Thermophysical and chemical characterization of charring ablative materials Final report

Thermophysical and chemical properties of charring ablative material

Disclination Asymmetry in Two-Dimensional Nematic Liquid Crystals with Unequal Frank Constants

The behavior of a thin film of nematic liquid crystal with unequal Frank constants is discussed. Distinct Frank constants are found to imply unequal core energies for $+1/2$ and $-1/2$ disclinations. Even so, a topological constraint is shown to ensure that the bulk densities of the two types of disclinations are the same. For a system with free boundary conditions, such as a liquid membrane, unequal core energies simply renormalize the Gaussian rigidity and line tension.Comment: RevTex forma

Multicanonical molecular dynamics by variable-temperature thermostats and variable-pressure barostats

Sampling from flat energy or density distributions has proven useful in equilibrating complex systems with large energy barriers. Several thermostats and barostats are presented to sample these flat distributions by molecular dynamics. These methods use a variable temperature or pressure that is updated on the fly in the thermodynamic controller. These methods are illustrated on a Lennard-Jones system and a structure-based model of proteins

A Multi-Scale Model for Correlation in B Cell VDJ Usage of Zebrafish

The zebrafish (\emph{Danio rerio}) is one of the model animals for study of immunology because the dynamics in the adaptive immune system of zebrafish are similar to that in higher animals. In this work, we built a multi-scale model to simulate the dynamics of B cells in the primary and secondary immune responses of zebrafish. We use this model to explain the reported correlation between VDJ usage of B cell repertoires in individual zebrafish. We use a delay ordinary differential equation (ODE) system to model the immune responses in the 6-month lifespan of a zebrafish. This mean field theory gives the number of high affinity B cells as a function of time during an infection. The sequences of those B cells are then taken from a distribution calculated by a "microscopic" random energy model. This generalized $NK$ model shows that mature B cells specific to one antigen largely possess a single VDJ recombination. The model allows first-principles calculation of the probability, $p$, that two zebrafish responding to the same antigen will select the same VDJ recombination. This probability $p$ increases with the B cell population size and the B cell selection intensity. The probability $p$ decreases with the B cell hypermutation rate. The multi-scale model predicts correlations in the immune system of the zebrafish that are highly similar to that from experiment.Comment: 29 pages, 10 figures, 1 tabl

Evolutionary processes in finite populations

We consider the evolution of large but finite populations on arbitrary fitness landscapes. We describe the evolutionary process by a Markov-Moran process.We show that toO(1/N), the time-averaged fitness is lower for the finite population than it is for the infinite population.We also showthat fluctuations in the number of individuals for a given genotype can be proportional to a power of the inverse of the mutation rate. Finally, we show that the probability for the system to take a given path through the fitness landscape can be nonmonotonic in system size

Dispersion Coefficients by a Field-Theoretic Renormalization of Fluid Mechanics

We consider subtle correlations in the scattering of fluid by randomly placed obstacles, which have been suggested to lead to a diverging dispersion coefficient at long times for high Peclet numbers, in contrast to finite mean-field predictions. We develop a new master equation description of the fluid mechanics that incorporates the physically relevant fluctuations, and we treat those fluctuations by a renormalization group procedure. We find a finite dispersion coefficient at low volume fraction of disorder and high Peclet numbers.Comment: 4 pages, 1 figure; to appear in Phys. Rev. Let

Shape Changes of Self-Assembled Actin Bilayer Composite Membranes

We report the self-assembly of thin actin shells beneath the membranes of giant vesicles. Ion-carrier mediated influx of Mg2+ induces actin polymerization in the initially spherical vesicles. Buckling of the vesicles and the formation of blisters after thermally induced bilayer expansion is demonstrated. Bilayer flickering is dominated by tension generated by its coupling to the actin cortex. Quantitative flicker analysis suggests the bilayer and the actin cortex are separated by 0.4 \mum to 0.5 \mum due to undulation forces.Comment: pdf-file, has been accepted by PR

Two-Dimensional Diffusion in the Presence of Topological Disorder

How topological defects affect the dynamics of particles hopping between lattice sites of a distorted, two-dimensional crystal is addressed. Perturbation theory and numerical simulations show that weak, short-ranged topological disorder leads to a finite reduction of the diffusion coefficient. Renormalization group theory and numerical simulations suggest that longer-ranged disorder, such as that from randomly placed dislocations or random disclinations with no net disclinicity, leads to subdiffusion at long times.Comment: 10 pages, 6 figure

Renormalization of Drift and Diffusivity in Random Gradient Flows

We investigate the relationship between the effective diffusivity and effective drift of a particle moving in a random medium. The velocity of the particle combines a white noise diffusion process with a local drift term that depends linearly on the gradient of a gaussian random field with homogeneous statistics. The theoretical analysis is confirmed by numerical simulation. For the purely isotropic case the simulation, which measures the effective drift directly in a constant gradient background field, confirms the result previously obtained theoretically, that the effective diffusivity and effective drift are renormalized by the same factor from their local values. For this isotropic case we provide an intuitive explanation, based on a {\it spatial} average of local drift, for the renormalization of the effective drift parameter relative to its local value. We also investigate situations in which the isotropy is broken by the tensorial relationship of the local drift to the gradient of the random field. We find that the numerical simulation confirms a relatively simple renormalization group calculation for the effective diffusivity and drift tensors.Comment: Latex 16 pages, 5 figures ep

Free Energies of Isolated 5- and 7-fold Disclinations in Hexatic Membranes

We examine the shapes and energies of 5- and 7-fold disclinations in low-temperature hexatic membranes. These defects buckle at different values of the ratio of the bending rigidity, $\kappa$, to the hexatic stiffness constant, $K_A$, suggesting {\em two} distinct Kosterlitz-Thouless defect proliferation temperatures. Seven-fold disclinations are studied in detail numerically for arbitrary $\kappa/K_A$. We argue that thermal fluctuations always drive $\kappa/K_A$ into an ``unbuckled'' regime at long wavelengths, so that disclinations should, in fact, proliferate at the {\em same} critical temperature. We show analytically that both types of defects have power law shapes with continuously variable exponents in the ``unbuckled'' regime. Thermal fluctuations then lock in specific power laws at long wavelengths, which we calculate for 5- and 7-fold defects at low temperatures.Comment: LaTeX format. 17 pages. To appear in Phys. Rev.