Mehran Kardar

Classical ecological models predict that diverse communities should be unstable, presenting a central challenge to explaining the stable biodiversity seen in nature. We revisit this long-standing problem by extending the generalized Lotka–Volterra model to include both spatial structure and environmental fluctuations across space and time. We find that neither space nor environmental noise alone can resolve the tension between diversity and stability, but that together they permit arbitrarily many species to stably coexist in a sufficiently large system, despite strongly disordered competitive interactions. We analytically characterize the noise-induced transition to coexistence, showing that spatiotemporal noise drives power-law abundance fluctuations, leading to an anomalous scaling of moments known empirically as Taylor’s law. At the metacommunity level, this manifests as an emergent sublinear self-inhibition that stabilizes diversity and renders the interaction disorder irrelevant in the high-diversity limit. Spatiotemporal noise thus provides a resolution to the diversity-stability paradox and a generic mechanism by which complex communities can persist.

We describe a contactless heat engine in which quantum and thermal electromagnetic fluctuations act as the working medium. The setup consists of two concentric cylinders held at different temperatures. The inner cylinder stably levitates within the outer one due to repulsive nonequilibrium Casimir forces. The chirality of the setup is broken by using nonreciprocal dielectric materials, akin to application of a magnetic field along the common cylinder axis. Using Rytov fluctuational electrodynamics, we show that heat transfer and torque can be expressed in terms of an angular-momentum-resolved heat flux density, Φn(ω): each exchanged photon carries energy ℏω and angular momentum ℏn. In reciprocal media, contributions from modes n and −n cancel and there is no net torque; nonreciprocity breaks this symmetry and powers rotation of the inner cylinder. Even in the absence of contact, electromagnetic fluctuations produce a frictional torque opposing rotation that we compute. This enables computation of characteristic steady state rotations, and estimation of the engine efficiency (which remains bounded by the Carnot limit). The cylindrical setup provides a natural realization of fluctuation-induced angular-momentum transfer and a possible route toward nanoscale contactless engines.

The formation of condensates by the Linker for the Activation of T cells (LAT) is a key signal gating and amplification step in the T-cell receptor signaling pathway. LAT condensation is challenging to study in vivo and is therefore often investigated using reconstitution experiments. While these experiments recapitulate key aspects of LAT condensation, they also exhibit some puzzling features. Here, we describe the mechanisms underlying these observations using two complementary models. First, we employ a Smoluchowski aggregation model to show that the delay time before condensation is observed arises from a low effective binding probability between LAT monomers. Second, we propose a field-theoretic model that reproduces all condensate morphologies observed in experiments, showing that they can arise from common underlying dynamics, modulated by variations in experimental conditions. This result unifies different experimental observations reported previously. While this article addresses open questions regarding the formation of LAT condensates, our results also provide a common framework for understanding the condensation of other multivalent membrane proteins such as EGFR, FGFR2, and nephrin.

We numerically revisit the transfer-matrix formulation of directed polymers in random media and show that a common finite-dimensional framework organizes the canonical one-point fluctuation laws in ( 1 + 1 ) dimensions. For a fixed realization of the bulk disorder, full-space partition functions are obtained from the same time-ordered product W ( t ) through endpoint contractions or a Brownian-weighted initial vector, while the half-space construction modifies only the transfer rule at the absorbing boundary. These choices yield distributions consistent with the standard KPZ subclasses: Tracy-Widom GUE for point-to-point geometry, Tracy-Widom GOE for point-to-line geometry, Tracy-Widom GSE for half-space point-to-point geometry, and Baik-Rains for the stationary line-to-point construction. In all four cases, the free-energy fluctuations grow as t 1 / 3 , and the low-order cumulants approach the corresponding universal benchmarks. The matrix-product formulation also provides access to intrinsic spectral observables. For the leading eigenvalue λ 1 ( t ) , the fluctuations of ln λ 1 ( t ) exhibit an intermediate t 1 / 3 regime, while the standardized distribution remains distinct from the canonical benchmark laws over the studied time range.

When competing species grow into new territory, the population is dominated by descendants of successful ancestors at the expansion front. Successful ancestry depends on both the reproductive advantage (fitness), as well as ability and opportunity to colonize new domains. We present a model that integrates both elements by coupling the classic description of one-dimensional competition (Fisher equation) to the minimal model of front shape (KPZ equation). Macroscopic manifestations of these equations are distinct growth morphologies controlled by expansion rates, competitive abilities, or spatial anisotropy. In some cases the ability to expand in space may overcome reproductive advantage in colonizing new territory. When new traits appear with accumulating mutations, we find that variations in fitness in range expansion may be described by the Tracy–Widom distribution.

In complex ecological communities, species may self-organize into clusters or clumps where highly similar species can coexist. The emergence of such species clusters can be captured by the interplay between neutral and niche theories. Based on the generalized Lotka-Volterra model of competition, we propose a minimal model for ecological communities in which the steady states contain self-organized clusters. In this model, species compete only with their neighbors in niche space through a common interaction strength. Unlike many previous theories, this model does not rely on random heterogeneity in interactions. Even in this minimal model where only the common interaction strength is varied, we find an exponentially large set of states that exhibit a rich variety of cluster patterns with different sizes and combinations. There are sharp phase transitions into the formation of clusters. There are also multiple phase transitions between different sets of possible cluster patterns, many of which accumulate near a small number of critical points. We analyze this phase structure using both numerical and analytical methods. In addition, the special case with only nearest-neighbor interactions is exactly solvable using the method of transfer matrices from statistical mechanics. We analyze the critical behavior of these systems.

Competition during range expansions is of great interest from both practical and theoretical viewpoints. Experimentally, range expansions are often studied in homogeneous Petri dishes, which lack spatial anisotropy that might be present in realistic populations. Here, we analyze a model of anisotropic growth, based on coupled Kardar-Parisi-Zhang and Fisher-Kolmogorov-Petrovsky-Piskunov equations that describe surface growth and lateral competition. The anisotropy is encoded in how strongly genetic boundaries between strains are moved as a result of the expansion front morphology. We completely characterize spatial patterns and invasion velocities in this generalized model. In particular, we find that strong anisotropy results in a distinct morphology of spatial invasion with a kink in the displaced strain ahead of the boundary between the strains. This morphology of the outcompeted strain is similar to a shock wave and serves as a signature of anisotropic growth. We confirm these predictions with a commonly employed reaction-diffusion model of anisotropic growth.

The formation of condensates by the Linker for the Activation of T-cells (LAT) is a key signal gating and amplification step in the T-cell receptor signaling pathway. LAT condensation is challenging to study in-vivo and is therefore often investigated using reconstitution experiments. While these experiments recapitulate key aspects of LAT condensation, they also exhibit some puzzling features. Here, we describe the mechanisms underlying these observations using two complementary models. First, we employ a Smoluchowski aggregation model to show that the delay time before condensation is observed arises from a low effective binding probability between LAT monomers. Second, we propose a field-theoretic model that reproduces all condensate morphologies observed in experiments, showing that they can arise from common underlying dynamics modulated by variations in experimental conditions. This result unifies different experimental observations reported previously. While this article addresses open questions regarding the formation of LAT condensates, our results also provide a common framework for understanding condensation of other multivalent membrane proteins such as EGFR, FGFR2, and nephrin.

We show that cancellation of internal forces together with spatially uncorrelated noise generically enforces a universal 1 / s scaling of the center-of-mass (COM) diffusivity for polymer segments of contour length s , independent of model details. Within an active generalized Rouse-Langevin (A-GRLE) framework for fractal polymers in a viscoelastic bath with weak activity, we derive closed-form links between segment COM motion and the short-time behavior of two-point fluctuations. The same COM law predicts transient s − 3 tangent-tangent correlations along the contour following a temperature quench. Reanalyzing recent two-locus chromatin tracking, we extract a dynamic COM exponent ξ = 0.77 ± 0.16 , suggesting topological constraints. These results identify model-independent signatures of collective polymer dynamics and clarify that the observed Rouse-like scaling of chromatin loci reflects transient, unentangled dynamics with an inevitable crossover to an entangled regime at longer times.