Search for: All records

Abstract We analytically study the emergence of instabilities and the consequent steady-state pattern formation in a stochastic partial differential equation (PDE) based, compartmental model of spatiotemporal epidemic spread. The model is characterized by: (1) strongly nonlinear forces representing the infection transmission mechanism and (2) random environmental forces represented by the Ornstein–Uhlenbeck (O–U) stochastic process which better approximates real-world uncertainties. Employing second-order perturbation analysis and computing the local Lyapunov exponent, we find the emergence of diffusion-induced instabilities and analyze the effects of O–U noise on these instabilities. We obtain a range of values of the diffusion coefficient and correlation time in parameter space that support the onset of instabilities. Notably, the stability and pattern formation results depend critically on the correlation time of the O–U stochastic process; specifically, we obtain lower values of steady-state infection density for higher correlation times. Also, for lower correlation times the results approach those obtained in the white noise case. The analytical results are valid for lower-order correlation times. In summary, the results provide insights into the onset of noise-induced, and Turing-type instabilities in a stochastic PDE epidemic model in the presence of strongly nonlinear deterministic infection forces and stochastic environmental forces represented by Ornstein–Uhlenbeck noise. 

Abstract Theoretical analysis of epidemic dynamics has attracted significant attention in the aftermath of the COVID–19 pandemic. In this article, we study dynamic instabilities in a spatiotemporal compartmental epidemic model represented by a stochastic system of coupled partial differential equations (SPDE). Saturation effects in infection spread–anchored in physical considerations–lead to strong nonlinearities in the SPDE. Our goal is to study the onset of dynamic, Turing–type instabilities, and the concomitant emergence of steady–state patterns under the interplay between three critical model parameters–the saturation parameter, the noise intensity, and the transmission rate. Employing a second–order perturbation analysis to investigate stability, we uncover both diffusion–driven and noise–induced instabilities and corresponding self–organized distinct patterns of infection spread in the steady state. We also analyze the effects of the saturation parameter and the transmission rate on the instabilities and the pattern formation. In summary, our results indicate that the nuanced interplay between the three parameters considered has a profound effect on the emergence of dynamical instabilities and therefore on pattern formation in the steady state. Moreover, due to the central role played by the Turing phenomenon in pattern formation in a variety of biological dynamic systems, the results are expected to have broader significance beyond epidemic dynamics. 

We present Jammed Interconnected Bilayer Emulsions (JIBEs) as a class of tissue-like materials with macroscopic scalability and rapid fabrication, comprising millions to billions of bilayer-separated aqueous compartments. These materials closely mimic the organizational structure and properties of biological tissues. Our rapid self-assembly method for producing JIBEs generates milliliter- to deciliter-scale volumes within minutes representing over 10,000-fold improvement in the fabrication speed of droplet-based artificial tissues compared to existing droplet-based methods, enabling the creation of a truly macroscopic material. The method is highly adaptable to a wide range of amphiphiles, including lipids and block-copolymers, providing flexibility in tailoring JIBEs for diverse applications. The jammed architecture of JIBEs imparts unique properties, such as direct 3D-printabilty into aqueous solutions or onto air-exposed surfaces. Their membrane-bound structure also allows functionalization with biological and artificial nanochannels, enabling the material to exhibit the specific properties of the incorporated channels. In this work, we demonstrate three key features of JIBEs using distinct ion channels: tunable conductance, selective transport, and memristance. Incorporating an E. coli outer membrane protein increased ionic conductance by approximately 4,400-fold compared to non-functionalized tissues. Introducing a peptide-based transporter produced ion-selective membranes capable of discriminating ammonium over sodium at a ratio greater than 15:1. Finally, incorporating a model voltage-gated pore enabled the construction of a massively networked memristive device. We propose that functionalizing JIBEs with additional membrane proteins or synthetic ion channels could unlock a broad range of applications, including separations, energy generation and storage, neuromorphic computing, tissue engineering, drug delivery, and soft robotics. 

Microfluidic experiments and numerical simulations are used to study dispersion in viscoelastic fluid flow through porous media, which we show can be understood through the Lagrangian stretching field that dynamically guides transport. 

Abstract Modifying the energy landscape of existing molecular emitters is an attractive challenge with favourable outcomes in chemistry and organic optoelectronic research. It has recently been explored through strong light–matter coupling studies where the organic emitters were placed in an optical cavity. Nonetheless, a debate revolves around whether the observed change in the material properties represents novel coupled system dynamics or the unmasking of pre-existing material properties induced by light–matter interactions. Here, for the first time, we examined the effect of strong coupling in polariton organic light-emitting diodes via time-resolved electroluminescence studies. We accompanied our experimental analysis with theoretical fits using a model of coupled rate equations accounting for all major mechanisms that can result in delayed electroluminescence in organic emitters. We found that in our devices the delayed electroluminescence was dominated by emission from trapped charges and this mechanism remained unmodified in the presence of strong coupling.