Characterizing Granular Networks Using Topological Metrics

We carry out a direct comparison of experimental and numerical realizations of the exact same granular system as it undergoes shear jamming. We adjust the numerical methods used to optimally represent the experimental settings and outcomes up to microscopic contact force dynamics. Measures presented here range form microscopic, through mesoscopic to system-wide characteristics of the system. Topological properties of the mesoscopic force networks provide a key link between micro and macro scales. We report two main findings: the number of particles in the packing that have at least two contacts is a good predictor for the mechanical state of the system, regardless of strain history and packing density. All measures explored in both experiments and numerics, including stress tensor derived measures and contact numbers depend in a universal manner on the fraction of non-rattler particles, $f_{NR}$. The force network topology also tends to show this universality, yet the shape of the master curve depends much more on the details of the numerical simulations. In particular we show that adding force noise to the numerical data set can significantly alter the topological features in the data. We conclude that both $f_{NR}$ and topological metrics are useful measures to consider when quantifying the state of a granular system.Comment: 8 pages, 8 figure

Exploring the Free Energy Landscape: From Dynamics to Networks and Back

The knowledge of the Free Energy Landscape topology is the essential key to understand many biochemical processes. The determination of the conformers of a protein and their basins of attraction takes a central role for studying molecular isomerization reactions. In this work, we present a novel framework to unveil the features of a Free Energy Landscape answering questions such as how many meta-stable conformers are, how the hierarchical relationship among them is, or what the structure and kinetics of the transition paths are. Exploring the landscape by molecular dynamics simulations, the microscopic data of the trajectory are encoded into a Conformational Markov Network. The structure of this graph reveals the regions of the conformational space corresponding to the basins of attraction. In addition, handling the Conformational Markov Network, relevant kinetic magnitudes as dwell times or rate constants, and the hierarchical relationship among basins, complete the global picture of the landscape. We show the power of the analysis studying a toy model of a funnel-like potential and computing efficiently the conformers of a short peptide, the dialanine, paving the way to a systematic study of the Free Energy Landscape in large peptides.Comment: PLoS Computational Biology (in press

Entanglement reduction induced by geometrical confinement in polymer thin films

We report simulation results on melts of entangled linear polymers confined in a free-standing thin film. We study how the geometric constraints imposed by the confinement alter the entanglement state of the system compared to the equivalent bulk system using various observables. We find that the confinement compresses the chain conformation uniaxially, decreasing the volume pervaded by the chain, which in turn reduces the number of the accessible inter-chain contact that could lead to entanglements. This local and non-uniform effect depends on the position of the chain within the film. We also test a recently presented theory that predicts how the number of entanglements decreases with geometrical confinement.Comment: 28 pages, 10 figure

Variational Methods for Biomolecular Modeling

Structure, function and dynamics of many biomolecular systems can be characterized by the energetic variational principle and the corresponding systems of partial differential equations (PDEs). This principle allows us to focus on the identification of essential energetic components, the optimal parametrization of energies, and the efficient computational implementation of energy variation or minimization. Given the fact that complex biomolecular systems are structurally non-uniform and their interactions occur through contact interfaces, their free energies are associated with various interfaces as well, such as solute-solvent interface, molecular binding interface, lipid domain interface, and membrane surfaces. This fact motivates the inclusion of interface geometry, particular its curvatures, to the parametrization of free energies. Applications of such interface geometry based energetic variational principles are illustrated through three concrete topics: the multiscale modeling of biomolecular electrostatics and solvation that includes the curvature energy of the molecular surface, the formation of microdomains on lipid membrane due to the geometric and molecular mechanics at the lipid interface, and the mean curvature driven protein localization on membrane surfaces. By further implicitly representing the interface using a phase field function over the entire domain, one can simulate the dynamics of the interface and the corresponding energy variation by evolving the phase field function, achieving significant reduction of the number of degrees of freedom and computational complexity. Strategies for improving the efficiency of computational implementations and for extending applications to coarse-graining or multiscale molecular simulations are outlined.Comment: 36 page

Flow rate of transport network controls uniform metabolite supply to tissue

Life and functioning of higher organisms depends on the continuous supply of metabolites to tissues and organs. What are the requirements on the transport network pervading a tissue to provide a uniform supply of nutrients, minerals, or hormones? To theoretically answer this question, we present an analytical scaling argument and numerical simulations on how flow dynamics and network architecture control active spread and uniform supply of metabolites by studying the example of xylem vessels in plants. We identify the fluid inflow rate as the key factor for uniform supply. While at low inflow rates metabolites are already exhausted close to flow inlets, too high inflow flushes metabolites through the network and deprives tissue close to inlets of supply. In between these two regimes, there exists an optimal inflow rate that yields a uniform supply of metabolites. We determine this optimal inflow analytically in quantitative agreement with numerical results. Optimizing network architecture by reducing the supply variance over all network tubes, we identify patterns of tube dilation or contraction that compensate sub-optimal supply for the case of too low or too high inflow rate.Comment: 11 pages, 4 figures, 8 pages supplemen

Phase behavior and material properties of hollow nanoparticles

Effective pair potentials for hollow nanoparticles like the ones made from carbon (fullerenes) or metal dichalcogenides (inorganic fullerenes) consist of a hard core repulsion and a deep, but short-ranged, van der Waals attraction. We investigate them for single- and multi-walled nanoparticles and show that in both cases, in the limit of large radii the interaction range scales inversely with the radius, $R$, while the well depth scales linearly with $R$. We predict the values of the radius $R$ and the wall thickness $h$ at which the gas-liquid coexistence disappears from the phase diagram. We also discuss unusual material properties of the solid, which include a large heat of sublimation and a small surface energy.Comment: Revtex, 13 pages with 8 Postscript files included, submitted to Phys. Rev.