Applied Mathematics Commons^™

On Solutions Of First Order Pde With Two-Dimensional Dirac Delta Forcing Terms, Ian Robinson

Rose-Hulman Undergraduate Mathematics Journal

We provide solutions of a first order, linear partial differential equation of two variables where the nonhomogeneous term is a two-dimensional Dirac delta function. Our results are achieved by applying the unilateral Laplace Transform, solving the subsequently transformed PDE, and reverting back to the original space-time domain. A discussion of existence and uniqueness of solutions, a derivation of solutions of the PDE coupled with a boundary and initial condition, as well as a few worked examples are provided.

Pathogen Emergence As Complex Biological Invasion: Lessons From Dynamical Systems Modeling, Sudam Surasinghe, Marisabel Rodriguez, Victor Meszaros, Jane Molofksy, Salvador Almagro-Moreno, Brandon Ogbunugafor

Northeast Journal of Complex Systems (NEJCS)

Infectious disease emergence has become the target of cross-disciplinary efforts
that aim to understand and predict the shape of outbreaks. The many challenges
involved with the prediction of disease emergence events is a characteristic that in-
fectious diseases share with biological invasions in many subfields of ecology (e.g.,
how certain plants are able to successfully invade a new niche). Like infectious
diseases, biological invasions by plants and animals involve interactions between
agents (pathogens and plants in their respective cases) and a recipient niche. In
this study, we examine the problem of pathogen emergence through the lens of a
framework first …

Accurate Covariance Estimation For Pose Data From Iterative Closest Point Algorithm, Rick H. Yuan, Clark N. Taylor, Scott L. Nykl

Faculty Publications

One of the fundamental problems of robotics and navigation is the estimation of the relative pose of an external object with respect to the observer. A common method for computing the relative pose is the iterative closest point (ICP) algorithm, where a reference point cloud of a known object is registered against a sensed point cloud to determine relative pose. To use this computed pose information in downstream processing algorithms, it is necessary to estimate the uncertainty of the ICP output, typically represented as a covariance matrix. In this paper, a novel method for estimating uncertainty from sensed data is …

Waste Treatment Facility Location For Hotel Chains, Dolores R. Santos-Peñate, Rafael R. Suárez-Vega, Carmen Florido De La Nuez

ITSA 2022 Gran Canaria - 9th Biennial Conference: Corporate Entrepreneurship and Global Tourism Strategies After Covid 19

Tourism generates huge amounts of waste. About half of the waste generated by hotels is food and garden bio-waste. This bio-waste can be used to make compost and pellets. In turn, pellets can be used as an absorbent material in composters and as an energy source. We consider the problem of locating composting and pellet-making facilities so that the bio-waste generated by a chain of hotels can be managed at or close to the generation points. An optimization model is applied to locate the facilities and allocate the waste and products, and several scenarios are analysed. The study shows that, …

Temporality-Induced Chaos In The Kuramoto Model, Keanu Mason Rock, Hamza Dirie, Sean P. Cornelius

Northeast Journal of Complex Systems (NEJCS)

Switched dynamical systems have been extensively studied in engineering literature in the context of system control. In these systems, the dynamical laws change between different subsystems depending on the environment, a process that is known to produce emergent behaviors---notably chaos. These dynamics are analogous to those of temporal networks, in which the network topology changes over time, thereby altering the dynamics on the network. It stands to reason that temporal networks may therefore produce emergent chaos and other exotic behaviors unanticipated in static networks, yet concrete examples remain elusive. Here, we present a minimal example of a networked system in …

Extending The Spectral Difference Method With Divergence Cleaning (Sddc) To The Hall Mhd Equations, Russell J. Hankey, Kuangxu Chen, Chunlei Liang

Northeast Journal of Complex Systems (NEJCS)

The Hall Magnetohydrodynamic (MHD) equations are an extension of the standard MHD equations that include the “Hall” term from the general Ohm’s law. The Hall term decouples ion and electron motion physically on the ion inertial length scales. Implementing the Hall MHD equations in a numerical solver allows more physical simulations for plasma dynamics on length scales less than the ion inertial scale length but greater than the electron inertial length. The present effort is an important step towards producing physically correct results to important problems, such as the Geospace Environmental Modeling (GEM) Magnetic Reconnection problem. The solver that is …

Balancing Sustainability, Profitability, And Resiliency In A 2-Prey, 1-Predator System, Jacob Kahn

Mathematica Militaris

Management decisions on sustainable harvesting of any species in our marine ecosystems benefit from mathematical modeling and simulations due to the underlying complex ecological interactions between species. Using basic mathematical analysis and numerical simulation tools, we consider the problem of investigating the maximum sustainable yield (MSY) and the maximum economic yield (MEY) when harvesting in a fishery system consisting of one predator and two competing prey species. Results show that the harvesting effort required to achieve MEY is less than what is needed to achieve MSY. This implies that increasing harvesting effort beyond what is needed to reach MEY will …

Numerical Analysis Of A Combustion Model For Layered Media Via Mathematical Homogenization, Jessica M. Riggs, Ana Maria Soane

Mathematica Militaris

We propose to investigate a mathematical model
for combustion in a rod made of periodically alternating thin
layers of two combustible materials such as those occurring in
gun propellants. We apply the homogenization theory to resolve
the fast oscillations of the model’s coefficients across adjacent
layers, and set up numerical simulations to better understand
the reactions occurring in such media.

(R2052) Flow Patterns For Newtonian And Non-Newtonian Fluids In A Cylindrical Pipe, Erick Sanchez, Dambaru Bhatta

Applications and Applied Mathematics: An International Journal (AAM)

A fully developed laminar steady flow of an incompressible, viscous fluid in a horizontal cylindrical pipe is considered here. Flow patterns for an incompressible, viscous fluid for both Newtonian and non-Newtonian fluids such as shear-thinning, shear-thickening and Bingham plastic fluids are analyzed in this study. Assuming that the flow is only due to the wall shear stress and the pressure drop, the velocity component in the axial direction for these cases is derived. Computational results of the velocity profiles for various cases are obtained using MATLAB and presented in graphical forms. It is observed that the velocity profile is parabolic …

(R2028) A Brief Note On Space Time Fractional Order Thermoelastic Response In A Layer, Navneet Lamba, Jyoti Verma, Kishor Deshmukh

Applications and Applied Mathematics: An International Journal (AAM)

In this study, a one-dimensional layer of a solid is used to investigate the exact analytical solution of the heat conduction equation with space-time fractional order derivatives and to analyze its associated thermoelastic response using a quasi-static approach. The assumed thermoelastic problem was subjected to certain initial and boundary conditions at the initial and final ends of the layer. The memory effects and long-range interaction were discussed with the help of the Caputo-type fractional-order derivative and finite Riesz fractional derivative. Laplace transform and Fourier transform techniques for spatial coordinates were used to investigate the solution of the temperature distribution and …

(R1966) Semi Analytical Approach To Study Mathematical Model Of Atmospheric Internal Waves Phenomenon, Patel Yogeshwari, Jayesh M. Dhodiya

Applications and Applied Mathematics: An International Journal (AAM)

This research aims to study atmospheric internal waves which occur within the fluid rather than on the surface. The mathematical model of the shallow fluid hypothesis leads to a coupled nonlinear system of partial differential equations. In the shallow flow model, the primary assumption is that vertical size is smaller than horizontal size. This model can precisely replicate atmospheric internal waves because waves are dispersed over a vast horizontal area. A semi-analytical approach, namely modified differential transform, is applied successfully in this research. The proposed method obtains an approximate analytical solution in the form of convergent series without any linearization, …

(R1951) Numerical Solution For A Class Of Nonlinear Emden-Fowler Equations By Exponential Collocation Method, Mohammad Aslefallah, Saeid Abbasbandy, Şuayip Yüzbaşi

Applications and Applied Mathematics: An International Journal (AAM)

In this research, exponential approximation is used to solve a class of nonlinear Emden-Fowler equations. This method is based on the matrix forms of exponential functions and their derivatives using collocation points. To demonstrate the usefulness of the method, we apply it to some different problems. The numerical approximate solutions are compared with available (existing) exact (analytical) solutions to show the accuracy of the proposed method. The method has been checked with several examples to show its validity and reliability. The reported examples illustrate that the method is reasonably efficient and accurate.

(R1954) Fractional Order On Modeling The Transmission Of Devastative Covid-19 Infection: Efficacy Of Vaccination, Ashutosh Rajput, Tanvi ., Rajiv Aggarwal, Arpana Sharma, Shiv Kumar Sahdev, Manoj Kumar, Jaimala .

Applications and Applied Mathematics: An International Journal (AAM)

The second wave of COVID-19 is an unprecedented condition in India and began in mid February 2021. Individuals who were already suffering from other comorbidities were found with lung infection, and hence, the number of disease induced deaths were rising faster during the second wave in relation to the first wave. This paper has proposed a mathematical model with fractional order derivatives by correlating the model based number of infectives with the real number of infectives in India. For the system of fractional differential equations, a disease-free state has been computed and proved to be locally asymptotically stable with certain …

(R1997) Distance Measures Of Complex Fermatean Fuzzy Number And Their Application To Multi-Criteria Decision-Making Problem, V. Chinnadurai, S. Thayalan, A. Bobin

Applications and Applied Mathematics: An International Journal (AAM)

Multi-criteria decision-making (MCDM) is the most widely used decision-making method to solve many complex problems. However, classical MCDM approaches tend to make decisions when the parameters are imprecise or uncertain. The concept of a complex fuzzy set is new in the field of fuzzy set theory. It is a set that can collect and interpret the membership grades from the unit circle in a plane instead of the interval [0,1]. CFS cannot deal with membership and non-membership grades, while complex intuitionistic fuzzy set and complex Pythagorean fuzzy set works only for a limited range of values. The concept of a …

(R1987) Hermite Wavelets Method For System Of Linear Differential Equations, Inderdeep Singh, Manbir Kaur

Applications and Applied Mathematics: An International Journal (AAM)

In this research paper, we present an accurate technique for solving the system of linear differential equations. Such equations often arise as a result of modeling in many systems and applications of engineering and science. The proposed scheme is based on Hermite wavelets basis functions and operational matrices of integration. The demonstrated scheme is simple as it converts the problem into algebraic matrix equation. To validate the applicability and efficacy of the developed scheme, some illustrative examples are also considered. The results so obtained with the help of the present proposed numerical technique by using Hermite wavelets are observed to …

Hydrodynamic And Physicochemical Interactions Between An Active Janus Particle And An Inactive Particle, Jessica S. Rosenberg

Dissertations, Theses, and Capstone Projects

Active matter is an area of soft matter science in which units consume energy and turn it into autonomous motion. Groups of these units – whether flocks of birds, bacterial colonies, or even collections of synthetically-made active particles – may exhibit complex behavior on large scales. While the large-scale picture is of great importance, so is the microscopic scale. Studying the individual particles that make up active matter will allow us to understand how they move, and whether and under what circumstances their activity can be controlled.

Here we delve into the world of active matter by studying colloidal-sized (100 …

(R2033) Resonant Curve Due To Perturbations Of Geo-Synchronous Satellite Including Effect Of Earth’S Equatorial Ellipticity, Sushil Yadav, Mukesh Kumar, Virendra Kumar

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we have investigated resonant curve due to frequencies − angular rate of rotation of the Earth and the rate of change of Earth’s equatorial ellipticity parameter. Perturbation equations are used to convert the non-linear equations of motion of geo-synchronous satellite to the linear form. With the help of graphs, we have shown the effect of Earth’s equatorial ellipticity parameter on oscillatory amplitude and variation in orbital radius of satellite. By defining different perturbations, we have also drawn resonant curve due to frequencies steady-state orbital angular rate of satellite and the rate of change of Earth’s equatorial ellipticity …

(R1975) Map/Ph(1), Ph(2)/2 Queue With Multiple Vacation, Optional Service, Consultations And Interruptions, G. Ayyappan, S. Sankeetha

Applications and Applied Mathematics: An International Journal (AAM)

Two types of services are explored in this paper: regular server and main server, both of which provide both regular and optional services. Customers arrive using the Markovian Arrival Process (MAP), and service time is allocated based on phase type. The regular server uses the main server as a resource. Customers’ service at the primary server is disrupted as a result. When the queue size is empty, the main server can take several vacations. This system has been represented as a QBD Process that investigates steady state with the use of matrix analytic techniques, employing finite-dimensional block matrices. Our model’s …

A Guide To Uncertainty And Global Sensitivity Analysis In Lumped-Parameter Models Of The Cardiovascular System, Raheem Gul, Aamir Shahzad, Syed Muhammad Jawwad Riaz

International Journal of Emerging Multidisciplinaries: Mathematics

In this paper, a general 5-steps framework of uncertainty analysis (UA) and sensitivity analysis (SA) in lumped parameter models of the cardiovascular system (partial or complete) is presented. In order to conduct proper UA and SA, a high number of model simulations is required. Therefore, lumped parameter (0D) models of the cardiovascular system (CVS) are suitable for UA and SA as compared to high or multi-dimensional models (3D,2D,1D). As an example, a linear elastic lumped-parameter model of arm arteries is considered and a 5-steps framework is applied to quantify the impact of input parameters on output variables. The framework uses …

Fem Simulations To Analyze Flow And Thermal Characteristics Of Carreau Non-Newtonian Fluid In A Square Cavity, Sardar Muhammad Bilal, Noor Zeb Khan, Rimsha Nisar

International Journal of Emerging Multidisciplinaries: Mathematics

Heat transfer aspects induced by natural convection in enclosures have promising utilizations and essence from theoretical as well as practical prospective like in, nuclear and chemical reactors, electronic devices, cooling, polymeric processes, solar power collection and so forth. After viewing aforementioned extensive practical importance present communicatn is addressed to explain the flow attributes of Non-Newtonian Carreau fluid model in a square cavity. For non-elastic Carreau fluid model expressing the stress and strain relations at infinite and zero stress magnitude. Mathematical formulation of problem is conceded by obliging conservation laws of momentum and energy. A square enclosure with unit dimension is …