+publisher:"Penn State University" +contributor:("Leonid Berlyand, Committee Chair/Co-Chair")

Penn State University

1. Ryan, Shawn David. Effective properties and collective dynamics in bacterial suspensions.

Degree: 2014, Penn State University

URL: https://submit-etda.libraries.psu.edu/catalog/22455

► This dissertation introduces novel computationally efficient PDE models, which are used to investigate the origin of self-organization in bacterial suspensions. The key feature of these… (more)

▼ This dissertation introduces novel computationally efficient PDE models, which are used to investigate the origin of self-organization in bacterial suspensions. The key feature of these models is the incorporation of interbacterial interactions motivated by recent experimental observations suggesting their importance in the emergence of collective swimming. Results on well-posedness, effective properties and the onset of the collective state are established through rigorous asymptotic and numerical analysis. Each problem considered is highly multiscale in that microscopic interactions result in changes in the macroscopic state. This work provides a better understanding of the physical mechanisms governing the transition to collective motion. Throughout this dissertation, novel models are employed where a bacterium is represented as a point force dipole subject to two types of interactions: hydrodynamic interactions and excluded volume type interactions introduced through the use of a short-range Lennard-Jones type repelling potential. The point dipole model accounts for the particle size through this potential and shape via Jeffery’s equations modeling how an ellipsoid interacts with the surrounding fluid. Confirming experimental observation, the mathematical analysis reveals that the alignment of asymmetrical particles and the presence of self-propulsion change the effective rheological properties of the suspension such as a drastic reduction in the effective viscosity. By providing explicit formulas for the effective viscosity as well as the effective normal stress differences, the theory presented herein can describe the complete rheological behavior of an active suspension undergoing planar shear in terms of known physical parameters. The first few chapters (1-4) of this dissertation are concerned with introducing the PDE/ODE model for the suspension allowing for the investigation of this decrease in the effective viscosity. The main challenge is added complexity due to the incorporation of interbacterial interactions, in contrast to previous models valid only in the dilute regime. Rigorous mathematical analysis is then performed on the associated nonlinear non-local kinetic equation governing the evolution of the particle distribution function for bacterial positions and orientations. Using this approach, an explicit asymptotic formula for the effective viscosity in terms of known physical parameters is derived. This formula reveals the physical mech- anisms responsible for the striking decrease in the effective viscosity observed in experiment; namely, the combination of self-propulsion, a non-uniform spatial distribution of bacteria due to interactions, and a non-spherical shape of bacteria. The model developed in this dissertation also allows for computationally efficient GPU numerical simulations containing a large number of particles, which are in agreement with the analytical results and experiment. This work is the first to capture the qualitative behavior of the effective viscosity observed in active… Advisors/Committee Members: Leonid Berlyand, Dissertation Advisor/Co-Advisor, Chair%22%29&pagesize-30">Leonid Berlyand, Committee Chair/Co-Chair, Anna L Mazzucato, Committee Member, Xiantao Li, Committee Member, Ralph H Colby, Committee Member.

Subjects/Keywords: mathematical biology; active biosystems; collective motion; effective viscosity; coupled PDE/ODE system; kinetic theory

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Ryan, S. D. (2014). Effective properties and collective dynamics in bacterial suspensions. (Thesis). Penn State University. Retrieved from https://submit-etda.libraries.psu.edu/catalog/22455

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Ryan, Shawn David. “Effective properties and collective dynamics in bacterial suspensions.” 2014. Thesis, Penn State University. Accessed April 11, 2021. https://submit-etda.libraries.psu.edu/catalog/22455.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Ryan, Shawn David. “Effective properties and collective dynamics in bacterial suspensions.” 2014. Web. 11 Apr 2021.

Vancouver:

Ryan SD. Effective properties and collective dynamics in bacterial suspensions. [Internet] [Thesis]. Penn State University; 2014. [cited 2021 Apr 11]. Available from: https://submit-etda.libraries.psu.edu/catalog/22455.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Ryan SD. Effective properties and collective dynamics in bacterial suspensions. [Thesis]. Penn State University; 2014. Available from: https://submit-etda.libraries.psu.edu/catalog/22455

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Penn State University

2. Mizuhara, Matthew S. Analytical and numerical studies on minimal models of crawling cell motion.

Degree: 2017, Penn State University

URL: https://submit-etda.libraries.psu.edu/catalog/14701msm344

► The motility of eukaryotic cells is ubiquitous in biological systems and is central to various processes such as wound healing and the immune response. Understanding… (more)

▼ The motility of eukaryotic cells is ubiquitous in biological systems and is central to various processes such as wound healing and the immune response. Understanding the biophysical mechanisms driving such crawling cell motion has long attracted biologists, biophysicists, and applied mathematicians alike. Experimental results exhibit a wide range of modes of motility including persistently moving cells, wobbling (bipedal) motion, and rotating cells. Although the biological pathways driving cell motility are complicated, various mathematical models have had great success in both replicating experimental results as well as predicting new phenomena. In this dissertation we study two minimal models of cell motion which are derived from a phase-field model of keratocyte motion. The first is derived via the so-called sharp interface limit of the phase-field model. In this limit one recovers a non-linear and non-local geometric evolution law for the motion of a planar curve representing the boundary of the cell membrane. In a particular physical parameter regime we prove well-posedness by establishing existence/uniqueness of solutions. We next demonstrate necessary conditions for the existence of traveling wave solutions which correspond to persistently moving cells. We additionally investigate the sharp interface limit equation numerically: we introduce novel algorithms which resolve the difficulties of non-linearity, non-locality, and non-uniqueness of solutions of the sharp interface limit equation. Simulations reveal wobbling motions as well as rotating cells corresponding to experimental results. The second minimal model is derived by reducing the full phase-field system to a differential algebraic equation (DAE) system. In this simplified system we investigate the effect of patterned substrates on the direction of cell motion. In particular we are interested in understanding the motility of cells on substrates with alternating adhesive and non-adhesive stripes. We validate the DAE system by showing qualitative agreement with full phase-field simulation results wherein either parallel and perpendicular motion to stripes are observed depending on physical parameters. Additionally we predict the effect of changing biophysical parameters and substrate geometry on the direction of cell motility; these results have applications to directed cell motion and sorting. Advisors/Committee Members: Leonid Berlyand, Dissertation Advisor/Co-Advisor, Chair%22%29&pagesize-30">Leonid Berlyand, Committee Chair/Co-Chair, Mark Levi, Committee Member, Anna Mazzucato, Committee Member, Lorraine Santy, Outside Member, Xiantao Li, Committee Member.

Subjects/Keywords: applied mathematics; mathematical biology; cell motility; partial differential equations; keratocyte motion

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Mizuhara, M. S. (2017). Analytical and numerical studies on minimal models of crawling cell motion. (Thesis). Penn State University. Retrieved from https://submit-etda.libraries.psu.edu/catalog/14701msm344

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Mizuhara, Matthew S. “Analytical and numerical studies on minimal models of crawling cell motion.” 2017. Thesis, Penn State University. Accessed April 11, 2021. https://submit-etda.libraries.psu.edu/catalog/14701msm344.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Mizuhara, Matthew S. “Analytical and numerical studies on minimal models of crawling cell motion.” 2017. Web. 11 Apr 2021.

Vancouver:

Mizuhara MS. Analytical and numerical studies on minimal models of crawling cell motion. [Internet] [Thesis]. Penn State University; 2017. [cited 2021 Apr 11]. Available from: https://submit-etda.libraries.psu.edu/catalog/14701msm344.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Mizuhara MS. Analytical and numerical studies on minimal models of crawling cell motion. [Thesis]. Penn State University; 2017. Available from: https://submit-etda.libraries.psu.edu/catalog/14701msm344

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Penn State University

3. Haines, Brian Michael. Effective Viscosity of Dilute Bacterial Suspensions.

Degree: 2011, Penn State University

URL: https://submit-etda.libraries.psu.edu/catalog/11996

► This dissertation explores the bulk (volume averaged) properties of suspensions of microswimmers in a fluid. A microswimmer is a microscopic object that propels itself through… (more)

▼ This dissertation explores the bulk (volume averaged) properties of suspensions of microswimmers in a fluid. A microswimmer is a microscopic object that propels itself through a fluid. A common example of a microswimmer is a bacterium, such as Bacillus subtilis. Our particular interest is the bulk rheological properties of suspensions of bacteria – that is, studying how such a suspension deforms under the application of an external force. In the simplest case, the rheology of a fluid can be described by a scalar effective viscosity. The goal of this dissertation is to find explicit formulae for the effective viscosity in terms of known geometric and physical parameters characterizing bacteria and use them to explain experimental observations. Throughout the dissertation, we consider bacterial suspensions in the dilute limit, where bacteria are assumed to be so far apart that interactions between them are negligible. This simplifies calculations significantly and is the regime in which the most striking experimental results have been observed. We first study suspensions of self-propelled particles using a two-dimensional (2D) Partial Differential Equation (PDE) model. A bacterium is modeled as a disk in 2D with self-propulsion provided by a point force in the fluid. A formula is obtained for the effective viscosity of such suspensions in the dilute limit. This formula includes the two terms that are found in the 2D version of Einstein's classical result for a passive suspension of spheres. To this, our main contribution is added, an additional term due to self-propulsion which depends on the physical and geometric properties of the suspension. This work demonstrates how bacterial self-propulsion can alter the viscosity of a fluid and highlights the importance of bacterial orientation. Next, we present a more realistic PDE model for dilute suspensions of swimming bacteria in a three-dimensional fluid. In this work, a bacterium is modeled as a prolate spheroid with self-propulsion once more provided by a point force. Furthermore, the bacterium is subject to a random torque in order to model tumbling (random reorientation). This model is used to calculate the effective viscosity of the suspension from the microscopic details of the interaction of an elongated body with a prescribed background flow, once more in the dilute limit. Due to a bacterium's asymmetric shape (in particular, unlike the case of rotationally symmetric bacteria used in the first model), interactions with generic planar background flows cause the bacterium to preferentially align in certain directions. Due to the random torque, the steady-state distribution of orientations is unique for a given background flow. Under this distribution of orientations, self-propulsion produces a reduction in the effective viscosity. For sufficiently weak background flows, the effect of self-propulsion on the effective viscosity dominates all other contributions, leading to an effective viscosity of the suspension that is lower than the viscosity of the ambient… Advisors/Committee Members: Leonid Berlyand, Dissertation Advisor/Co-Advisor, Chair%22%29&pagesize-30">Leonid Berlyand, Committee Chair/Co-Chair, Alberto Bressan, Committee Member, Helge Kristian Jenssen, Committee Member, Anna L Mazzucato, Committee Member, Jayanth R Banavar, Committee Member.

Subjects/Keywords: rheology; effective viscosity; bacterial suspensions

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Haines, B. M. (2011). Effective Viscosity of Dilute Bacterial Suspensions. (Thesis). Penn State University. Retrieved from https://submit-etda.libraries.psu.edu/catalog/11996

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Haines, Brian Michael. “Effective Viscosity of Dilute Bacterial Suspensions.” 2011. Thesis, Penn State University. Accessed April 11, 2021. https://submit-etda.libraries.psu.edu/catalog/11996.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Haines, Brian Michael. “Effective Viscosity of Dilute Bacterial Suspensions.” 2011. Web. 11 Apr 2021.

Vancouver:

Haines BM. Effective Viscosity of Dilute Bacterial Suspensions. [Internet] [Thesis]. Penn State University; 2011. [cited 2021 Apr 11]. Available from: https://submit-etda.libraries.psu.edu/catalog/11996.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Haines BM. Effective Viscosity of Dilute Bacterial Suspensions. [Thesis]. Penn State University; 2011. Available from: https://submit-etda.libraries.psu.edu/catalog/11996

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Penn State University

4. Gorb, Yuliya. Asymptotic Analysis of Effective Properties of Highly Concentrated Composites.

Degree: 2008, Penn State University

URL: https://submit-etda.libraries.psu.edu/catalog/7155

► The modeling and design of composite materials, which are at the forefront of modern technology, raises fundamental questions of physics, materials science, and mathematics. Many… (more)

Subjects/Keywords: effective properties; high contrast composites; homogenization; asymptotics; discrete network; error estimate; variational bounds; Poiseuille flow

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Gorb, Y. (2008). Asymptotic Analysis of Effective Properties of Highly Concentrated Composites. (Thesis). Penn State University. Retrieved from https://submit-etda.libraries.psu.edu/catalog/7155

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Gorb, Yuliya. “Asymptotic Analysis of Effective Properties of Highly Concentrated Composites.” 2008. Thesis, Penn State University. Accessed April 11, 2021. https://submit-etda.libraries.psu.edu/catalog/7155.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Gorb, Yuliya. “Asymptotic Analysis of Effective Properties of Highly Concentrated Composites.” 2008. Web. 11 Apr 2021.

Vancouver:

Gorb Y. Asymptotic Analysis of Effective Properties of Highly Concentrated Composites. [Internet] [Thesis]. Penn State University; 2008. [cited 2021 Apr 11]. Available from: https://submit-etda.libraries.psu.edu/catalog/7155.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Gorb Y. Asymptotic Analysis of Effective Properties of Highly Concentrated Composites. [Thesis]. Penn State University; 2008. Available from: https://submit-etda.libraries.psu.edu/catalog/7155

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Penn State University

5. Gyrya, Vitaliy. Effective viscosity and dynamics of suspensions of micro-swimmers .

Degree: 2010, Penn State University

URL: https://submit-etda.libraries.psu.edu/catalog/11317

► This dissertation explores two problems, all related to modeling and analysis of hydrodynamic interactions between microswimmers, most common example of which are swimming microorganisms, e.g.… (more)

▼ This dissertation explores two problems, all related to modeling and analysis of hydrodynamic interactions between microswimmers, most common example of which are swimming microorganisms, e.g. Bacillus subtilis. Results for both problems were published in peer-reviewed journals. In Chapter 1 we introduce the subject of the study, its origins and goals, as well as its current state of development. In Chapter 2 we present the first problem, in which we study the dynamics and interaction of two microswimmers, modeled by self-propelled dumbbell-type structures. We focus on alignment dynamics of a coplanar pair of elongated swimmers, which propel themselves either by “pushing” or “pulling” both in three- and quasi-two-dimensional geometries of space. We derive asymptotic expressions for the dynamics of the pair, which, complemented by numerical experiments, indicate that the tendency of bacteria to align with one another strongly depends on the position of the propulsion force. In particular, we observe that positioning of the effective propulsion force inside the dumbbell results in qualitative agreement with the dynamics observed in experiments, such as mutual alignment of converging bacteria. In Chapter 3 we present the second problem, where we develop a 2D model for a suspension of microswimmers in a fluid and analyze it analytically in the dilute regime when swimmer-swimmer interactions can be neglected and numerically in the moderate concentration regime accounting for all hydrodynamic interactions, using a Mimetic Finite Difference method – efficient method for problems with complex geometries. Our analysis shows that in the dilute regime (in the absence of rotational diffusion) the effective shear viscosity is not affected by self-propulsion. But at the moderate concentrations (due to swimmer-swimmer interactions) the effective viscosity decreases linearly as a function of the propulsion strength of the swimmers. These results prove that (i) a physically observable decrease of viscosity for a suspension of self-propelled microswimmers can be explained purely from the view of hydrodynamics, i.e. “higher order” phenomena such as chemotaxis and chemical constitution of fluid can be neglected (ii) self-propulsion and interactions among swimmers are both essential to the reduction of the effective shear viscosity. In Chapter 3 we also present a number of numerical experiments for the dynamics of swimmers resulting from pairwise interactions at moderate distances from one another. The numerical results agree with the physically observed phenomena (e.g., attraction of swimmer to swimmer and swimmer to the wall). This is viewed as an additional validation of the model and the numerical scheme. Advisors/Committee Members: Leonid Berlyand, Dissertation Advisor/Co-Advisor, Chair%22%29&pagesize-30">Leonid Berlyand, Committee Chair/Co-Chair, Andrew Leonard Belmonte, Committee Member, Anna L Mazzucato, Committee Member, Timothy Reluga, Committee Member, Reka Z Albert, Committee Member.

Subjects/Keywords: Stokes; bacteria; microswimmers; effective viscosity; rheology; interactions; self-propulsion

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Gyrya, V. (2010). Effective viscosity and dynamics of suspensions of micro-swimmers . (Thesis). Penn State University. Retrieved from https://submit-etda.libraries.psu.edu/catalog/11317

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Gyrya, Vitaliy. “Effective viscosity and dynamics of suspensions of micro-swimmers .” 2010. Thesis, Penn State University. Accessed April 11, 2021. https://submit-etda.libraries.psu.edu/catalog/11317.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Gyrya, Vitaliy. “Effective viscosity and dynamics of suspensions of micro-swimmers .” 2010. Web. 11 Apr 2021.

Vancouver:

Gyrya V. Effective viscosity and dynamics of suspensions of micro-swimmers . [Internet] [Thesis]. Penn State University; 2010. [cited 2021 Apr 11]. Available from: https://submit-etda.libraries.psu.edu/catalog/11317.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Gyrya V. Effective viscosity and dynamics of suspensions of micro-swimmers . [Thesis]. Penn State University; 2010. Available from: https://submit-etda.libraries.psu.edu/catalog/11317

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

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