Search results for: brownian dynamics

Authors: Mounir Zili

Abstract:

We will introduce a new extension of the Brownian motion, that could serve to get a good model of many natural phenomena. It is a linear combination of a finite number of sub-fractional Brownian motions; that is why we will call it the mixed sub-fractional Brownian motion. We will present some basic properties of this process. Among others, we will check that our process is non-Markovian and that it has non-stationary increments. We will also give the conditions under which it is a semimartingale. Finally, the main features of its sample paths will be specified.

Keywords: mixed Gaussian processes, Sub-fractional Brownian motion, sample paths

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Authors: Mounir Zili

Abstract:

We will introduce a new extension of the Brownian motion, that could serve to get a good model of many natural phenomena. It is a linear combination of a finite number of sub-fractional Brownian motions; that is why we will call it the mixed sub-fractional Brownian motion. We will present some basic properties of this process. Among others, we will check that our process is non-markovian and that it has non-stationary increments. We will also give the conditions under which it is a semi-martingale. Finally, the main features of its sample paths will be specified.

Keywords: fractal dimensions, mixed gaussian processes, sample paths, sub-fractional brownian motion

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Authors: Sujoy Das, M. M. Ghosh

Abstract:

The thermal conductivity of a fluid can be significantly enhanced by dispersing nano-sized particles in it, and the resultant fluid is termed as "nanofluid". A theoretical model for estimating the thermal conductivity of a nanofluid has been proposed here. It is based on the mechanism that evenly dispersed nanoparticles within a nanofluid undergo Brownian motion in course of which the nanoparticles repeatedly collide with the heat source. During each collision a rapid heat transfer occurs owing to the solid-solid contact. Molecular dynamics (MD) simulation of the collision of nanoparticles with the heat source has shown that there is a pulse-like pick up of heat by the nanoparticles within 20-100 ps, the extent of which depends not only on thermal conductivity of the nanoparticles, but also on the elastic and other physical properties of the nanoparticle. After the collision the nanoparticles undergo Brownian motion in the base fluid and release the excess heat to the surrounding base fluid within 2-10 ms. The Brownian motion and associated temperature variation of the nanoparticles have been modeled by stochastic analysis. Repeated occurrence of these events by the suspended nanoparticles significantly contributes to the characteristic thermal conductivity of the nanofluids, which has been estimated by the present model for a ethylene glycol based nanofluid containing Cu-nanoparticles of size ranging from 8 to 20 nm, with Gaussian size distribution. The prediction of the present model has shown a reasonable agreement with the experimental data available in literature.

Keywords: brownian dynamics, molecular dynamics, nanofluid, thermal conductivity

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Authors: Valeria Bondarenko

Abstract:

In this paper, we propose two problems related to fractal Brownian motion. First problem is simultaneous estimation of two parameters, Hurst exponent and the volatility, that describe this random process. Numerical tests for the simulated fBm provided an efficient method. Second problem is approximation of the increments of the observed time series by a power function by increments from the fractional Brownian motion. Approximation and estimation are shown on the example of real data, daily deposit interest rates.

Keywords: fractional Brownian motion, Gausssian processes, approximation, time series, estimation of properties of the model

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Authors: Changhong Guo, Shaomei Fang, Yong He

Abstract:

In this paper, fractional Black-Scholes models for the European option pricing were established based on the fractional G-Brownian motion (fGBm), which generalizes the concepts of the classical Brownian motion, fractional Brownian motion and the G-Brownian motion, and that can be used to be a tool for considering the long range dependence and uncertain volatility for the financial markets simultaneously. A generalized fractional Black-Scholes equation (FBSE) was derived by using the Taylor’s series of fractional order and the theory of absence of arbitrage. Finally, some explicit option pricing formulas for the European call option and put option under the FBSE were also solved, which extended the classical option pricing formulas given by F. Black and M. Scholes.

Keywords: European option pricing, fractional Black-Scholes equations, fractional g-Brownian motion, Taylor's series of fractional order, uncertain volatility

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Authors: N. Bachok, N. L. Aleng, N. M. Arifin, A. Ishak, N. Senu

Abstract:

The problem of laminar fluid flow which results from the shrinking of a permeable surface in a nanofluid has been investigated numerically. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. A similarity solution is presented which depends on the mass suction parameter S, Prandtl number Pr, Lewis number Le, Brownian motion number Nb and thermophoresis number Nt. It was found that the reduced Nusselt number is decreasing function of each dimensionless number.

Keywords: Boundary layer, nanofluid, shrinking sheet, Brownian motion, thermophoresis, similarity solution

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Authors: Samaneh Rahimirshnani, Hossein Jafari

Abstract:

In this paper, we consider fluid queueing processes fed by an isonormal Gaussian process. We study the correlation structure of the queueing process and the rate of convergence of the running supremum in the queueing process. The Malliavin calculus techniques are applied to obtain relations that show the workload process inherits the dependence properties of the input process. As examples, we consider two isonormal Gaussian processes, the sub-fractional Brownian motion (SFBM) and the fractional Brownian motion (FBM). For these examples, we obtain upper bounds for the covariance function of the queueing process and its rate of convergence to zero. We also discover that the rate of convergence of the queueing process is related to the structure of the covariance function of the input process.

Keywords: queue length process, Malliavin calculus, covariance function, fractional Brownian motion, sub-fractional Brownian motion

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Authors: B. F. Nteumagne, E. Pindza, E. Mare

Abstract:

We apply Lie symmetries analysis to price and hedge options in the fractional Brownian framework. The reputation of Lie groups is well spread in the area of Mathematical sciences and lately, in Finance. In the presence of transactions costs and under fractional Brownian motions, analytical solutions become difficult to obtain. Lie symmetries analysis allows us to simplify the problem and obtain new analytical solution. In this paper, we investigate the use of symmetries to reduce the partial differential equation obtained and obtain the analytical solution. We then proposed a hedging procedure and calibration technique for these types of options, and test the model on real market data. We show the robustness of our methodology by its application to the pricing of digital options.

Keywords: fractional brownian model, symmetry, transaction cost, option pricing

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Authors: Mohsen Farshad

Abstract:

Information and force definition has been intertwined with the concept of entropy for many years. The displacement information of degrees of freedom with Brownian motions at a given temperature in space emerges as an entropic force between species. Here, we use this concept of entropy to understand the underlying physics behind the formation of attractive and repulsive forces by imagining that space is filled with free Brownian degrees of freedom. We incorporate the radius of bodies and the distance between them into entropic force relation systematically. Using this modified gravitational entropic force, we derive the attractive entropic force between bodies without considering their spin. We further hypothesize a possible mechanism for the formation of the repulsive force between two bodies. We visually elaborate that the repulsive entropic force will be manifested through the rotation of degrees of freedom around the spinning particles.

Keywords: entropy, information, force, Brownian Motions

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Authors: Sina Dehghani, Zhikang Rong

Abstract:

Historically, a variety of approaches have been taken to forecast commodity prices due to the significant implications of these values on the global economy. An accurate forecasting tool for a valuable commodity would significantly benefit investors and governmental agencies. Silver, in particular, has grown significantly as a commodity in recent years due to its use in healthcare and technology. This manuscript aims to utilize the Geometric Brownian Motion predictive model to forecast silver commodity prices over multiple 3-year periods. The results of the study indicate that the model has several limitations, particularly its inability to work effectively over longer periods of time, but still was extremely effective over shorter time frames. This study sets a baseline for silver commodity forecasting with GBM, and the model could be further strengthened with refinement.

Keywords: geometric Brownian motion, commodity, risk management, volatility, stochastic behavior, price forecasting

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Authors: Ceren Vardar Acar, Mine Caglar

Abstract:

In finance, the price of a volatile asset can be modeled using fractional Brownian motion (fBm) with Hurst parameter H>1/2. The Black-Scholes model for the values of returns of an asset using fBm is given as, 〖Y_t=Y_0 e^((r+μ)t+σB)〗_t^H, 0≤t≤T where Y_0 is the initial value, r is constant interest rate, μ is constant drift and σ is constant diffusion coefficient of fBm, which is denoted by B_t^H where t≥0. Black-Scholes model can be constructed with some Markov processes such as Brownian motion. The advantage of modeling with fBm to Markov processes is its capability of exposing the dependence between returns. The real life data for a volatile asset display long-range dependence property. For this reason, using fBm is a more realistic model compared to Markov processes. Investors would be interested in any kind of information on the risk in order to manage it or hedge it. The maximum possible loss is one way to measure highest possible risk. Therefore, it is an important variable for investors. In our study, we give some theoretical bounds on the distribution of maximum possible loss of fBm. We provide both asymptotical and strong estimates for the tail probability of maximum loss of standard fBm and fBm with drift and diffusion coefficients. In the investment point of view, these results explain, how large values of possible loss behave and its bounds.

Keywords: maximum drawdown, maximum loss, fractional brownian motion, large deviation, Gaussian process

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Authors: Madhu Aneja, Sapna Sharma

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Thermal conductivity of ordinary heat transfer fluids is not adequate to meet today’s cooling rate requirements. Nanoparticles have been shown to increase the thermal conductivity and convective heat transfer to the base fluids. One of the possible mechanisms for anomalous increase in the thermal conductivity of nanofluids is the Brownian motions of the nanoparticles in the basefluid. In this paper, the natural convection of incompressible nanofluid over a nonlinear stretching sheet in the presence of magnetic field is studied. The flow and heat transfer induced by stretching sheets is important in the study of extrusion processes and is a subject of considerable interest in the contemporary literature. Appropriate similarity variables are used to transform the governing nonlinear partial differential equations to a system of nonlinear ordinary (similarity) differential equations. For computational purpose, Finite Element Method is used. The effective thermal conductivity and viscosity of nanofluid are calculated by KKL (Koo – Klienstreuer – Li) correlation. In this model effect of Brownian motion on thermal conductivity is considered. The effect of important parameter i.e. nonlinear parameter, volume fraction, Hartmann number, heat source parameter is studied on velocity and temperature. Skin friction and heat transfer coefficients are also calculated for concerned parameters.

Keywords: Brownian motion, convection, finite element method, magnetic field, nanofluid, stretching sheet

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Authors: Zakiya Shireen, Sujin B. Babu

Abstract:

Irreversible diffusion-limited cluster aggregation (DLCA) of binary sticky spheres was simulated by modifying the Brownian Cluster Dynamics (BCD). We randomly distribute N spheres in a 3D box of size L, the volume fraction is given by Φtot = (π/6)N/L³. We identify NA and NB number of spheres as species A and B in our system both having identical size. In these systems, both A and B particles undergo Brownian motion. Irreversible bond formation happens only between intra-species particles and inter-species interact only through hard-core repulsions. As we perform simulation using BCD we start to observe binary gels. In our study, we have observed that species B always percolate (cluster size equal to L) as expected for the monomeric case and species A does not percolate below a critical ratio which is different for different volume fractions. We will also show that the accessible volume of the system increases when compared to the monomeric case, which means that species A is aggregating inside the cage created by B. We have also observed that for moderate Φtot the system undergoes a transition from flocculation region to percolation region indicated by the change in fractal dimension from 1.8 to 2.5. For smaller ratio of A, it stays in the flocculation regime even though B have already crossed over to the percolation regime. Thus, we observe two fractal dimension in the same system.

Keywords: BCD, fractals, percolation, sticky spheres

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Authors: Ognjen Vukovic

Abstract:

Chern-Simons equation represents the cornerstone of quantum physics. The question that is often asked is if the aforementioned equation can be successfully applied to the interaction in international financial markets. By analysing the time series in financial theory, it is proved that Chern-Simons equation can be successfully applied to financial time-series. The aforementioned statement is based on one important premise and that is that the financial time series follow the fractional Brownian motion. All variants of Chern-Simons equation and theory are applied and analysed. Financial theory time series movement is, firstly, topologically analysed. The main idea is that exchange rate represents two-dimensional projections of three-dimensional Brownian motion movement. Main principles of knot theory and topology are applied to financial time series and setting is created so the Chern-Simons equation can be applied. As Chern-Simons equation is based on small particles, it is multiplied by the magnifying factor to mimic the real world movement. Afterwards, the following equation is optimised using Solver. The equation is applied to n financial time series in order to see if it can capture the interaction between financial time series and consequently explain it. The aforementioned equation represents a novel approach to financial time series analysis and hopefully it will direct further research.

Keywords: Brownian motion, Chern-Simons theory, financial time series, econophysics

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Authors: M. J. Uddin, M. M. Rahman

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Transient natural convective flow dynamics of nanofluids in a horizontal homocentric annulus using nonhomogeneous dynamic model has been experimented numerically. The simulation is carried out for four different shapes of the inner wall, which is either cylindrical, elliptical, square or triangular. The outer surface of the annulus is maintained at constant low temperature while the inner wall is maintained at a uniform temperature; higher than the outer one. The enclosure is permeated by a uniform magnetic field having variable orientation. The Brownian motion and thermophoretic deposition phenomena of the nanoparticles are taken into account in model construction. The governing nonlinear momentum, energy, and concentration equations are solved numerically using Galerkin weighted residual finite element method. To find the best performer, the local Nusselt number is demonstrated for different shapes of the inner wall. The heat transfer enhancement for different nanofluids for four different shapes of the inner wall is exhibited.

Keywords: nanofluids, annulus, nonhomogeneous dynamic model, heat transfer

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Authors: Rangoli Goyal, Rama Bhargava

Abstract:

The triple diffusive boundary layer flow of nanofluid under the action of constant magnetic field over a non-linear stretching sheet has been investigated numerically. The model includes the effect of Brownian motion, thermophoresis, and cross-diffusion; slip mechanisms which are primarily responsible for the enhancement of the convective features of nanofluid. The governing partial differential equations are transformed into a system of ordinary differential equations (by using group theory transformations) and solved numerically by using variational finite element method. The effects of various controlling parameters, such as the magnetic influence number, thermophoresis parameter, Brownian motion parameter, modified Dufour parameter, and Dufour solutal Lewis number, on the fluid flow as well as on heat and mass transfer coefficients (both of solute and nanofluid) are presented graphically and discussed quantitatively. The present study has industrial applications in aerodynamic extrusion of plastic sheets, coating and suspensions, melt spinning, hot rolling, wire drawing, glass-fibre production, and manufacture of polymer and rubber sheets, where the quality of the desired product depends on the stretching rate as well as external field including magnetic effects.

Keywords: FEM, thermophoresis, diffusiophoresis, Brownian motion

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Authors: G. Sarojamma, K. Vendabai

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An analysis is carried out to investigate the effect of magnetic field and heat source on the steady boundary layer flow and heat transfer of a Casson nanofluid over a vertical cylinder stretching exponentially along its radial direction. Using a similarity transformation, the governing mathematical equations, with the boundary conditions are reduced to a system of coupled, non –linear ordinary differential equations. The resulting system is solved numerically by the fourth order Runge – Kutta scheme with shooting technique. The influence of various physical parameters such as Reynolds number, Prandtl number, magnetic field, Brownian motion parameter, thermophoresis parameter, Lewis number and the natural convection parameter are presented graphically and discussed for non – dimensional velocity, temperature and nanoparticle volume fraction. Numerical data for the skin – friction coefficient, local Nusselt number and the local Sherwood number have been tabulated for various parametric conditions. It is found that the local Nusselt number is a decreasing function of Brownian motion parameter Nb and the thermophoresis parameter Nt.

Keywords: casson nanofluid, boundary layer flow, internal heat generation/absorption, exponentially stretching cylinder, heat transfer, brownian motion, thermophoresis

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Authors: Zeeshan Ahmed, Ajinkya Sarode, Pratik Basarkar, Atul Bhargav, Debjyoti Banerjee

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The use of CO₂ in oil recovery and in CO₂ capture and storage is gaining traction in recent years. These applications involve heat transfer between CO₂ and the base fluid, and hence, there arises a need to improve the thermal conductivity of CO₂ to increase the process efficiency and reduce cost. One way to improve the thermal conductivity is through nanoparticle addition in the base fluid. The nanofluid model in this study consisted of copper (Cu) nanoparticles in varying concentrations with CO₂ as a base fluid. No experimental data are available on thermal conductivity of CO₂ based nanofluid. Molecular dynamics (MD) simulations are an increasingly adopted tool to perform preliminary assessments of nanoparticle (NP) fluid interactions. In this study, the effect of the formation of a nanolayer (or molecular layering) at the gas-solid interface on thermal conductivity is investigated using equilibrium MD simulations by varying NP diameter and keeping the volume fraction (1.413%) of nanofluid constant to check the diameter effect of NP on the nanolayer and thermal conductivity. A dense semi-solid fluid layer was seen to be formed at the NP-gas interface, and the thickness increases with increase in particle diameter, which also moves with the NP Brownian motion. Density distribution has been done to see the effect of nanolayer, and its thickness around the NP. These findings are extremely beneficial, especially to industries employed in oil recovery as increased thermal conductivity of CO₂ will lead to enhanced oil recovery and thermal energy storage.

Keywords: copper-CO2 nanofluid, molecular dynamics simulation, molecular interfacial layer, thermal conductivity

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Authors: S. Etaig, R. Hasan, N. Perera

Abstract:

This paper analyses the heat transfer performance and fluid flow using different nanofluids in a square enclosure. The energy equation and Navier-Stokes equation are solved numerically using finite volume scheme. The effect of volume fraction concentration on the enhancement of heat transfer has been studied icorporating the Brownian motion; the influence of effective thermal conductivity on the enhancement was also investigated for a range of volume fraction concentration. The velocity profile for different Rayleigh number. Water-Cu, water AL2O3 and water-TiO2 were tested.

Keywords: computational fluid dynamics, natural convection, nanofluid and thermal conductivity

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Authors: Elysia Barker, Jian Guo Zhou, Ling Qian, Steve Decent

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A method of modelling topography used in the simulation of riverbeds is proposed in this paper, which removes the need for datapoints and measurements of physical terrain. While complex scans of the contours of a surface can be achieved with other methods, this requires specialised tools, which the proposed method overcomes by using fractional Brownian motion (FBM) as a basis to estimate the real surface within a 15% margin of error while attempting to optimise algorithmic efficiency. This removes the need for complex, expensive equipment and reduces resources spent modelling bed topography. This method also accounts for the change in topography over time due to erosion, sediment transport, and other external factors which could affect the topography of the ground by updating its parameters and generating a new bed. The lattice Boltzmann method (LBM) is used to simulate both stationary and steady flow cases in a side-by-side comparison over the generated bed topography using the proposed method and a test case taken from an external source. The method, if successful, will be incorporated into the current LBM program used in the testing phase, which will allow an automatic generation of topography for the given situation in future research, removing the need for bed data to be specified.

Keywords: bed topography, FBM, LBM, shallow water, simulations

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Authors: Jorge Lopez

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In this work, we introduce fractional calculus in order to study the dynamics of a damped multistory building with some symmetry. Initially we make a review of the dynamics of a free and damped multistory building. Then we introduce those concepts of fractional calculus that will be involved in our study. It has been noticed that fractional calculus provides models with less parameters than those based on classical calculus. In particular, a damped classical oscilator is more naturally described by using fractional derivatives. Accordingly, we model our multistory building as a set of coupled fractional oscillators and compare its dynamics with the results coming from traditional methods.

Keywords: coupled oscillators, fractional calculus, fractional oscillator, structural dynamics

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Authors: Shuyi Wu, Chuang Li, Quanshui Zheng, Luping Xu

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Stretching and snipping DNA molecule by microfluidic has important application value in gene analysis by lab on a chip. Movement, deformation and fragmenting of DNA in microfluidic are typical fluid-solid coupling problems. An efficient and common simulation system for researching the movement, deformation and fragmenting of DNA by microfluidic has not been well developed. In our study, Brownian dynamics-finite element method (BD-FEM) is used to simulate the dynamic process of stretching and fragmenting DNA by contraction flow. The shape and parameters of micro-channels are changed to optimize the stretching and fragmenting properties of DNA. Our results indicate that strain rate, resulting from contraction microchannel, is the main control parameter for stretching and fragmenting DNA. There is good consistency between the simulation data and previous experimental result about the single DNA molecule behavior and averaged fragmenting properties in this study. BD-FEM method is an efficient calculating tool to research stretching and fragmenting behavior of single DNA molecule and optimize microfluidic devices for manipulating, stretching and fragmenting DNA.

Keywords: fragmenting, DNA, microfluidic, optimize.

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Authors: Ali Oveysi Sarabi

Abstract:

In this paper, controller design for the attitude and altitude dynamics of an outdoor quadrotor, which is constructed with low cost actuators and drivers, is aimed. Before designing the controller, the quadrotor is modeled mathematically in Matlab-Simulink environment. To control attitude dynamics, linear quadratic regulator (LQR) based controllers are designed, simulated and applied to the system. Two different proportional-integral-derivative action (PID) controllers are designed to control yaw and altitude dynamics. During the implementation of the designed controllers, different test setups are used. Designed controllers are implemented and tuned on the real system using xPC Target. Tests show that these basic control structures are successful to control the attitude and altitude dynamics.

Keywords: helicopter balance, flight dynamics, autonomous landing, control robotics

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Authors: Massimiliano Frezza, Sergio Bianchi, Augusto Pianese

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The relation between stock price volatility and trading volume represents a controversial issue which has received a remarkable attention over the past decades. In fact, an extensive literature shows a positive relation between price volatility and trading volume in the financial markets, but the causal relationship which originates such association is an open question, from both a theoretical and empirical point of view. In this regard, various models, which can be considered as complementary rather than competitive, have been introduced to explain this relationship. They include the long debated Mixture of Distributions Hypothesis (MDH); the Sequential Arrival of Information Hypothesis (SAIH); the Dispersion of Beliefs Hypothesis (DBH); the Noise Trader Hypothesis (NTH). In this work, we analyze whether stock market efficiency can explain the diversity of results achieved during the years. For this purpose, we propose an alternative measure of market efficiency, based on the pointwise regularity of a stochastic process, which is the Hurst–H¨older dynamic exponent. In particular, we model the stock market by means of the multifractional Brownian motion (mBm) that displays the property of a time-changing regularity. Mostly, such models have in common the fact that they locally behave as a fractional Brownian motion, in the sense that their local regularity at time t0 (measured by the local Hurst–H¨older exponent in a neighborhood of t0 equals the exponent of a fractional Brownian motion of parameter H(t0)). Assuming that the stock price follows an mBm, we introduce and theoretically justify the Hurst–H¨older dynamical exponent as a measure of market efficiency. This allows to measure, at any time t, markets’ departures from the martingale property, i.e. from efficiency as stated by the Efficient Market Hypothesis. This approach is applied to financial markets; using data for the SP500 index from 1978 to 2017, on the one hand we find that when efficiency is not accounted for, a positive contemporaneous relationship emerges and is stable over time. Conversely, it disappears as soon as efficiency is taken into account. In particular, this association is more pronounced during time frames of high volatility and tends to disappear when market becomes fully efficient.

Keywords: volume–volatility relationship, efficient market hypothesis, martingale model, Hurst–Hölder exponent

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Authors: Mohammad Bqoor, Mohammad Hamdan, Isam Janajreh, Sufian Abedrabbo

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This extensive theoretical study on a novel Ionized Gas Thermoelectric Generator (IG-TEG) system has shown the ability of continuous energy extracting from the thermal energy of ambient air around standard room temperature and even below. This system does not need a temperature gradient in order to work, unlike the other TEGs that use the Seebeck effect, and therefore this new system can be utilized in sustainable energy systems, as well as in green cooling solutions, by extracting energy instead of wasting energy in compressing the gas for cooling. This novel system was designed based on Static Ratchet Potential (SRP), which is known as a spatially asymmetric electric potential produced by an array of positive and negative electrodes. The ratchet potential produces an electrical current from the random Brownian Motion of charged particles that are driven by thermal energy. The key parameter of the system is particle transportation, and it was studied under the condition of flashing ratchet potentials utilizing several methods and examined experimentally, ensuring its functionality. In this study, a different approach is pursued to estimate particle transportation by evaluating the charged particle distribution and applying the other conditions of the SRP, and showing continued energy harvesting potency from the particles’ transportation. Ultimately, power levels of 10 Watt proved to be achievable from a 1 m long system tube of 10 cm radius.

Keywords: thermoelectric generator, ratchet potential, Brownian ratchet, energy harvesting, sustainable energy, green technology

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Authors: Salman Piri

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In this study, a two-dimensional lattice Boltzmann method (LBM) was considered for the numerical simulation of fluid flow in a channel. Also, the Lagrangian method was used for particle tracking in one-way coupling. Three hundred spherical particles with specific diameters were released in the channel entry and an elliptical object was placed in the channel for flow obstruction. The effect of gravity, the drag force, the Saffman lift and the Brownian forces were evaluated in the particle motion trajectories. Also, the effect of the geometrical parameter, ellipse aspect ratio, and the flow characteristic or Reynolds number was surveyed for the transport and deposition of particles. Moreover, the influence of particle diameter between 0.01 and 10 µm was investigated. Results indicated that in small Reynolds, more inertial and gravitational trapping occurred on the obstacle surface for particles with larger diameters. Whereas, for nano-particles, influenced by Brownian diffusion and vortices behind the obstacle, the inertial and gravitational mechanisms were insignificant and diffusion was the dominant deposition mechanism. In addition, in Reynolds numbers larger than 400, there was no significant difference between the deposition of finer and larger particles. Also, in higher aspect ratios of the ellipse, more inertial trapping occurred for particles of larger diameter (10 micrometers), while in lower cases, interception and gravitational mechanisms were dominant.

Keywords: ellipse aspect elito, particle tracking diffusion, lattice boltzman method, larangain particle tracking

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Authors: Sathish Kumar Jayaraj

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The study of urban traffic dynamics, underpinned by the principles of fluid dynamics, offers a distinct perspective to comprehend and enhance the efficiency of traffic flow within bustling cityscapes. Leveraging the concept of the Traffic Flow Factor (TFF) as an analog to the Reynolds number, this research delves into the intricate interplay between traffic density, velocity, and road category, drawing compelling parallels to fluid dynamics phenomena. By introducing the notion of Vehicle Shearing Resistance (VSR) as an analogy to dynamic viscosity, the study sheds light on the multifaceted influence of traffic regulations, lane management, and road infrastructure on the smoothness and resilience of traffic flow. The TFF equation serves as a comprehensive metric for quantifying traffic dynamics, enabling the identification of congestion hotspots, the optimization of traffic signal timings, and the formulation of data-driven traffic management strategies. The study underscores the critical significance of integrating fluid dynamics principles into the domain of urban traffic management, fostering sustainable transportation practices, and paving the way for a more seamless and resilient urban mobility ecosystem.

Keywords: traffic flow factor (TFF), urban traffic dynamics, fluid dynamics principles, vehicle shearing resistance (VSR), traffic congestion management, sustainable urban mobility

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Authors: Madhu Aneja, Sapna Sharma

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The water-based bioconvection of a nanofluid containing motile gyrotactic micro-organisms over nonlinear inclined stretching sheet has been investigated. The governing nonlinear boundary layer equations of the model are reduced to a system of ordinary differential equations via Oberbeck-Boussinesq approximation and similarity transformations. Further, the modified set of equations with associated boundary conditions are solved using Finite Element Method. The impact of various pertinent parameters on the velocity, temperature, nanoparticles concentration, density of motile micro-organisms profiles are obtained and analyzed in details. The results show that with the increase in angle of inclination δ, velocity decreases while temperature, nanoparticles concentration, a density of motile micro-organisms increases. Additionally, the skin friction coefficient, Nusselt number, Sherwood number, density number are computed for various thermophysical parameters. It is noticed that increasing Brownian motion and thermophoresis parameter leads to an increase in temperature of fluid which results in a reduction in Nusselt number. On the contrary, Sherwood number rises with an increase in Brownian motion and thermophoresis parameter. The findings have been validated by comparing the results of special cases with existing studies.

Keywords: bioconvection, finite element method, gyrotactic micro-organisms, inclined stretching sheet, nanofluid

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Authors: Anca Radulescu, Danae Evans

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The relationship between a network’s hardwiring and its emergent dynamics are central to neuroscience. We study the principles of this correspondence in a canonical setup (in which network nodes exhibit well-studied complex quadratic dynamics), then test their universality in biological networks. By extending methods from discrete dynamics, we study the effects of network connectivity on temporal patterns, encapsulating long-term behavior into the rich topology of network Mandelbrot sets. Then elements of fractal geometry can be used to predict and classify network behavior.

Keywords: canonical model, complex dynamics, dynamic networks, fractals, Mandelbrot set, network connectivity

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Authors: Ana M. Korol, Bibiana Riquelme, Osvaldo A. Rosso

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Since erythrocyte deformability analysis is mostly qualitative, the development of quantitative nonlinear methods is crucial for restricting subjectivity in the study of cell behaviour. An electro-optic mechanic system called erythrodeformeter has been developed and constructed in our laboratory in order to evaluate the erythrocytes' viscoelasticity. A numerical method formulated on the basis of fractal approximation for ordinary (OBM) and fractionary Brownian motion (FBM), as well as wavelet transform analysis, are proposed to distinguish chaos from noise based on the assumption that diffractometric data involves both deterministic and stochastic components, so it could be modelled as a system of bounded correlated random walk. Here we report studies on 25 donors: 4 alpha thalassaemic patients, 11 beta thalassaemic patients, and 10 healthy controls non-alcoholic and non-smoker individuals. The Correlation Coefficient, a nonlinear parameter, showed evidence of the changes in the erythrocyte deformability; the Wavelet Entropy could quantify those differences which are detected by the light diffraction patterns. Such quantifiers allow a good deal of promise and the possibility of a better understanding of the rheological erythrocytes aspects and also could help in clinical diagnosis.

Keywords: red blood cells, deformability, nonlinear dynamics, chaos theory, wavelet trannsform

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