Modifying continuous-time random walks to model finite-size particle diffusion in granular porous media

The continuous-time random walk (CTRW) model is useful for alleviating the computational burden of simulating diffusion in actual media. In principle, isotropic CTRW only requires knowledge of the step-size, $P_l$, and waiting-time, $P_t$, distributions of the random walk in the medium and it then generates presumably equivalent walks in free space, which are much faster. Here we test the usefulness of CTRW to modelling diffusion of finite-size particles in porous medium generated by loose granular packs. This is done by first simulating the diffusion process in a model porous medium of mean coordination number, which corresponds to marginal rigidity (the loosest possible structure), computing the resulting distributions $P_l$ and $P_t$ as functions of the particle size, and then using these as input for a free space CTRW. The CTRW walks are then compared to the ones simulated in the actual media. In particular, we study the normal-to-anomalous transition of the diffusion as a function of increasing particle size. We find that, given the same $P_l$ and $P_t$ for the simulation and the CTRW, the latter predicts incorrectly the size at which the transition occurs. We show that the discrepancy is related to the dependence of the effective connectivity of the porous media on the diffusing particle size, which is not captured simply by these distributions. We propose a correcting modification to the CTRW model -- adding anisotropy -- and show that it yields good agreement with the simulated diffusion process. We also present a method to obtain $P_l$ and $P_t$ directly from the porous sample, without having to simulate an actual diffusion process. This extends the use of CTRW, with all its advantages, to modelling diffusion processes of finite-size particles in such confined geometries.Comment: 9 pages, 7 figure

Affine and topogical structural entropies in granular statistical mechanics: Explicit calculations and equation of state.

We identify two orthogonal sources of structural entropy in rattler-free granular systems: affine, involving structural changes that only deform the contact network, and topological, corresponding to different topologies of the contact network. We show that a recently developed connectivity-based granular statistical mechanics separates the two naturally by identifying the structural degrees of freedom with spanning trees on the graph of the contact network. We extend the connectivity-based formalism to include constraints on, and correlations between, degrees of freedom as interactions between branches of the spanning tree. We then use the statistical mechanics formalism to calculate the partition function generally and the different entropies in the high-angoricity limit. We also calculate the degeneracy of the affine entropy and a number of expectation values. From the latter, we derive an equipartition principle and an equation of state relating the macroscopic volume and boundary stress to the analog of the temperature, the contactivity

Failure of the Volume Function in Granular Statistical Mechanics and an Alternative Formulation

We first show that the currently accepted statistical mechanics for granular matter is flawed. The reason is that it is based on the volume function, which depends only on a minute fraction of all the structural degrees of freedom and is unaffected by most of the configurational microstates. Consequently, the commonly used partition function underestimates the entropy severely. We then propose a new formulation, replacing the volume function with a ${\it connectivity}$ function that depends on all the structural degrees of freedom and accounts correctly for the entire entropy. We discuss the advantages of the new formalism and derive explicit results for two- and three-dimensional systems. We test the formalism by calculating the entropy of an experimental two-dimensional system, as a function of system size, and showing that it is an extensive variable.Comment: 5 pages, 3 figure

Theory-based design of sintered granular composites triples three-phase boundary in fuel cells.

Solid-oxide fuel cells produce electric current from energy released by a spontaneous electrochemical reaction. The efficiency of these devices depends crucially on the microstructure of their electrodes and in particular on the three-phase boundary (TPB) length, along which the energy-producing reaction occurs. We present a systematic maximization of the TPB length as a function of four readily controllable microstructural parameters, for any given mean hydraulic radius, which is a conventional measure of the permeability to gas flow. We identify the maximizing parameters and show that the TPB length can be increased by a factor of over 300% compared to current common practices. We support this result by calculating the TPB of several numerically simulated structures. We also compare four models for a single intergranular contact in the sintered electrode and show that the model commonly used in the literature is oversimplified and unphysical. We then propose two alternatives

Bacterial Programmed Cell Death and Multicellular Behavior in Bacteria

Traditionally, programmed cell death (PCD) is associated with eukaryotic multicellular organisms. However, recently, PCD systems have also been observed in bacteria. Here we review recent research on two kinds of genetic programs that promote bacterial cell death. The first is mediated by mazEF, a toxin–antitoxin module found in the chromosomes of many kinds of bacteria, and mainly studied in Escherichia coli. The second program is found in Bacillus subtilis, in which the skf and sdp operons mediate the death of a subpopulation of sporulating bacterial cells. We relate these two bacterial PCD systems to the ways in which bacterial populations resemble multicellular organisms

Escherichia coli MazF Leads to the Simultaneous Selective Synthesis of Both “Death Proteins” and “Survival Proteins”

The Escherichia coli mazEF module is one of the most thoroughly studied toxin–antitoxin systems. mazF encodes a stable toxin, MazF, and mazE encodes a labile antitoxin, MazE, which prevents the lethal effect of MazF. MazF is an endoribonuclease that leads to the inhibition of protein synthesis by cleaving mRNAs at ACA sequences. Here, using 2D-gels, we show that in E. coli, although MazF induction leads to the inhibition of the synthesis of most proteins, the synthesis of an exclusive group of proteins, mostly smaller than about 20 kDa, is still permitted. We identified some of those small proteins by mass spectrometry. By deleting the genes encoding those proteins from the E. coli chromosome, we showed that they were required for the death of most of the cellular population. Under the same experimental conditions, which induce mazEF-mediated cell death, other such proteins were found to be required for the survival of a small sub-population of cells. Thus, MazF appears to be a regulator that induces downstream pathways leading to death of most of the population and the continued survival of a small sub-population, which will likely become the nucleus of a new population when growth conditions become less stressful