Search results for: dynamical

Authors: Sanjay K. Behera, Debasish Saha, Paramesh Gadige, Ranjini Bandyopadhyay

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The zero shear viscosity (η₀) of a suspension of hard sphere colloids characterized by a significant polydispersity (≈10%) increases with increase in volume fraction (ϕ) and shows a dramatic increase at ϕ=ϕg with the system entering a colloidal glassy state. Fragility which is the measure of the rapidity of approach of these suspensions towards the glassy state is sensitive to its size polydispersity and stiffness of the particles. Soft poly(N-isopropylacrylamide) (PNIPAM) particles deform in the presence of neighboring particles at volume fraction above the random close packing volume fraction of undeformed monodisperse spheres. Softness, therefore, enhances the packing efficiency of these particles. In this study PNIPAM particles of a nearly constant swelling ratio and with polydispersities varying over a wide range (7.4%-48.9%) are synthesized to study the effects of polydispersity on the dynamics of suspensions of soft PNIPAM colloidal particles. The size and polydispersity of these particles are characterized using dynamic light scattering (DLS) and scanning electron microscopy (SEM). As these particles are deformable, their packing in aqueous suspensions is quantified in terms of effective volume fraction (ϕeff). The zero shear viscosity (η₀) data of these colloidal suspensions, estimated from rheometric experiments as a function of the effective volume fraction ϕeff of the suspensions, increases with increase in ϕeff and shows a dramatic increase at ϕeff = ϕ₀. The data for η₀ as a function of ϕeff fits well to the Vogel-Fulcher-Tammann equation. It is observed that increasing polydispersity results in increasingly fragile supercooled liquid-like behavior, with the parameter ϕ₀, extracted from the fits to the VFT equation shifting towards higher ϕeff. The observed increase in fragility is attributed to the prevalence of dynamical heterogeneities (DHs) in these polydisperse suspensions, while the simultaneous shift in ϕ₀ is ascribed to the decoupling of the dynamics of the smallest and largest particles. Finally, it is observed that the intrinsic nonlinearity of these suspensions, estimated at the third harmonic near ϕ₀ in Fourier transform oscillatory rheological experiments, increases with increase in polydispersity. These results are in agreement with theoretical predictions and simulation results for polydisperse hard sphere colloidal glasses and clearly demonstrate that jammed suspensions of polydisperse colloidal particles can be effectively fluidized with increasing polydispersity. Suspensions of these particles are therefore excellent candidates for detailed experimental studies of the effects of polydispersity on the dynamics of glass formation.

Keywords: dynamical heterogeneity, effective volume fraction, fragility, intrinsic nonlinearity

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Authors: Feng Wang, Vladislav Vasilyev

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Ferrocene (Fe(C5H5)2, i.e., di-cyclopentadienyle iron (FeCp2) or Fc) is a unique example of ‘wrong but seminal’ in chemistry history. It has significant applications in a number of areas such as homogeneous catalysis, polymer chemistry, molecular sensing, and nonlinear optical materials. However, the ‘molecular carousel’ has been a ‘notoriously difficult example’ and subject to long debate for its conformation and properties. Ferrocene is a dynamic molecule. As a result, understanding of the dynamical properties of ferrocene is very important to understand the conformational properties of Fc. In the present study, molecular dynamic (MD) simulations are performed. In the simulation, we use 5 geometrical parameters to define the overall conformation of Fc and all the rest is a thermal noise. The five parameters are defined as: three parameters d---the distance between two Cp planes, α and δ to define the relative positions of the Cp planes, in which α is the angle of the Cp tilt and δ the angle the two Cp plane rotation like a carousel. Two parameters to position the Fe atom between two Cps, i.e., d1 for Fe-Cp1 and d2 for Fe-Cp2 distances. Our preliminary MD simulation discovered the five parameters behave differently. Distances of Fe to the Cp planes show that they are independent, practically identical without correlation. The relative position of two Cp rings, α, indicates that the two Cp planes are most likely not in a parallel position, rather, they tilt in a small angle α≠ 0°. The mean plane dihedral angle δ ≠ 0°. Moreover, δ is neither 0° nor 36°, indicating under those conditions, Fc is neither in a perfect eclipsed structure nor a perfect staggered structure. The simulations show that when the temperature is above 80K, the conformers are virtually in free rotations, A very interesting result from the MD simulation is the five C-Fe bond distances from the same Cp ring. They are surprisingly not identical but in three groups of 2, 2 and 1. We describe the pentagon formed by five carbon atoms as ‘turtle swimming’ for the motion of the Cp rings of Fc as shown in their dynamical animation video. The Fe- C(1) and Fe-C(2) which are identical as ‘the turtle back legs’, Fe-C(3) and Fe-C(4) which are also identical as turtle front paws’, and Fe-C(5) ---’the turtle head’. Such as ‘turtle swimming’ analog may be able to explain the single substituted derivatives of Fc. Again, the mean Fe-C distance obtained from MD simulation is larger than the quantum mechanically calculated Fe-C distances for eclipsed and staggered Fc, with larger deviation with respect to the eclipsed Fc than the staggered Fc. The same trend is obtained for the five Fe-C-H angles from same Cp ring of Fc. The simulated mean IR spectrum at 7K shows split spectral peaks at approximately 470 cm-1 and 488 cm-1, in excellent agreement with quantum mechanically calculated gas phase IR spectrum for eclipsed Fc. As the temperature increases over 80K, the clearly splitting IR spectrum become a very board single peak. Preliminary MD results will be presented.

Keywords: ferrocene conformation, molecular dynamics simulation, conformer orientation, eclipsed and staggered ferrocene

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Authors: K. Raghuwaiya, B. Sharma, J. Vanualailai

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This paper presents a set of artificial potential field functions that improves upon; in general, the motion planning and posture control, with theoretically guaranteed point and posture stabilities, convergence and collision avoidance properties of the general 3-trailer system in a priori known environment. We basically design and inject two new concepts; ghost walls and the distance optimization technique (DOT) to strengthen point and posture stabilities, in the sense of Lyapunov, of our dynamical model. This new combination of techniques emerges as a convenient mechanism for obtaining feasible orientations at the target positions with an overall reduction in the complexity of the navigation laws. Simulations are provided to demonstrate the effectiveness of the controls laws.

Keywords: artificial potential fields, 3-trailer systems, motion planning, posture

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Authors: Joon-Hoon Park

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In this paper the rationalized Haar transform is applied for distributed parameter system identification and estimation. A distributed parameter system is a dynamical and mathematical model described by a partial differential equation. And system identification concerns the problem of determining mathematical models from observed data. The Haar function has some disadvantages of calculation because it contains irrational numbers, for these reasons the rationalized Haar function that has only rational numbers. The algorithm adopted in this paper is based on the transform and operational matrix of the rationalized Haar function. This approach provides more convenient and efficient computational results.

Keywords: distributed parameter system, rationalized Haar transform, operational matrix, system identification

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Authors: Jade Martínez-Llinàs, Pere Colet

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By exploring the possible dynamical regimes in a prototypical model for mutually delay-coupled OEOs, here it is shown that two mutually coupled non-identical OEOs, besides in- and out-of-phase square-waves, can generate stable square-wave pulses synchronized at a quarter of the period (T/4) in a broad parameter region. The key point to obtain T/4 solutions is that the two OEO operate with mixed feedback, namely with negative feedback in one and positive in the other. Furthermore, the coexistence of multiple solutions provides a large degree of flexibility for tuning the frequency in the GHz range without changing any parameter. As a result the two coupled OEOs system is good candidate to be implemented for information encoding as a high-capacity memory device.

Keywords: nonlinear optics, optoelectronic oscillators, square waves, synchronization

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Authors: Anuj Abraham, N. Pappa, Daniel Honc, Rahul Sharma

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In this paper, an analysis of some model order reduction techniques is presented. A new hybrid algorithm for model order reduction of linear time invariant systems is compared with the conventional techniques namely Balanced Truncation, Hankel Norm reduction and Dominant Pole Algorithm (DPA). The proposed hybrid algorithm is known as Clustering Dominant Pole Algorithm (CDPA) is able to compute the full set of dominant poles and its cluster center efficiently. The dominant poles of a transfer function are specific eigenvalues of the state space matrix of the corresponding dynamical system. The effectiveness of this novel technique is shown through the simulation results.

Keywords: balanced truncation, clustering, dominant pole, Hankel norm, model reduction

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Authors: Manuel Meranza-Castillon, Rolando Diaz-Castillo, Adrian Arellano-Delgado, Cesar Cruz-Hernandez, Rosa Martha Lopez-Gutierrez

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In this work, we deal with experimental network synchronization of chaotic nodes with different topologies. Our approach is based on complex system theory, and we use a master-slave configuration to couple the nodes in the networks. In particular, we design and implement electronically complex dynamical networks composed by nine coupled chaotic Chua’s circuits with topologies: in nearest-neighbor, small-world, open ring, star, and global. Also, network synchronization is evaluated according to a particular coupling strength for each topology. This study is important by the possible applications to private transmission of information in a chaotic communication network of multiple users.

Keywords: complex networks, Chua's circuit, experimental synchronization, multiple users

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Authors: Sadia Arshad, Ayesha Sohail, Sana Javed, Khadija Maqbool, Salma Kanwal

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The dynamical study of the carriers play an essential role in the evolution and global transmission of infectious diseases and will be discussed in this study. To make this approach novel, we will consider the fractional order model which is generalization of integer order derivative to an arbitrary number. Since the integration involved is non local therefore this property of fractional operator is very useful to study epidemic model for infectious diseases. An extended numerical method (ODE solver) is implemented on the model equations and we will present the simulations of the model for different values of fractional order to study the effect of carriers on transmission dynamics. Global dynamics of fractional model are established by using the reproduction number.

Keywords: Fractional differential equation, Numerical simulations, epidemic model, transmission dynamics

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Authors: Mustapha El Mataouy, Abellatif Aaliti, Mouhamed Khaddor

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Erbium actived silica-hafnia planar waveguides have been prepared by sol-gel route. The films were deposited on vitreous silica substrates using dip-coating technique. The parameters of preparation have been chosen to optimize the waveguides for operation in the near infrared (NIR) region, and to increase the luminescence efficiency of the metastable 4I13/2 state of Erbium ions. The waveguides properties were determined by m-lines spectroscopy, loss measurements. Waveguide Raman and luminescence spectroscopy were used to obtain information about the structure of the prepared films and about the dynamical process related to the emission in the C telecom band (1530nm-1565nm) of the Erbium ions. The results are discussed with the aim of comparing the structural and optical properties of Erbium activated silica-hafnia planar waveguides with different molar ratio of Si / Hf.

Keywords: erbium, optical amplifiers, silica-hafnia, sol-gel, waveguide

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Authors: H. Y. Jung, Ju H. Park, S. M. Lee

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A sampled-data controller is presented for solid oxide fuel cell systems which is expressed by a sector bounded nonlinear model. The sector bounded nonlinear systems, which have a feedback connection with a linear dynamical system and nonlinearity satisfying certain sector type constraints. Also, the sampled-data control scheme is very useful since it is possible to handle digital controller and increasing research efforts have been devoted to sampled-data control systems with the development of modern high-speed computers. The proposed control law is obtained by solving a convex problem satisfying several linear matrix inequalities. Simulation results are given to show the effectiveness of the proposed design method.

Keywords: sampled-data control, fuel cell, linear matrix inequalities, nonlinear control

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Authors: K. Raghuwaiya, S. Singh, B. Sharma, J. Vanualailai

Abstract:

This paper presents a set of artificial potential field functions that improves upon; in general, the motion planning and posture control, with theoretically guaranteed point and posture stabilities, convergence and collision avoidance properties of 3-trailer systems in a priori known environment. We basically design and inject two new concepts; ghost walls and the Distance Optimization Technique (DOT) to strengthen point and posture stabilities, in the sense of Lyapunov, of our dynamical model. This new combination of techniques emerges as a convenient mechanism for obtaining feasible orientations at the target positions with an overall reduction in the complexity of the navigation laws. The effectiveness of the proposed control laws were demonstrated via simulations of two traffic scenarios.

Keywords: artificial potential fields, 3-trailer systems, motion planning, posture, parking and collision, free trajectories

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Authors: Sanjay Narayan Deo, Badam Singh Kushvah

Abstract:

Bennu(101955) is a half kilometer potentially hazardous near-Earth asteroid. We analyze the influence of Yarkovsky effect and relativistic effect of the Sun on the motion of the asteroid Bennu. The transverse model is used to compute Yarkovsky force on asteroid Bennu. Our dynamical model includes Newtonian perturbations of eight planets, the Moon, the Sun and three massive asteroid (1Ceres, 2Palas and 4Vesta). We showed the variation in orbital elements of nominal orbit of the asteroid. In the presence of Yarkovsky effect, the Semi-major axis of the orbit of the asteroid is decreases by 350 m over one period of orbital motion. The magnitude of Yarkovsky force is computed. We find that maximum magnitude of Yarkovsky force is 0.09 N at the perihelion . We also found that the magnitude of the Sun relativity effect is greater than the Yarkovsky effect on the motion the asteroid Bennu.

Keywords: Bennu, orbital elements, relativistic effect, Yarkovsky effect

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Authors: Weihua Ruan, Kuan-Chou Chen

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This paper is concerned with a system of Hamilton-Jacobi-Bellman equations coupled with an autonomous dynamical system. The mathematical system arises in the differential game formulation of political economy models as an infinite-horizon continuous-time differential game with discounted instantaneous payoff rates and continuously and discretely varying state variables. The existence of a weak solution of the PDE system is proven and a computational scheme of approximate solution is developed for a class of such systems. A model of democratization is mathematically analyzed as an illustration of application.

Keywords: Hamilton-Jacobi-Bellman equations, infinite-horizon differential games, continuous and discrete state variables, political-economy models

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Authors: Hassan Mohammad Alkomy, Hesham Elkaranshawy, Ahmed Ibrahim Ashour, Khaled Tawfik Mohamed

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For a rigid body sliding on a rough surface, a range of uncertainty or non-uniqueness of solution could be found, which is termed: Painlevé paradox. Painlevé paradox is the reason of a wide range of bouncing motion, observed during sliding of robotic manipulators on rough surfaces. In this research work, the existence of the paradox zone during the sliding motion of a two-link (P-R) robotic manipulator with a unilateral constraint is investigated. Parametric study is performed to investigate the effect of friction, link-length ratio, total height and link-mass ratio on the paradox zone.

Keywords: dynamical system, friction, multibody system, painlevé paradox, robotic systems, sliding robots, unilateral constraint

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Authors: Surbhi Rani, Sunita Gakkhar

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The four-dimensional food web system consisting of two prey species for a generalist middle predator and a top predator is proposed and investigated. The middle predator is predating both the prey species with a modified Holling type-II functional response. The food web model is found to be well-posed, bounded, and dissipative. The proposed model's essential dynamical features are studied in terms of local stability. The four species' survival is explored, and persistence conditions are established. The numerical simulations reveal the persistence in the form of a chaotic attractor or stable focus. The conclusion is that providing additional food to the middle predator may help to control the food chain's chaos.

Keywords: predator-prey model, existence of equilibrium points, local stability, chaos, numerical simulations

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Authors: S. Lecheb, A. Nour, A. Chellil, H. Mechakra, N. Hamad, H. Kebir

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The work involves develops attended by a numerical execution of the eXtend Finite Element Method premises a measurement by the fracture process cracked so many cracked plates an application will be processed for the calculation of the stress intensity factor SIF. In the first we give in statically part the distribution of stress, displacement field and strain of composite plate in two cases uncrack/edge crack, also in dynamical part the first six modes shape. Secondly, we calculate Stress Intensity Factor SIF for different orientation angle θ of central crack with length (2a=0.4mm) in plan strain condition, KI and KII are obtained for mode I and mode II respectively using X-FEM method. Finally from crack inclined involving mixed modes results, the comparison we chose dangerous inclination and the best crack angle when K is minimal.

Keywords: stress intensity factor (SIF), crack orientation, glass/epoxy, natural frequencies, X-FEM

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Authors: Ram Kishor

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The Lyapunov characteristic exponent (LCE) is an important tool to describe behavior of a dynamical system, which measures the average rate of divergence (or convergence) of a trajectory emanating in the vicinity of initial point. To analyze the behavior of nearby trajectory emanating in the neighborhood of an equilibrium point in the restricted three-body problem under the influence of perturbations in the form of radiation pressure and oblateness, we compute LCEs of first order with the help of slandered method which is based on variational equation of the system. It is observed that trajectories are chaotic in nature due positive LCEs. Also, we analyze the effect of radiation pressure and oblateness on the LCEs. Results are applicable to study the behavior of more generalized RTBP in the presence of perturbations such as PR drag, solar wind drag etc.

Keywords: Lyapunov characteristic exponent, RTBP, radiation pressure, oblateness

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Authors: Matthaios Katsanikas

Abstract:

We study the structure of the invariant manifolds of complex unstable periodic orbits of a family of periodic orbits, in a 3D autonomous Hamiltonian system of galactic type, after a transition of this family from stability to complex instability (Hamiltonian Hopf bifurcation). We consider the case of a supercritical Hamiltonian Hopf bifurcation. The invariant manifolds of complex unstable periodic orbits have two kinds of structures. The first kind is represented by a disk confined structure on the 4D space of section. The second kind is represented by a complicated central tube structure that is associated with an extended network of tube structures, strips and flat structures of sheet type on the 4D space of section.

Keywords: dynamical systems, galactic dynamics, chaos, phase space

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Authors: M. Zemouli, K. Amara, M. Elkeurti, Y. Benallou

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We present the molecular dynamic simulations results of the structural and dynamical properties of the zinc-blende GaBi over a wide range of temperature (300-1000) K. Our simulation where performed in the framework of the three-body Tersoff potential, which accurately reproduces the lattice constants and elastic constants of the GaBi. A good agreement was found between our calculated results and the available theoretical data of the lattice constant, the bulk modulus and the cohesive energy. Our study allows us to predict the thermodynamic properties such as the specific heat and the lattice thermal expansion. In addition, this method allows us to check its ability to predict the phase transition of this compound. In particular, the transition pressure to the rock-salt phase is calculated and the results are compared with other available works.

Keywords: Gallium compounds, molecular dynamics simulations, interatomic potential thermodynamic properties, structural phase transition

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Authors: Motahare Aali, Fatemeh Tajik

Abstract:

Here, we investigate the sensitivity the Casimir force and consequently dynamical actuation of a three-layer microswitch to some ambient conditions. In fact, we have considered the effect of optical properties on the stable operation of the microswitch for both good (e.g. metals) and poor conductors via a three layer Casimir oscillator. Indeed, gold (Au) has been chosen as a good conductor which is widely used for Casimir force measurements, and highly doped conductive silicon carbide (SiC) has been considered as a poor conductor which is a promising material for device operating under harsh environments. Also, the intervening stratum is considered ethanol or water. It is also supposed that the microswitches are frictionless and autonomous. Using reduction factor diagrams and bifurcation curves, it has been shown how performance of the microswitches is sensitive to temperature and intervening stratum, moreover it is investigated how the conductivity of the components can affect this sensitivity.

Keywords: Casimir force, optical properties, Lifshitz theory, dielectric function

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Authors: N. F. Jamaluddin, N. A. H. Aizam

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This paper explains the educational timetabling problem, a type of scheduling problem that is considered as one of the most challenging problem in optimization and operational research. The university examination timetabling problem (UETP), which involves assigning a set number of exams into a set number of timeslots whilst fulfilling all required conditions, has been widely investigated. The limitation of available timeslots and resources with the increasing number of examinations are the main reasons in the difficulty of solving this problem. Dynamical change in the examination scheduling system adds up the complication particularly in coping up with the demand and new requirements by the communities. Our objective is to investigate these demands and requirements with subjects taken from Universiti Malaysia Terengganu (UMT), through questionnaires. Integer linear programming model which reflects the preferences obtained to produce an effective examination timetabling was formed.

Keywords: demands, educational timetabling, integer linear programming, scheduling, university examination timetabling problem (UETP)

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Authors: Ashwini Umale

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Trajectory planning and optimization is a fundamental problem in articulated robotics. It is often viewed as a two phase problem of initial feasible path planning around obstacles and subsequent optimization of a trajectory satisfying dynamical constraints. An optimized trajectory of multi-axis robot is important and directly influences the Performance of the executing task. Optimal is defined to be the minimum time to transition from the current speed to the set speed. In optimization of trajectory through virtual environment explores the most suitable way to represent robot motion from virtual environment to real environment. This paper aims to review the research of trajectory optimization in virtual environment using simulation software Robcad. Improvements are to be expected in trajectory optimization to generate smooth and collision free trajectories with minimization of overall robot cycle time.

Keywords: trajectory optimization, forward kinematics and reverse kinematics, dynamic constraints, robcad simulation software

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Authors: Jiangbo Pu, Hanhui Xu, Yazhou Wang, Hongyan Cui, Yong Hu

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Spinal cord injury (SCI) brings great negative influence to the patients and society. Neurological loss in human after SCI is a major challenge in clinical. Instead, neural regeneration could have been seen in animals after SCI, and such regeneration could be retarded by blocking neural plasticity pathways, showing the importance of neural plasticity in functional recovery. Here we used sample entropy as an indicator of nonlinear dynamical in the brain to quantify plasticity changes in spontaneous EEG recordings of rats before and after SCI. The results showed that the entropy values were increased after the injury during the recovery in one week. The increasing tendency of sample entropy values is consistent with that of behavioral evaluation scores. It is indicated the potential application of sample entropy analysis for the evaluation of neural plasticity in spinal cord injury rat model.

Keywords: spinal cord injury (SCI), sample entropy, nonlinear, complex system, firing pattern, EEG, spontaneous activity, Basso Beattie Bresnahan (BBB) score

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Authors: Gilbert Makanda

Abstract:

The problem of the teaching of mathematics is studied using differential equations. A mathematical model for knowledge acquisition in mathematics is developed. In this study we adopt the mathematical model that is normally used for disease modelling in the teaching of mathematics. It is assumed that teaching is 'infecting' students with knowledge thereby spreading this knowledge to the students. It is also assumed that students who gain this knowledge spread it to other students making disease model appropriate to adopt for this problem. The results of this study show that increasing recruitment rates, learning contact with teachers and learning materials improves the number of knowledgeable students. High dropout rates and forgetting taught concepts also negatively affect the number of knowledgeable students. The developed model is then solved using Matlab ODE45 and \verb"lsqnonlin" to estimate parameters for the actual data.

Keywords: differential equations, knowledge acquisition, least squares, dynamical systems

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Authors: Ruben Lopez-Rodriguez

Abstract:

In a microgrid, diverse energy sources (both renewable and non-renewable) are combined with energy storage units to form a localized power system. Microgrids function as independent entities, capable of meeting the energy needs of specific areas or communities. This paper introduces a Model Predictive Control (MPC) approach tailored for grid-connected microgrids, aiming to optimize their operation. The formulation employs Mixed-Integer Programming (MIP) to find optimal trajectories. This entails the fulfillment of continuous and binary constraints, all while accounting for commutations between various operating conditions such as storage unit charge/discharge, import/export from/towards the main grid, as well as asset connection/disconnection. To validate the proposed approach, a microgrid case study is conducted, and the simulation results are compared with those obtained using a rule-based strategy.

Keywords: microgrids, mixed logical dynamical systems, mixed-integer optimization, model predictive control

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Authors: Paras Ram, Vikas Kumar

Abstract:

The transmission of Malaria with seasonal were studied through the use of mathematical models. The data from the annual number of Malaria cases reported to the Division of Epidemiology, Ministry of Public Health, Thailand during the period 1997-2011 were analyzed. The transmission of Malaria with seasonal was studied by formulating a mathematical model which had been modified to describe different situations encountered in the transmission of Malaria. In our model, the population was separated into two groups: the human and vector groups, and then constructed a system of nonlinear differential equations. Each human group was divided into susceptible, infectious in hot season, infectious in rainy season, infectious in cool season and recovered classes. The vector population was separated into two classes only: susceptible and infectious vectors. The analysis of the models was given by the standard dynamical modeling.

Keywords: ferrofluid, magnetic field, porous medium, rotating disk, Neuringer-Rosensweig Model

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Authors: Chanyuan Gu, Shouming Zhong

Abstract:

Synchronization is a fundamental phenomenon that enables coherent behavior in networks as a result of interactions. The purpose of this research had been to investigate the problem of anti-phase synchronization for complex delayed dynamical networks with output coupling. The coupling configuration is general, with the coupling matrix not assumed to be symmetric or irreducible. The amount of the coupling variables between two connected nodes is flexible, the nodes in the drive and response systems need not to be identical and there is not any extra constraint on the coupling matrix. Some pinning controllers are designed to make the drive-response system achieve the anti-phase synchronization. For the convenience of description, we applied the matrix Kronecker product. Some new criteria are proposed based on the Lyapunov stability theory, linear matrix inequalities (LMI) and Schur complement. Lastly, some simulation examples are provided to illustrate the effectiveness of our proposed conditions.

Keywords: anti-phase synchronization, complex networks, output coupling, pinning control

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Authors: Neelam Singha

Abstract:

The present work intends to analyze the system dynamics of Hashimoto’s thyroiditis with the assistance of fractional calculus. Hashimoto’s thyroiditis or chronic lymphocytic thyroiditis is an autoimmune disorder in which the immune system attacks the thyroid gland, which gradually results in interrupting the normal thyroid operation. Consequently, the feedback control of the system gets disrupted due to thyroid follicle cell lysis. And, the patient perceives life-threatening clinical conditions like goiter, hyperactivity, euthyroidism, hyperthyroidism, etc. In this work, we aim to obtain the approximate solution to the posed fractional-order problem describing Hashimoto’s thyroiditis. We employ the Adomian decomposition method to solve the system of fractional-order differential equations, and the solutions obtained shall be useful to provide information about the effect of medical care. The numerical technique is executed in an organized manner to furnish the associated details of the progression of the disease and to visualize it graphically with suitable plots.

Keywords: adomian decomposition method, fractional derivatives, Hashimoto's thyroiditis, mathematical modeling

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Authors: G. Santamato, M. Solazzi, A. Frisoli

Abstract:

Systems for detection of damages in railway pantographs effectively reduce the cost of maintenance and improve time scheduling. In this paper, we present an approach to design a monitoring tool fitting strong customer requirements such as portability and ease of use. Pantograph has been modeled to estimate its dynamical properties, since no data are available. With the aim to focus on suspensions health, a two Degrees of Freedom (DOF) scheme has been adopted. Parameters have been calculated by means of analytical dynamics. A Finite Element Method (FEM) modal analysis verified the former model with an acceptable error. The detection strategy seeks phase-plots topology alteration, induced by defects. In order to test the suitability of the method, leakage in the dashpot was simulated on the lumped model. Results are interesting because changes in phase plots are more appreciable than frequency-shift. Further calculations as well as experimental tests will support future developments of this smart strategy.

Keywords: pantograph models, phase plots, structural health monitoring, damage detection

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Authors: Rajkumar N. Ingle

Abstract:

In this paper, the existence of a solution of nonlinear functional random differential equations of the first order is proved under caratheodory condition. The study of the functional random differential equation has got importance in the random analysis of the dynamical systems of universal phenomena. Objectives: Nonlinear functional random differential equation is useful to the scientists, engineers, and mathematicians, who are engaged in N.F.R.D.E. analyzing a universal random phenomenon, govern by nonlinear random initial value problems of D.E. Applications of this in the theory of diffusion or heat conduction. Methodology: Using the concepts of probability theory, functional analysis, generally the existence theorems for the nonlinear F.R.D.E. are prove by using some tools such as fixed point theorem. The significance of the study: Our contribution will be the generalization of some well-known results in the theory of Nonlinear F.R.D.E.s. Further, it seems that our study will be useful to scientist, engineers, economists and mathematicians in their endeavors to analyses the nonlinear random problems of the universe in a better way.

Keywords: Random Fixed Point Theorem, functional random differential equation, N.F.R.D.E., universal random phenomenon

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