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Articles 1 - 9 of 9
Full-Text Articles in Physical Sciences and Mathematics
Regional Mapping Of Flow And Wall Characteristics Of Intracranial Aneurysms, Juan R. Cebral, Xinjie Duan, Piyusha S. Gade, Bong Jae Chung, Fernando Mut, Khaled Aziz, Anne M. Robertson
Regional Mapping Of Flow And Wall Characteristics Of Intracranial Aneurysms, Juan R. Cebral, Xinjie Duan, Piyusha S. Gade, Bong Jae Chung, Fernando Mut, Khaled Aziz, Anne M. Robertson
Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works
The evolution of intracranial aneurysms (IAs) is thought to be driven by progressive wall degradation in response to abnormal hemodynamics. Previous studies focused on the relationship between global hemodynamics and wall properties. However, hemodynamics, wall structure and mechanical properties of cerebral aneurysms can be non-uniform across the aneurysm wall. Therefore, the aim of this work is to introduce a methodology for mapping local hemodynamics to local wall structure in resected aneurysm specimens. This methodology combines image-based computational fluid dynamics, tissue resection, micro-CT imaging of resected specimens mounted on 3D-printed aneurysm models, alignment to 3D vascular models, multi-photon microscopy of the …
The Mechanics Of Clearance In A Non-Newtonian Lubrication Layer, Bong Jae Chung, Douglas Platt, Ashuwin Vaidya
The Mechanics Of Clearance In A Non-Newtonian Lubrication Layer, Bong Jae Chung, Douglas Platt, Ashuwin Vaidya
Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works
This paper investigates the mechanics of clearance of an embedded particle in a lubrication layer of viscoelastic fluid. We show theoretically that in a slider bearing domain containing a viscoelastic fluid, the oscillating shearing motion of a wall aids in transporting away any embedded particle towards the moving boundary. The impact of geometry and material properties of the fluid layer are explored by coupling theoretical and numerical methods. Our approach suggests a possible mechanism by which the human eye could clear out any debris beneath the eyelid, under responsive blinking. Our simplified analysis brings to bear interesting approaches from physics …
Computing The Optimal Path In Stochastic Dynamical Systems, Martha Bauver, Eric Forgoston, Lora Billings
Computing The Optimal Path In Stochastic Dynamical Systems, Martha Bauver, Eric Forgoston, Lora Billings
Department of Mathematics Facuty Scholarship and Creative Works
In stochastic systems, one is often interested in finding the optimal path that maximizes the probability of escape from a metastable state or of switching between metastable states. Even for simple systems, it may be impossible to find an analytic form of the optimal path, and in high- dimensional systems, this is almost always the case. In this article, we formulate a constructive methodology that is used to compute the optimal path numerically. The method utilizes finite-time Lyapunov exponents, statistical selection criteria, and a Newton-based iterative minimizing scheme. The method is applied to four examples. The first example is a …
A Two-Strain Tb Model With Multiple Latent Stages, Azizeh Jabbari, Carlos Castillo-Chavez, Fereshteh Nazari, Baojun Song, Hossein Kheiri
A Two-Strain Tb Model With Multiple Latent Stages, Azizeh Jabbari, Carlos Castillo-Chavez, Fereshteh Nazari, Baojun Song, Hossein Kheiri
Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works
A two-strain tuberculosis (TB) transmission model incorporating antibiotic-generated TB resistant strains and long and variable waiting periods within the latently infected class is introduced. The mathematical analysis is carried out when the waiting periods are modeled via parametrically friendly gamma distributions, a reasonable alternative to the use of exponential distributed waiting periods or to integral equations involving "arbitrary" distributions. The model supports a globally-asymptotically stable disease-free equilibrium when the reproduction number is less than one and an endemic equilibriums, shown to be locally asymptotically stable, or l.a.s., whenever the basic reproduction number is greater than one. Conditions for the existence …
Splash Dynamics Of Paint On Dry, Wet, And Cooled Surfaces, David Baron, Haiyan Su, Ashuwin Vaidya
Splash Dynamics Of Paint On Dry, Wet, And Cooled Surfaces, David Baron, Haiyan Su, Ashuwin Vaidya
Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works
In his classic study in 1908, A.M. Worthington gave a thorough account of splashes and their formation through visualization experiments. In more recent times, there has been renewed interest in this subject, and much of the underlying physics behind Worthington's experiments has now been clarified. One specific set of such recent studies, which motivates this paper, concerns the fluid dynamics behind Jackson Pollock's drip paintings. The physical processes and the mathematical structures hidden in his works have received serious attention and made the scientific pursuit of art a compelling area of exploration. Our current work explores the interaction of watercolors …
The Importance Of Prediction Model Validation And Assessment In Obesity And Nutrition Research, Andrada Ivanescu, P. Li, B. George, A. W. Brown, S. W. Keith, D. Raju, D. B. Allison
The Importance Of Prediction Model Validation And Assessment In Obesity And Nutrition Research, Andrada Ivanescu, P. Li, B. George, A. W. Brown, S. W. Keith, D. Raju, D. B. Allison
Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works
Deriving statistical models to predict one variable from one or more other variables, or predictive modeling, is an important activity in obesity and nutrition research. To determine the quality of the model, it is necessary to quantify and report the predictive validity of the derived models. Conducting validation of the predictive measures provides essential information to the research community about the model. Unfortunately, many articles fail to account for the nearly inevitable reduction in predictive ability that occurs when a model derived on one data set is applied to a new data set. Under some circumstances, the predictive validity can …
Wake–Cylinder Interactions Of A Hinged Cylinder At Low And Intermediate Reynolds Numbers, Bong Jae Chung, M. Cohrs, Wayne Ernst, G. P. Galdi, Ashuwin Vaidya
Wake–Cylinder Interactions Of A Hinged Cylinder At Low And Intermediate Reynolds Numbers, Bong Jae Chung, M. Cohrs, Wayne Ernst, G. P. Galdi, Ashuwin Vaidya
Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works
This paper is devoted to the study and classification of vortex-induced oscillation and the wake structure of flow past finite cylinders. Experiments were performed in a water tunnel using cylindrical particles hinged in the center of the test section while allowing them one degree of rotational freedom. The speed of flow and aspect ratio of the cylinders were used to vary the Reynolds number in the study between 100 and 5000. The cylinders display different responses to the fluid flow depending upon the Re, ranging from steady orientation, periodic oscillation to autorotation. A hydrogen bubble flow visualization technique was used …
Thermally Induced Aggregation Of Rigid Spheres On A Liquid Surface, Eric Forgoston, Leo Hentschker, Siobhan Soltau, Patrick Truitt, Ashuwin Vaidya
Thermally Induced Aggregation Of Rigid Spheres On A Liquid Surface, Eric Forgoston, Leo Hentschker, Siobhan Soltau, Patrick Truitt, Ashuwin Vaidya
Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works
Fluids provide the optimal setting to explore natural patterns far from thermodynamic equilibrium. Experiments suggest that randomly dispersed particles on a liquid surface tend to aggregate on the surface of liquid over time, and the process is enhanced by an increase in the temperature of the liquid. We show that the agglomeration radii increases monotonically with temperature up until the point where all particles in the system form a single, large aggregate. The aggregation dynamics is related to changes in the material properties of the liquid including its viscosity and surface tension as well as the convection driven flow generated …
Modelling Subject-Specific Childhood Growth Using Linear Mixed-Effect Models With Cubic Regression Splines, Laura M. Grajeda, Andrada Ivanescu, Mayuko Saito, Ciprian Crainiceanu, Devan Jaganath, Robert H. Gilman, Jean E. Crabtree, Dermott Kelleher, Lilia Cabrera, Vitaliano Cama, William Checkley
Modelling Subject-Specific Childhood Growth Using Linear Mixed-Effect Models With Cubic Regression Splines, Laura M. Grajeda, Andrada Ivanescu, Mayuko Saito, Ciprian Crainiceanu, Devan Jaganath, Robert H. Gilman, Jean E. Crabtree, Dermott Kelleher, Lilia Cabrera, Vitaliano Cama, William Checkley
Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works
Background: Childhood growth is a cornerstone of pediatric research. Statistical models need to consider individual trajectories to adequately describe growth outcomes. Specifically, well-defined longitudinal models are essential to characterize both population and subject-specific growth. Linear mixed-effect models with cubic regression splines can account for the nonlinearity of growth curves and provide reasonable estimators of population and subject-specific growth, velocity and acceleration. Methods: We provide a stepwise approach that builds from simple to complex models, and account for the intrinsic complexity of the data. We start with standard cubic splines regression models and build up to a model that includes subject-specific …