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MAA Intermountain Section Conference March 23-24, 2018 ABSTRACTS

An Unconditionally Stable Numerical Scheme for a Competition System Involving Diffusion Terms

Seth Armstrong

Southern Utah University


A system of difference equations is presented to approximate the solution to a system of partial differential equations that is used to model competing species with diffusion. The approximation is a semi-implicit finite-difference scheme that mimics the dynamical properties of the true solution. The scheme is uniquely solvable and is unconditionally stable. The asymptotic behavior of the difference scheme is studied by constructing upper and lower solutions for the difference scheme. The convergence rate of the numerical solution to the true solution is given. This is based on joint work with Dr. Jianlong Han.

 Zero Curvature Representations of Darboux Integrable Systems

Brandon P. Ashley

Utah State University


One of the most important properties of integrable nonlinear differential equations is their characterization of having zero curvature representations (ZCRs) which give rise to conservation laws and large classes of exact solutions.  However, there is no general method for finding ZCRs which satisfy these goals.  In this talk, we give a brief introduction to ZCRs and demonstrate our algorithm for finding ZCRs of a subclass of integrable systems known as Darboux integrable systems via the quotient construction of Anderson and Fels.


Technical Analysis: Some mathematical tools used to analyze stock prices direction
Saïd Bahi

Southern Utah University


Technical analysis is used for forecasting stock price direction based on historical data. Some of the current techniques used will be presented using actual data. For the weak-form efficient market hypothesis, such techniques are useless, since it argues that prices follow a random walk. However, they are very wildly used by analysts among other statistical tools.


Classifying the Schur Rings Over the Infinite Cyclic Group

Nicholas Bastian and Jaden Brewer and

Southern Utah University

Schur rings are a type of algebra that is spanned by a partition of finite groups that

meets other conditions. Schur rings were originally developed by Schur and Wielandt in the first

half of the 20th century. They were originally developed to study permutation groups and have

since been more widely studied. They were especially studied in the 1980s and 1990s to look at

finite cyclic groups, which are finite sets that cycle through their elements equipped with an

operation satisfying certain properties.

Past research has provided a classification of Schur rings over finite cyclic groups. We will

provide an extension of this classification to Schur rings over infinite cyclic groups. This will be

accomplished by using a mapping technique involving what we call freshman exponentiation.

Using this we will show that there are only two types of Schur Rings over the integers up to

isomorphism. As all infinite cyclic groups are isomorphic to the integers this will prove our



Using Desmos to Explore Function Transformations and Modeling

Bryan Bradford

Southern Utah University


This presentation shows how to use the computer website Desmos to teach how function transformations work. Some Desmos functionalities that will be highlighted are instantly updating graphs, defining functions, defining variables and doing piecewise graphing. Afterwards, I will be showing how to use Desmos to help students create mathematical models based on data values.


Rényi a-Entropy of Directed Graphs

David Brown, Eric Culver, Bryce Frederickson, Sidney Tate, Brent Thomas

Utah State University


Abstract (on separate page)

Channeling Pythagoras, Killing Him, then Resurrecting Him in the Heart of a Renaissance Boy

Bill Bynum

Westminster College


A demonstration of inquiry-based learning, Pythagorean-style, using poker-chips to explore basic number theory relationships related to divisibility and primality, infused with Pythagorean banter referencing

their religious practices and philosophy of music, alas, leading to the destruction of their rational philosophy, then, thankfully, finding Pythagoreanism alive in the thinking of a famous renaissance scientist.  Ages 8 - 108.


Machine learning model that classifies suicide vulnerability of Twitter users based on their interactions.

Felipe Cancino

Brigham Young University-Idaho


I model machine learning algorithms to classify if a twitter user is at risk of committing suicide. The factors of the model are the tweets that are interactions between a user closest friends. The best accuracy obtained is 75%.


Modeling the impact climate change has in the fragility of states

Felipe Cancino, Andrew Wolfe, and Jason Meziere

Brigham Young University-Idaho


A fragile state “is one where the government is not able to, or chooses not to, provide basic essentials to

its people” (ICM 2018 problem E). Fragile countries are more vulnerable to the impact of climate change such as natural disasters, increase or decrease of temperatures, unpredictable weather among others. We quantify a countries’ fragility based on political descriptors such as GDP per year, GNI, political corruption, etc. We create a mathematical model that analyzes and predicts the impact climate change has in countries’ fragility.


Sensitivity Analysis for contingency tables

Julian Chan

Weber State University


In this talk we discuss measures of confounding variables for contingency tables. We discuss an

application to a toy data set of CDC Zika virus, present simulation results, and theoretical

results. In addition, we define several types of reversals including Simpson’s Paradox and explain the relations between these reversals and statistics conditions. This presentation is based on joint with

with Dr. Knaeble of Utah Valley University.


Seifert Genus and Turaev Genus of Knots

Leslie Colton

Brigham Young University


The Turaev genus is a property of a knot. The Seifert genus of certain knots is another property of a knot, and for positive knots is related to the Turaev genus through an inequality. The alternating decomposition of a knot diagram can tell us the Turaev genus of a link through a simple algorithm. The Turaev genus of positive knots might be related to the Seifert genus more strongly than is currently proven.


Modeling the Spread of Whirling Disease in Salmonids

Neil Duncan

Dixie State University


Whirling Disease (WD) is an ecologically and economically devastating parasitic disease

of salmonid fish. Young fish (fry) are the most susceptible to the disease, which causes skeletal

deformation, neurological damage, and early mortality. It is responsible for the decimation of wild trout populations in the Rocky Mountain region of the United States, killing up to 90% of the population of some rivers. As a result, there have already been large economical losses to fisheries, recreational fishing, and the tourism industry of many western states. If not controlled, the negative effects could be magnified.


The parasite known as Myxobolus Cerebralis is the source of WD. To complete its life cycle the parasite needs two specific hosts; a salmonid fish and a Tubifex worm. The spores of M. Cerebralis are released when infected fish die. The spores are then ingested by Tubifex worms which live in the mud of river bottoms. Inside the worm, the parasite takes on a new form, called a Triactinomyxon (TAM). The TAMs become capable of infecting young susceptible fish who eat the Tubifex worms or come into contact with released TAMs.


The TAM gets into the cartilage near a fish's organ of equilibrium and multiplies very rapidly into new spores, pressuring the organ and causing the victim to swim erratically, losing its ability to forage or to escape predation. The fish dies and releases spores, propagating the life cycle of the parasite. The effects of WD are more significant in some areas than others due to environmental conditions, namely water temperature. Experiments have been conducted showing that varying water temperatures have a significant effect on the production and release of TAMs.


Rényi Ordering of Tournaments

Bryce Frederickson

Utah State University


In the early 1900’s, when H. G. Landau popularized the idea of tournaments, he defined a hierarchy parameter that measures how closely a tournament resembles the transitive tournament based on its score sequence. This parameter partitions the set of tournaments into equivalence classes and orders them from ‘most regular’ to ‘most transitive.’ In recent years, new ‘entropy’ parameters have been defined for graphs based on the spectrum of its normalized Laplacian matrix. By extending these definitions to tournaments, we find that the Rényi a-entropy in fact refines Landau’s hierarchy classes and even distinguishes between tournaments of the same score sequence. From these classes, we establish a Rényi order in which entropy is minimized for transitive tournaments and maximized for doubly regular tournaments.


Timescale Analysis for Eco-evolutionary Time Series Data

Guen Grosklos

Utah State University


Traditionally, evolution, or changes in gene frequencies, is perceived as occurring very slowly

compared to ecological rates of change (e.g., changes in population abundances).  Recent empirical

studies suggest that ecology and evolution may change at similar rates.  However, there is debate

about how fast evolution can be relative to ecology.  We present a method based on the theory of

fast-slow dynamical systems to estimate the relative rates of ecological and evolutionary change

from abundance and phenotypic time series data.  When applied to a suite of empirical data sets,

we find in many cases that ecology and evolution have comparable time scales.  These results show

that the traditional assumption of slow evolution does not always hold in empirical systems.  In

addition, this reinforces the idea that a new theory addressing the concurrent interactions between

ecological and evolutionary processes (i.e., eco-evolutionary dynamics) is needed.


A semi-implicit difference scheme for a reaction diffusion Brusselator system

Jianlong Han

Southern Utah University


A semi-implicit finite difference scheme is proposed for a reaction diffusion Brusselator system. The numerical scheme preserves the similar dynamic properties of the true solution of the system. The asymptotic behavior of the numerical scheme is analyzed.


Cyclic Decompositions of λKn into LWO Graphs

Derek W. Hein

Southern Utah University


In this talk, we identify LWO graphs, find the minimum λ for decomposition of λKn into these graphs, and show that for all viable values of λ, the necessary conditions are sufficient for LWO–decompositions using cyclic decompositions from base graphs.


Dispersal attributes of Alfalfa Stem Nematode

Scott Jordan

Utah State University


The speed of a traveling pest invasive front can be determined through the moment generating function associated to the so-called contact distribution of the dispersal process, which captures the non-local character of the underlying spatial component in an invasion event. This presentation reports the results of a laboratory experiment aimed to approximate the contact distribution for the spread of alfalfa stem nematodes. We fit a Gaussian distribution to the experimental data and approximate the speed of nematode invasive fronts in absence of advection, which is generally associated to nematode transport by flood irrigation. The probability kernel is then used to calculate front speeds when resistant varieties of alfalfa are introduced. We found that, unsurprisingly, invasive speeds are relatively low and cannot

support the rapid dispersal of the disease among fields as seen in practice. However, this result

leads to conjecture that changing current irrigation practices, from flood to sprinkle irrigation, could effectively contribute to control the spread of alfalfa stem nematodes.


Linear Algebra--Flipped but only in part.

Martha Lee Hollist Kilpack

Brigham Young University


I have jumped on the flipped classroom train and I took my Linear Algebra students with me. The concept that enticed me onto the train was the partially flipped model: you have students learn simpler concepts outside of class, creating more time in class to discuss and work with the harder material. We will look at a travel plan for partially flipping a linear algebra class, examples of how topics were taught, and reviews from students who took this trip.


Representing Pinecone and Christmas Tree Lattices as Algebraic Structures

Ryan Janai Kurth

Brigham Young University


For an algebraic structure A, one can easily build a lattice from its subalgebras with the partial order of set inclusion. There is a constructive proof that every algebraic lattice is isomorphic to a subalgebra lattice. Although this construction works well for the purposes of the proof, in practice it will result in a surplus of functions. Given certain types of lattices, including the pinecone and the christmas tree, we will construct algebras that contain a more reasonable number of operations.


Graduate Student Professional Development on Writing Assessments for Undergraduate Mathematics Classrooms

Hannah Mae Lewis

Utah State University


Providing professional development for graduate teaching assistants is becoming more common in mathematics departments in the United States in recent years. The purpose of this talk is to give a research-based example of a professional development session. The seminar discussed is focused on developing good assessments by writing and critiquing exam questions or mini-experiments. This seminar is one in a series of talks over the course of a semester. Previously to this seminar presentation, the graduate teaching assistants would have learned about writing weighted objectives and seen examples of good test questions. This seminar leads them through the typical test writing process, discusses why this is not the correct method, and then each graduate student has the opportunity to write their own question with a corresponding rubric and course objective. Various discussions of these questions are analyzed in pairs and as a group. Through this process graduate teaching assistants have the opportunity to improve their test writing skills and learn how to analyze objectives, prompts, and rubrics.


(Mis)Adventures in Experiential Learning: 10 years of hands-on learning in college algebra

Matthew Lewis and Paul Cox

Brigham Young University-Idaho


We will share our experience over the last 10 years of transforming our traditional, lecture-based course

into a student-centered class where students learn through experience.

We share the original vision of the course, lessons we’ve learned over the years and our vision

for the future of the class.


Computer Toolkit for Integrable Systems

Phillip Linson           

Utah State University


An integrable system is a system of partial differential equations which admits one or more of

the following properties: Lax pair, zero curvature formulation, Hamiltonian operator, recursion

operator, Hirota-bilinear formulation, or a number of others.  In this talk I will discuss my efforts to create a database of integrable systems and their properties. This effort has involved referencing previous incomplete databases as well as compiling other systems and their properties from the literature, and finally deriving some properties by hand. Currently I’m working on compiling Lax pair and zero curvature formulations. To this end, I am writing programs to automatically calculate these properties from the system itself. During my talk I will give brief Maple presentations of these programs, as well as the database itself.


Algebraic Representations for a Finite Lattice

Madeline May

Brigham Young University


For any group the subgroups form a lattice under set inclusion. Further, the subalgebras of any algebra form a lattice. For a finite lattice L, Birkhoff-Frink provided a method to construct an algebra whose subalgebra is isomorphic to L. However, this method gives an excess of operations. We consider methods for certain types of lattices that provide necessary functions. In this presentation we look at power sets lattices and the Mn lattice. We also consider what happens when adding a greatest or least element to a preexisting lattice.


Parameterizing Landscape-Level Movement Models in Hetergeneous Environments

Ian McGahan

Utah State University


The study of animal movement is undergoing a revolution due to the boom in availability of individual telemetry data (GPS tracking) and the increase in resolution of remotely-sensed environmental data (landscape classification from satellite imagery). This data is a time series of correlated locations embedded in landscape patches of known type and varying effect on animal movement.  A long history of mathematical research describes probabilistic consequences of animal movement using partial differential equations. Solutions, with appropriate initial data, are probability density functions (PDFs) of future locations in a time series of individual telemetry data.  Such a PDF can be used in a maximum likelihood estimation procedure to estimate animal movement parameters. The diffusion equation is commonly used but does not allow for variable landscape resistance to movement, spatial aggregation of populations in favorable habitats, or correlation in individual movement.  All three are significant for animals like mule deer. The ecological telegrapher’s equation (ETE) naturally aggregates populations in preferred habitats and accommodates both correlated movement and variable landscape resistance.  We

use the ETE to derive a PDF describing individual movement.  Using asymptotic techniques and homogenization over short scale variation we find a closed form solution to parameterize a landscape-level population model for mule deer in Southern Utah.


Multiparticle Dynamics in a Lattice Gas System

Stewart McGinnis

Brigham Young University


We consider a deterministic dynamical system of particles traveling along the bonds of the triangular lattice. When a particle arrives at a lattice site it is scattered either to the left or right depending on whether the lattice site is oriented to either the left or right, respectively. After scattering a particle the scatterer switches orientation. As a result there is an interplay between the configuration of scatterers, i.e. the medium the particle travels through, and the particle’s trajectory. Under the given rule, it is known that a single particle will propagate through the lattice. We extend the system to include multiple particles, and describe the rich resulting dynamics. The addition of multiple particles gives rise to periodic structures and tangles in which at least two particles have an infinite number of indirect interactions via the medium. We

prove time-invertibility of the dynamics, and provide a number of necessary conditions for aperiodicity and unboundedness of a given initial configuration.  Despite a fair amount of research on the subject, there has not been a mathematical model created which predicts the spread of WD in salmonid populations based on environmental factors.


Our purpose in this research is to work towards a novel and accurate model which effectively predicts what will happen to an ecosystem of fish, worms, and parasites based on initial conditions of populations considering infection rates and fluctuations in water temperature. Once fully developed, the results of this model could be used by wildlife agencies, recreational fishers, and fisheries to implement factors to reduce the spread of WD.


An Agent Based Model of Hand, Foot, and Mouth Disease

Alexander Mitchell

Dixie State University


Hand, Foot, and Mouth Disease (HFMD) is a common viral illness that typically affects children of 5 years old or younger. HFMD spreads through bodily fluids, close contact, and occasionally air, and can lead to fever, sore throat, and painful sores. Outbreaks of HFMD are typically mild; however, recent outbreaks in China have caused multiple infant deaths, leading to socioeconomic disturbances. Several studies have shown that quarantine measures could potentially help suppress the spread of HFMD in future outbreaks. Thus, to better mitigate the spread of HFMD we must better understand how it propagates through a population and how it would be effected by quarantine measures. In order to accomplish this we developed an agent-based model with the goal of simulating HFMD infections and outbreaks, and compared the result with real-world data from past outbreaks. We then analyzed the model and found an R0 value for the disease. Furthermore, we simulated outbreaks with differing amounts of intervention to quantify the usefulness of possible control measures.


Optimal Brewery Crawl Through Montana: An Applied Traveling Salesman Problem

Daniel Olszewski

Carroll College


This talk will briefly cover the Traveling Salesman Problem, and look at a specific application to the 67 breweries in Montana. The algorithms employed to find a near-optimal solution include the nearest neighbor, genetic, and simulated annealing.


Spherical Triangles, Platonic Solids, and Computer Animation.

Bob Palais

Utah Valley University


The 8 octants divide the unit sphere into 8 congruent triangles whose vertices are those of the regular octahedron. Motivated by this example, we consider regular tilings of the sphere. We review a `lune-y proof’ of the classical Girard formula for the area of a spherical triangle and use the formula to show that the number of faces meeting at a vertex can only be 3,4, or 5, and only two more regular polyhedral with triangular faces exist. We find the remaining Platonic solids by using a duality, to show the number of face vertices can also only be 3,4, or 5. We show where Olinde Rodrigues made explicit the analogy of spherical triangle vector addition for composing rotations with rectilinear vector addition for composing translations. We explain how the non-commutative product on the 3-sphere he found from this observation has been used in computer animation, and by Cartan to study linear representations of closed groups.


Classification of Resistance Distances in Simple Graphs

Marcellus Randall

Carroll College


Within graph theory, there are multiple distance metrics which can describe the concept of “distance” between nodes on a simple graph, which are of particular interest to researchers studying link prediction and network evolution. This talk will focus on the relationship between measures of distance in simple graphs and various features of these graphs. I will discuss classifying graphs in which any edge resistance is greater than any non-edge resistance, using Katz centrality scores and classical graph theoretical features.


On Fractional Realizations of Tournament Score Sequences

Kaitlin Murphy and David Brown, Bryce Frederickson, Braden Mindrum, Brent Thomas,

Utah State University


Abstract (on separate page)


Dynamical Stability despite Time-Varying Network Structure

David Reber and Benjamin Webb

Brigham Young University


Dynamic processes on real-world networks are inherently time-delayed due to finite processing speeds, the need to transmit data over distances, or other interruptions in the network’s dynamics.  These time-delays, which correspond to bisecting edges in the network’s underlying graph of interactions, can and often do have a destabilizing effect on the network’s dynamics.  We demonstrate that networks whose underlying graph of interactions satisfy the criteria which we refer to as intrinsic stability are able to maintain their stability even in the presence of time-varying time-delays.  These time-varying delays can be of any form, e.g. deterministic, stochastic, etc.  Furthermore, determining whether a network is intrinsically stable is straightforward and can be implemented on large-scale networks.


Linear Systems of PDEs and Geometry of Calabi-Yau manifolds

Michael Schultz

Utah State University


Given two linear differential equations of finite rank (i.e., the dimension of the solution space) defined on the same space, one may define their tensor product, symmetric product, and exterior product. In this talk, I will discuss a 3-parameter rank-5 system of linear partial differential equations that

arises from the exterior product of the connection forms of two Pfaffian systems; this differential system governs the periods of the Jacobian of a generic smooth genus-two elliptic curve. I will explain the connection of this differential system to the Picard-Fuchs system of a family of lattice polarized K3 surfaces of Picard-rank 17.


Theta Relations from Low Degree Coverings

Shantel Spatig and Thomas Hill and

Utah State University


A genus two curve with symmetries can cover pairs of elliptic curves by two low-degree coverings. In degree two, this classical fact is known as Jacobi Reduction. The coordinates of the Jacobian variety of a genus two curve and of an elliptic curve are theta functions of genus two and genus one, respectively, and their moduli are modular forms given by the corresponding theta constants. By understanding the geometric relation between the genus-two curve with symmetry and the pair of elliptic curves, we are able to derive functional relations between theta functions of genus two and genus one along Humbert varieties of low discriminant.


Hidden Symmetries in Real and Theoretical Networks

Dallas Smith

Brigham Young University


Real-world networks often have a high degree of symmetry. Understanding a network's symmetry can often provide insight into the network's form or function. To this end, we have proposed a novel generalization of the notion of network (graph) symmetry which we refer to as latent symmetry. In this talk I will define latent symmetries and present a number of examples real and theoretical networks which contain them. I will also explain properties of latent symmetries which suggest that they are potentially useful for revealing hidden structures in networks.


Strong Tournaments That are not Cycle Extendable

Brent Thomas and LeRoy Beasley, David Brown

Utah State University


Abstract (on separate page)


Modeling Memorization and Forgetfulness for the Application to a Learning Module

Will Tidwell

Utah State University


Memorization and forgetfulness can be modeled using an ordinary differential equation

that allows for different individual absorption and retention rates of material. By measuring

memorization percentages at specific time increments we can gather data to parameterize the

model. There are many different ways to construct the best fit including transforming the data

and using various tools in MATLAB. Various methods to find a best fit have been investigated

and in each case advantages and limitations were found. This investigation is being used to

help develop this memorization and forgetfulness model into a problem-based learning module

for an undergraduate course focusing on mathematical modeling for preservice teachers.

Applying this model in a sequence of lessons is beneficial as problem-based learning targets

higher learning levels, deepens understanding, and presents mathematical concepts in the

context of a real-world situation.


Zero Forcing Number for Lexicographic Products of Graphs

Violeta Vasilevska

Utah Valley University


Zero forcing is a process on a graph that consists of finding a minimum set of vertices by following certain rules. At the end of this process, all vertices in the graph are ‘observed’ (‘colored’ with the same color). In this talk, we show how to compute the zero forcing number for lexicographic products of certain graphs. This is joint work with several co-authors (REUF research group 2015: K. Benson, D. Ferrero,

  1. Flagg, V. Frust, L. Hogben, and B. Wissman).


Implementing Daily Group Work in Calculus Classes

Violeta Vasilevska

Utah Valley University


This presentation will highlight the group work implementation in Calculus I and II classes. Namely, in these classes, after the new concepts/ideas are introduced, students almost solely work in groups on carefully assigned problems (contained in the provided lecture worksheets). In this talk, the structure of the in-class group work, the benefits to students (and teacher), and the students’ feedback on the in-class group work/worksheets will be discussed.


Isospectral Graph Reductions and Improved Estimates of Matrices Spectra.

Ben Webb

Brigham Young University


Via an isospectral graph reduction the adjacency matrix of a graph can be reduced to a smaller matrix while its spectrum is maintained up to some known (and possibly empty) set. It is then possible to estimate the spectrum of the original matrix by considering Gershgorin-type estimates associated with the reduced matrix. The main result we present is that the eigenvalue estimates associated with Gershgorin, Brauer, Brualdi, and Varga improve as the matrix is reduced. Given that such estimates improve with each successive reduction, it is also possible to estimate the eigenvalues of a matrix with increasing accuracy by repeated use the isospectral reduction process.


Applications of Network Flows

Erica Wiens

Carroll College


Have you ever played a board game or a video game where you mentally figured out the shortest path between two locations before moving? Or have you ever followed a sports team only to discover three quarters of the way through the season that they have no possible chance at winning because they are so far behind? Then you have unknowingly used network flows. Network flows can be used to optimize a variety of problems including shortest path, maximum flow, and finding the minimum cost  of a flow. Through applications, we will explore a few ways to approach each of these problems to determine the most computationally efficient way to solve each problem.


A Ring Walks into a Bar . . .

James S. Wolper

Idaho State University


Sometimes one can rewrite a theorem as a joke. Some jokes are told well, and some fall flat.

What can jokes teach us about writing about, talking about, and even doing Mathematics?


Introduction of nonlocal diffusion models

Xiaoxia Xie

Idaho State University


Long range dispersal is a common phenomenon in biology and ecology. In this talk, I will introduce the nonlocal diffusion operators by an approach that is understandable for undergrads. And then I will briefly discuss the applications in population models.


Plots, Puppies, and Deadly Disease

Elisabeth (Lizzy) Younce

Carroll College


The Serengeti Health Initiative began in 2003 as a collaboration of the Lincoln Park Zoo and various universities around the world in which a team of veterinarians and researchers have been running a campaign to eliminate rabies from the Serengeti Region of Tanzania. To track the impact of the program, survey data has been collected in sixteen villages over thirteen years of the campaign. In this talk I will explain the dynamics of dog populations within the Serengeti from the unusual perspective of evolving shape versus traditional differential equation-based models. Fluctuations in the survey populations and specific villages surveyed over time created challenges in data organization and in applying traditional time series and population analyses. In the talk I will explain the results obtained via traditional exploratory and regression data analytics, as well alternative statistical methods to discover data patterns and shapes and observe their evolution over time. Finally, I will connect these data discoveries back to their original purpose, the campaign to eliminate rabies in the Serengeti.


On Accurate, Stable and Efficient Numerical Approximation for Phase Field Models with Applications in Cell Biology

Jia Zhao

Utah State University


In this talk, I will first discuss the generalized Onsager principle for deriving hydrodynamic theories (equations) for multiphase complex fluids. The generalized Onsager principle combined with variational principle would give a dissipative system that the total energy is decreasing in time. Then I will introduce the newly proposed energy quadratization (EQ) approach to develop efficient, accurate and energy stable numerical approximations for dissipative systems. In the end, applications in cell mitosis and biofilm formation/treatment would be discussed to demonstrate the effectiveness of the modeling and numerical tools.