Mathematical modeling of the growth and coarsening of ice particles in the context of high pressure shift freezing processes.

High pressure shift freezing (HPSF) has been proven more beneficial for ice crystal size and shape than traditional (at atmospheric pressure) freezing.1-3 A model for growth and coarsening of ice crystals inside a frozen food sample (either at atmospheric or high pressure) is developed, and some numerical experiments are given, with which the model is validated by using experimental data. To the best of our knowledge, this is the first model suited for freezing crystallization in the context of high pressure.

Synaptic bistability due to nucleation and evaporation of receptor clusters.

We introduce a bistability mechanism for long-term synaptic plasticity based on switching between two metastable states that contain significantly different numbers of synaptic receptors. One state is characterized by a two-dimensional gas of mobile interacting receptors and is stabilized against clustering by a high nucleation barrier. The other state contains a receptor gas in equilibrium with a large cluster of immobile receptors, which is stabilized by the turnover rate of receptors into and out of the synapse. Transitions between the two states can be initiated by either an increase (potentiation) or a decrease (depotentiation) of the net receptor flux into the synapse. This changes the saturation level of the receptor gas and triggers nucleation or evaporation of receptor clusters.

Ostwald ripening of binary alloy particles.

Classical Lifshitz-Slyozov-Wagner theory is generalized for Ostwald ripening of particles composed of random binary alloy. We show that the steady state ripening process is characterized by self-similar particle size and composition distributions. The shape of particle size distribution depends on whether the process is diffusion controlled (Lifshitz-Slyozov) or reaction controlled (Wagner) and is consistent with the predictions of classical theory for one-component materials. The steady state composition distribution, in contrast, has the same functional form in both extreme cases featuring a universal dependence of the composition upon particle size. We also found that transients in particle's composition can be very quick resulting in a steady state distribution well before it is reached by particles sizes. These transients involve significant changes in particle sizes and open an opportunity for producing metastable particle size distributions of required shape.

Analysis of microscopic parameters of single-particle trajectories in neurons.

We performed a comparative study of the statistical uncertainties that arise when calculating the velocity and diffusion coefficients from single-particle trajectories. We show that a method where particle mean displacement is used to calculate velocity and mean square fluctuation is used to calculate diffusion coefficient offers greater accuracy than analysis of time-dependent mean square displacement. Our assessment of the performance of the two analysis strategies is conducted in two ways. First, we apply each of the methods to simulated trajectories where each parameter term is known. Second, we analyze the motion of previously uncharacterized EphB2 receptors in the membrane of hippocampal neurons. We find that EphB2 receptors display different types of motion mode and transition between these modes. We present our data as a distribution of microscopic diffusion coefficients for each particle trajectory, which we refer to as partial distributions. Partial distributions are summed to form a cumulative distribution of diffusion coefficients for EphB2 receptors in hippocampal neurons. The structure and interpretation of the EphB2 cumulative distribution are discussed.

Role of interaction anisotropy in the formation and stability of molecular templates.

Surface templating via self-assembly of hydrogen-bonded molecular networks is a rapidly developing bottom-up approach in nanotechnology. Using the melamine-PTCDI molecular system as an example we show theoretically that the network stability in the parameter space of temperature versus molecular coupling anisotropy is highly restricted. Our kinetic Monte Carlo simulations predict a structural stability diagram that contains domains of stability of an open honeycomb network, a compact phase, and a high-temperature disordered phase. The results are in agreement with recent experiments, and reveal a relationship between the molecular size and the network stability, which may be used to predict an upper limit on pore-cavity sizes.

Modeling phase separation in nonstoichiometric silica.

We have modeled the decomposition of nonstoichiometric amorphous SiOx upon annealing into silicon and stoichiometric silica, using a new method based on mapping Metropolis Monte Carlo simulations onto rate equations. The concentrations of all oxidation states of silicon are derived as a function of time and found to attain steady-state values at long times dependent on temperature T and oxygen content x. The degree of phase separation and the sizes of Si particles are predicted as a function of T and x, enabling greater control over the size of silicon quantum dots in silica matrices.

Monte Carlo simulation of growth of porous SiOx by vapor deposition.

A random network model containing defects has been developed and applied to the deposition of amorphous SiOx films on a flat substrate. A new Monte Carlo procedure enables dangling bonds to migrate and annihilate. The degree of porosity in the films is found to increase with oxygen content. As the oxygen content increases a larger fraction of pore surfaces is covered with oxygen, and the density of dangling bonds on pore surfaces decreases. Oxygen plays the role of a surfactant, lowering the energies of pore surfaces and enhancing the porosity of amorphous SiO2 compared to amorphous Si.