Publications
95 results found
Killeen A, Bertrand T, Lee CF, 2024, Machine learning topological defects in confluenttissues, Biophysical Reports, Vol: 4, ISSN: 2667-0747
Active nematics is an emerging paradigm for characterizing biological systems. One aspect of particularly intense focus is the role active nematic defects play in these systems, as they have been found to mediate a growing number of biological processes. Accurately detecting and classifying these defects in biological systems is, therefore, of vital importance to improving our understanding of such processes. While robust methods for defect detection exist for systems of elongated constituents, other systems, such as epithelial layers, are not well suited to such methods. Here, we address this problem by developing a convolutional neural network to detect and classify nematic defects in confluent cell layers. Crucially, our method is readily implementable on experimental images of cell layers and is specifically designed to be suitable for cells that are not rod shaped, which we demonstrate by detecting defects on experimental data using the trained model. We show that our machine learning model outperforms current defect detection techniques and that this manifests itself in our method as requiring less data to accurately capture defect properties. This could drastically improve the accuracy of experimental data interpretation while also reducing costs, advancing the study of nematic defects in biological systems.
Anand S, Lee CF, Bertrand T, 2024, Active Jamming at Criticality, Physical Review Research, ISSN: 2643-1564
Chen L, Lee CF, Maitra A, et al., 2024, Dynamics of packed swarms: time-displaced correlators of two dimensional incompressible flocks, Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, Vol: 109, ISSN: 1539-3755
We analytically calculate the scaling exponents of a two-dimensional KPZ-like system: coherentlymoving incompressible polar active fluids. Using three different renormalization group approxima-tion schemes, we obtain values for the “roughness” exponent χ and anisotropy exponent ζ that areextremely near the known exact results. This implies our prediction for the previously completelyunknown dynamic exponent z is likely to be quantitatively accurate.
Killeen A, Bertrand T, Lee CF, 2023, Modeling growing confluent tissues using a lattice Boltzmann method: interface stability and fluctuations, Physical Review Research, Vol: 5, ISSN: 2643-1564
Tissue growth underpins a wide array of biological and developmental processes, and numerical modeling of growing systems has been shown to be a useful tool for understanding these processes. However, the phenomena that can be captured are often limited by the size of systems that can be modeled. Here, we address this limitation by introducing a lattice Boltzmann method (LBM) for a growing system that is able to efficiently model hydrodynamic length scales. The model incorporates a bounce-back approach to describing the growing front of a tissue, which we use to investigate the dynamics of the interface of growing model tissues. We find that the interface grows with scaling in agreement with the Kardar-Parisi-Zhang (KPZ) universality class when growth in the system is bulk driven. Interestingly, we also find the emergence of a previously unreported hydrodynamic instability when proliferation is restricted to the tissue edge. We then develop an analytical theory to show that the instability arises due to a coupling between the number of cells actively proliferating and the position of the interface.
Jentsch P, Lee CF, 2023, Critical phenomena in compressible polar active fluids: dynamical and functional renormalization group studies, Physical Review Research, Vol: 5, Pages: 1-24, ISSN: 2643-1564
Active matter is not only relevant to living matter and diverse nonequilibrium systems, but also constitutes a fertile ground for novel physics. Indeed, dynamic renormalization group (DRG) analyses have uncovered many new universality classes (UCs) in polar active fluids (PAFs)—an archetype of active matter systems. However, due to the inherent technical difficulties in the DRG methodology, almost all previous studies have been restricted to polar active fluids in the incompressible or infinitely compressible (i.e., Malthusian) limits, and, when the ε expansion was used in conjunction, to the one-loop level. Here, we use functional renormalization group (FRG) methods to overcome some of these difficulties and unveil critical behavior in compressible polar active fluids, and calculate the corresponding critical exponents beyond the one-loop level. Specifically, we investigate the multicritical point of compressible PAFs, where the critical order-disorder transition coincides with critical phase separation. We first study the critical phenomenon using a DRG analysis and find that it is insufficient since two-loop effects are important to obtain a nontrivial correction to the scaling exponents. We then remedy this defect by using a FRG analysis. We find three universality classes and obtain their critical exponents, which we then use to show that at least two of these universality classes are out of equilibrium because they violate the fluctuation-dissipation relation.
Cairoli A, Spenlehauer A, Overby D, et al., 2023, Model of inverse bleb growth explains giant vacuole dynamics during cell mechanoadaptation, PNAS Nexus, Vol: 2, Pages: 1-11, ISSN: 2752-6542
Cells can withstand hostile environmental conditions manifest as large mechanical forces such as pressure gradients and/or shear stresses by dynamically changing their shape. Such conditions are realized in the Schlemm’s canal of the eye where endothelial cells that cover the inner vessel wall are subjected to the hydrodynamic pressure gradients exerted by the aqueous humor outflow. These cells form fluid-filled dynamic outpouchings of their basal membrane called giant vacuoles. The inverses of giant vacuoles are reminiscent of cellular blebs, extracellular cytoplasmic protrusions triggered by local temporary disruption of the contractile actomyosin cortex. Inverse blebbing has also been first observed experimentally during sprouting angiogenesis, but its underlying physical mechanisms are poorly understood. Here, we hypothesize that giant vacuole formation can be described as inverse blebbing and formulate a biophysical model of this process. Our model elucidates how cell membrane mechanical properties affect the morphology and dynamics of giant vacuoles and predicts coarsening akin to Ostwald ripening between multiple invaginating vacuoles. Our results are in qualitative agreement with observations from the formation of giant vacuoles during perfusion experiments. Our model not only elucidates the biophysical mechanisms driving inverse blebbing and giant vacuole dynamics, but also identifies universal features of the cellular response to pressure loads that are relevant to many experimental contexts.
Chen L, Lee CF, Maitra A, et al., 2022, Incompressible polar active fluids with quenched random field disorder in dimensions d>2, Physical Review Letters, Vol: 129, ISSN: 0031-9007
We present a hydrodynamic theory of incompressible polar active fluids with quenched random field disorder. This theory shows that such fluids can overcome the disruption caused by the quenched disorder and move coherently, in the sense of having a nonzero mean velocity in the hydrodynamic limit. However, the scaling behavior of this class of active systems cannot be described by linearized hydrodynamics in spatial dimensions between 2 and 5. Nonetheless, we obtain the exact dimension-dependent scaling exponents in these dimensions.
Chen L, Lee CF, Maitra A, et al., 2022, Packed swarms on dirt: two-dimensional incompressible flocks with quenched and annealed disorder, Physical Review Letters, Vol: 129, ISSN: 0031-9007
We show that incompressible polar active fluids can exhibit an ordered, coherently moving phase even in the presence of quenched disorder in two dimensions. Unlike such active fluids with annealed disorder (i.e., time-dependent random white noise) only, which behave like equilibrium ferromagnets with long-range interactions, this robustness against quenched disorder is a fundamentally non-equilibrium phenomenon. The ordered state belongs to a new universality class, whose scaling laws we calculate using three different renormalization group schemes, which all give scaling exponents within 0.02 of each other, indicating that our results are quite accurate. Our predictions can be quantitatively tested in readily available artificial active systems, and imply that biological systems such as cell layers can move coherently in vivo, where disorder is inevitable.
Chen L, Lee CF, Maitra A, et al., 2022, Hydrodynamic theory of two-dimensional incompressible polar active fluids with quenched and annealed disorder, Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, Vol: 106, Pages: 1-29, ISSN: 1539-3755
We study the moving phase of two-dimensional (2D) incompressible polar active fluids in the presence of both quenched and annealed disorder. We show that long-range polar order persists even in this defect-ridden two-dimensional system. We obtain the large-distance, long-time scaling laws of the velocity fluctuations using three distinct dynamic renormalization group schemes. These are an uncontrolled one-loop calculation in exactly two dimensions, and two d=(dc−ε) expansions to O(ε), obtained by two different analytic continuations of our 2D model to higher spatial dimensions: a “hard” continuation which has dc=73, and a “soft” continuation with dc=52. Surprisingly, the quenched and annealed parts of the velocity correlation function have the same anisotropy exponent and the relaxational and propagating parts of the dispersion relation have the same dynamic exponent in the nonlinear theory even though they are distinct in the linearized theory. This is due to anomalous hydrodynamics. Furthermore, all three renormalization schemes yield very similar values for the universal exponents, and therefore we expect the numerical values that we predict for them to be highly accurate.
Partridge B, Gonzalez Anton S, Khorshed R, et al., 2022, Heterogeneous run-and-tumble motion accounts for transient non-Gaussian super-diffusion in haematopoietic multi-potent progenitor cells, PLoS One, Vol: 17, Pages: 1-26, ISSN: 1932-6203
Multi-potent progenitor (MPP) cells act as a key intermediary step between haematopoietic stem cells and the entirety of the mature blood cell system. Their eventual fate determination is thought to be achieved through migration in and out of spatially distinct niches. Here we first analyze statistically MPP cell trajectory data obtained from a series of long time-course 3D in vivo imaging experiments on irradiated mouse calvaria, and report that MPPs display transient super-diffusion with apparent non-Gaussian displacement distributions. Second, we explain these experimental findings using a run-and-tumble model of cell motion which incorporates the observed dynamical heterogeneity of the MPPs. Third, we use our model to extrapolate the dynamics to time-periods currently inaccessible experimentally, which enables us to quantitatively estimate the time and length scales at which super-diffusion transitions to Fickian diffusion. Our work sheds light on the potential importance of motility in early haematopoietic progenitor function.
Cairoli A, Spenlehauer A, Overby DR, et al., 2022, Model of inverse bleb growth explains giant vacuole dynamics during cell mechanoadaptation
<jats:title>Abstract</jats:title><jats:p>Cells can withstand hostile environmental conditions manifest as large mechanical forces such as pressure gradients and/or shear stresses by dynamically changing their shape. Such conditions are realized in the Schlemm’s canal of the eye where endothelial cells that cover the inner vessel wall are subjected to the hydrodynamic pressure gradients exerted by the aqueous humor outflow. These cells form fluid-filled dynamic outpouchings of their basal membrane called<jats:italic>giant vacuoles</jats:italic>. The inverse of giant vacuoles are reminiscent of cellular blebs, extracellular cytoplasmic protrusions triggered by local temporary disruption of the contractile actomyosin cortex. Inverse blebbing has been first observed experimentally during sprouting angiogenesis, but its underlying physical mechanisms are poorly understood. Here, we identify giant vacuole formation as inverse blebbing and formulate a biophysical model of this process. Our model elucidates how cell membrane mechanical properties affect the morphology and dynamics of giant vacuoles and predicts coarsening akin to Ostwald ripening between multiple invaginating vacuoles. Our results are in qualitative agreement with observations from the formation of giant vacuoles during perfusion experiments. Our model not only elucidates the biophysical mechanisms driving inverse blebbing and giant vacuole dynamics, but also identifies universal features of the cellular response to pressure loads that are relevant to many experimental contexts.</jats:p><jats:sec><jats:title>Significance statement</jats:title><jats:p>Human Schlemm’s canal endothelial cells in physiological conditions are subjected to a pressure gradient caused by the flow of aqueous humor in the basal-to-apical direction across the endothelium leading to the formation of cellular outpouchings called giant vacuoles. The physical mechanis
Bertrand T, Lee CF, 2022, Diversity of phase transitions and phase separations in active fluids, Physical Review Research, Vol: 4, ISSN: 2643-1564
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 active systems. These emergent features include motility-induced phase separation, a long-ranged ordered (collective motion) phase in two dimensions, and order-disorder phase coexistences (banding and reverse-banding regimes). Here, we unify these diverse phase transitions and phase coexistences into a single formulation based on generic hydrodynamic equations for active fluids. We also reveal a novel comoving coexistence phase and a multicritical point.
Pirillo C, Birch F, Tissot FS, et al., 2022, Metalloproteinase inhibition reduces AML growth, prevents stem cell loss, and improves chemotherapy effectiveness, BLOOD ADVANCES, Vol: 6, Pages: 3126-3141, ISSN: 2473-9529
Lee CF, 2022, An infinite set of integral formulae for polar, nematic, and higher order structures at the interface of motility-induced phase separation, NEW JOURNAL OF PHYSICS, Vol: 24, ISSN: 1367-2630
Killeen A, Bertrand T, Lee CF, 2022, Polar fluctuations lead to extensile nematic behavior in confluent tissues, Physical Review Letters, Vol: 128, Pages: 1-6, ISSN: 0031-9007
How can a collection of motile cells, each generating contractile nematic stresses in isolation, become an extensile nematic at the tissue-level? Understanding this seemingly contradictory experimental observation, which occurs irrespective of whether the tissue is in the liquid or solid states, is not only crucial to our understanding of diverse biological processes, but is also of fundamental interest to soft matter and many-body physics. Here, we resolve this cellular to tissue level disconnect in the small fluctuation regime by using analytical theories based on hydrodynamic descriptions of confluent tissues, in both liquid and solid states. Specifically, we show that a collection of microscopic constituents with no inherently nematic extensile forces can exhibit active extensile nematic behavior when subject to polar fluctuating forces. We further support our findings byperforming cell level simulations of minimal models of confluent tissues.
Lee CF, 2022, An infinite set of integral formulae for polar, nematic, and higher order structures at the interface of motility-induced phase separation, New Journal of Physics, Vol: 24, ISSN: 1367-2630
Motility-induced phase separation (MIPS) is a purely non-equilibriumphenomenon in which self-propelled particles phase separate without any attractive interactions. One surprising feature of MIPS is the emergence of polar, nematic, and higher order structures at the interfacial region, whose underlying physics remains poorly understood. Starting with a model of MIPS in which all many-body interactions are captured by an effective speed function and an effective pressure function that depend solely on the local particle density, I derive analytically an infinite set of integral formulae for the ordering structures at the interface. I then test these integral formulae by applying them to numerical data from direct particle dynamics simulation and find that they remain valid with a high accuracy.
Partridge B, Anton SG, Khorshed R, et al., 2021, Heterogeneous run-and-tumble motion accounts for transient non-Gaussian super-diffusion in haematopoietic multi-potent progenitor cells
<jats:p>Multi-potent progenitor (MPP) cells act as a key intermediary step between haematopoietic stem cells and the entirety of the mature blood cell system. Their eventual fate determination is thought to be achieved through migration in and out of spatially distinct niches. Here we first analyze statistically MPP cell trajectory data obtained from a series of long time-course 3D <jats:italic>in-vivo</jats:italic> imaging experiments on irradiated mouse calvaria, and report that MPPs display transient super-diffusion with apparent non-Gaussian displacement distributions. Second, we explain these experimental findings using a run-and-tumble model of cell motion which incorporates the observed dynamical heterogeneity of the MPPs. Third, we use our model to extrapolate the dynamics to time-periods currently inaccessible experimentally, which enables us to quantitatively estimate the time and length scales at which super-diffusion transitions to Fickian diffusion. Our work sheds light on the potential importance of motility in early haematopoietic progenitor function.</jats:p>
Lee CF, 2021, Scaling law and universal drop size distribution of coarsening in conversion-limited phase separation, Physical Review Research, Vol: 3, Pages: 1-6, ISSN: 2643-1564
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. [Science 373, 1218 (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. One implication of this conversion-limited picture is that standard theories of coarsening in phase separation (Lifshitz-Slyozov-Wagner theory of Ostwald ripening and drop coalescence schemes) no longer apply. Surprisingly, I show here that the model equations of conversion-limited phase separation can instead be mapped onto a grain growth model in a single-phase material in three dimensions. I further elucidate the universal coarsening behavior in the late stage using analytical and numerical methods.
Folkmann A, Putnam A, Lee CF, et al., 2021, Regulation of biomolecular condensates by interfacial protein clusters, Science, Vol: 373, Pages: 1218-1224, ISSN: 0036-8075
Pickering emulsions, droplet suspensions stabilized by solid particles, were discovered more than 100 years ago and are well studied in foods, oils, cosmetics, and pharmaceuticals. The particles adsorb to the droplet interface and prevent the emulsion from coarsening. Folkmann et al. report that P granules, biomolecular condensates in Caenorhabditis elegans, are an example of an intracellular Pickering emulsion (see the Perspective by Snead and Gladfelter). Biomolecular condensates are cellular compartments that form without traditional lipid membranes. This work raises the possibility that Pickering agents fulfill the role of membranes in biomolecular condensates. —DJ
Nesbitt D, Pruessner G, Lee CF, 2021, Uncovering novel phase transitions in dense dry polar active fluids using a lattice Boltzmann method, New Journal of Physics, Vol: 23, ISSN: 1367-2630
The dynamics of dry active matter have implications for a diverse collection of biological phenomena spanning a range of length and time scales, such as animal flocking, cell tissue dynamics, and swarming of inserts and bacteria. Uniting these systems are a common set of symmetries and conservation laws, defining dry active fluids as a class of physical system. Many interesting behaviours have been observed at high densities, which remain difficult to simulate due to the computational demand. Here, we show how two-dimensional dry active fluids in a dense regime can be studied using a simple modification of the lattice Boltzmann method. We apply our method on a model that exhibits motility-induced phase separation, and an active model with contact inhibition of locomotion, which has relevance to collective cell migration. For the latter, we uncover multiple novel phase transitions: two first-order and one potentially critical. We further support our simulation results with an analytical treatment of the hydrodynamic equations obtained via the Chapman-Enskog coarse-graining procedure.
Chen L, Lee CF, Toner J, 2020, Moving, Reproducing, and Dying Beyond Flatland: Malthusian Flocks in Dimensions <i>d</i> > 2, PHYSICAL REVIEW LETTERS, Vol: 125, ISSN: 0031-9007
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- Citations: 7
Chen L, Lee CF, Toner J, 2020, Universality class for a nonequilibrium state of matter: A d=4−ε expansion study of Malthusian flocks, Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, Vol: 102, Pages: 1-40, ISSN: 1539-3755
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 toa new universality class in spatial dimensionsd >2. We calculate the universal exponents andscaling laws of this new universality class toO( ) in ad= 4− expansion, and find these aredifferent 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 dimensionsin the range of 2< d≤4. We also obtain a universal amplitude ratio relating the damping oftransverse and longitudinal velocity and density fluctuations in these systems. Furthermore, wefind a universal separatrix in real (r) space between two regions in which the equal time densitycorrelation〈δρ(r,t)δρ(0,t)〉has opposite signs. Our expansion should be quite accurate ind= 3,allowing precise quantitative comparisons between our theory, simulations, and experiments.
Chen L, Lee CF, Toner J, 2020, Moving, reproducing, and dying beyond Flatland: Malthusian flocks in dimensions d>2, Physical Review Letters, ISSN: 0031-9007
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 calculate the universal exponents and scaling laws of this new universality class to O(ϵ) in an ϵ=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.
Pytowski L, Lee CF, Foley AC, et al., 2020, Liquid–liquid phase separation of type II diabetes-associated IAPP initiates hydrogelation and aggregation, Proceedings of the National Academy of Sciences of USA, Vol: 117, Pages: 12050-12061, ISSN: 0027-8424
Amyloidoses (misfolded polypeptide accumulation) are among the most debilitating diseases our aging societies face. Amyloidogenesis can be catalyzed by hydrophobic–hydrophilic interfaces (e.g., air–water interface in vitro [AWI]). We recently demonstrated hydrogelation of the amyloidogenic type II diabetes-associated islet amyloid polypeptide (IAPP), a hydrophobic–hydrophilic interface-dependent process with complex kinetics. We demonstrate that human IAPP undergoes AWI-catalyzed liquid–liquid phase separation (LLPS), which initiates hydrogelation and aggregation. Insulin modulates these processes but does not prevent them. Using nonamyloidogenic rat IAPP, we show that, whereas LLPS does not require the amyloidogenic sequence, hydrogelation and aggregation do. Interestingly, both insulin and rat sequence delayed IAPP LLPS, which may reflect physiology. By developing an experimental setup and analysis tools, we show that, within the whole system (beyond the droplet stage), macroscopic interconnected aggregate clusters form, grow, fuse, and evolve via internal rearrangement, leading to overall hydrogelation. As the AWI-adsorbed gelled layer matures, its microviscosity increases. LLPS-driven aggregation may be a common amyloid feature and integral to pathology.
Lee CF, 2020, Formation of liquid-like cellular organelles depends on their composition, NATURE, Vol: 581, Pages: 144-145, ISSN: 0028-0836
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- Citations: 3
Partridge B, Lee CF, 2019, Critical motility-induced phase separation belongs to the Ising universality class, Physical Review Letters, Vol: 123, Pages: 1-6, ISSN: 0031-9007
A collection of self-propelled particles with volume exclusion interactions can exhibit the phenomenology of a gas-liquid phase separation, known as motility-induced phase separation (MIPS). The nonequilibrium nature of the system is fundamental to the phase transition; however, it is unclear whether MIPS at criticality contributes a novel universality class to nonequilibrium 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.
Sartori P, Lee CF, 2019, Scaling behaviour of non-equilibrium planar N-atic spin systems under weak fluctuations, New Journal of Physics, Vol: 21, Pages: 1-6, ISSN: 1367-2630
Starting from symmetry considerations, we derive the generic hydrodynamic equation of nonequilibrium XY spin systems with N-atic symmetry under weak fluctuations. Through a systematictreatment we demonstrate that, in two dimensions, these systems exhibit two types of scalingbehaviours. For N = 1, they have long-range order and are described by the flocking phase of drypolar active fluids. For all other values of N, the systems exhibit quasi long-range order, as in theequilibrium XY model at low temperature.
Overby DR, Spenlehauer A, Cairoli A, et al., 2019, Actomyosin contractility and the vimentin cytoskeleton influence giant vacuole life-cycle in Schlemm's canal endothelial cells, Annual Meeting of the Association-for-Research-in-Vision-and-Ophthalmology (ARVO), Publisher: ASSOC RESEARCH VISION OPHTHALMOLOGY INC, ISSN: 0146-0404
Weber C, Zwicker D, Juelicher F, et al., 2019, Physics of active emulsions, Reports on Progress in Physics, Vol: 82, Pages: 1-40, ISSN: 0034-4885
Phase separating systems that are maintained away from thermodynamic equilibrium via molecular processes represent a class of active systems, which we call \textit{ active emulsions}. These systems are driven by external energy input for example provided by an external fuel reservoir. The external energy input gives rise to novel phenomena that are not present in passive systems. For instance, concentration gradients can spatially organise emulsions and cause novel droplet size distributions. Another example are active droplets that are subject to chemical reactions such that their nucleation and size can be controlled and they can spontaneously divide. In this review we discuss the physics of phase separation and emulsions and show how the concepts that governs such phenomena can be extended to capture the physics of active emulsions. This physics is relevant to the spatial organisation of the biochemistry in living cells, for the development novel applications in chemical engineering and models for the origin of life.
Cairoli A, Lee CF, 2019, Active Lévy Matter: Anomalous Diffusion, Hydrodynamics and Linear Stability
Anomalous diffusion, manifest as a nonlinear temporal evolution of theposition mean square displacement, and/or non-Gaussian features of the positionstatistics, is prevalent in biological transport processes. Likewise,collective behavior is often observed to emerge spontaneously from the mutualinteractions between constituent motile units in biological systems. Exampleswhere these phenomena can be observed simultaneously have been identified inrecent experiments on bird flocks, fish schools and bacterial swarms. Theseresults pose an intriguing question, which cannot be resolved by existingtheories of active matter: How is the collective motion of these systemsaffected by the anomalous diffusion of the constituent units? Here, we answerthis question for a microscopic model of active L\'evy matter -- a collectionof active particles that perform superdiffusion akin to a L\'evy flight andinteract by promoting polar alignment of their orientations. We present indetails the derivation of the hydrodynamic equations of motion of the model,obtain from these equations the criteria for a disordered or ordered state, andapply linear stability analysis on these states at the onset of collectivemotion. Our analysis reveals that the disorder-order phase transition in activeL\'evy matter is critical, in contrast to ordinary active fluids where thephase transition is, instead, first-order. Correspondingly, we estimate thecritical exponents of the transition by finite size scaling analysis and usethese numerical estimates to relate our findings to known universality classes.These results highlight the novel physics exhibited by active matterintegrating both anomalous diffusive single-particle motility andinter-particle interactions.
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