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In a geographically distributed population, assortative clustering plays an important role in evolution by modifying local environments. To examine its effects in a linear habitat, we consider a one-dimensional grid of cells, where each cell is either empty or occupied by an organism whose replication strategy is genetically inherited to offspring. PEG300 research buy The strategy determines whether to have offspring in surrounding cells, as a function of the neighborhood configuration. If more than one offspring compete for a cell, then they can be all exterminated due to the cost of conflict depending on environmental conditions. We find that the system is more densely populated in an unfavorable environment than in a favorable one because only the latter has to pay the cost of conflict. This observation agrees reasonably well with a mean-field analysis which takes assortative clustering of strategies into consideration. Our finding suggests a possibility of intrinsic nonlinearity between environmental conditions and population density when an evolutionary process is involved.We derive and asymptotically analyze mass-action models for disease spread that include transient pair formation and dissociation. Populations of unpaired susceptible individuals and infected individuals are distinguished from the population of three types of pairs of individuals both susceptible, one susceptible and one infected, and both infected. Disease transmission can occur only within a pair consisting of one susceptible individual and one infected individual. We use perturbation expansion to formally derive uniformly valid approximations for the dynamics of the total infected and susceptible populations under different conditions including combinations of fast association, fast transmission, and fast dissociation limits. The effective equations are derived from the fundamental mass-action system without implicitly imposing transmission mechanisms, such as those used in frequency-dependent models. Our results represent submodels that show how effective nonlinear transmission can arise from pairing dynamics and are juxtaposed with density-based mass-action and frequency-based models.Engineered swift equilibration (ESE) is a class of driving protocols that enforce an equilibrium distribution with respect to external control parameters at the beginning and end of rapid state transformations of open, classical nonequilibrium systems. ESE protocols have previously been derived and experimentally realized for Brownian particles in simple, one-dimensional, time-varying trapping potentials; one recent study considered ESE in two-dimensional Euclidean configuration space. Here we extend the ESE framework to generic, overdamped Brownian systems in arbitrary curved configuration space and illustrate our results with specific examples not amenable to previous techniques. Our approach may be used to impose the necessary dynamics to control the full temporal configurational distribution in a wide variety of experimentally realizable settings.Simple models of infectious diseases tend to assume random mixing of individuals, but real interactions are not random pairwise encounters they occur within various types of gatherings such as workplaces, households, schools, and concerts, best described by a higher-order network structure. We model contagions on higher-order networks using group-based approximate master equations, in which we track all states and interactions within a group of nodes and assume a mean-field coupling between them. Using the susceptible-infected-susceptible dynamics, our approach reveals the existence of a mesoscopic localization regime, where a disease can concentrate and self-sustain only around large groups in the network overall organization. In this regime, the phase transition is smeared, characterized by an inhomogeneous activation of the groups. At the mesoscopic level, we observe that the distribution of infected nodes within groups of the same size can be very dispersed, even bimodal. When considering heterogeneous networks, both at the level of nodes and at the level of groups, we characterize analytically the region associated with mesoscopic localization in the structural parameter space. We put in perspective this phenomenon with eigenvector localization and discuss how a focus on higher-order structures is needed to discern the more subtle localization at the mesoscopic level. Finally, we discuss how mesoscopic localization affects the response to structural interventions and how this framework could provide important insights for a broad range of dynamics.The sampling of conformations in the molecular simulations for systems with complicated free energy landscapes is always difficult. Here, we report a method for enhanced sampling based on the coarse-graining of conformational space. In this method, the locally converged region of the conformational space is coarse-grained with its population characterized by the related average residence time and visiting number, and at the same time, the direct simulations inside it are eliminated. The detailed balance is satisfied by updating the visiting number and generating outgoing trajectories of this region. This kind of coarse-graining operation can be further carried out by merging all the neighboring regions which are already converged together. The global equilibrium is achieved when the local equilibrated regions cover all the interested areas of the landscape. We tested the method by applying it to two model potentials and one protein system with multiple-basin energy landscapes. The sampling efficiency is found to be enhanced by more than three orders of magnitude compared to conventional molecular simulations, and are comparable with other widely used enhanced sampling methods. In addition, the kinetic information can also be well captured. All these results demonstrate that our method can help to solve the sampling problems efficiently and precisely without applying high temperatures or biasing potentials.Desiccation cracks in colloidal deposits occur to release the excess strain energy arising from the competition between the drying induced shrinkage of the deposit and its adhesion to the substrate. Here we report remarkably different morphology of desiccation cracks in the dried patterns formed by the evaporation of sessile drops containing colloids on elastomer (soft) or glass (stiff) substrates. The change in the crack pattern, i.e., from radial cracks on stiff substrates to circular cracks on soft substrates, is shown to arise solely due to the variation in elasticity of the underlying substrates. Our experiments and calculations reveal an intricate correlation between the desiccation crack patterns and the substrate's elasticity. The mismatch in modulus of elasticity between the substrate and that of the particulate deposit significantly alters the energy release rate during the nucleation and propagation of cracks. The stark variation in crack morphology is attributed to the tensile or compressive nature of the drying-induced in-plane stresses.
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