具有守恒律的反应扩散系统的普适极限行为
Universal limiting behaviour of reaction-diffusion systems with conservation laws
AI总结：
本文证明多物种反应扩散系统中的守恒律使守恒量演化遵循类 Cahn-Hilliard 方程，并基于零倾线建立几何框架以构造粗粒化场论系数，从而为复杂多物种系统提供简化而准确的描述。
摘要：
理解由许多相互作用的物种组成的复杂非均匀系统，是贯穿几乎所有自然科学的一个重大挑战。反应扩散系统中的相分离和图案形成，在很大程度上被作为两个独立的范式加以研究。在此我们表明，在由许多物种组成的反应扩散系统中，守恒律的存在约束了守恒量的演化，使其由类似 Cahn-Hilliard 的方程支配。这建立了与共存范式以及近期“活性”场论之间的直接联系。因此，即使对于复杂的多物种系统，在粗粒化时空尺度上也会涌现出一种大幅简化但准确的描述。以零倾线（均匀稳态线）作为核心图景，我们发展了一个几何框架，赋予化学空间以基和合适的坐标。该框架使我们能够捕捉并理解消除快速非守恒自由度所带来的效应，并显式构造粗粒化场论的系数。我们期望，本文发展的理论将对推进我们对生物分子凝聚体的理解特别相关。
英文摘要：
Making sense of complex inhomogeneous systems composed of many interacting species is a grand challenge that pervades basically all natural sciences. Phase separation and pattern formation in reaction-diffusion systems have been largely studied as two separate paradigms. Here we show that in reaction-diffusion systems composed of many species, the presence of a conservation law constrains the evolution of the conserved quantity to be governed by a Cahn-Hilliard-like equation. This establishes a direct link with the paradigm of coexistence and recent "active" field theories. Hence, even for complex many-species systems a dramatically simplified but accurate description emerges over coarse spatio-temporal scales. Using the nullcline (the line of homogeneous steady states) as the central motif, we develop a geometrical framework which endows chemical space with a basis and suitable coordinates. This framework allows us to capture and understand the effect of eliminating fast non-conserved degrees of freedom, and to explicitly construct coefficients of the coarse field theory. We expect that the theory we develop here will be particularly relevant to advance our understanding of biomolecular condensates.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
