Navdeep Rana

We present the phenomenology of the one-dimensional nonreciprocal Cahn-Hilliard model for varying nonreciprocity ( α ) and different boundary conditions. At small α , a perturbed uniform state evolves to a defect-laden configuration that lacks global polar order. Defects are the sources and sinks of traveling waves. For a given α , defects with a unique wave number that increases monotonically with α are selected. A critical threshold α c marks the onset of a transition to states with finite global polar order. For periodic boundary conditions, above α c , the system shows traveling waves that are completely ordered. In contrast, traveling waves are incompatible with the Neumann and Dirichlet boundary conditions. Instead, for α ≳ α c , we find fluctuating domains that show intermittent polar order, and at large α , the system partitions into two domains with opposite polar order.

We present stochastic variants of the exponential time differencing schemes for stiff stochastic differential equations. We derive three explicit schemes that offer better stability compared to Euler-Maruyama and Milstein's method, and achieve strong convergence up to order O(h) in the time step h. We combine these schemes with a pseudo-spectral approach to outline efficient algorithms for simulating stochastic field theories with additive noise. To illustrate the effectiveness of this approach, we study several systems in and out of equilibrium, including Model A, Model B, the Kardar-Parisi-Zhang equation, and the Complex Ginzburg-Landau equation. We outline procedures for computing physical observables such as the critical exponents, correlation functions, and dynamic linear response, and provide our implementation as open source code.

The ordered state of microswimmers can be destroyed by an instability created by their swimming stresses. This leads to chaotic flows that resemble turbulence characterized by the presence of topological defects, a phenomenon known as active turbulence. We show that for pushers, the defect turbulent state transitions to a novel concentration-wave turbulent state reported earlier, where defects coexist along with concentration waves. This state emerges from an instability where fluctuations in the concentration of swimmers play a dominant role. Our study aims to provide a comprehensive understanding of the instabilities and turbulence in weakly inertial suspensions of pushers.

The collective chasing dynamics of nonreciprocally coupled densities leads to stable traveling waves which can be mapped to a model for emergent flocking. In this Letter, we couple the nonreciprocal Cahn-Hilliard model to a fluid to minimally describe scalar active mixtures in a suspension, with the aim to explore the stability of the waves, i.e., the emergent flock in the presence of self-generated fluid flows. We show that the emergent polarity is linearly unstable to perturbations for a specific sign of the active stress recalling instabilities of orientational order in a fluid. Using numerical simulations, we find, however, that nonreciprocity stabilizes the waves against the linear instability in a large region of the phase space.

Random nonreciprocal interactions between a large number of conserved densities are shown to enhance the stability of the system toward pattern formation. The enhanced stability is an exact result when the number of species approaches infinity and is confirmed numerically by simulations of the multispecies nonreciprocal Cahn-Hilliard model. Furthermore, the diversity in dynamical patterns increases with an increasing number of components, and novel steady states such as pulsating or spatiotemporally chaotic condensates are observed. Our results may help to unravel the mechanisms by which living systems self-organize via metabolism.

We present a computational study of the pairwise interactions between defects in the recently introduced non-reciprocal Cahn–Hilliard model. The evolution of a defect pair exhibits dependence upon their corresponding topological charges, initial separation, and the non-reciprocity coupling constant α. We find that the stability of isolated topologically neutral targets significantly affects the pairwise defect interactions. At large separations, defect interactions are small and a defect pair is stable. When positioned in relatively close proximity, a pair of oppositely charged spirals or targets merge to form a single target. At low α, like-charged spirals form rotating bound pairs, which are however torn apart by spontaneously formed targets at high α. Similar preference for charged or neutral solutions is also seen for a spiral target pair where the spiral dominates at low α, but concedes to the target at large α. Our work sheds light on the complex phenomenology of non-reciprocal active matter systems when their collective dynamics involves topological defects.

We discover an instability mechanism in suspensions of self-propelled particles that does not involve active stress. Instead, it is driven by a subtle interplay of inertia, swimmer motility, and concentration fluctuations, through a crucial time lag between the velocity and the concentration field. The resulting time-persistent state seen in our high-resolution numerical simulations consists of self-sustained waves of concentration and orientation, transiting from regular oscillations to wave turbulence. We analyze the statistical features of this active turbulence, including an intriguing connection to the Batchelor spectrum of passive scalars.