No description available.

No description available.

No description available.

No description available.

No description available.

Many interesting problems in cellular biophysics involve the dynamics of filamentary elastic objects with bend and twist degrees of freedom, moving in a viscous environment. Motivated by the mysterious macrofiber formation in B. subtilis and the rotational dynamics of bacterial flagella, we have sought to establish a general theoretical structure to deal with elastic filament dynamics, analyze these equations for model systems, and to determine the important physical parameters that set the dynamical scales for these systems. We first studied the novel problem of a rotationally forced elastic filament in a viscous fluid [1] to examine the competition between twist injection, twist diffusion, and writhing motions. Two dynamical regimes separated by a Hopf bifurcation were discovered: (i) diffusion-dominated axial rotation, or twirling, and (ii) steady-state crankshafting motion, or whirling. Next, we extended elasticity theory of filaments to encompass systems, such as bacterial flagella, that display competition between two helical structures of opposite chirality [2]. A general, fully intrinsic formulation of the dynamics of bend and twist degrees of freedom was developed using the natural frame of space curves, spanning from the inviscid limit to the viscously-overdamped regime applicable to cellular biology. To be able to measure the elastic properties of cell-sized objects, such as bacterial fibers [3], we utilized an optical trapping system to study the relaxation of a single fiber of B. subtilis which was bent and then released. By analyzing the relaxation time, the bending modulus of the bacterial cell wall was measured to be 1.6 ± 0.6 x 10⁻¹² erg·cm. This number is important in understanding the scales of forces and torques that are present in macrofiber formation and motion, lending insight into the mechanism behind these phenomena.

Two models are presented to describe the immediate environment surrounding negatively charged contaminants in an idealized plasma. The first model uses Poisson's equation to determine the contaminant charge and voltage. This model predicts a critical radius of 40 microns or less below which Poisson's equation is no longer valid. For contaminant radii less than 40 microns, the Coulomb potential is used to find the contaminant charge and voltage. Both models predict negative charges on the order of 10-14 Coulombs, and voltages on the same order of magnitude as the electron energy.

The hydrodynamic stability of a plane, two-dimensional, incompressible wall jet subjected to small disturbances is investigated by direct numerical integration of the complete Navier-Stokes equations. The numerical model allows growing or decaying of disturbances in the downstream direction as in physical experiments. In the past, various numerical investigations were published using the linear stability theory for the case of temporally growing disturbances. In this work, the investigations are made for the case of spatially growing disturbances. The neutral curves of the linear stability theory are displayed, and in addition, the downstream development of spatial growing disturbances is provided by using the complete Navier-Stokes equations. It is shown that the behavior of the disturbances is as predicted by the linear stability theory for a certain frequency using small disturbances. The changes in the downstream development of the flow subjected to large disturbances compared to the results using small disturbances is discussed. For large disturbance amplitudes, it was found that for the frequency of the disturbance waves used in the investigations the boundary layer mode clearly dominates the hydrodynamic stability.

<p> The goal of this work was to develop, introduce, and test a promising computational paradigm for the development of turbulence models for incompressible magnetohydrodynamics (MHD). MHD governs the behavior of an electrically conducting fluid in the presence of an external electromagnetic (EM) field. The incompressible MHD model is used in many engineering and scientific disciplines from the development of nuclear fusion as a sustainable energy source to the study of space weather and solar physics. Many interesting MHD systems exhibit the phenomenon of turbulence which remains an elusive problem from all scientific perspectives. This work focuses on the computational perspective and proposes techniques that enable the study of systems involving MHD turbulence. Direct numerical simulation (DNS) is not a feasible approach for studying MHD turbulence. In this work, turbulence models for incompressible MHD were developed from the variational multiscale (VMS) formulation wherein the solution fields were decomposed into resolved and unresolved components. The unresolved components were modeled with a term that is proportional to the residual of the resolved scales. Two additional MHD models were developed based off of the VMS formulation: a residual-based eddy viscosity (RBEV) model and a mixed model that partners the VMS formulation with the RBEV model. These models are endowed with several special numerical and physics features. Included in the numerical features is the internal numerical consistency of each of the models. Physically, the new models are able to capture desirable MHD physics such as the inverse cascade of magnetic energy and the subgrid dynamo effect. The models were tested with a Fourier-spectral numerical method and the finite element method (FEM). The primary test problem was the Taylor-Green vortex. Results comparing the performance of the new models to DNS were obtained. The performance of the new models was compared to classic and cutting-edge dynamic Smagorinsky eddy viscosity (DSEV) models. The new models typically outperform the classical models.</p>

<p> In inertial confinement fusion (ICF), the kinetic ion and charge separation field effects may play a significant role in the difference between the measured neutron yield in experiments and the predicted yield from fluid codes. Two distinct of approaches exists in modeling plasma physics phenomena: fluid and kinetic approaches. While the fluid approach is computationally less expensive, robust closures are difficult to obtain for a wide separation in temperature and density. While the kinetic approach is a closed system, it resolves the full 6D phase space and classic explicit numerical schemes restrict both the spatial and time-step size to a point where the method becomes intractable. Classic implicit system require the storage and inversion of a very large linear system which also becomes intractable. This dissertation will develop a new implicit method based on an emerging moment-based accelerator which allows one to step over stiff kinetic time-scales. The new method converges the solution per time-step stably and efficiently compared to a standard Picard iteration. This new algorithm will be used to investigate mixing in Omega ICF fuel-pusher interface at early time of the implosion process, fully kinetically. </p>