable and unstable solutions are explored; also Hop-bifurcation and
frequency interpretation when current varies is examined. This study
allows having control of neuron dynamics and neuron response when
these parameters change. Analysis like this is particularly important
for several applications such as: tuning parameters in learning
process, neuron excitability tests, measure bursting properties of the
neuron, etc. Finally, a hardware implementation results were
developed to corroborate these results.
Abstract: The effectiveness of microchannels in enhancing heat
transfer has been demonstrated in the semiconductor industry. In
order to tap the microscale heat transfer effects into macro
geometries, overcoming the cost and technological constraints,
microscale passages were created in macro geometries machined
using conventional fabrication methods. A cylindrical insert was
placed within a pipe, and geometrical profiles were created on the
outer surface of the insert to enhance heat transfer under steady-state
single-phase liquid flow conditions. However, while heat transfer
coefficient values of above 10 kW/m2·K were achieved, the heat
transfer enhancement was accompanied by undesirable pressure drop
increment. Therefore, this study aims to address the high pressure
drop issue using Constructal theory, a universal design law for both
animate and inanimate systems. Two designs based on Constructal theory were developed to study
the effectiveness of Constructal features in reducing the pressure drop
increment as compared to parallel channels, which are commonly
found in microchannel fabrication. The hydrodynamic and heat
transfer performance for the Tree insert and Constructal fin (Cfin)
insert were studied using experimental methods, and the underlying
mechanisms were substantiated by numerical results. In technical
terms, the objective is to achieve at least comparable increment in
both heat transfer coefficient and pressure drop, if not higher
increment in the former parameter. Results show that the Tree insert improved the heat transfer
performance by more than 16 percent at low flow rates, as compared
to the Tree-parallel insert. However, the heat transfer enhancement
reduced to less than 5 percent at high Reynolds numbers. On the
other hand, the pressure drop increment stayed almost constant at 20
percent. This suggests that the Tree insert has better heat transfer
performance in the low Reynolds number region. More importantly,
the Cfin insert displayed improved heat transfer performance along
with favourable hydrodynamic performance, as compared to Cfinparallel
insert, at all flow rates in this study. At 2 L/min, the
enhancement of heat transfer was more than 30 percent, with 20
percent pressure drop increment, as compared to Cfin-parallel insert.
Furthermore, comparable increment in both heat transfer coefficient
and pressure drop was observed at 8 L/min. In other words, the Cfin
insert successfully achieved the objective of this study. Analysis of the results suggests that bifurcation of flows is
effective in reducing the increment in pressure drop relative to heat
transfer enhancement. Optimising the geometries of the Constructal
fins is therefore the potential future study in achieving a bigger stride
in energy efficiency at much lower costs.
Abstract: Cholera is a disease that is predominately common in
developing countries due to poor sanitation and overcrowding
population. In this paper, a deterministic model for the dynamics of
cholera is developed and control measures such as health educational
message, therapeutic treatment, and vaccination are incorporated in
the model. The effective reproduction number is computed in terms
of the model parameters. The existence and stability of the
equilibrium states, disease free and endemic equilibrium states are
established and showed to be locally and globally asymptotically
stable when R0 < 1 and R0 > 1 respectively. The existence of
backward bifurcation of the model is investigated. Furthermore,
numerical simulation of the model developed is carried out to show
the impact of the control measures and the result indicates that
combined control measures will help to reduce the spread of cholera
in the population.
Abstract: The numerical simulation has made tremendous
advances in investigating the blood flow phenomenon through elastic
arteries. Such study can be useful in demonstrating the disease
progression and hemodynamics of cardiovascular diseases such as
atherosclerosis. In the present study, patient specific case diagnosed
with partially stenosed complete right ICA and normal left carotid
bifurcation without any atherosclerotic plaque formation is
considered. 3D patient specific carotid bifurcation model is generated
based on CT scan data using MIMICS-4.0 and numerical analysis is
performed using FSI solver in ANSYS-14.5. The blood flow is
assumed to be incompressible, homogenous and Newtonian, while
the artery wall is assumed to be linearly elastic. The two-way
sequentially coupled transient FSI analysis is performed using FSI
solver for three pulse cycles. The hemodynamic parameters such as
flow pattern, Wall Shear Stress, pressure contours and arterial wall
deformation are studied at the bifurcation and critical zones such as
stenosis. The variation in flow behavior is studied throughout the
pulse cycle. Also, the simulation results reveal that there is a
considerable increase in the flow behavior in stenosed carotid in
contrast to the normal carotid bifurcation system. The investigation
also demonstrates the disturbed flow pattern especially at the
bifurcation and stenosed zone elevating the hemodynamics,
particularly during peak systole and later part of the pulse cycle. The
results obtained agree well with the clinical observation and
demonstrates the potential of patient specific numerical studies in
prognosis of disease progression and plaque rupture.
Abstract: A cyclostationary Gaussian linearization method is
formulated for investigating the time average response of nonlinear
system under sinusoidal signal and white noise excitation. The
quantitative measure of cyclostationary mean, variance, spectrum of
mean amplitude, and mean power spectral density of noise are
analyzed. The qualitative response behavior of stochastic jump and
bifurcation are investigated. The validity of the present approach in
predicting the quantitative and qualitative statistical responses is
supported by utilizing Monte Carlo simulations. The present analysis
without imposing restrictive analytical conditions can be directly
derived by solving non-linear algebraic equations. The analytical
solution gives reliable quantitative and qualitative prediction of mean
and noise response for the Duffing system subjected to both sinusoidal
signal and white noise excitation.
Abstract: For the treatment of acute and chronic lung diseases it is preferred to deliver medicaments by inhalation. The drug is delivered directly to tracheobronchial tree. This way allows the given medicament to get directly into the place of action and it makes rapid onset of action and maximum efficiency. The transport of aerosol particles in the particular part of the lung is influenced by their size, anatomy of the lungs, breathing pattern and airway resistance. This article deals with calculation of airway resistance in the lung model of Horsfield. It solves the problem of determination of the pressure losses in bifurcation and thus defines the pressure drop at a given location in the bronchial tree. The obtained data will be used as boundary conditions for transport of aerosol particles in a central part of bronchial tree realized by Computational Fluid Dynamics (CFD) approach. The results obtained from CFD simulation will allow us to provide information on the required particle size and optimal inhalation technique for particle transport into particular part of the lung.
Abstract: In this report we have discussed the theoretical aspects
of the flow transformation, occurring through a series of bifurcations.
The parameters and their continuous diversion, the intermittent bursts
in the transition zone, variation of velocity and pressure with time,
effect of roughness in turbulent zone, and changes in friction factor
and head loss coefficient as a function of Reynolds number for a
transverse flow across a cylinder have been discussed. An analysis of
the variation in the wake length with Reynolds number was done in
FORTRAN.
Abstract: This paper is devoted to the study of a viscous
incompressible flow around a circular cylinder performing harmonic
oscillations, especially the steady streaming phenomenon. The
research methodology is based on the asymptotic explanation method
combined with the computational bifurcation analysis. The research
approach develops Schlichting and Wang decomposition method.
Present studies allow to identify several regimes of the secondary
streaming with different flow structures. The results of the research
are in good agreement with experimental and numerical simulation
data.
Abstract: An accurate study of blood flow is associated with an accurate vascular pattern and geometrical properties of the organ of interest. Due to the complexity of vascular networks and poor accessibility in vivo, it is challenging to reconstruct the entire vasculature of any organ experimentally. The objective of this study is to introduce an innovative approach for the reconstruction of a full vascular tree from available morphometric data. Our method consists of implementing morphometric data on those parts of the vascular tree that are smaller than the resolution of medical imaging methods. This technique reconstructs the entire arterial tree down to the capillaries. Vessels greater than 2 mm are obtained from direct volume and surface analysis using contrast enhanced computed tomography (CT). Vessels smaller than 2mm are reconstructed from available morphometric and distensibility data and rearranged by applying Murray’s Laws. Implementation of morphometric data to reconstruct the branching pattern and applying Murray’s Laws to every vessel bifurcation simultaneously, lead to an accurate vascular tree reconstruction. The reconstruction algorithm generates full arterial tree topography down to the first capillary bifurcation. Geometry of each order of the vascular tree is generated separately to minimize the construction and simulation time. The node-to-node connectivity along with the diameter and length of every vessel segment is established and order numbers, according to the diameter-defined Strahler system, are assigned. During the simulation, we used the averaged flow rate for each order to predict the pressure drop and once the pressure drop is predicted, the flow rate is corrected to match the computed pressure drop for each vessel. The final results for 3 cardiac cycles is presented and compared to the clinical data.