Protein microparticles visualize the contact network and rigidity onset in the gelation of model proteins

Protein aggregation into gel networks is of immense importance in diverse areas from food science to medical research; however, it remains a grand challenge as the underlying molecular interactions are complex, difficult to access experimentally, and to model computationally. Early stages of gelation often involve protein aggregation into protein clusters that later on aggregate into a gel network. Recently synthesized protein microparticles allow direct control of these early stages of aggregation, decoupling them from the subsequent gelation stages. Here, by following the gelation of protein microparticles directly at the particle scale, we elucidate in detail the emergence of a percolating structure and the onset of rigidity as measured by microrheology. We find that the largest particle cluster, correlation length, and degree of polymerization all diverge with power laws, while the particles bind irreversibly indicating a nonequilibrium percolation process, in agreement with recent results on weakly attractive colloids. Concomitantly, the elastic modulus increases in a power-law fashion as determined by microrheology. These results give a consistent microscopic picture of the emergence of rigidity in a nonequilibrium percolation process that likely underlies the gelation in many more systems such as proteins, and other strongly interacting structures originating from (bio)molecules.

Network percolation reveals adaptive bridges of the mobility network response to COVID-19

Human mobility is crucial to understand the transmission pattern of COVID-19 on spatially embedded geographic networks. This pattern seems unpredictable, and the propagation appears unstoppable, resulting in over 350,000 death tolls in the U.S. by the end of 2020. Here, we create the spatiotemporal inter-county mobility network using 10 TB (Terabytes) trajectory data of 30 million smart devices in the U.S. in the first six months of 2020. We investigate the bond percolation process by removing the weakly connected edges. As we increase the threshold, the mobility network nodes become less interconnected and thus experience surprisingly abrupt phase transitions. Despite the complex behaviors of the mobility network, we devised a novel approach to identify a small, manageable set of recurrent critical bridges, connecting the giant component and the second-largest component. These adaptive links, located across the United States, played a key role as valves connecting components in divisions and regions during the pandemic. Beyond, our numerical results unveil that network characteristics determine the critical thresholds and the bridge locations. The findings provide new insights into managing and controlling the connectivity of mobility networks during unprecedented disruptions. The work can also potentially offer practical future infectious diseases both globally and locally.

Influence of coffee brewing methods on the chromatographic and spectroscopic profiles, antioxidant and sensory properties

Cold brewing coffee has gained increasing popularity as a novel brewing method. A completely different flavour profile during cold brewing extraction (smooth and mild) is a result of the low-energy process, prolonged water-grind contact times and long preparation time. The aim of our research was to compare coffee drinks obtained with an innovative device for a faster, dynamic cold coffee extraction process (Hardtank) to drinks prepared traditionally in 24 h and hot brewed drinks. This study investigated the differences in chemical composition (volatile, non-volatile and lipid compounds), sensory properties and antioxidant capacity of coffee drinks from various extraction processes carried out at variable brewing temperatures, times and percolation modes. The results showed that the new cold maceration technique using coffee bed percolation (Hardtank) improved the quality of cold coffee drinks, making them similar in taste to hot coffee drinks. Among the studied extractions, the combination of a lower temperature (19.3 °C) and percolation process appeared to be the ideal setting for the most efficient extraction of compounds such as chlorogenic acids, gallic acid, caffeine, trigonelline, 5-(hydroxymethyl)furfural and lipids and consequently for their intake. In addition, FTIR spectra indicated an even 4 times greater quantity of lipids in Hardtank drinks than in classic cold brew and up to 5 times more lipids than in hot brew coffee, which contribute to the formation of the aroma and flavour. The decreased extraction time and use of coffee bed percolation could be beneficial for the quality and taste of cold brew products.

Development of a Method for Determining the Main Parameters of the Percolation Process in Antistatic Composite Polymer Materials

Polymer composite materials based on thermoplastic polymer and carbon nanoparticles with different axial ratio were obtained by melt technology. The values of the electrical resistance of polymer composites have been determined. Development of a methodology for assessing the parameters of the percolation process: the percolation threshold and the required resistance values of the polymer, to obtain a material with antistatic properties.

Random fractals and their intersection with winning sets

We show that fractal percolation sets in $\mathbb{R}^{d}$ almost surely intersect every hyperplane absolutely winning (HAW) set with full Hausdorff dimension. In particular, if $E\subset\mathbb{R}^{d}$ is a realisation of a fractal percolation process, then almost surely (conditioned on $E\neq\emptyset$ ), for every countable collection $\left(f_{i}\right)_{i\in\mathbb{N}}$ of $C^{1}$ diffeomorphisms of $\mathbb{R}^{d}$ , $\dim_{H}\left(E\cap\left(\bigcap_{i\in\mathbb{N}}f_{i}\left(\text{BA}_{d}\right)\right)\right)=\dim_{H}\left(E\right)$ , where $\text{BA}_{d}$ is the set of badly approximable vectors in $\mathbb{R}^{d}$ . We show this by proving that E almost surely contains hyperplane diffuse subsets which are Ahlfors-regular with dimensions arbitrarily close to $\dim_{H}\left(E\right)$ . We achieve this by analysing Galton–Watson trees and showing that they almost surely contain appropriate subtrees whose projections to $\mathbb{R}^{d}$ yield the aforementioned subsets of E. This method allows us to obtain a more general result by projecting the Galton–Watson trees against any similarity IFS whose attractor is not contained in a single affine hyperplane. Thus our general result relates to a broader class of random fractals than fractal percolation.

Human mobility in response to COVID-19 in France, Italy and UK

The COVID-19 pandemic is one of the defining events of our time. National Governments responded to the global crisis by implementing mobility restrictions to slow down the spread of the virus. To assess the impact of those policies on human mobility, we perform a massive comparative analysis on geolocalized data from 13 M Facebook users in France, Italy, and the UK. We find that lockdown generally affects national mobility efficiency and smallworldness—i.e., a substantial reduction of long-range connections in favor of local paths. The impact, however, differs among nations according to their mobility infrastructure. We find that mobility is more concentrated in France and UK and more distributed in Italy. In this paper we provide a framework to quantify the substantial impact of the mobility restrictions. We introduce a percolation model mimicking mobility network disruption and find that node persistence in the percolation process is significantly correlated with the economic and demographic characteristics of countries: areas showing higher resilience to mobility disruptions are those where Value Added per Capita and Population Density are high. Our methods and findings provide important insights to enhance preparedness for global critical events and to incorporate resilience as a relevant dimension to estimate the socio-economic consequences of mobility restriction policies.

Geometric functionals of fractal percolation

Fractal percolation exhibits a dramatic topological phase transition, changing abruptly from a dust-like set to a system-spanning cluster. The transition points are unknown and difficult to estimate. In many classical percolation models the percolation thresholds have been approximated well using additive geometric functionals, known as intrinsic volumes. Motivated by the question of whether a similar approach is possible for fractal models, we introduce corresponding geometric functionals for the fractal percolation process F. They arise as limits of expected functionals of finite approximations of F. We establish the existence of these limit functionals and obtain explicit formulas for them as well as for their finite approximations.

The Brooks and Corey Capillary Pressure Model Revisited from Pore Network Simulations of Capillarity-Controlled Invasion Percolation Process

Relating the macroscopic properties of porous media such as capillary pressure with saturation is an on-going problem in many fields, but examining their correlations with microstructural traits of the porous medium is a challenging task due to the heterogeneity of the solid matrix and the limitations of laboratory instruments. Considering a capillarity-controlled invasion percolation process, we examined the macroscopic properties as functions of matrix saturation and pore structure by applying the throat and pore network model. We obtained a relationship of the capillary pressure with the effective saturation from systematic pore network simulations. Then, we revisited and identified the microstructure parameters in the Brooks and Corey capillary pressure model. The wetting phase residual saturation is related to the ratio of standard deviation to the mean radius, the ratio of pore radius to the throat length, and pore connectivity. The size distribution index in the Brooks and Corey capillary pressure model should be more reasonably considered as a meniscus size distribution index rather than a pore size distribution index, relating this parameter with the invasion process and the structural properties. The size distribution index is associated with pore connectivity and the ratio of standard deviation to mean radius (σ0/r¯), increasing with the decline of σ0/r¯ but the same for networks with same σ0/r¯. The identified parameters of the Brooks and Corey model might be further utilized for correlations with other transport properties such as permeability.