Modelling Saccharomyces Cerevisiae For The Production Of Fermented Beverages, 2024 Tecnológico Nacional de México/IT Tijuana

#### Modelling Saccharomyces Cerevisiae For The Production Of Fermented Beverages, Paul A. Valle Dr., Yolocuauhtli Salazar Dr., Luis N. Coria Dr., Oscar N. Soto Dr., Jesus B. Paez Dr.

*Annual Symposium on Biomathematics and Ecology Education and Research*

No abstract provided.

Bayesian Networks And Machine Learning For Predicting Breast Cancer Growth From In Vitro Cell Count Data, 2024 Jarvis Christian College

#### Bayesian Networks And Machine Learning For Predicting Breast Cancer Growth From In Vitro Cell Count Data, Widodo Samyono

*Annual Symposium on Biomathematics and Ecology Education and Research*

No abstract provided.

Seshaiyer: Understanding Non-Linear Dynamics Of Interacting Subpopulations And Implicit Human Behavior Using Physics-Informed Neural Networks, 2024 George Mason University

#### Seshaiyer: Understanding Non-Linear Dynamics Of Interacting Subpopulations And Implicit Human Behavior Using Physics-Informed Neural Networks, Naima Aubry-Romero, Alonso Ogueda-Oliva, Padmanabhan Seshaiyer

*Annual Symposium on Biomathematics and Ecology Education and Research*

No abstract provided.

An Introduction To The Time-Independent Schrödinger Equation And Methods To Solve It, 2024 Old Dominion University

#### An Introduction To The Time-Independent Schrödinger Equation And Methods To Solve It, Vu Giang, Alex Gnech

*OUR Journal: ODU Undergraduate Research Journal*

The Time-Independent Schrödinger Equation is a linear elliptic PDE that describes quantum-mechanical systems. Its significance in the science of submicroscopic phenomena, particularly quantum mechanics, is as central as Newton’s laws of motion are to classical mechanics. This study uses various methods, including novel neural networks and finite difference schemes, to solve the one-dimensional two-body equation.

(Si13-09) Numerical Methods For Solving Nonlinear Fisher Equation Using Backward Differentiation Formula, 2024 National Institute of Technology, India

#### (Si13-09) Numerical Methods For Solving Nonlinear Fisher Equation Using Backward Differentiation Formula, Vikash Vimal, Rajesh Kumar Sinha, Liju Pannikkal

*Applications and Applied Mathematics: An International Journal (AAM)*

This paper examines the numerical solution of the nonlinear Fisher equation that is used to find the growth of tumour cells in the brain. By employing new methods that transform nonlinear partial differential equations (PDE) into nonlinear ordinary differential equations (ODE) through spatial discretization. The stability of the resulting nonlinear system is evaluated using Lyapunov’s criteria. Implicit stiff solvers, including various orders of backward differentiation formulas, are used to address the ODE system. The efficiency of these numerical methods is demonstrated through two examples, and a comparison with existing methods from the literature is conducted. Compared to traditional methods, the …

(Si13-02) Approximate Solution Of Fuzzy Volterra Integro-Differential Equations Using Numerical Techniques, 2024 Integral University, India

#### (Si13-02) Approximate Solution Of Fuzzy Volterra Integro-Differential Equations Using Numerical Techniques, Asiya Ansari, Najmuddin Ahmad

*Applications and Applied Mathematics: An International Journal (AAM)*

To determine the approximate solution to fuzzy Volterra integro-differential equations, the Adomian Decomposition Method (ADM), Modified Adomian Decomposition Method (MADM), Variational Iteration Method (VIM), and Homotopy Perturbation Method (HPM) are proposed in this study. We present two examples to support the methodology, and the results are presented in tables to demonstrate the method’s efficiency and correctness. Wolfram Mathematica 11.3 is used to perform the computations.

Production Box Cost Estimating Relationships For Dod Avionics, 2024 Air Force Cost Analysis Agency

#### Production Box Cost Estimating Relationships For Dod Avionics, Carla J. Cisneros, Edward D. White, Brandon M. Lucas, Jonathan D. Ritschel, Robert D. Fass, Shawn M. Valentine

*Faculty Publications*

The authors use historical information obtained from the Cost Assessment Data Enterprise to estimate recurring production unit cost for DoD avionics via cost estimating relationships (CERs). The specific modeled responses include mean unit cost, median unit cost, and the 100th production unit cost (T100) utilizing learning curve theory. For T100, the authors adopt both a multiplicative and an additive error for CER comparison. Recommended CERs consist of the mean unit cost and the T100 utilizing a multiplicative error. Moreover, results reveal that weight has a significant effect on cost as well as a potential underaccounting of real price change or …

Performance Studies Of An Axial Flow Waterjet Pump Using An Unsteady Reynolds-Averaged Navier-Stokes Model, 2024 Clarkson University

#### Performance Studies Of An Axial Flow Waterjet Pump Using An Unsteady Reynolds-Averaged Navier-Stokes Model, Stephen E. Monroe, Junfeng Wang, Chunlei Liang

*Northeast Journal of Complex Systems (NEJCS)*

In this study, an Unsteady Reynolds-Averaged Navier-Stokes (URANS) model is demonstrated its suitability for studying the flow and performance of open marine propellers and waterjet pumps. First, the accuracy of the URANS model is validated by studying turbulent flow past counter-rotating propellers (CRPs). Specifically, experimental data from Miller (1976) is employed for comparison against the URANS results. Subsequently, URANS is used to study the flow and performance of an Office of Naval Research (ONR) axial flow waterjet pump (AxWJ-2). Due to the large number of degrees of freedom for both simulations, parallel computations over 80 cores are performed. For the …

Certifying Stability In Runge-Kutta Schemes: Algebraic Conditions And Semidefinite Programming, 2024 New Jersey Institute of Technology

#### Certifying Stability In Runge-Kutta Schemes: Algebraic Conditions And Semidefinite Programming, Austin Juhl

*Dissertations*

Numerical stability is a critical property for a time-integration scheme. In the context of Runge-Kutta methods applied to stiff differential equations, A-stability is one of the most basic and practically important notions of stability. Dating back to the work of Dahlquist, it has been known that A-stability is equivalent to the Runge-Kutta stability function satisfying a particular convex feasibility problem. Specifically, up to a transformation, the stability function lies in the convex cone of positive functions. In recent years, sum-of-squares optimization and semidefinite programming have become valuable tools in developing rigorous certificates of stability in dynamical systems. Therefore, it is …

Mathematical Modeling, Analysis, And Simulation Of Patient Addiction Journey, 2024 University of Arizona

#### Mathematical Modeling, Analysis, And Simulation Of Patient Addiction Journey, Adan Baca, Diego Gonzalez, Alonso G. Ogueda, Holly C. Matto, Padmanabhan Seshaiyer

*CODEE Journal*

This paper aims to develop a mathematical model to study the dynamics of addiction as individuals go through their detox journey. The motivation for this work is three fold. First, there has been a significant increase in drug overdose and drug addiction following the COVID-19 pandemic, and addiction may be interpreted as a infectious disease. Secondly, the dynamics of infectious disease could be modeled via compartmental models described by differential equations and one can therefore leverage the existing analytical and numerical methods to model addiction as a disease. Finally, the work helps to inform how mathematical models governed by differential …

Hypogene Speleogenesis In Carbonates By Cooling Hydrothermal Flow: The Case Of Mt. Berenike Caves, Israel, 2024 Duke University, Durahm, USA

#### Hypogene Speleogenesis In Carbonates By Cooling Hydrothermal Flow: The Case Of Mt. Berenike Caves, Israel, Roi Roded, Boaz Langford, Einat Aharonov, Piotr Szymczak, Micka Ullman, Shemesh Yaaran, Boaz Lazar, Amos Frumkin

*International Journal of Speleology*

The Berenike hypogenic cave system near Lake Kinneret, Israel, provides a valuable case study for investigating the recently proposed Confined-Cooling-Flow (CCF) speleogenesis model. Field and speleological surveys, along with existing research, are used to provide a thorough analysis. The CCF model relies on a simple thermo-hydro-chemical scenario, involving the rise of CO2-rich hydrothermal fluids discharging into a confined layer. The cooling of these CO2-rich fluids turns them into aggressive solutions due to the inverse relation between temperature and solubility of carbonates (retrograde solubility). Previous geochemical and numerical analyses of the CCF model predict localized and persistent dissolution and speleogenesis on …

Computation Of Moving Interface Flows In Biophysical Applications, 2024 University of Tennessee at Chattanooga

#### Computation Of Moving Interface Flows In Biophysical Applications, Mohammad Murshed

*Masters Theses and Doctoral Dissertations*

This dissertation is concerned with the modeling, simulation, and analysis of moving interface problems involving viscous fluids and solid structures. The main computational technique employed in this work is the immersed boundary method, a widely known numerical method for fluid-structure interaction (FSI). In this technique, the fluid equations are solved in an Eulerian grid and the structure is treated as a network of Lagrangian nodes. The communication between the fluid and structure dynamics is established by the use of the Dirac delta function. Utilizing the immersed boundary method, we have studied three biophysical applications. In the first application, we computed …

Mathematical Modeling And Numerical Approximations Of Combustion Instability Frequencies And Growth Rates, 2024 University of Tennessee, Knoxville

#### Mathematical Modeling And Numerical Approximations Of Combustion Instability Frequencies And Growth Rates, Harvey B. Ring Iii

*Doctoral Dissertations*

This dissertation presents a mathematical model and numerical simulations to determine the resonant frequencies and their associated growth rates for longitudinal modes in a combustion system similar to that found in a rocket engine. The mathematical model, which is applicable to a two-duct system with a thin flame between the two ducts, each of which having constant area and properties, considers the case of axial mean velocity and uses a vibrating wall at the inlet to select the frequency so that all modes may be found. The model is applied to the acoustics equations describing pressure and velocity fluctuations, derived …

Uniformly Distributing Points On A Sphere, 2024 Institute of Analysis and Number Theory

#### Uniformly Distributing Points On A Sphere, Flavio Arrigoni

*Rose-Hulman Undergraduate Mathematics Journal*

In this paper, we are going to present and discuss different procedures for distributing points on a sphere's surface. Furthermore, we will assess their quality with three different distribution tests. The MATHEMATICA package that we created for testing and plotting the points is publicly available.

Approximating Equilibria In Restricted Games, 2024 Phillips Academy Andover

#### Approximating Equilibria In Restricted Games, Jack W. Doyle

*Rose-Hulman Undergraduate Mathematics Journal*

We consider optimal play in restricted games with linear constraints, and use ϵ-equilibria to find near-equilibrium states in these games. We present three mathematical optimization formulations -- a mixed-integer linear program (MILP), a quadratic program with linear constraints (QP), and a quadratically constrained program (QCP) -- to both approximate and identify these states. The MILP has a short runtime relative to the QP and QCP for large games (a factor 100 faster for |S|=9) and exhibits linear growth in run time, but provides only relatively weak upper bound. The QP and QCP provide a tight bound and the precise value …

Numerical Issues For A Non-Autonomous Logistic Model, 2024 Los Alamos National Laboratory

#### Numerical Issues For A Non-Autonomous Logistic Model, Marina Mancuso, Kaitlyn M. Martinez, Carrie Manore, Fabio Milner

*CODEE Journal*

The user-friendly aspects of standardized, built-in numerical solvers in

computational software aid in the simulations of many problems solved using

differential equations. The tendency to trust output from built-in numerical

solvers may stem from their ease-of-use or the user’s unfamiliarity with the

inner workings of the numerical methods. Here, we show a case where the

most frequently used and trusted built-in numerical methods in Python’s

SciPy library produce incorrect, inconsistent, and even unstable approxima-

tions for a the non-autonomous logistic equation, which is used to model

biological phenomena across a variety of disciplines. Some of the most com-

monly used …

(R2067) Solutions Of Hyperbolic System Of Time Fractional Partial Differential Equations For Heat Propagation, 2024 NMIMS Deemed to be University

#### (R2067) Solutions Of Hyperbolic System Of Time Fractional Partial Differential Equations For Heat Propagation, Sagar Sankeshwari, Vinayak Kulkarni

*Applications and Applied Mathematics: An International Journal (AAM)*

Hyperbolic linear theory of heat propagation has been established in the framework of a Caputo time fractional order derivative. The solution of a system of integer and fractional order initial value problems is achieved by employing the Adomian decomposition approach. The obtained solution is in convergent infinite series form, demonstrating the method’s strengths in solving fractional differential equations. Moreover, the double Laplace transform method is employed to acquire the solution of a system of integer and fractional order boundary conditions in the Laplace domain. An inversion of double Laplace transforms has been achieved numerically by employing the Xiao algorithm in …

Advances In Computational And Statistical Inverse Problems, 2024 Dartmouth College

#### Advances In Computational And Statistical Inverse Problems, Dylan Green

*Dartmouth College Ph.D Dissertations*

Inverse problems are prevalent in many fields of science and engineering, such as signal processing and medical imaging. In such problems, indirect data are used to recover information regarding some unknown parameters of interest. When these problems fail to be well-posed, the original problems must be modified to include additional constraints or optimization terms, giving rise to so-called regularization techniques. Classical methods for solving inverse problems are often deterministic and focus on finding point estimates for the unknowns. Some newer methods approach the solving of inverse problems by instead casting them in a statistical framework, allowing for novel point estimate …

Pt-Symmetry And Eigenmodes, 2024 Portland State University

#### Pt-Symmetry And Eigenmodes, Tamara Gratcheva

*University Honors Theses*

Spectra of systems with balanced gain and loss, described by Hamiltonians with parity and time-reversal (*PT*) symmetry is a rich area of research. This work studies by means of numerical techniques, how eigenvalues and eigenfunctions of a Schrodinger operator change as a gain-loss parameter changes. Two cases on a disk with zero boundary conditions are considered. In the first case, within the enclosing disk, we place a parity (*P*) symmetric configuration of three smaller disks containing gain and loss media, which does not have *PT*-symmetry. In the second case, we study a *PT*-symmetric configuration …

Identifiability For Pde Models Of Fluorescence Microscopy Experiments, 2024 Duke University

#### Identifiability For Pde Models Of Fluorescence Microscopy Experiments, Veronica Ciocanel

*Biology and Medicine Through Mathematics Conference*

No abstract provided.