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تسجيل مستخدم جديدActive Levy Matter: Anomalous Diffusion, Hydrodynamics and Linear Stability
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Anomalous diffusion, manifest as a nonlinear temporal evolution of the position mean square displacement, and/or non-Gaussian features of the position statistics, is prevalent in biological transport processes. Likewise, collective behavior is often observed to emerge spontaneously from the mutual interactions between constituent motile units in biological systems. Examples where these phenomena can be observed simultaneously have been identified in recent experiments on bird flocks, fish schools and bacterial swarms. These results pose an intriguing question, which cannot be resolved by existing theories of active matter: How is the collective motion of these systems affected by the anomalous diffusion of the constituent units? Here, we answer this question for a microscopic model of active Levy matter -- a collection of active particles that perform superdiffusion akin to a Levy flight and interact by promoting polar alignment of their orientations. We present in details the derivation of the hydrodynamic equations of motion of the model, obtain from these equations the criteria for a disordered or ordered state, and apply linear stability analysis on these states at the onset of collective motion. Our analysis reveals that the disorder-order phase transition in active Levy matter is critical, in contrast to ordinary active fluids where the phase transition is, instead, first-order. Correspondingly, we estimate the critical exponents of the transition by finite size scaling analysis and use these numerical estimates to relate our findings to known universality classes. These results highlight the novel physics exhibited by active matter integrating both anomalous diffusive single-particle motility and inter-particle interactions.
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Collective motion is often modeled within the framework of active fluids, where the constituent active particles, when interactions with other particles are switched off, perform normal diffusion at long times. However, in biology, single-particle su
perdiffusion and fat-tailed displacement statistics are also widespread. The collective properties of interacting systems exhibiting such anomalous diffusive dynamics, which we call active Levy matter, cannot be captured by current active fluid theories. Here, we formulate a hydrodynamic theory of active Levy matter by coarse-graining a microscopic model of aligning polar active particles that perform superdiffusion akin to Levy flights. Applying a linear stability analysis on the hydrodynamic equations at the onset of collective motion, we find that, in contrast to its conventional counterpart, the order-disorder transition can become critical. We then estimate the corresponding critical exponents by finite size scaling analysis of numerical simulations. Our work highlights the novel physics in active matter that integrates both anomalous diffusive motility and inter-particle interactions.
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Active matter represents a broad class of systems that evolve far from equilibrium due to the local injection of energy. Like their passive analogues, transformations between distinct metastable states in active matter proceed through rare fluctuatio
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The characterization of diffusion processes is a keystone in our understanding of a variety of physical phenomena. Many of these deviate from Brownian motion, giving rise to anomalous diffusion. Various theoretical models exists nowadays to describe
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