Hydrodynamic Approaches to Active Matter: Successes and Future Challenges

Smectic layering can be observed in biological systems such as the acto-myosin network in lamellipodia (1) and also monolayer tissues, endoplasmic reticulum, myelin sheets etc, but also in many out-of-equilibrium patterns. Such systems are often not mono-crystalline and display dislocations densities, dynamical behavior etc. This raises the question of the description of active smectics in the presence of dislocation densities in two and three dimensions. After discussing the existence or non-existence of a steady state depending on boundary conditions, I'll give a few examples of non-equilibrium behavior.

Universality, Scaling and the framework of Wilson’s Renormalization Group are seminal concepts that have shaped our understanding of phase transitions and complex phase behavior in thermal systems. Generalizing these ideas to non-thermal systems, ones that explore configuration space without any thermal motion, pose significant challenges. Recently, a combination of experiments, simulations and theoretical analysis have been used to establish scaling and universality in non-Brownian suspensions that are close to jamming. In this talk, I will present my perspective on the implications of this result and how we can build on it to develop predictive theories.

Active matter systems described by a slow, conserved scalar density field possess a very rich phase diagram which reveals striking, intrinsically out-of-equilibrium dynamics. Domains might undergo reversed Ostwald ripening, or dilute bubbles nucleated inside dense, bounded domains can grow and migrate towards their boundaries. Although these dynamics have been observed and predicted across different models of such active systems (such as in active Model B+), a quantitative explanation of the coupled growth and migration of these structures has remained incomplete. In this talk, I will present a joint incoming work with R.Ginelli, J.F Joanny, and F. Jülicher where we show that in many cases, one can describe such active systems with a simple sharp-interface theory that combines simple diffusive transport in the bulk with active interfacial kinetics. This enables analytical predictions for the growth and motion of interacting dense droplets and dilute bubbles. For two separated droplets, shrinking promotes attraction, while growth promotes repulsion. Together with reversed Ostwald ripening, this constitutes an elegant physical mechanism describing the steady state of macrophase separation. We also show how an off-centered bubble-in-droplet structure, relevant to bubbly phase separation, move together, with the bubble's relative migration strongly enhanced as the bubble approaches the outer interface.

Unlike coffee and cream that homogenize when stirred, growing micro-organisms (e.g., bacteria and unicellular marine organisms) can actively kill each other and avoid mixing. How do such antagonistic interactions impact the growth and survival of competing strains, while being spatially advected by turbulent flows? By using analytic arguments and numerical simulations of a continuum model, we describe the dynamics of two antagonistic strains that are dispersed by both compressible and incompressible turbulent flows in two spatial dimensions. A key parameter is the ratio of the fluid transport time to that of biological reproduction, which determines the winning organism that ultimately takes over the whole population from an initial heterogeneous state, a process known as fixation. By quantifying the probability and mean time for fixation, we discuss how turbulence raises the threshold for biological nucleation and antagonism suppresses flow-induced mixing by depleting the population at interfaces. We highlight the unusual biological consequences of the interplay of turbulent fluid flows with antagonistic population dynamics, with potential implications for marine microbial ecology and origins of biological chirality.

I will discuss type-II superconductors in a magnetic field applied transversely to correlated columnar disorder, showing that it drives a phase transition to a distinct "smectic" vortex glass (SmVG) state. SmVG is characterized by an infinitely anisotropic electrical transport, resistive (dissipationless) for current perpendicular to (along) columnar defects. Its positional order is also quite unusual, long-ranged with true Bragg peaks along columnar defects and logarithmically rough vortex lattice distortions with quasi-Bragg peaks transverse to columnar defects. For low temperatures and sufficiently weak columnar-only disorder, SmVG is a true topologically-ordered "Bragg glass", characterized by a vanishing dislocation density. At sufficiently long scales the residual ever-present point disorder converts this state to a more standard, but highly anisotropic vortex glass.

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Universality explains how systems with vastly different microscopic dynamics can exhibit identical large-scale behaviour through the fixed point structure of the renormalization-group (RG): ``universality classes''. While this framework is well established in equilibrium statistical mechanics, many active and living systems operate intrinsically far from equilibrium, where much of universality's structure remains a mystery. In this letter, we analyse a minimal non-equilibrium (NE) extension of the critical $O(N)$ model obtained by coupling orientational fluctuations to real-space propagation; converting passive diffusion of spin distortions into directed transport of orientational information. Using a symmetry motivated model, we further use a perturbative dynamical RG analysis, within a one-loop $\epsilon$-expansion, to show that the space--spin coupling generically destabilises the equilibrium $O(N)$ universality class (UC) and instead drives the system towards a new NE UC. We further identify two additional multicritical non-equilibrium RG fixed points, alongside several special multi-critical UCs associated with critical incompressible polar active fluids, randomly stirred fluids and long-range interacting ferromagnets. Our results place NE spin criticality, flocking hydrodynamics, and several previously known multi-critical systems within a common RG framework generated by space--spin coupling.

The Ising universality class is remarkably robust to non-equilibrium perturbations, which generically flow to zero under renormalization. We show that this robustness fails when an order parameter is coupled nonreciprocally to a conserved diffusive density. Below $d_c=4$, the renormalization group flows to a fast-diffusion fixed point at which the density acts as a long-range multiplicative noise, producing a novel universality class. The non-equilibrium nature of the fixed point is manifest in the large-scale violation of the fluctuation-dissipation relations, reflected in a splitting of the scaling exponents of the two-point correlation and response functions--a measurable hallmark of non-equilibrium critical fluctuations. A two-loop calculation establishes the stability of this fixed point but yields a small correction-to-scaling exponent $\omega\approx0.020$ in $d=3$, implying strong finite-size corrections. An all-orders modified Harris criterion $\nu>2/(d+z-2)$ confirms that the BIM fixed point governs criticality in $d=3$, with Ising universality recovered only at $d=2$.

Chiral active matter, which breaks both parity symmetry and time-reversal symmetry is ubiquitous in living systems. Here, we introduce a minimal two-dimensional chiral active lattice gas by incorporating stochastic, biased local rotations. At low temperatures, the system coarsens into condensates with chiral orientations and faceted, crystal-like shapes. The interfaces align at characteristic angles with respect to the lattice axes and exhibit edge currents that are persistent, unidirectional, and angle-dependent. To generalise these findings, we propose a continuum theory by adding an active chiral edge current term to Model B, which reveals the essential role of active chiral transport in the interfacial dynamics of phase separation. Edge currents with n-fold symmetry produce condensates whose shapes resemble regular n-sided polygons. In the thin-interface limit, we construct an effective interface potential governing edge currents, from which the steady-state condensate geometry can be obtained, both in the lattice model and the continuum description. Ref:B. Wang, P. Pietzonka, and F. Jülicher, arXiv:2603.20064 [cond-mat.stat-mech] (2026).

I'll describe the hydrodynamic behavior of two-dimensional chiral flocks; that is, chiral polar-ordered active matter with neither number nor momentum conservation. I'll show that such systems generically, in the absence of fluctuations , form a ``time crystal", in which the velocity of the entire system rotates uniformly at a fixed frequency $b$. Fluctuations about this state belong to the universality class of a sort of extended($2+1$)-Kardar-Parisi-Zhang (KPZ) equation, which implies exotic non-universal orientational order in these systems.

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Chemically active cortical condensates orchestrate the emergence of the actomyosin layer at the oocyte-to-embryo transition in the nematode worm. In this talk I will report on new work that utilizes an inference approach that includes 3D phase portraits and that investigates fluctuations, to identify additional molecular players that contribute to the generation of such non-equilibrium biomolecular condensates in the cortex that assemble and disassemble.

Computation is the controlled evolution of a state. Asynchronous evolutions, where all parts of the state change in their own time without stopping each other, put this control in jeopardy. It is in fact a mystery how natural processes perform asynchronous computations using many units with no global orchestration. In this talk, we demonstrate how collective computational abilities can emerge in asynchronous many-body systems. The key insight is to split the physical "hardware" underlying the computation into two asymmetrically coupled parts, analogous to position and momentum in a harmonic oscillator. The resulting inertia nudges the evolution of the state so that the asynchronous computation proceeds in the right order. By treating our inertial asynchronous computer as a nonequilibrium material, we map out its phase diagram numerically and analytically using a framework we dub loop dynamical mean-field theory. We experimentally demonstrate our approach using analog spiking neuromorphic chips designed to mimic actual neurons in the brain. In addition, we construct software that can run on asynchronous hardware: we denoise movies whose clean versions were never seen during training, an instantiation of the generalization transition underlying modern machine learning. Our results point to a general strategy for reliable, decentralized computation in energy-constrained settings from dynamics self-assembly to cell differentiation.

Many examples of collective biological function--such as biochemical signaling networks--arise in systems whose physical degrees of freedom satisfy coupled ordinary differential equations. The networks have been tuned by biological evolution or other processes so that e.g., effective rate constants that enter into the dynamical equations are tuned so that the network as a whole exhibits desired collective behavior. I will argue that many biological systems with complex function are forms of tunable active matter--an area that is ripe for theoretical study.

I will present a very general relation between correlation functions and response or relaxation functions that holds both in equilibrium, when the usual fluctuation-dissipation theorem is valid, and to linear order in an expansion about arbitrary nonequilibrium states, when it is not. I will explain the relation, and discuss its utility, by means of various examples, including fluids in equilibrium and nonequilibrium states, as well as active-matter systems.

not yet prepared

At low Reynolds number, propulsion is constrained by time reversal symmetry. According to Purcell's scallop theorem, the net displacement over any reciprocal actuation cycle is zero, so directed motion requires a non reciprocal drive or deformation. Here we show that magnetic achiral bent rod microstructures realize a mechanism in which non reciprocity emerges dynamically. Using experiments on magnetic achiral bent rods suspended in a viscous fluid and actuated by rotating magnetic fields, we observe that these simple microstructures exhibit two symmetry related propulsion states (1). Above a critical actuation frequency, the particles behave as polar particles whose propulsion direction is determined by their head orientation and becomes decoupled from the sense (clockwise or counterclockwise) of the driving field. Once the system locks into one propulsion branch, reversing the applied magnetic field rotation no longer reverses the swimming direction, thereby breaking the direction reversal symmetry characteristic of conventional field driven micro swimmers. Consequently, under an oscillating field, the swimmers transition from reciprocal to non reciprocal motion observed once it enters the bistable field range. This bistability therefore overcomes the constraint imposed by Purcell's scallop theorem, enabling sustained net propulsion without structural chirality or shape reconfiguration. Compared with previously studied oscillating field driven active chiral structures (2,3), the achiral bent rods exhibit substantially enhanced diffusivities and stronger inter swimmer interactions. Investigating both quasi 1D and 2D confinement, we experimentally observe that these enhanced interactions give rise to distinct collective states and self organization. Simple toy model calculations indicate that hydrodynamic interactions are the dominant mechanism underlying the observed collective behaviour, establishing this experimentally accessible system as a model platform for studying emergent active hydrodynamics. 1. Sachs, Johannes & Morozov, Konstantin & Kenneth, Oded & Qiu, Tian & Segreto, Nico & Fischer, Peer & Leshansky, Alexander. (2018). Role of symmetry in driven propulsion at low Reynolds number. Physical Review E. 98. 10.1103/PhysRevE.98.063105. 2. Mandal, Pranay, and Ambarish Ghosh. "Observation of enhanced diffusivity in magnetically powered reciprocal swimmers." Physical Review Letters 111.24 (2013): 248101. 3. Patil Gouri, Pranay Mandal, and Ambarish Ghosh. "Using the thermal ratchet mechanism to achieve net motility in magnetic microswimmers." Physical Review Letters 129.19 (2022): 198002.

Turnover of microscopic components is ubiquitous in living matter across levels of biological organisation, e.g., through cell division and death in tissues or assembly and disassembly of cytoskeletal filaments. The hydrodynamic theory of Malthusian flocks describes the long-wavelength ordering of such polar active matter, but its phase diagram and nonlinear scaling behavior is not yet well understood in two dimensions. Using a nonperturbative renormalization group approach, fully compatible with rotational symmetry, and in the absence of defects, we explicitly obtain the fixed point governing true long-range order and uncover a new regime of quasi long-range order. A critical point similar to, but distinct from the Berezinskii-Kosterlitz-Thouless universality class governs the transition between true and quasi long-range order. Our results reveal a richer phase structure for two-dimensional Malthusian flocks than previously anticipated and, subject to our approximation, establish the nonlinear scaling behavior governing the two phases and the novel phase transition.

Chiral symmetry breaking is a defining feature of life, visible at all scales from molecules to tissues and organisms. Its intrinsically out-of-equilibrium nature has recently attracted great interest in the active matter community. Experimental realizations of chiral living matter have been so far largely limited to crystals, while chiral fluids were typically externally driven. Here, we show that a living chiral fluid behaves fundamentally differently from a driven one. We introduce an experimental system of spinning microalgae that are very well described by a minimal hydrodynamic model of 2d active rotors. The cells self-assemble into a percolating chiral fluid as their density increases. Strikingly, microscopic and macroscopic vorticity have opposite handednesses: while individual cells spin counterclockwise, clusters orbit clockwise, leading to odd transport coefficients with reversed signs. Combining experiments, theory and simulations, we show that this chirality inversion is a direct consequence of the active (i.e. internally driven) nature of the particles.

I shall discuss recent work with SJ Kole, GP Alexander, and A Maitra on three-dimensional chiral active systems with translational order. I will answer the title question, contrast the properties of 3D chiral active elastomers and solids, and discuss an inertial instability of the latter.

Collective turns in starling flocks propagate linearly with negligible attenuation, indicating the existence of an underdamped sector in the dispersion relation. According to linear response theory, beside granting linear propagation of the phase perturbations, the real part of the frequency should also yield a spin-wave form of the unperturbed correlation function. However, new high-resolution experiments on real flocks show that underdamped traveling waves coexist with an overdamped Lorentzian correlation function. Theory and experiments are reconciled once we add to the dynamics a nonlinear Fermi-Pasta-Ulam-Tsingou term.

Motility regulation via external stimuli provides novel strategies for controlling active matter, including photo-responsive bacteria. In this talk, we investigate photo-responsive structure formation in a minimal model of dry active nematics. Combining microscopic simulations with analysis of the corresponding hydrodynamic theory, we show that the system generically self-assembles into dense, nematically ordered structures at the boundaries of compact illumination patterns. Remarkably, these structures enclose a protected disordered core whose density is self-selected and independent of the global density. Our analysis reveals that these protected states are robust across model parameters and confining geometries, and emerge from a generic interplay between local nematic alignment and curvature-driven active currents. Our results provide a minimal theoretical framework with concrete, experimentally testable predictions, and establish new avenues for controlling active materials without relying on mechanical confinement.

Active chiral fluids can support a nondissipative transport coefficient known as odd (or Hall) viscosity. Hydrodynamic descriptions of such fluids typically introduce odd viscosity phenomenologically. How such a response emerges from specific microscopic interactions remains incompletely understood. Here, building on classical shear rheology, we microscopically derive an odd rheological response in active chiral films: thin layers of torque-exerting, elongated particles anchored to a no-slip surface. A canonical realization of such a film is the bacterial carpet, in which flagellated bacteria are tethered head-down to a solid surface while their flagella remain free to spin and inject angular momentum into the surrounding fluid. Using a kinetic theory for the orientational dynamics of these anchored particles, we derive their stress response to an imposed shear flow. We reveal that shear-induced reorientation leads to a flow-aligned polarization and a transverse surface traction from which the odd-viscosity tensor follows in closed form. Numerical solutions of the nonlinear kinetic theory further highlight saturation of the transverse traction at strong shear, driven by shear-induced orientation dynamics -- signaling departure from linear response. Our results demonstrate how odd viscosity can emerge self-consistently as a coarse-grained rheological signature of active fluid-structure interaction and establish active chiral films as a new controllable setting for odd hydrodynamics.

In recent years, non-equilibrium interfaces such as those in motility-induced phase separation have attracted intense interest. Although striking non-equilibrium effects, including effective negative surface tension, have been reported, numerical studies have repeatedly found an apparently equilibrium-like interface spectrum, $S=\langle h_k h_{-k}\rangle\sim k^{-2}$. We introduce a new non-equilibrium particle system in which energy is injected during collisions. The particles are hard disks that dissipate energy through viscous drag during free flight, while acquiring variable energy upon impact. With interparticle attractions or density-dependent energy injection, the system phase separates, forming interfaces with a rich variety of non-equilibrium fluctuations. Remarkably, when the two coexisting bulk phases are hyperuniform, interface fluctuations are strongly suppressed, giving $S\sim k^{-1}$. By tuning the driving mechanism and the underlying conservation laws, we also uncover regimes of enhanced fluctuations, $S\sim k^{-3}$, as well as behavior consistent with the recently identified qKPZ universality class. We further show that chirality can change the interface universality class. We fully explain this phenomenology by deriving an effective interface equation from the underlying order-parameter dynamics and using the renormalization group. All in all, we link the microscopic driving to emergent interfacial universality.

In suspensions of swimming bacteria, individual cells interact via long-range hydrodynamic forces and self-organize into collective states that drive large-scale chaotic flows, commonly referred to as ``bacterial turbulence.'' Despite extensive experimental and theoretical work, it remains unclear whether an intrinsic length scale underlies the observed patterns. To directly address this question and shed light on the mechanisms driving active turbulence, we investigate the emergence of large-scale flows in E. coli suspensions confined within flat cylindrical chambers, systematically varying the confinement height over more than two orders of magnitude. We first demonstrate that the critical density for the onset of collective motion scales inversely with the confinement height without saturation. Near the onset, both the observed length and time scales increase sharply, with the length scale limited only by the vertical confinement. Importantly, both scales exhibit clear power-law dependence on the confinement height, demonstrating the absence of an intrinsic length scale in bacterial collective motion. Close to the instability onset, we observed transient coherent vortices, reaching up to 4000 times the size of a single bacterium and spanning the full chamber width, further reinforcing the conclusion that bacterial turbulence is scale-free. Our experimental results, which characterize the onset of collective motion and demonstrate that bacterial turbulence is scale-free, discriminate between competing theoretical models and provide essential input for theories seeking to capture the dynamics and constitutive relations of wet active matter.

Propagating, storing and processing information is key to take smart decisions – for organisms as well as for autonomous devices. In search for the minimal units that allow for complex behaviour, the slime mould Physarum polycephalum stands out by solving complex optimization problems despite its simple make-up. Physarum’s body is an interlaced network of fluid-filled tubes lacking any nervous system, in fact being a single gigantic cell. Yet, Physarum finds the shortest path through a maze. We unravel that Physarum’s complex behaviour emerges from the physics of active flows shuffling through its tubular networks. Flows transport information, information that is stored in the architecture and mechanical state of the network. Thus, tubular adaptation drives processing of information into complex behaviour. Taking inspiration from the mechanisms in Physarum we outline how to embed complex behaviour in active microfluidic devices and how to program human vasculature.

The transition to collective motion is arguably the most studied phase transition in active matter. It leads to an ordered phase whose properties have attracted much attention. In this talk I will discuss the role played by non-linear structures in the transition to collective motion. I will show how the transition is generically first order and discuss the nature of the coexistence state. Then, I will show how the nucleation of non-linear structures destroys the ordered phase in systems with scalar symmetries. Contrary to the equilibrium case, I will then show how continuous symmetries prove more robust to these non-linear excitations.

Hydrodynamic theories of active matter are commonly organiZed by the symmetry of the ordered state. Non-reciprocal spin systems show why this can be insufficient. Their microscopic interactions contain two independent symmetries: alignment determines the orientational order, whereas sensing determines the geometry through which neighbours influence one another. Directional sensing makes this influence non-reciprocal, since one element may respond strongly to another without an equivalent reverse response. Starting from stochastic angular dynamics, a kinetic hierarchy provides a general route to the continuum theory. Alignment selects the critical angular mode and the eventual emerging order (polar, nematic, or higher-fold). Sensing instead fixes the angular structure and derivative order of the anisotropic spatial couplings. The same ordered symmetry can therefore support different transport mechanisms and different deformations of its topological defects, depending on how the environment is sensed. Thus, two complementary hydrodynamic limits emerge. These descriptions connect smoothly only when the sensing geometry respects all symmetry-equivalent orientations of the ordered field.

In pulsating active matter, topological defects are motile despite the absence of any macroscopic flows and microscopic self-propulsion. We reveal that this motility arises from a ratchet effect: the mechanochemical coupling between local oscillations and repulsive interactions breaks both spatial and time-reversal symmetries, thus leading asymmetric rotating defects to drift under fluctuations. This mechanism regulates a crossover between spiral waves connecting slow defects and fiber-like waves connecting fast defects, in analogy with the onset of heart rhythm disorder in cardiac tissues. We rationalize this crossover in terms of a fluctuating hydrodynamics that captures how motile defects spontaneously nucleate and move within an ordered background.

It is now well established that chiral active matter shows a wealth of intriguing phenomena that are absent in its achiral counterparts. One of the striking features of such chiral active systems is edge currents. While several studies suggest that edge currents in chiral active matter can be robust against changes in confinement geometries, the microscopic rules that render these edge currents robust remain elusive. Here, we introduce a simple particle model of two-dimensional chiral active swimmers that undergo chirality switching and demonstrate that the model exhibits robust edge currents. When a single particle is confined, edge currents arise regardless of the confinement geometry or the presence of defects. We also investigate the collective behavior of interacting particles in bulk and find that chirality switching induces phase separation accompanied by edge currents along interfaces. This phase separation is distinct from motility-induced phase separation and is qualitatively explained by an effective hydrodynamic theory derived via bottom-up coarse-graining. Furthermore, by analyzing the topological properties of the linearized hydrodynamic equations, we show that the edge currents in our system are genuine topological edge modes. Notably, phase separation induced by chirality switching can be regarded as the coexistence of two topologically distinct domains.

Classical nucleation theory (CNT) constructs a free energy $F(R)$ as a function of droplet radius (the reaction coordinate) and estimates the nucleation rate via the barrier height $F(R_c)$ at the critical radius. For systems without detailed balance, the free energy is replaced by a quasipotential whose only calculation is from dynamics. For the case of a conserved scalar field --- liquid-vapour nucleation, Active Model B+ --- the calculation goes through with little fuss, so long as the correct nonequilibrium interfacial tension is identified. (In passing, this calculation proves nonlocality of the stationary measure in AMB+.) For a nonconserved scalar (kinetic Ising models, Active Model A) things are more subtle. Specifically, to find the mobility of the reaction coordinate, one cannot assume that the interfacial profile of a growing droplet is the same as that of a relaxing droplet of the same size --- as would be demanded in equilibrium, and assumed in CNT. To overcome this problem we have developed Nonequilibrium Nucleation Theory (NNT) which can be formulated either by deriving a Langevin equation for $R$, or by minimizing the stochastic action at field level. Exploiting (or in our case rediscovering) a long-established protocol, NNT makes a specific definition of the reaction coordinate that projects out the dynamical deviations of the interfacial shape, allowing these to remain undetermined.

Active networks of cytoskeletal filaments and motor proteins provide powerful in vitro models for studying intracellular processes and dynamic structures within the framework of active matter physics. These systems enable investigation of self-driven assemblies that operate far from thermodynamic equilibrium generating dynamic patterns on length scales far larger than those of their individual components. In our study we investigate the emergent behaviour of active microtubule–kinesin networks subjected to external mechanical forces acting at the air–liquid interface. To this end, we use a simple approach by confining active networks composed of microtubules, kinesin motors, and ATP within a sessile droplet. We observe that evaporation-driven flows generate shear stresses that couple with motor activity and this interplay produces non-trivial dynamics that lead to wetting followed by dewetting of the droplet. Interestingly, the temporal evolution of these dynamics strongly depends on motor crosslinking, ATP availability, and the ionic strength of the bulk solution. We believe that our findings can contribute to understanding how intracellular ionic strength may regulate cytoskeletal mechanics and organization through electrostatic interactions between microtubules and motor proteins.

Motion turns out to anomalously stabilise ordered phases. While this stabilising effect has been discussed in "clean" (i.e. disorder-free) systems for thirty years since the pioneering work of Toner and Tu, it is more pronounced in "dirty" (i.e., materials with quenched, random field disorder) systems. Indeed, I will show that a particular kind of active polar fluids can retain orientational order in two dimensions even in the presence of random-field disorder. This is because motility has an "annealising" effect on time-independent disorder. In the second part of the talk, I will shift my attention to active phases that break translational symmetry––specifically, polar smectics and solids––and demonstrate that, even here, motility anomalously stabilises order. Indeed, the equal-time statistics of displacement fluctuations of motile smectics in d dimensions with quenched disorder are equivalent to time-displaced correlations of the height field in the d-1-dimensional KPZ equation. For one class of motile solids, I will show that the equal-time displacement correlations in the presence of quenched disorder are only as large as the equal-time displacement correlations of passive solids in the absence of quenched disorder, again attesting to the annealising effect of motion.