Condensed Matter Theory

Abstract:

We consider a binary mixture of chemically active particles that produce or consume solute molecules and that interact with each other through the long-range concentration fields they generate. We analytically calculate the effective phoretic mobility of these particles when the mixture is submitted to a constant, external concentration gradient, at leading order in the overall concentration. Relying on an analogy with the modeling of strong electrolytes, we show that the effective phoretic mobility decays with the square root of the concentration: our result is, therefore, a nonequilibrium counterpart to the celebrated Kohlrausch and Debye-Hückel-Onsager conductivity laws for electrolytes, which are extended here to particles with long-range nonreciprocal interactions. The effective mobility law we derive reveals the existence of a regime of maximal mobility and could find applications in the description of nanoscale transport phenomena in living cells.

Abstract:

We have studied the rich dynamics of a damped particle inside an external double-well potential under the influence of state-dependent time-delayed feedback. In certain regions of the parameter space, we observe multistability with the existence of two different attractors (limit cycle or strange attractor) with well separated mean Lyapunov energies forming a two-level system. Bifurcation analysis reveals that, as the effects of the time-delay feedback are enhanced, chaotic transitions emerge between the two wells of the double-well potential for the attractor corresponding to the fundamental energy level. By computing the residence time distributions and the scaling laws near the onset of chaotic transitions, we rationalize this apparent tunneling-like effect in terms of the crisis-induced intermittency phenomenon. Further, we investigate the first passage times in this regime and observe the appearance of a Cantor-like fractal set in the initial history space, a characteristic feature of hyperbolic chaotic scattering. The non-integer value of the uncertainty dimension indicates that the residence time inside each well is unpredictable. Finally, we demonstrate the robustness of this tunneling intermittency as a function of the memory parameter by calculating the largest Lyapunov exponent.

Abstract:

Biomorphs, Richard Dawkins’s iconic model of morphological evolution, are traditionally used to demonstrate the power of natural selection to generate biological order from random mutations. Here we show that biomorphs can also be used to illustrate how developmental bias shapes adaptive evolutionary outcomes. In particular, we find that biomorphs exhibit phenotype bias, a type of developmental bias where certain phenotypes can be many orders of magnitude more likely than others to appear through random mutations. Moreover, this bias exhibits a strong preference for simpler phenotypes with low descriptional complexity. Such bias towards simplicity is formalised by an information-theoretic principle that can be intuitively understood from a picture of evolution randomly searching in the space of algorithms. By using population genetics simulations, we demonstrate how moderately adaptive phenotypic variation that appears more frequently upon random mutations can fix at the expense of more highly adaptive biomorph phenotypes that are less frequent. This result, as well as many other patterns found in the structure of variation for the biomorphs, such as high mutational robustness and a positive correlation between phenotype evolvability and robustness, closely resemble findings in molecular genotype-phenotype maps. Many of these patterns can be explained with an analytic model based on constrained and unconstrained sections of the genome. We postulate that the phenotype bias towards simplicity and other patterns biomorphs share with molecular genotype-phenotype maps may hold more widely for developmental systems.