Search

Abstract: This work aims to describe the spatial distribution of flow from characteristics of the underlying pore structure in heterogeneous porous media. Thousands of two-dimensional samples of polydispersed granular media are used to (1) obtain the velocity field via direct numerical simulations, and (2) conceptualize the pore network as a graph in each sample. Analysis of the flow field allows us to distinguish preferential from stagnant flow regions and to quantify how channelized the flow is. Then, the graph’s edges are weighted by geometric attributes of their corresponding pores to find the path of minimum resistance of each sample. Overlap between the preferential flow paths and the predicted minimum resistance path determines the accuracy in individual samples. An evolutionary algorithm is employed to determine the “fittest” weighting scheme (here, the channel’s arc length to pore throat ratio) that maximizes accuracy across the entire dataset while minimizing over-parameterization. Finally, the structural similarity of neighboring edges is analyzed to explain the spatial arrangement of preferential flow within the pore network. We find that connected edges within the preferential flow subnetwork are highly similar, while those within the stagnant flow subnetwork are dissimilar. The contrast in similarity between these regions increases with flow channelization, explaining the structural constraints to local flow. The proposed framework may be used for fast characterization of porous media heterogeneity relative to computationally expensive direct numerical simulations. Article Highlights: 1.A quantitative assessment of flow channeling is proposed that distinguishes pore-scale flow fields into preferential and stagnant flow regions.2.Geometry and topology of the pore network are used to predict the spatial distribution of fast flow paths from structural data alone.3.Local disorder of pore networks provides structural constraints for flow separation into preferential v stagnant regions and informs on their velocity contrast.

Objectives: This study aims to analyse age-specific all-cause mortality trends in the UK before and after COVID-19 emergence to determine if pre-pandemic trends contributed to increased mortality levels in the post-pandemic era., Study Design: Statistical analysis of UK mortality data., Methods: We utilised age-structured population and mortality data for all UK countries from 2005 to 2023. Mortality rates were calculated for each age group, and excess mortality was estimated using the Office for National Statistics (ONS) method., Results: Our most concerning finding is an increase in all-cause mortality rates for middle-aged adults (30-54 years) starting around 2012. The COVID-19 pandemic may have further impacted these rates, but the pre-existing upward trend suggests that current elevated mortality rates might have been reached regardless of the pandemic. This finding is more alarming than the slowdown in the decline of cardiovascular disease death rates for individuals under 75 noted by the British Heart Foundation., Conclusion: Our results highlight the importance of considering both immediate pandemic impacts and long-term mortality trends in public health strategies. This underscores the need for targeted interventions and improved healthcare planning to address both ongoing and future challenges., (Copyright © 2024 The Author. Published by Elsevier Ltd.. All rights reserved.)

Campylobacter jejuni is a bacterial pathogen recognised as a major cause of foodborne illness worldwide. While Campylobacter jejuni generally does not grow outside its host, it can survive outside of the host long enough to pose a health concern. This review presents an up-to-date description and evaluation of biological, mathematical, and statistical approaches used to understand the behaviour of this foodborne pathogen and suggests future avenues which can be explored. Specifically, the incorporation of mathematical modelling may aid the understanding of C. jejuni biofilm formation both outside and inside the host. Predictive studies may be improved by the introduction of more standardised protocols for assessments of disinfection methods and by assessment of novel physical disinfection strategies as well as assessment of the efficiency of plant extracts on C. jejuni eradication. A full description of the metabolic pathways of C. jejuni , which is needed for the successful application of metabolic models, is yet to be achieved. Finally, a shift from animal models (except for those that are a source of human campylobacteriosis) to human-specific data may be made possible due to recent technological advancements, and this may lead to more accurate predictions of human infections.

We study the avalanche statistics observed in a minimal random growth model. The growth is governed by a reproduction rate obeying a probability distribution with finite mean a[over ¯] and variance v_{a}. These two control parameters determine if the avalanche size tends to a stationary distribution (finite scale statistics with finite mean and variance, or power-law tailed statistics with exponent ∈(1,3]), or instead to a nonstationary regime with log-normal statistics. Numerical results and their statistical analysis are presented for a uniformly distributed growth rate, which are corroborated and generalized by mathematical results. The latter show that the numerically observed avalanche regimes exist for a wide family of growth rate distributions, and they provide a precise definition of the boundaries between the three regimes.

The impact of the extent of testing infectious individuals on suppression of COVID-19 is illustrated from the early stages of outbreaks in Germany, the Hubei province of China, Italy, Spain and the UK. The predicted percentage of untested infected individuals depends on the specific outbreak but we found that they typically represent 60-80% of all infected individuals during the early stages of the outbreaks. We propose that reducing the underlying transmission from untested cases is crucial to suppress the virus. This can be achieved through enhanced testing in combination with social distancing and other interventions that reduce transmission such as wearing face masks. Once transmission from silent carriers is kept under control by these means, the virus could have been fully suppressed through fast isolation and contact tracing of tested cases., (© 2021. The Author(s).)

Policymakers require consistent and accessible tools to monitor the progress of an epidemic and the impact of control measures in real time. One such measure is the Estimated Dissemination Ratio (EDR), a straightforward, easily replicable, and robust measure of the trajectory of an outbreak that has been used for many years in the control of infectious disease in livestock. It is simple to calculate and explain. Its calculation and use are discussed below together with examples from the current COVID-19 outbreak in the UK. These applications illustrate that EDR can demonstrate changes in transmission rate before they may be clear from the epidemic curve. Thus, EDR can provide an early warning that an epidemic is resuming growth, allowing earlier intervention. A conceptual comparison between EDR and the commonly used reproduction number is also provided., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2021 Pérez-Reche, Taylor, McGuigan, Conaglen, Forbes, Strachan and Honhold.)

Whole genome sequence (WGS) data could transform our ability to attribute individuals to source populations. However, methods that efficiently mine these data are yet to be developed. We present a minimal multilocus distance (MMD) method which rapidly deals with these large data sets as well as methods for optimally selecting loci. This was applied on WGS data to determine the source of human campylobacteriosis, the geographical origin of diverse biological species including humans and proteomic data to classify breast cancer tumours. The MMD method provides a highly accurate attribution which is computationally efficient for extended genotypes. These methods are generic, easy to implement for WGS and proteomic data and have wide application.

This article reviews modern applications of mathematical descriptions of biofilm formation. The focus is on theoretically obtained results which have implications for areas including the medical sector, food industry and wastewater treatment. Examples are given as to how models have contributed to the overall knowledge on biofilms and how they are used to predict biofilm behaviour. We conclude that the use of mathematical models of biofilms has demonstrated over the years the ability to significantly contribute to the vast field of biofilm research. Among other things, they have been used to test various hypotheses on the nature of interspecies interactions, viability of biofilm treatment methods or forces behind observed biofilm pattern formations. Mathematical models can also play a key role in future biofilm research. Many models nowadays are analysed through computer simulations and continue to improve along with computational capabilities. We predict that models will keep on providing answers to important challenges involving biofilm formation. However, further strengthening of the ties between various disciplines is necessary to fully use the tools of collective knowledge in tackling the biofilm phenomenon.

A new method ("explosive immunization") is proposed for immunization and targeted destruction of networks. It combines the explosive percolation (EP) paradigm with the idea of maintaining a fragmented distribution of clusters. The ability of each node to block the spread of an infection (or to prevent the existence of a large cluster of connected nodes) is estimated by a score. The algorithm proceeds by first identifying low score nodes that should not be vaccinated or destroyed, analogously to the links selected in EP if they do not lead to large clusters. As in EP, this is done by selecting the worst node (weakest blocker) from a finite set of randomly chosen "candidates." Tests on several real-world and model networks suggest that the method is more efficient and faster than any existing immunization strategy. Because of the latter property it can deal with very large networks.

The spread of social phenomena such as behaviors, ideas or products is an ubiquitous but remarkably complex phenomenon. A successful avenue to study the spread of social phenomena relies on epidemic models by establishing analogies between the transmission of social phenomena and infectious diseases. Such models typically assume simple social interactions restricted to pairs of individuals; effects of the context are often neglected. Here we show that local synergistic effects associated with acquaintances of pairs of individuals can have striking consequences on the spread of social phenomena at large scales. The most interesting predictions are found for a scenario in which the contagion ability of a spreader decreases with the number of ignorant individuals surrounding the target ignorant. This mechanism mimics ubiquitous situations in which the willingness of individuals to adopt a new product depends not only on the intrinsic value of the product but also on whether his acquaintances will adopt this product or not. In these situations, we show that the typically smooth (second order) transitions towards large social contagion become explosive (first order). The proposed synergistic mechanisms therefore explain why ideas, rumours or products can suddenly and sometimes unexpectedly catch on.

Epidemics in networks can be affected by cooperation in transmission of infection and also connectivity between nodes. An interplay between these two properties and their influence on epidemic spread are addressed in the paper. A particular type of cooperative effects (called synergy effects) is considered, where the transmission rate between a pair of nodes depends on the number of infected neighbors. The connectivity effects are studied by constructing networks of different topology, starting with lattices with only local connectivity and then with networks that have both local and global connectivity obtained by random bond-rewiring to nodes within a certain distance. The susceptible-infected-removed epidemics were found to exhibit several interesting effects: (i) for epidemics with strong constructive synergy spreading in networks with high local connectivity, the bond rewiring has a negative role in epidemic spread, i.e., it reduces invasion probability; (ii) in contrast, for epidemics with destructive or weak constructive synergy spreading on networks of arbitrary local connectivity, rewiring helps epidemics to spread; (iii) and, finally, rewiring always enhances the spread of epidemics, independent of synergy, if the local connectivity is low.

This study underpins quantitative relationships that account for the combined effects that starting biomass and peak pyrolysis temperature have on physico-chemical properties of biochar. Meta-data was assembled from published data of diverse biochar samples (n=102) to (i) obtain networks of intercorrelated properties and (ii) derive models that predict biochar properties. Assembled correlation networks provide a qualitative overview of the combinations of biochar properties likely to occur in a sample. Generalized Linear Models are constructed to account for situations of varying complexity, including: dependence of biochar properties on single or multiple predictor variables, where dependence on multiple variables can have additive and/or interactive effects; non-linear relation between the response and predictors; and non-Gaussian data distributions. The web-tool Biochar Engineering implements the derived models to maximize their utility and distribution. Provided examples illustrate the practical use of the networks, models and web-tool to engineer biochars with prescribed properties desirable for hypothetical scenarios., (Copyright © 2015 Elsevier Ltd. All rights reserved.)

The lattice gas model of condensation in a heterogeneous pore system, represented by a random graph of cells, is studied using an exact analytical solution. A binary mixture of pore cells with different coordination numbers is shown to exhibit two phase transitions as a function of chemical potential in a certain temperature range. Heterogeneity in interaction strengths is demonstrated to reduce the critical temperature and, for large-enough degreeS of disorder, divides the cells into ones which are either on average occupied or unoccupied. Despite treating the pore space loops in a simplified manner, the random-graph model provides a good description of condensation in porous structures containing loops. This is illustrated by considering capillary condensation in a structural model of mesoporous silica SBA-15.

A theoretical framework for the description of susceptible-infected-removed (SIR) spreading processes with synergistic transmission of infection on a lattice is developed. The model incorporates explicitly the effects of time-dependence of the state of the hosts in the neighborhood of transmission events. Exact solution of the model shows that time-dependence of the state of nearest neighbors of recipient hosts is a key factor for synergistic spreading processes. It is demonstrated that the higher the connectivity of a lattice, the more prominent is the effect of synergy on spread.

The zero-temperature random-field Ising model is solved analytically for magnetization versus external field for a bilayered Bethe lattice. The mechanisms of infinite avalanches which are observed for small values of disorder are established. The effects of variable interlayer interaction strengths on infinite avalanches are investigated. The spin-field correlation length is calculated and its critical behavior is discussed. Direct Monte Carlo simulations of spin-flip dynamics are shown to support the analytical findings. We find, paradoxically, that a reduction of the interlayer bond strength can cause a phase transition from a regime with continuous magnetization reversal to a regime where magnetization exhibits a discontinuity associated with an infinite avalanche. This effect is understood in terms of the proposed mechanisms for the infinite avalanche.

A lattice-gas model with heterogeneity is developed for the description of fluid condensation in finite sized one-dimensional pores of arbitrary shape. Mapping to the random-field Ising model allows an exact solution of the model to be obtained at zero-temperature, reproducing the experimentally observed dependence of the amount of fluid adsorbed in the pore on external pressure. It is demonstrated that the disorder controls the sorption for long pores and can result in H2-type hysteresis. Finite-temperature Metropolis dynamics simulations support analytical findings in the limit of low temperatures. The proposed framework is viewed as a fundamental building block of the theory of capillary condensation necessary for reliable structural analysis of complex porous media from adsorption-desorption data.

A mapping of avalanches occurring in the zero-temperature random-field Ising model to life periods of a population experiencing immigration is established. Such a mapping allows the microscopic criteria for the occurrence of an infinite avalanche in a q-regular graph to be determined. A key factor for an avalanche of spin flips to become infinite is that it interacts in an optimal way with previously flipped spins. Based on these criteria, we explain why an infinite avalanche can occur in q-regular graphs only for q>3 and suggest that this criterion might be relevant for other systems. The generating function techniques developed for branching processes are applied to obtain analytical expressions for the durations, pulse shapes, and power spectra of the avalanches. The results show that only very long avalanches exhibit a significant degree of universality.

This study demonstrates that the pattern assembly and attachment strength of colloids in an evaporating sessile droplet resting on a smooth substrate can be controlled by adding nonionic solutes (surfactant) to the solution. As expected, increasing the surfactant concentration leads to a decrease in initial surface tension of the drop, σ(0). For the range of initial surface tensions investigated (39-72 mN m(-1)), three distinct deposition patterns were produced: amorphous stains (σ(0) = 63-72 mN m(-1)), coffee-ring stains (σ(0) = 48-53 mN m(-1)), and concentric rings (σ(0) = 39-45 mN m(-1)). A flow-displacement system was used to measure the attachment strength of the dried colloids. Characteristic drying regimes associated with the three unique pattern formations are attributed to abrupt transitions of contact line dynamics during evaporation. The first transition from slipping- to pinned-contact line was found to be a direct result of the competition between mechanical instability of the droplet and the friction generated by pinned colloids at the contact line. The second transition from pinned- to recurrent-stick-rip-slip-contact line was caused by repeated liquid film rupturing from evaporation-intensified surfactant concentration. Data from flow-displacement tests indicate that attachment strength of dried particles is strongest for amorphous stains (lowest surfactant concentration) and weakest for concentric rings (highest surfactant concentration). The mechanism behind these observations was ascribed to the formation and adsorption of micelles onto colloid and substrate surfaces as the droplet solution evaporates. The range of attachment forces observed between the colloids and the solid substrate were well captured by extended-DLVO interactions accounting for van der Waals attraction, electric double layer repulsion, and micelle-protrusion repulsion. Both empirical and theoretical results suggest that an increasingly dense layer of adsorbed micellar-protrusions on colloid and substrate surfaces acts as a physical barrier that hinders strong van der Waals attractive interactions at close proximity. Thereby, colloid stains dried at higher surfactant concentrations are more easily detached from the substrate when dislodging forces are applied than stains dried at lower surfactant concentrations.

Predictability of undesired events is a question of great interest in many scientific disciplines including seismology, economy and epidemiology. Here, we focus on the predictability of invasion of a broad class of epidemics caused by diseases that lead to permanent immunity of infected hosts after recovery or death. We approach the problem from the perspective of the science of complexity by proposing and testing several strategies for the estimation of important characteristics of epidemics, such as the probability of invasion. Our results suggest that parsimonious approximate methodologies may lead to the most reliable and robust predictions. The proposed methodologies are first applied to analysis of experimentally observed epidemics: invasion of the fungal plant pathogen Rhizoctonia solani in replicated host microcosms. We then consider numerical experiments of the susceptible-infected-removed model to investigate the performance of the proposed methods in further detail. The suggested framework can be used as a valuable tool for quick assessment of epidemic threat at the stage when epidemics only start developing. Moreover, our work amplifies the significance of the small-scale and finite-time microcosm realizations of epidemics revealing their predictive power.

Using a network representation for real soil samples and mathematical models for microbial spread, we show that the structural heterogeneity of the soil habitat may have a very significant influence on the size of microbial invasions of the soil pore space. In particular, neglecting the soil structural heterogeneity may lead to a substantial underestimation of microbial invasion. Such effects are explained in terms of a crucial interplay between heterogeneity in microbial spread and heterogeneity in the topology of soil networks. The main influence of network topology on invasion is linked to the existence of long channels in soil networks that may act as bridges for transmission of microorganisms between distant parts of soil.

Heterogeneity in host populations is an important factor affecting the ability of a pathogen to invade, yet the quantitative investigation of its effects on epidemic spread is still an open problem. In this paper, we test recent theoretical results, which extend the established "percolation paradigm" to the spread of a pathogen in discrete heterogeneous host populations. In particular, we test the hypothesis that the probability of epidemic invasion decreases when host heterogeneity is increased. We use replicated experimental microcosms, in which the ubiquitous pathogenic fungus Rhizoctonia solani grows through a population of discrete nutrient sites on a lattice, with nutrient sites representing hosts. The degree of host heterogeneity within different populations is adjusted by changing the proportion and the nutrient concentration of nutrient sites. The experimental data are analysed via Bayesian inference methods, estimating pathogen transmission parameters for each individual population. We find a significant, negative correlation between heterogeneity and the probability of pathogen invasion, thereby validating the theory. The value of the correlation is also in remarkably good agreement with the theoretical predictions. We briefly discuss how our results can be exploited in the design and implementation of disease control strategies.

An epidemiological model which incorporates synergistic effects that allow the infectivity and/or susceptibility of hosts to be dependent on the number of infected neighbors is proposed. Constructive synergy induces an exploitative behavior which results in a rapid invasion that infects a large number of hosts. Interfering synergy leads to a slower and sparser explorative foraging strategy that traverses larger distances by infecting fewer hosts. The model can be mapped to a dynamical bond percolation with spatial correlations that affect the mechanism of spread but do not influence the critical behavior of epidemics., (© 2011 American Physical Society)

Using digitized images of the three-dimensional, branching structures for root systems of bean seedlings, together with analytical and numerical methods that map a common susceptible-infected-recovered ('SIR') epidemiological model onto the bond percolation problem, we show how the spatially correlated branching structures of plant roots affect transmission efficiencies, and hence the invasion criterion, for a soil-borne pathogen as it spreads through ensembles of morphologically complex hosts. We conclude that the inherent heterogeneities in transmissibilities arising from correlations in the degrees of overlap between neighbouring plants render a population of root systems less susceptible to epidemic invasion than a corresponding homogeneous system. Several components of morphological complexity are analysed that contribute to disorder and heterogeneities in the transmissibility of infection. Anisotropy in root shape is shown to increase resilience to epidemic invasion, while increasing the degree of branching enhances the spread of epidemics in the population of roots. Some extension of the methods for other epidemiological systems are discussed.

The percolation paradigm is widely used in spatially explicit epidemic models where disease spreads between neighbouring hosts. It has been successful in identifying epidemic thresholds for invasion, separating non-invasive regimes, where the disease never invades the system, from invasive regimes where the probability of invasion is positive. However, its power is mainly limited to homogeneous systems. When heterogeneity (environmental stochasticity) is introduced, the value of the epidemic threshold is, in general, not predictable without numerical simulations. Here, we analyse the role of heterogeneity in a stochastic susceptible-infected-removed epidemic model on a two-dimensional lattice. In the homogeneous case, equivalent to bond percolation, the probability of invasion is controlled by a single parameter, the transmissibility of the pathogen between neighbouring hosts. In the heterogeneous model, the transmissibility becomes a random variable drawn from a probability distribution. We investigate how heterogeneity in transmissibility influences the value of the invasion threshold, and find that the resilience of the system to invasion can be suitably described by two control parameters, the mean and variance of the transmissibility. We analyse a two-dimensional phase diagram, where the threshold is represented by a phase boundary separating an invasive regime in the high-mean, low-variance region from a non-invasive regime in the low-mean, high-variance region of the parameter space. We thus show that the percolation paradigm can be extended to the heterogeneous case. Our results have practical implications for the analysis of disease control strategies in realistic heterogeneous epidemic systems.

One of the challenges in epidemiology is to account for the complex morphological structure of hosts such as plant roots, crop fields, farms, cells, animal habitats and social networks, when the transmission of infection occurs between contiguous hosts. Morphological complexity brings an inherent heterogeneity in populations and affects the dynamics of pathogen spread in such systems. We have analysed the influence of realistically complex host morphology on the threshold for invasion and epidemic outbreak in an SIR (susceptible-infected-recovered) epidemiological model. We show that disorder expressed in the host morphology and anisotropy reduces the probability of epidemic outbreak and thus makes the system more resistant to epidemic outbreaks. We obtain general analytical estimates for minimally safe bounds for an invasion threshold and then illustrate their validity by considering an example of host data for branching hosts (salamander retinal ganglion cells). Several spatial arrangements of hosts with different degrees of heterogeneity have been considered in order to separately analyse the role of shape complexity and anisotropy in the host population. The estimates for invasion threshold are linked to morphological characteristics of the hosts that can be used for determining the threshold for invasion in practical applications.

We propose a spin model with quenched disorder which exhibits in slow driving two drastically different types of critical nonequilibrium steady states. One of them corresponds to classical criticality requiring fine-tuning of the disorder. The other is a self-organized criticality which is insensitive to disorder. The crossover between the two types of criticality is determined by the mode of driving. As one moves from "soft" to "hard" driving the universality class of the critical point changes from a classical order-disorder to a quenched Edwards-Wilkinson universality class. The model is viewed as prototypical for a broad class of physical phenomena ranging from magnetism to earthquakes.

We propose an explanation for the self-organization towards criticality observed in martensites during the cyclic process known as "training." The scale-free behavior originates from the interplay between the reversible phase transformation and the concurrent activity of lattice defects. The basis of the model is a continuous dynamical system on a rugged energy landscape, which in the quasistatic limit reduces to a sandpile automaton. We reproduce all the principal observations in thermally driven martensites, including power-law statistics, hysteresis shakedown, asymmetric signal shapes, and correlated disorder.

We study the driving-rate and temperature dependence of the power-law exponents that characterize the avalanche distribution in first-order phase transitions. Measurements of acoustic emission in structural transitions in Cu-Zn-Al and Cu-Al-Ni are presented. We show how the observed behavior emerges within a general framework of competing time scales of avalanche relaxation, driving rate, and thermal fluctuations. We confirm our findings by numerical simulations of a prototype model.

The significance of thermal fluctuations in nucleation in structural first-order phase transitions has been examined. The prototypical case of martensitic transitions has been experimentally investigated by means of acoustic emission techniques. We propose a model based on the mean first-passage time to account for the experimental observations. Our study provides a unified framework to establish the conditions for isothermal and athermal transitions to be observed.