Evolution of force networks during stick-slip motion of an intruder in a granular material: Topological measures extracted from experimental data.

In quasi-two-dimensional experiments with photoelastic particles confined to an annular region, an intruder constrained to move in a circular path halfway between the annular walls experiences stick-slip dynamics. We discuss the response of the granular medium to the driven intruder, focusing on the evolution of the force network during sticking periods. Because the available experimental data do not include precise information about individual contact forces, we use an approach developed in our previous work [Basak et al., J. Eng. Mech. 147, 04021100 (2021)0733-939910.1061/(ASCE)EM.1943-7889.0002003] based on networks constructed from measurements of the integrated strain magnitude on each particle. These networks are analyzed using topological measures based on persistence diagrams, revealing that force networks evolve smoothly but in a nontrivial manner throughout each sticking period, even though the intruder and granular particles are stationary. Characteristic features of persistence diagrams show identifiable slip precursors. In particular, the number of generators describing the structure and complexity of force networks increases consistently before slips. Key features of the dynamics are similar for granular materials composed of disks or pentagons, but some details are consistently different. In particular, we find significantly larger fluctuations of the measures computed based on persistence diagrams and, therefore, of the underlying networks, for systems of pentagonal particles.

Lipid exchange in crystal-confined fatty acid binding proteins: X-ray evidence and molecular dynamics explanation.

Fatty acid binding proteins (FABPs) are responsible for the long-chain fatty acids (FAs) transport inside the cell. However, despite the years, since their structure is known and the many studies published, there is no definitive answer about the stages of the lipid entry-exit mechanism. Their structure forms a ß -barrel of 10 anti-parallel strands with a cap in a helix-turn-helix motif, and there is some consensus on the role of the so-called portal region, involving the second α -helix from the cap ( α 2), ß C- ß D, and ß E- ß F turns in FAs exchange. To test the idea of a lid that opens, we performed a soaking experiment on an h-FABP crystal in which the cap is part of the packing contacts, and its movement is strongly restricted. Even in these conditions, we observed the replacement of palmitic acid by 2-Bromohexadecanoic acid (Br-palmitic acid). Our MD simulations reveal a two-step lipid entry process: (i) The travel of the lipid head through the cavity in the order of tens of nanoseconds, and (ii) The accommodation of its hydrophobic tail in hundreds to thousands of nanoseconds. We observed this even in the cases in which the FAs enter the cavity by their tail. During this process, the FAs do not follow a single trajectory, but multiple ones through which they get into the protein cavity. Thanks to the complementary views between experiment and simulation, we can give an approach to a mechanistic view of the exchange process.

Molecular basis of the anchoring and stabilization of human islet amyloid polypeptide in lipid hydroperoxidized bilayers.

The molecular structure of membrane lipids is formed by mono- or polyunsaturations on their aliphatic tails that make them susceptible to oxidation, facilitating the incorporation of hydroperoxide (R-OOH) functional groups. Such groups promote changes in both composition and complexity of the membrane significantly modifying its physicochemical properties. Human Langerhans islets amyloid polypeptide (hIAPP) is the main component of amyloid deposits found in the pancreas of patients with type-2 diabetes (T2D). hIAPP in the presence of membranes with oxidized lipid species accelerates the formation of amyloid fibrils or the formation of intermediate oligomeric structures. However, the molecular bases at the initial stage of the anchoring and stabilization of the hIAPP in a hydroperoxidized membrane are not yet well understood. To shed some light on this matter, in this contribution, three bilayer models were modeled: neutral (POPC), anionic (POPS), and oxidized (POPCOOH), and full atom Molecular Dynamics (MD) simulations were performed. Our results show that the POPCOOH bilayer increases the helicity in hIAPP when compared to POPC or POPS bilayer. The modification in the secondary structure covers the residues of the so-called amyloidogenic core of the hIAPP. Overall, the hydroperoxidation of the neutral lipids modifies both the anchoring and the stabilization of the peptide hIAPP by reducing the random conformations of the peptide and increasing of hydrogen bond population with the hydroperoxidized lipids.

Universal features of the stick-slip dynamics of an intruder moving through a confined granular medium.

Experiments and simulations of an intruder dragged by a spring through a two-dimensional annulus of granular material exhibit robust force fluctuations. At low packing fractions (ϕ<ϕ_{0}), the intruder clears an open channel. Above ϕ_{0}, stick-slip dynamics develop, with an average energy release that is independent of the particle-particle and particle-base friction coefficients but does depend on the width W of the annulus and the diameter D of the intruder. A simple model predicts the dependence of ϕ_{0} on W and D, allowing for a data collapse for the average energy release as a function of ϕ/ϕ_{0}. These results pose challenges for theories of mechanical failure in amorphous materials.

Enhancement of the flow of vibrated grains through narrow apertures by addition of small particles.

We analyze the flow and clogging of circular grains passing through a small aperture under vibration in two dimensions. Via discrete element method simulations, we show that when grains smaller than the original ones are introduced in the system as an additive, the net flow of the original species can be significantly increased. Moreover, there is an optimal radius of the additive particles that maximizes the effect. This finding may constitute the basis for technological applications not only concerning the flow of granular materials but also regarding active matter, including pedestrian evacuation.

Molecular dynamics simulation of the heart type fatty acid binding protein in a crystal environment.

Crystallographic data comes from a space-time average over all the unit cells within the crystal, so dynamic phenomena do not contribute significantly to the diffraction data. Many efforts have been made to reconstitute the movement of the macromolecules and explore the microstates that the confined proteins can adopt in the crystalline network. We explored different strategies to simulate a heart fatty acid binding protein (H-FABP) crystal by means of Molecular Dynamics (MD) simulations. We evaluate the effect of introducing restraints according to experimental isotropic B-factors and we analyzed the H-FABP motions in the crystal using Principal Component Analysis (PCA), isotropic and anisotropic B-factors. We compared the behavior of the protein simulated in the crystal confinement versus in solution, and we observed the effect of that confinement in the mobility of the protein residues. Restraining one-third of Cα atoms based on experimental B-factors produce lower B-factors than simulations without restraints, showing that the position restraint of the atoms with the lowest experimental B-factor is a good strategy to maintain the geometry of the crystal with an obvious decrease in the degrees of motion of the protein. PCA shows that, as position restraint reduces the conformational space explored by the system, the motion of the crystal is better recovered, for an essential subspace of the same size, in the simulations without restraints. Restraining only one Cα seems to be a good balance between giving flexibility to the system and preserving its structure. Communicated by Ramaswamy H. Sarma.

Intruder in a two-dimensional granular system: Effects of dynamic and static basal friction on stick-slip and clogging dynamics.

We present simulation results for an intruder pulled through a two-dimensional granular system by a spring using a model designed to mimic the experiments described by Kozlowski et al. [Phys. Rev. E 100, 032905 (2019)2470-004510.1103/PhysRevE.100.032905]. In that previous study the presence of basal friction between the grains and the base was observed to change the intruder dynamics from clogging to stick-slip. Here we first show that our simulation results are in excellent agreement with the experimental data for a variety of experimentally accessible friction coefficients governing interactions of particles with each other and with boundaries. We then use simulations to explore a broader range of parameter space, focusing on the friction between the particles and the base. We consider both static and dynamic basal friction coefficients, which are difficult to vary smoothly in experiments. The simulations show that dynamic friction strongly affects the stick-slip behavior when the coefficient is decreased below 0.1, while static friction plays only a marginal role.

Dynamics of a grain-scale intruder in a two-dimensional granular medium with and without basal friction.

We report on a series of experiments in which a grain-sized intruder is pushed by a spring through a two-dimensional granular material composed of photoelastic disks in a Couette geometry. We study the intruder dynamics as a function of packing fraction for two types of supporting substrates: A frictional glass plate and a layer of water for which basal friction forces are negligible. We observe two dynamical regimes: Intermittent flow, in which the intruder moves freely most of the time but occasionally gets stuck, and stick-slip dynamics, in which the intruder advances via a sequence of distinct, rapid events. When basal friction is present, we observe a smooth crossover between the two regimes as a function of packing fraction, and we find that reducing the interparticle friction coefficient causes the stick-slip regime to shift to higher packing fractions. When basal friction is eliminated, we observe intermittent flow at all accessible packing fractions. For all cases, we present results for the statistics of stick events, the intruder velocity, and the force exerted on the intruder by the grains. Our results indicate the qualitative importance of basal friction at high packing fractions and suggest a possible connection between intruder dynamics in a static material and clogging dynamics in granular flows.

Effect of the trabecular bone microstructure on measuring its thermal conductivity: A computer modeling-based study.

The objective of this work is to quantify the relation between the value of the effective thermal conductivity of trabecular bone and its microstructure and marrow content. The thermal conductivity of twenty bovine trabecular bone samples was measured prior to and after defatting at 37, 47, and 57 °C. Computer models were built including the microstructure geometry and the gap between the tissue and measurement probe. The thermal conductivity (k) measured was 0.39 ±â€¯0.06 W m-1 K-1 at 37 °C, with a temperature dependence of + 0.2%°C-1. Replacing marrow by phosphate-buffered saline (defatting) increased both the computer simulations and measurement results by 0.04 W m-1 K-1. The computer simulations showed that k increases by 0.02-0.04 W m-1 K-1 when the model includes a gap filled by phosphate-buffered saline between the tissue and measurement probe. In the presence of microstructure and fatty red marrow, k varies by ±â€¯0.01 W m-1 K-1 compared with the case considering matrix only, which suggests that there are no significant differences between cortical and trabecular bone in terms of k. The computer results showed that the presence of a gap filled by phosphate-buffered saline around the energy applicator changes maximum temperature by < 0.7 °C, while including the bone microstructure involved a variation of < 0.2 mm in the isotherm location. Future experimental studies on measuring the value of k involving the insertion of a probe into the bone through a drill hole should consider the bias found in the simulations. Thermal models based on a homogeneous geometry (i.e. ignoring the microstructure) could provide sufficient accuracy.

Structure of force networks in tapped particulate systems of disks and pentagons. I. Clusters and loops.

The force network of a granular assembly, defined by the contact network and the corresponding contact forces, carries valuable information about the state of the packing. Simple analysis of these networks based on the distribution of force strengths is rather insensitive to the changes in preparation protocols or to the types of particles. In this and the companion paper [Kondic et al., Phys. Rev. E 93, 062903 (2016)10.1103/PhysRevE.93.062903], we consider two-dimensional simulations of tapped systems built from frictional disks and pentagons, and study the structure of the force networks of granular packings by considering network's topology as force thresholds are varied. We show that the number of clusters and loops observed in the force networks as a function of the force threshold are markedly different for disks and pentagons if the tangential contact forces are considered, whereas they are surprisingly similar for the network defined by the normal forces. In particular, the results indicate that, overall, the force network is more heterogeneous for disks than for pentagons. Such differences in network properties are expected to lead to different macroscale response of the considered systems, despite the fact that averaged measures (such as force probability density function) do not show any obvious differences. Additionally, we show that the states obtained by tapping with different intensities that display similar packing fraction are difficult to distinguish based on simple topological invariants.

Structure of force networks in tapped particulate systems of disks and pentagons. II. Persistence analysis.

In the companion paper [Pugnaloni et al., Phys. Rev. E 93, 062902 (2016)10.1103/PhysRevE.93.062902], we use classical measures based on force probability density functions (PDFs), as well as Betti numbers (quantifying the number of components, related to force chains, and loops), to describe the force networks in tapped systems of disks and pentagons. In the present work, we focus on the use of persistence analysis, which allows us to describe these networks in much more detail. This approach allows us not only to describe but also to quantify the differences between the force networks in different realizations of a system, in different parts of the considered domain, or in different systems. We show that persistence analysis clearly distinguishes the systems that are very difficult or impossible to differentiate using other means. One important finding is that the differences in force networks between disks and pentagons are most apparent when loops are considered: the quantities describing properties of the loops may differ significantly even if other measures (properties of components, Betti numbers, force PDFs, or the stress tensor) do not distinguish clearly or at all the investigated systems.

Quaternionic representation of the genetic code.

A heuristic diagram of the evolution of the standard genetic code is presented. It incorporates, in a way that resembles the energy levels of an atom, the physical notion of broken symmetry and it is consistent with original ideas by Crick on the origin and evolution of the code as well as with the chronological order of appearance of the amino acids along the evolution as inferred from work that mixtures known experimental results with theoretical speculations. Suggested by the diagram we propose a Hamilton quaternions based mathematical representation of the code as it stands now-a-days. The central object in the description is a codon function that assigns to each amino acid an integer quaternion in such a way that the observed code degeneration is preserved. We emphasize the advantages of a quaternionic representation of amino acids taking as an example the folding of proteins. With this aim we propose an algorithm to go from the quaternions sequence to the protein three dimensional structure which can be compared with the corresponding experimental one stored at the Protein Data Bank. In our criterion the mathematical representation of the genetic code in terms of quaternions merits to be taken into account because it describes not only most of the known properties of the genetic code but also opens new perspectives that are mainly derived from the close relationship between quaternions and rotations.

Genetic algorithm for the pair distribution function of the electron gas.

The pair distribution function of the electron gas is calculated using a parameterized generalization of hypernetted chain approximation with the parameters being obtained by optimizing the system energy with a genetic algorithm. The functions so obtained are compared with Monte Carlo simulations performed by other authors in its variational and di_usion versions showing a very good agreement especially with the di_usion Monte Carlo results.