Phase separation is not only ubiquitous in diverse physical systems, but also plays an important organizational role inside biological cells. However, experimental studies of intracellular condensates (drops with condensed concentrations of specific
collections of proteins and nucleic acids) have challenged the standard coarsening theories of phase separation. Specifically, the coarsening rates observed are unexpectedly slow for many intracellular condensates. Recently, Folkmann, et al. [bioRxiv 2021.06.22.449249 (2021)] argued that the slow coarsening rate can be caused by the slow conversion of a condensate constituent between the state in the dilute phase and the condensate state. A consequence of this conversion-limited picture is that standard theories of coarsening (Lifshitz-Slyozov--Wagner Ostwald ripening and drop coalescence schemes) no longer apply. Here, I elucidate the novel universal coarsening behavior of the conversion-limited scheme in the late stage using both analytical and numerical methods.
Motility-induced phase separation is a purely non-equilibrium phenomenon in which self-propelled particles aggregate without any attractive interactions. One surprising feature of MIPS is the emergence of polar-nematic order at the interfacial region
, whose underlying physics remains poorly understood. Here, I will show analytically and numerically that the many-body physics leading to the interfacial ordering behavior can be captured by an effective speed model. In this model, each particles speed depends on the systems density a short distance ahead of its direction of motion.
Active matter is not only indispensable to our understanding of diverse biological processes, but also provides a fertile ground for discovering novel physics. Many emergent properties impossible for equilibrium systems have been demonstrated in acti
ve systems. These emergent features include motility-induced phase separation, long-ranged ordered (collective motion) phase in two dimensions, and order-disorder phase co-existences (banding and reverse-banding regimes). Here, we unify these diverse phase transitions and phase co-existences into a single formulation based on generic hydrodynamic equations for active fluids. We also reveal a novel co-moving co-existence phase and a putative novel critical point.
We show that Malthusian flocks -- i.e., coherently moving collections of self-propelled entities (such as living creatures) which are being born and dying during their motion -- belong to a new universality class in spatial dimensions $d>2$. We calcu
late the universal exponents and scaling laws of this new universality class to $O(epsilon)$ in a $d=4-epsilon$ expansion, and find these are different from the canonical exponents previously conjectured to hold for immortal flocks (i.e., those without birth and death) and shown to hold for incompressible flocks with spatial dimensions in the range of $2 < d leq 4$. We also obtain a universal amplitude ratio relating the damping of transverse and longitudinal velocity and density fluctuations in these systems. Furthermore, we find a universal separatrix in real (${bf r}$) space between two regions in which the equal time density correlation $langledeltarho({bf r}, t)deltarho(0, t)rangle$ has opposite signs. Our expansion should be quite accurate in $d=3$, allowing precise quantitative comparisons between our theory, simulations, and experiments.
We show that Malthusian flocks -- i.e., coherently moving collections of self-propelled entities (such as living creatures) which are being born and dying during their motion -- belong to a new universality class in spatial dimensions $d>2$. We calcu
late the universal exponents and scaling laws of this new universality class to $O(epsilon)$ in an $epsilon=4-d$ expansion, and find these are different from the canonical exponents previously conjectured to hold for immortal flocks (i.e., those without birth and death) and shown to hold for incompressible flocks in $d>2$. Our expansion should be quite accurate in $d=3$, allowing precise quantitative comparisons between our theory, simulations, and experiments.
Starting from symmetry considerations, we derive the generic hydrodynamic equation of non-equilibrium $XY$ spin systems with $N$-atic symmetry under weak fluctuations. Through a systematic treatment we demonstrate that, in two dimensions, these syste
ms exhibit two types of scaling behaviours. For $N=1$, they have long-range order and are described by the flocking phase of dry polar active fluids. For all other values of $N$, the systems exhibit quasi long-range order, as in the equilibrium $XY$ model at low temperature.
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.
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.
A collection of self-propelled particles with volume exclusion interactions can exhibit the phenomenology of gas-liquid phase separation, known as motility-induced phase separation (MIPS). The non-equilibrium nature of the system is fundamental to th
e phase transition, however, it is unclear whether MIPS at criticality contributes a novel universality class to non-equilibrium physics. We demonstrate here that this is not the case by showing that a generic critical MIPS belongs to the Ising universality class with conservative dynamics.
We study universal behavior in the moving phase of a generic system of motile particles with alignment interactions in the incompressible limit for spatial dimensions $d>2$. Using a dynamical renormalization group analysis, we obtain the exact dynami
c, roughness, and anisotropy exponents that describe the scaling behavior of such incompressible systems. This is the first time a compelling argument has been given for the exact values of the anomalous scaling exponents of a flock moving through an isotropic medium in $d>2$.
