An Interface-Capturing Regularization Method For Solving The Equations For Two-Fluid Mixtures,
2013
Florida Institute of Technology - Melbourne
An Interface-Capturing Regularization Method For Solving The Equations For Two-Fluid Mixtures, Jian Du, Robert D. Guy, Aaron L. Fogelson, Grady B. Wright, James P. Keener
Mathematics Faculty Publications and Presentations
Many problems in biology involve gels which are mixtures composed of a polymer network permeated by a fluid solvent (water). The two-fluid model is a widely used approach to described gel mechanics, in which both network and solvent coexist at each point of space and their relative abundance is described by their volume fractions. Each phase is modeled as a continuum with its own velocity and constitutive law. In some biological applications, free boundaries separate regions of gel and regions of pure solvent, resulting in a degenerate network momentum equation where the network volume fraction vanishes. To overcome this difficulty, …
Correlation Properties Of Collective Motion In Bacterial Suspensions,
2013
Cleveland State University
Correlation Properties Of Collective Motion In Bacterial Suspensions, Shawn D. Ryan, Andrey Sokolov, Leonid Berlyand, Igor S. Aranson
Mathematics and Statistics Faculty Publications
The study of collective motion in bacterial suspensions has been of significant recent interest. To better understand the non-trivial spatio-temporal correlations emerging in the course of collective swimming in suspensions of motile bacteria, a simple model is employed: a bacterium is represented as a force dipole with size, through the use of a short-range repelling potential, and shape. The model emphasizes two fundamental mechanisms: dipolar hydrodynamic interactions and short-range bacterial collisions. Using direct particle simulations validated by a dedicated experiment, we show that changing the swimming speed or concentration alters the time scale of sustained collective motion, consistent with experiment. …
Progressive Reliability Method And Its Application To Offshore Mooring Systems,
2013
Texas A & M University
Progressive Reliability Method And Its Application To Offshore Mooring Systems, Mir Emad Mousavi, Paolo Gardoni, Mehdi Maadooliat
Mathematics, Statistics and Computer Science Faculty Research and Publications
Assessing the reliability of complex systems (e.g. structures) is essential for a reliability-based optimal design that balances safety and costs of such systems. This paper proposes the Progressive Reliability Method (PRM) for the quantification of the reliability of complex systems. The proposed method is a closed-form solution for calculating the probability of failure. The new method is flexible to the definition of “failure” (i.e., can consider serviceability and ultimate-strength failures) and uses the rules of probability theory to estimate the failure probability of the system or its components. The method is first discussed in general and then illustrated in two …
Assessing Protein Conformational Sampling Methods Based On Bivariate Lag-Distributions Of Backbone Angles,
2013
Marquette University
Assessing Protein Conformational Sampling Methods Based On Bivariate Lag-Distributions Of Backbone Angles, Mehdi Maadooliat, Xin Gao, Jianhua Z. Huang
Mathematics, Statistics and Computer Science Faculty Research and Publications
Despite considerable progress in the past decades, protein structure prediction remains one of the major unsolved problems in computational biology. Angular-sampling-based methods have been extensively studied recently due to their ability to capture the continuous conformational space of protein structures. The literature has focused on using a variety of parametric models of the sequential dependencies between angle pairs along the protein chains. In this article, we present a thorough review of angular-sampling-based methods by assessing three main questions: What is the best distribution type to model the protein angles? What is a reasonable number of components in a mixture model …
The Behavior Of Normality When Iteratively Finding The Normal To A Line In An Lp Geometry,
2013
Rochester Institute of Technology
The Behavior Of Normality When Iteratively Finding The Normal To A Line In An Lp Geometry, David L. Farnsworth, Joshua M. Fitzhugh
Articles
The normal direction to the normal direction to a line in Minkowski geometries generally does not give the original line. We show that in lp geometries with p > 1 repeatedly finding the normal line through the origin gives sequences of lines that monotonically approach specific lines of symmetry of the unit circle. Which lines of symmetry that are approached depends upon the value of p and the slope of the initial line.
Supplementary Balance Laws For Cattaneo Heat Propagation,
2013
Portland State University
Supplementary Balance Laws For Cattaneo Heat Propagation, Serge Preston
Mathematics and Statistics Faculty Publications and Presentations
In this work we determine for the Cattaneo heat propagation system all the supplementary balance laws (conservation laws ) of the same order (zero) as the system itself and extract the constitutive relations (expression for the internal energy) dictated by the Entropy Principle. The space of all supplementary balance laws (having the functional dimension 8) contains four original balance laws and their deformations depending on 4 functions of temperature (λ0(ϑ),KA (ϑ), A = 1, 2, 3). The requirements of the II law of thermodynamics leads to the exclusion of three functional degrees (KA= 0, A …
Ct Angiography In The Detection Of Carotid Body Enlargement In Patients With Hypertension And Heart Failure,
2013
Weill Cornell Medical College
Ct Angiography In The Detection Of Carotid Body Enlargement In Patients With Hypertension And Heart Failure, Sreejit Nair, Ajay Gupta, Marat Fudim, Christopher Robinson, Vinay Ravi, Sandra M. Hurtado Rua, Zoar Engelman, Kyungmouk S. Lee, C. Douglas Philips, Akhilesh K. Sista
Mathematics and Statistics Faculty Publications
Introduction: The carotid body (CB) has previously been found to be enlarged and hyperactive in various disease states such as heart failure (HF), hypertension (HTN), and respiratory disease. Evaluation of CB size in these disease states using imaging has not been performed. The purpose of this case–control study was to compare CB sizes in patients with HF and HTN with those of controls using CT angiography. Methods: A retrospective review was performed on 323 consecutive patients who had neck computed tomography angiography (CTA) exams in 2011. Following extensive review, 17 HF and HTN patients and 14 controls were identified. Two …
A Subelliptic Analogue Of Aronson-Serrin's Harnack Inequality,
2013
University of Minnesota Twin Cities
A Subelliptic Analogue Of Aronson-Serrin's Harnack Inequality, Luca Capogna, Giovanna Citti, Garrett Rea
Mathematics Sciences: Faculty Publications
We study the Harnack inequality for weak solutions of a class of degenerate parabolic quasilinear PDE,(Formula presented.) in cylinders Ω × (0,T) where Ω ⊂ M is an open subset of a manifold M endowed with control metric d corresponding to a system of Lipschitz continuous vector fields X=(X_1,..., X_m) and a measure dσ. We show that the Harnack inequality follows from the basic hypothesis of doubling condition and a weak Poincaré inequality in the metric measure space (M,d,dσ). We also show that such hypothesis hold for a class of Riemannian metrics gε collapsing to a sub-Riemannian metric limε → …
Relationships Between Body Roundness With Body Fat And Visceral Adipose Tissue Emerging From A New Geometrical Model,
2013
United States Military Academy at West Point
Relationships Between Body Roundness With Body Fat And Visceral Adipose Tissue Emerging From A New Geometrical Model, Diana M. Thomas, Carl Bredlau, Anja Bosy-Westphal, Manfred Mueller, Wei Shen, Dympna Gallagher, Yuna Maeda, Andrew Mcdougall, Courtney M. Peterson, Eric Ravussin, Steven B. Heymsfield
Department of Mathematics Faculty Scholarship and Creative Works
Objective To develop a new geometrical index that combines height, waist circumference (WC), and hip circumference (HC) and relate this index to total and visceral body fat. Design and Methods Subject data were pooled from three databases that contained demographic, anthropometric, dual energy X-ray absorptiometry (DXA) measured fat mass, and magnetic resonance imaging measured visceral adipose tissue (VAT) volume. Two elliptical models of the human body were developed. Body roundness was calculated from the model using a well-established constant arising from the theory. Regression models based on eccentricity and other variables were used to predict %body fat and %VAT. Results …
On Closed Subsets Of Non-Commutative Association Schemes Of Rank 6,
2013
University of Texas at Brownsville
On Closed Subsets Of Non-Commutative Association Schemes Of Rank 6, Jose Vera
Theses and Dissertations - UTB/UTPA
The notion of an association scheme is a generalization of the concept of a group. In fact, the so-called thin association schemes correspond in a well-understood way to groups. In this thesis, we look at the structure of non-commutative association schemes of rank 6. We will show that a non-normal closed subset of a noncommutative association scheme of rank 6, must have rank 2. The so-called Coxeter schemes of rank 6 which we present in Section 4 provide examples of association schemes of rank 6 with non-normal closed subsets of rank 2. It is shown that normal closed subsets of …
Mathematical Engineering And Control With Applications,
2013
Missouri University of Science and Technology
Mathematical Engineering And Control With Applications, Mamdouh M. El Kady, Martin Bohner, J. Liang, Mouffak Benchohra
Mathematics and Statistics Faculty Research & Creative Works
No abstract provided.
A Topics Analysis Model For Health Insurance Claims,
2013
Brigham Young University - Provo
A Topics Analysis Model For Health Insurance Claims, Jared Anthony Webb
Theses and Dissertations
Mathematical probability has a rich theory and powerful applications. Of particular note is the Markov chain Monte Carlo (MCMC) method for sampling from high dimensional distributions that may not admit a naive analysis. We develop the theory of the MCMC method from first principles and prove its relevance. We also define a Bayesian hierarchical model for generating data. By understanding how data are generated we may infer hidden structure about these models. We use a specific MCMC method called a Gibbs' sampler to discover topic distributions in a hierarchical Bayesian model called Topics Over Time. We propose an innovative use …
The Kalman Filter For Linear Systems On Time Scales,
2013
Missouri University of Science and Technology
The Kalman Filter For Linear Systems On Time Scales, Martin Bohner, Nick Wintz
Mathematics and Statistics Faculty Research & Creative Works
We introduce the Kalman filter for linear systems on time scales, which includes the discrete and continuous versions as special cases. When the system is also stochastic, we show that the Kalman filter is an observer that estimates the system when the state is corrupted by noisy measurements. Finally, we show that the duality of the Kalman filter and the Linear Quadratic Regulator (LQR) is preserved in their unification on time scales. A numerical example is provided. © 2013 Elsevier Ltd.
The Kalman Filter For Linear Systems On Time Scales,
2013
Missouri University of Science and Technology
The Kalman Filter For Linear Systems On Time Scales, Martin Bohner, Nick Wintz
Faculty Scholarship
We introduce the Kalman filter for linear systems on time scales, which includes the discrete and continuous versions as special cases. When the system is also stochastic, we show that the Kalman filter is an observer that estimates the system when the state is corrupted by noisy measurements. Finally, we show that the duality of the Kalman filter and the Linear Quadratic Regulator (LQR) is preserved in their unification on time scales. A numerical example is provided.
Minkowski And Beckenbach-Dresher Inequalities And Functionals On Time Scales,
2013
Missouri University of Science and Technology
Minkowski And Beckenbach-Dresher Inequalities And Functionals On Time Scales, Rabia Bibi, Martin Bohner, Josip Pečarić, Sanja Varǒsanec
Mathematics and Statistics Faculty Research & Creative Works
We obtain integral forms of the Minkowski inequality and Beckenbach-Dresher inequality on time scales. Also, we investigate a converse of Minkowski's inequality and several functionals arising from the Minkowski inequality and the Beckenbach-Dresher inequality. © ELEMENT, Zagreb.
Probable Frames: Using A Probability Task To Explore Fraction Multiplication,
2013
Brigham Young University
Probable Frames: Using A Probability Task To Explore Fraction Multiplication, Joseph G. Curtis, Dr. Robert Speiser
Journal of Undergraduate Research
When you toss a coin at the start of a football game and call “Heads!” the probability the coin will land “heads-up” is one-half. If the referee does not hear your prediction, he must toss again. The probability the second toss will land heads is again one-half. But what is the probability that both tosses were heads? In the double coin toss, the probability of two heads in a row is one-half times one-half: one-fourth. Although the rule (multiply the probabilities of the two independent events in order to calculate the probability of both events) is simple to carry out, …
Orca,
2013
Brigham Young University
Orca, Kourtney Peters
Journal of Undergraduate Research
Throughout my research, the students were rarely given a verbal introduction to the tasks they faced. Instead, they had to rely on their intuition, pre-conceptions, and any previous knowledge to find solutions to the tasks at hand. They were given time and resources to explore their already existing understanding. This balance of time to think and distance from the teacher’s guidance is key, I think, to encouraging students to use their intuition and past experience to solve problems. According to Duckworth (Bransford, 2000), “Accomplished teachers ‘give learners reason’ by respecting and understanding learners’ prior experiences and understandings, assuming that these …
Function And Distribution Of Apolipoprotein A1 In The Artery Wall Are Markedly Distinct From Those In Plasma,
2013
Cleveland State University
Function And Distribution Of Apolipoprotein A1 In The Artery Wall Are Markedly Distinct From Those In Plasma, Joseph A. Didonato, Ying Huang, Kulwant S. Aulak, Orli Even-Or, Gary Gerstenecker, Valentin Gogonea, Yuping Wu, Paul L. Fox, W.H. Wilson Tang, Edward F. Plow, Jonathan D. Smith, Edward A. Fisher, Stanley L. Hazen
Mathematics and Statistics Faculty Publications
Background—Prior studies show that apolipoprotein A1 (apoA1) recovered from human atherosclerotic lesions is highly oxidized. Ex vivo oxidation of apoA1 or high-density lipoprotein (HDL) cross-links apoA1 and impairs lipid binding, cholesterol efflux, and lecithin-cholesterol acyltransferase activities of the lipoprotein. Remarkably, no studies to date directly quantify either the function or HDL particle distribution of apoA1 recovered from the human artery wall. Methods and Results—A monoclonal antibody (10G1.5) was developed that equally recognizes lipid-free and HDL-associated apoA1 in both native and oxidized forms. Examination of homogenates of atherosclerotic plaque–laden aorta showed >100-fold enrichment of apoA1 compared with normal aorta (P<0.001). Surprisingly, buoyant density fractionation revealed that only a minority (<3% of total) of apoA1 recovered from either lesions or normal aorta resides within an HDL-like particle (1.063≤d≤1.21). In contrast, the majority (>90%) …
Rainich-Type Conditions For Null Electrovacuum Spacetimes Ii,
2013
Department of Physics, Utah State University
Rainich-Type Conditions For Null Electrovacuum Spacetimes Ii, Charles G. Torre
Research Vignettes
In this second of two worksheets I continue describing local Rainich-type conditions which are necessary and sufficient for the metric to define a null electrovacuum. In other words, these conditions, which I will call the null electrovacuum conditions, guarantee the existence of a null electromagnetic field such that the metric and electromagnetic field satisfy the Einstein-Maxwell equations. When it exists, the electromagnetic field is easily constructed from the metric. In this worksheet I consider the null electrovacuum conditions which apply when a certain null geodesic congruence determined by the metric is twisting. I shall illustrate the these conditions using a …
Stability Analysis Of 4-Species Aβ Aggregation Model: A Novel Approach To Obtaining Physically Meaningful Rate Constants,
2013
University of Southern Mississippi
Stability Analysis Of 4-Species Aβ Aggregation Model: A Novel Approach To Obtaining Physically Meaningful Rate Constants, G. Ghag, P. Ghosh, A. Mauro, V. Rangachari, Ashuwin Vaidya
Department of Mathematics Faculty Scholarship and Creative Works
Protein misfolding and concomitant aggregation towards amyloid formation is the underlying biochemical commonality among a wide range of human pathologies. Amyloid formation involves the conversion of proteins from their native monomeric states (intrinsically disordered or globular) to well-organized, fibrillar aggregates in a nucleation-dependent manner. Understanding the mechanism of aggregation is important not only to gain better insight into amyloid pathology but also to simulate and predict molecular pathways. One of the main impediments in doing so is the stochastic nature of interactions that impedes thorough experimental characterization and the development of meaningful insights. In this study, we have utilized a …
