Spatial correlations in geographical spreading of COVID-19 in the United States

The global spread of the COVID-19 pandemic has followed complex pathways, largely attributed to the high virus infectivity, human travel patterns, and the implementation of multiple mitigation measures. The resulting geographic patterns describe the evolution of the epidemic and can indicate areas that are at risk of an outbreak. Here, we analyze the spatial correlations of new active cases in the USA at the county level and characterize the extent of these correlations at different times. We show that the epidemic did not progress uniformly and we identify various stages which are distinguished by significant differences in the correlation length. Our results indicate that the correlation length may be large even during periods when the number of cases declines. We find that correlations between urban centers were much more significant than between rural areas and this finding indicates that long-range spreading was mainly facilitated by travel between cities, especially at the first months of the epidemic. We also show the existence of a percolation transition in November 2020, when the largest part of the country was connected to a spanning cluster, and a smaller-scale transition in January 2021, with both times corresponding to the peak of the epidemic in the country.

Scanning-probe and information-concealing machine learning intermediate hexatic phase and critical scaling of solid-hexatic phase transition in deformable particles

We investigate the two-dimensional melting of deformable polymeric particles with multi-body interactions described by the Voronoi model. We report machine learning evidence for the existence of the intermediate hexatic phase in this system, and extract the critical exponent $\nu\approx0.65$ for the divergence of the correlation length of the associated solid-hexatic phase transition. Moreover, we clarify the discontinuous nature of the hexatic-liquid phase transition in this system. These findings are achieved by directly analyzing system's spatial configurations with two generic machine learning approaches developed in this work, dubbed ``scanning-probe'' via which the possible existence of intermediate phases can be efficiently detected, and ``information-concealing'' via which the critical scaling of the correlation length in the vicinity of generic continuous phase transition can be extracted. Our work provides new physical insights into the fundamental nature of the two-dimensional melting of deformable particles, and establishes a new type of generic toolbox to investigate fundamental properties of phase transitions in various complex systems.

Morphology and Rheology of a Cool-Gel (Protein) Blended with a Thermo-Gel (Hydroxypropyl Methylcellulose)

This study investigates the morphological and rheological properties of blended gelatin (GA; a cooling-induced gel (cool-gel)) and hydroxypropyl methylcellulose (HPMC; a heating-induced gel (thermo-gel)) systems using a fluorescence microscope, small angle X-ray scattering (SAXS), and a rheometer. The results clearly indicate that the two biopolymers are immiscible and have low compatibility. Moreover, the rheological behavior and morphology of the GA/HPMC blends significantly depend on the blending ratio and concentration. Higher polysaccharide contents decrease the gelling temperature and improve the gel viscoelasticity character of GA/HPMC blended gels. The SAXS results reveal that the correlation length (ξ) of the blended gels decreases from 5.16 to 1.89 nm as the HPMC concentration increases from 1 to 6%, which suggests that much denser networks are formed in blended gels with higher HPMC concentrations. Overall, the data reported herein indicate that the gel properties of gelatin can be enhanced by blending with a heating-induced gel.

Dual Superconductor Model of Confinement: Quantum-String Representation of the 4D Yang–Mills Theory on a Torus and the Correlation Length away from the London Limit

This paper is devoted to the dual superconductor model of confinement in the 4D Yang–Mills theory. In the first part, we consider the latter theory compactified on a torus, and use the dual superconductor model in order to obtain the Polchinski–Strominger term in the string representation of a Wilson loop. For a certain realistic critical value of the product of circumferences of the compactification circles, which is expressed in terms of the gluon condensate and the vacuum correlation length, the coupling of the Polchinski–Strominger term turns out to be such that the string conformal anomaly cancels out, making the string representation fully quantum. In the second part, we use the analogy between the London limit of the dual superconductor and the low-energy limit of the 4D compact QED, to obtain the partition function of the dual superconductor model away from the London limit. There, we find a decrease of the vacuum correlation length, and derive the corresponding potential of monopole currents.

Burst Dynamics, Upscaling and Dissipation of Slow Drainage in Porous Media

We present a theoretical and experimental investigation of drainage in porous media. The study is limited to stabilized fluid fronts at moderate injection rates, but it takes into account capillary, viscous, and gravitational forces. In the theoretical framework presented, the work applied on the system, the energy dissipation, the final saturation and the width of the stabilized fluid front can all be calculated if we know the dimensionless fluctuation number, the wetting properties, the surface tension between the fluids, the fractal dimensions of the invading structure and its boundary, and the exponent describing the divergence of the correlation length in percolation. Furthermore, our theoretical description explains how the Haines jumps’ local activity and dissipation relate to dissipation on larger scales.

Generalized Transport Equation of The Autocovariance Function of the Density Field and Mass Invariant in Star-forming Clouds

In this Letter, we study the evolution of the autocovariance function of density-field fluctuations in star-forming clouds and thus of the correlation length l c (ρ) of these fluctuations, which can be identified as the average size of the most correlated structures within the cloud. Generalizing the transport equation derived by Chandrasekhar for static, homogeneous turbulence, we show that the mass contained within these structures is an invariant, i.e., that the average mass contained in the most correlated structures remains constant during the evolution of the cloud, whatever dominates the global dynamics (gravity or turbulence). We show that the growing impact of gravity on the turbulent flow yields an increase of the variance of the density fluctuations and thus a drastic decrease of the correlation length. Theoretical relations are successfully compared to numerical simulations. This picture brings a robust support to star formation paradigms where the mass concentration in turbulent star-forming clouds evolves from initially large, weakly correlated filamentary structures to smaller, denser, more correlated ones, and eventually to small, tightly correlated, prestellar cores. We stress that the present results rely on a pure statistical approach of density fluctuations and do not involve any specific condition for the formation of prestellar cores. Interestingly enough, we show that, under average conditions typical of Milky-Way molecular clouds, this invariant average mass is about a solar mass, providing an appealing explanation for the apparent universality of the IMF in such environments.

Spatial Correlation Length Scales of Sea-Ice Concentration Errors for High-Concentration Pack Ice

The European Organisation for the Exploitation of Meteorological Satellites-Ocean and Sea Ice Satellite Application Facility–European Space Agency-Climate Change Initiative (EUMETSAT-OSISAF–ESA-CCI) Level-4 sea-ice concentration (SIC) climate data records (CDRs), named SICCI-25km, SICCI-50km and OSI-450, provide gridded SIC error estimates in addition to SIC. These error estimates, called total error henceforth, comprise a random, uncorrelated error contribution from retrieval and sensor noise, aka the algorithm standard error, and a locally-to-regionally correlated contribution from gridding and averaging Level-2 SIC into the Level-4 SIC CDRs, aka the representativity error. However, these CDRs do not yet provide an error covariance matrix. Therefore, correlation scales of these error contributions and the total error in particular are unknown. In addition, larger-scale SIC errors due to, e.g., unaccounted weather influence or mismatch between the actual ice type and the algorithm setup are neither well represented by the total error, nor are their correlation scales known for these CDRs. In this study, I attempt to contribute to filling this knowledge gap by deriving spatial correlation length scales for the total error and the large-scale SIC error for high-concentration pack ice. For every grid cell with >90% SIC, I derive circular one-point correlation maps of 1000 km radius by computing the cross-correlation between the central 31-day time series of the errors and all other 31-day error time series within that circular area (disc) with 1000 km radius. I approximate the observed decrease in the correlation away from the disc’s center with an exponential function that best fits this decrease and thereby obtain the correlation length scale L sought. With this approach, I derive L separately for the total error and the large-scale SIC error for every high-concentration grid cell, and map, present and discuss these for the Arctic and the Southern Ocean for the year 2010 for the above-mentioned products. I find correlation length scales are substantially smaller for the total error, mostly below ~200 km, than the SIC error, ~200 km to ~700 km, in both hemispheres. I observe considerable spatiotemporal variability of the SIC error correlation length scales in both hemispheres and provide first directions to explain these. For SICCI-50km, I present the first evidence of the method’s robustness for other years and time series of L for 2003–2010.

Correlation length critical exponent as a function of the percolation radius for one-dimensional chains in bond problems

A one-dimensional lattice percolation model is constructed for the problem of constraints flowing along non-nearest neighbors. In this work, we calculated the critical exponent of the correlation length in the one-dimensional bond problem for a percolation radius of up to 6. In the calculations, we used a method without constructing a covering lattice or an adjacency matrix (to find the percolation threshold). The values of the critical exponent of the correlation length were obtained in the one-dimensional bond problem depending on the size of the system and at different percolation radii. Based on original algorithms that operate on a computer faster than standard ones (associated with the construction of a covering lattice), these results are obtained with corresponding errors.

Speckle patterns formed by broadband terahertz radiation and their applications for ghost imaging

Speckle patterns can be very promising for many applications due to their unique properties. This paper presents the possibility of numerically and experimentally formation of speckle patterns using broadband THz radiation. Strong dependence of the statistical parameters of speckles, such as size and sharpness on the parameters of the diffuser are demonstrated: the correlation length and the mean square deviation of the phase surface inhomogeneity. As the surface correlation length is increasing, the speckle size also increases and its sharpness goes down. Alternatively, the magnification of the standard deviation of the surface height leads to the speckle size diminishing and growth of the speckle sharpness. The dimensions of the experimentally formed speckles correspond to the results of numerical simulation. The possibility of utilizing formed speckle patterns for the implementation of the ghost imaging technique has been demonstrated by methods of numerical modeling.