Numerical Analysis and Computation Commons^™

(R1894) Invariant Solution For Two-Dimensional And Axisymmetric Jet Of Power-Law Fluids, Bhavixa Bhagat, M. G. Timol

Applications and Applied Mathematics: An International Journal (AAM)

An invariant solution is derived using the Lie symmetry technique for steady laminar two-dimensional and axisymmetric boundary layer jet flow of incompressible power-law fluids with appropriate boundary conditions. Using symmetry, the nonlinear partial differential equation of the jet flow problem is transformed into a nonlinear ordinary differential equation. The resultant nonlinear ordinary differential equation with boundary conditions is converted to an initial value problem using the Lie symmetry technique. A numerical solution for the resulting initial value problem is derived using Fehlberg’s fourth-fifth order Runge-Kutta method through Maple software. The graphical representation of the characteristics of the velocity field for …

Improving Efficiency Of Rational Krylov Subspace Methods, Shengjie Xu

All Dissertations

This thesis studies two classes of numerical linear algebra problems, approximating the product of a function of a matrix with a vector, and solving the linear eigenvalue problem $Av=\lambda Bv$ for a small number of eigenvalues. These problems are solved by rational Krylov subspace methods (RKSM). We present several improvements in two directions: pole selection and applying inexact methods.

In Chapter 3, a flexible extended Krylov subspace method ($\mathcal{F}$-EKSM) is considered for numerical approximation of the action of a matrix function $f(A)$ to a vector $b$, where the function $f$ is of Markov type. $\mathcal{F}$-EKSM has the same framework as …

Lyubeznik Numbers Of Unmixed Edge Ideals, Sara Rae Jones

Graduate Theses and Dissertations

Lyubeznik numbers, defined in terms of local cohomology, are invariants of local rings that are able to detect many algebraic and geometric properties. Notably they recognize topological behaviors of various structures associated to their rings. We will discuss computations of these numbers for unmixed edge ideals by giving a completely combinatorial construction which realizes the connectedness information captured by these numbers.

Efficient Hierarchical Space-Time Models For Large Areal Datasets With Application To Forest Inventory Mapping Using Remote Sensing Imagery, Md Kamrul Hasan Khan

Graduate Theses and Dissertations

The focus of this dissertation is development of a novel hierarchical framework, that can be used for predictive modeling of Forest Inventory and Analysis (FIA) data over large regions. This dissertation has two significant contributions. Based on a study region in north-central Wisconsin, we analyze satellite imagery, along with a sample of national forest inventory field plots, to monitor and predict changes in forest conditions over time. The auxiliary data from the satellite imagery of this region are relatively dense in space and time, and can be used to learn how forest conditions changed over that decade. However, these records …

Response Of Planetary Waves And Tides To The 2019 Southern Hemisphere Ssw And Q2dw Enhancement In Jan-Feb 2020 Observed By Condor Meteor Radar In Chile And Adelaide Meteor Radar In Australia, Alan Liu, Zishun Qiao, Iain Reid, Javier Fuentes, Chris Adami

Publications

A new multi-static meteor radar (CONDOR) has recently been installed in northern Chile. This CONDOR meteor radar (30.3°S, 70.7°W) and the Adelaide meteor radar (35°S, 138°E) have provided longitudinally spaced observations of the mean winds, tides and planetary waves of the PW-tides interaction cases we present here. We have observed a Quasi-6-Day Wave (Q6DW) enhancement in MLT winds at the middle latitudes (30.3°S, 35°S) during the unusual minor South Hemisphere SSW 2019 by the ground-based meteor radars. Tidal analysis also indicates modulation of the Q6DW w/ amplitude ~15 [m/s] and diurnal tides w/ amplitude ~60 [m/s]. Another case we present …

An Implementation Of The Method Of Moments On Chemical Systems With Constant And Time-Dependent Rates, Emmanuel Adara

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Physics-Informed Neural Networks For Informed Vaccine Distribution In Heterogeneously Mixed Populations, Alvan Arulandu, Padmanabhan Seshaiyer

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

On Analysis Of Effectiveness Controlling Covid-19 With Quarantine And Vaccination Compartments In Indonesia, Prihantini Prihantini

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Manufacturability And Analysis Of Topologically Optimized Continuous Fiber Reinforced Composites, Jesus A. Ferrand

Doctoral Dissertations and Master's Theses

Researchers are unlocking the potential of Continuous Fiber Reinforced Composites for producing components with greater strength-to-weight ratios than state of the art metal alloys and unidirectional composites. The key is the emerging technology of topology optimization and advances in additive manufacturing. Topology optimization can fine tune component geometry and fiber placement all while satisfying stress constraints. However, the technology cannot yet robustly guarantee manufacturability. For this reason, substantial post-processing of an optimized design consisting of manual fiber replacement and subsequent Finite Element Analysis (FEA) is still required.

To automate this post-processing in two dimensions, two (2) algorithms were developed. The …

Improved Operational Matrices Of Dp-Ball Polynomials For Solving Singular Second Order Linear Dirichlet-Type Boundary Value Problems, Ahmed Kherd, Salim F. Bamsaoud, Omar Bazighifan, Mobarek A. Assabaai

Hadhramout University Journal of Natural & Applied Sciences

Solving Dirichlet-type boundary value problems (BVPs) using a novel numerical approach is presented in this study. The operational matrices of DP-Ball Polynomials are used to solve the linear second-order BVPs. The modification of the operational matrix eliminates the BVP's singularity. Consequently, guaranteeing a solution is reached. In this article, three different examples were taken into consideration in order to demonstrate the applicability of the method. Based on the findings, it seems that the methodology may be used effectively to provide accurate solutions.

(Si10-067) Numerical Study Of The Time Fractional Burgers’ Equation By Using Explicit And Implicit Schemes, Swapnali Doley, A. Vanav Kumar, L. Jino

Applications and Applied Mathematics: An International Journal (AAM)

The study discusses the numerical solution for a time fractional Burgers’ equation using explicit (scheme 1) and implicit scheme (scheme 2), respectively. The approximation of the differential equation is discretized using the finite difference method (FDM). A non-linear term present in the Burgers’ equation is approximated using the time-averaged values. The Von-Neumann analysis shows that the Scheme 1 is conditionally stable and Scheme 2 is unconditionally stable. The numerical solutions are compared with the exact solutions and are good in agreement. Also, the error is estimated between exact and numerical solutions.

(Si10-056) Fear Effect In A Three Species Prey-Predator Food-Web System With Harvesting, R. P. Gupta, Dinesh K. Yadav

Applications and Applied Mathematics: An International Journal (AAM)

Some recent studies and field experiments show that predators affect their prey not only by direct capture; they also induce fear in prey species, which reduces their reproduction rate. Considering this fact, we propose a mathematical model to study the fear effect of a middle predator on its prey in a three-species food web system with harvesting. The ecological feasibility of solutions to the proposed system is guaranteed in terms of positivity and boundedness. The local stability of stationary points in the proposed system is derived. Multiple co-existing stationary points for the proposed system are observed, which makes the problem …

(Si10-062) Comprehensive Study On Methodology Of Orthogonal Interleavers, Priyanka Agarwal, Shivani Dixit, M. Shukla, Gaurish Joshi

Applications and Applied Mathematics: An International Journal (AAM)

Interleaving permutes the data bits by employing a user defined sequence to reduce burst error which at times exceeds the minimum hamming distance. It serves as the sole medium to distinguish user data in the overlapping channel and is the heart of Interleave Division Multiple Access (IDMA) scheme. Versatility of interleavers relies on various design parameters such as orthogonality, correlation, latency and performance parameters like bit error rate (BER), memory occupancy and computation complexity. In this paper, a comprehensive study of interleaving phenomenon and discussion on numerous interleavers is presented. Also, the BER performance of interleavers using IDMA scheme is …

A Data Driven Modeling Approach For Store Distributed Load And Trajectory Prediction, Nicholas Peters

Doctoral Dissertations and Master's Theses

The task of achieving successful store separation from aircraft and spacecraft has historically been and continues to be, a critical issue for the aerospace industry. Whether it be from store-on-store wake interactions, store-parent body interactions or free stream turbulence, a failed case of store separation poses a serious risk to aircraft operators. Cases of failed store separation do not simply imply missing an intended target, but also bring the risk of collision with, and destruction of, the parent body vehicle. Given this risk, numerous well-tested procedures have been developed to help analyze store separation within the safe confines of wind …

Approximation By Basis Pursuit: Background And Application To The Construction Of Efficient Spline Approximations, Babita Timalsina

Graduate Student Scholarship

Basis Pursuit was developed primarily as a tool in the field of signal processing, beginning in the mid 1990’s. The idea is to model the behavior of discrete signals using a wide range of functional behaviors and scales and to obtain an accurate and efficient representation of the signal using a minimal number of functions from a large “dictionary” of possible behaviors. The key observation is by formulating the representation as an ℓ1 optimization, the problem can be posed as a linear program so that the optimal solution uses no more than the number of constraints - it must be …

The Art Of Landslides: How Stochastic Mass Wasting Shapes Topography And Influences Landscape Dynamics, Benjamin Campforts, Charles Shobe, Irina Overeem, Gregory Tucker

Faculty & Staff Scholarship

Bedrock landslides shape topography and mobilize large volumes of sediment. Yet, interactions between landslide-produced sediment and fluvial systems that together govern large-scale landscape evolution are not well understood. To explain morphological patterns observed in steep, landslide-prone terrain, we explicitly model stochastic landsliding and associated sediment dynamics. The model accounts for several common landscape features such as slope frequency distributions, which include values in excess of regional stability limits, quasi-planar hillslopes decorated with straight, closely spaced channel-like features, and accumulation of sediment in valley networks rather than on hillslopes. Stochastic landsliding strongly affects the magnitude and timing of sediment supply to …

Spectral Analysis Of Multiscale Cultural Traits On Twitter, Chandler Squires, Nikhil Kunapuli, Yaneer Bar-Yam, Alfredo Morales

Northeast Journal of Complex Systems (NEJCS)

Understanding and mapping the emergence and boundaries of cultural areas is a challenge for social sciences. In this paper, we present a method for analyzing the cultural composition of regions via Twitter hashtags. Cultures can be described as distinct combination of traits which we capture via principal component analysis (PCA). We investigate the top 8 PCA components of an area including France, Spain, and Portugal, in terms of the geographic distribution of their hashtag composition. We also discuss relationships between components and the insights those relationships can provide into the structure of a cultural space. Finally, we compare the spatial …

Automating Defeasible Reasoning In Law With Answer Set Programming, How Khang Lim, Avishkar Mahajar, Martin Strecker, Meng Weng Wong

Centre for Computational Law (2022-2025)

The paper studies defeasible reasoning in rule-based systems, in particular about legal norms and contracts. We identify rule modifiers that specify how rules interact and how they can be overridden. We then define rule transformations that eliminate these modifiers, leading in the end to a translation of rules to formulas. For reasoning with and about rules, we contrast two approaches, one in a classical logic with SMT solvers, which is only briefly sketched, and one using non-monotonic logic with Answer Set Programming solvers, described in more detail.

Cohomology Of The Symmetric Group With Twisted Coefficients And Quotients Of The Braid Group, Trevor Nakamura

Graduate Theses and Dissertations

In 2014 Brendle and Margalit proved the level $4$ congruence subgroup of the braid group, $B_{n}[4]$, is the subgroup of the pure braid group generated by squares of all elements, $PB_{n}^{2}$. We define the mod $4$ braid group, $\Z_{n}$, to be the quotient of the braid group by the level 4 congruence subgroup, $B_{n}/B_{n}[4]$. In this dissertation we construct a group presentation for $\Z_{n}$ and determine a normal generating set for $B_{n}[4]$ as a subgroup of the braid group. Further work by Kordek and Margalit in 2019 proved $\Z_{n}$ is an extension of the symmetric group, $S_{n}$, by $\mathbb{Z}_{2}^{\binom{n}{2}}$. A …

Academic Hats And Ice Cream: Two Optimization Problems, Valery F. Ochkov, Yulia V. Chudova

Journal of Humanistic Mathematics

This article describes the use of computer software to optimize the design of an academic hat and an ice cream cone!