A thin-walled tube, e.g., a drinking straw, manifests an instability when bent by localizing the curvature change in a small region. This instability has been extensively studied since the seminal work of Brazier nearly a century ago. However, the sc
enario of pressurized tubes has received much less attention. Motivated by rod-shaped bacteria such as E. coli, whose cell walls are much thinner than their radius and are subject to a substantial internal pressure, we study, theoretically, how this instability is affected by this internal pressure. In the parameter range relevant to the bacteria, we find that the internal pressure significantly postpones the onset of the instability, while the bending stiffness of the cell wall has almost no influence. This study suggests a new method to infer turgor pressure in rod-shaped bacteria from bending experiments.
We study the dynamics of flow-networks in porous media using a pore-network model. First, we consider a class of erosion dynamics assuming a constitutive law depending on flow rate, local velocities, or shear stress at the walls. We show that dependi
ng on the erosion law, the flow may become uniform and homogenized or become unstable and develop channels. By defining an order parameter capturing these different behaviors we show that a phase transition occurs depending on the erosion dynamics. Using a simple model, we identify quantitative criteria to distinguish these regimes and correctly predict the fate of the network, and discuss the experimental relevance of our result.
Scientists have observed and studied diffusive waves in contexts as disparate as population genetics and cell signaling. Often, these waves are propagated by discrete entities or agents, such as individual cells in the case of cell signaling. For a b
road class of diffusive waves, we characterize the transition between the collective propagation of diffusive waves -- in which the wave speed is well-described by continuum theory -- and the propagation of diffusive waves by individual agents. We show that this transition depends heavily on the dimensionality of the system in which the wave propagates and that disordered systems yield dynamics largely consistent with lattice systems. In some system dimensionalities, the intuition that closely packed sources more accurately mimic a continuum can be grossly violated.
Many unicellular organisms allocate their key proteins asymmetrically between the mother and daughter cells, especially in a stressed environment. A recent theoretical model is able to predict when the asymmetry in segregation of key proteins enhance
s the population fitness, extrapolating the solution at two limits where the segregation is perfectly asymmetric (asymmetry $a$ = 1) and when the asymmetry is small ($0 leq a ll 1$). We generalize the model by introducing stochasticity and use a transport equation to obtain a self-consistent equation for the population growth rate and the distribution of the amount of key proteins. We provide two ways of solving the self-consistent equation: numerically by updating the solution for the self-consistent equation iteratively and analytically by expanding moments of the distribution. With these more powerful tools, we can extend the previous model by Lin et al. to include stochasticity to the segregation asymmetry. We show the stochastic model is equivalent to the deterministic one with a modified effective asymmetry parameter ($a_{rm eff}$). We discuss the biological implication of our models and compare with other theoretical models.
Homeostasis of protein concentrations in cells is crucial for their proper functioning, and this requires concentrations (at their steady-state levels) to be stable to fluctuations. Since gene expression is regulated by proteins such as transcription
factors (TFs), the full set of proteins within the cell constitutes a large system of interacting components. Here, we explore factors affecting the stability of this system by coupling the dynamics of mRNAs and protein concentrations in a growing cell. We find that it is possible for protein concentrations to become unstable if the regulation strengths or system size becomes too large, and that other global structural features of the networks can dramatically enhance the stability of the system. In particular, given the same number of proteins, TFs, number of interactions, and regulation strengths, a network that resembles a bipartite graph with a lower fraction of interactions that target TFs has a higher chance of being stable. By scrambling the $textit{E. coli.}$ transcription network, we find that the randomized network with the same number of regulatory interactions is much more likely to be unstable than the real network. These findings suggest that constraints imposed by system stability could have played a role in shaping the existing regulatory network during the evolutionary process. We also find that contrary to what one might expect from random matrix theory and what has been argued in the literature, the degradation rate of mRNA does not affect whether the system is stable.
In exponentially proliferating populations of microbes, the population typically doubles at a rate less than the average doubling time of a single-cell due to variability at the single-cell level. It is known that the distribution of generation times
obtained from a single lineage is, in general, insufficient to determine a populations growth rate. Is there an explicit relationship between observables obtained from a single lineage and the population growth rate? We show that a populations growth rate can be represented in terms of averages over isolated lineages. This lineage representation is related to a large deviation principle that is a generic feature of exponentially proliferating populations. Due to the large deviation structure of growing populations, the number of lineages needed to obtain an accurate estimate of the growth rate depends exponentially on the duration of the lineages, leading to a non-monotonic convergence of the estimate, which we verify in both synthetic and experimental data sets.
We study heat conduction mediated by longitudinal phonons in one dimensional disordered harmonic chains. Using scaling properties of the phonon density of states and localization in disordered systems, we find non-trivial scaling of the thermal condu
ctance with the system size. Our findings are corroborated by extensive numerical analysis. We show that a system with strong disorder, characterized by a `heavy-tailed probability distribution, and with large impedance mismatch between the bath and the system satisfies Fouriers law. We identify a dimensionless scaling parameter, related to the temperature scale and the localization length of the phonons, through which the thermal conductance for different models of disorder and different temperatures follows a universal behavior.
The Generalized Central Limit Theorem is a remarkable generalization of the Central Limit Theorem, showing that the sum of a large number of independent, identically-distributed (i.i.d) random variables with infinite variance may converge under appro
priate scaling to a distribution belonging to a special family known as Levy stable distributions. Similarly, the maximum of i.i.d. variables may converge to a distribution belonging to one of three universality classes (Gumbel, Weibull and Frechet). Here, we rederive these known results following a mathematically non-rigorous yet highly transparent renormalization-group-like approach that captures both of these universal results following a nearly identical procedure.
We study the spread of a quantum-mechanical wavepacket in a noisy environment, modeled using a tight-binding Hamiltonian. Despite the coherent dynamics, the fluctuating environment may give rise to diffusive behavior. When correlations between differ
ent level-crossing events can be neglected, we use the solution of the Landau-Zener problem to find how the diffusion constant depends on the noise. We also show that when an electric field or external disordered potential is applied to the system, the diffusion constant is suppressed with no drift term arising. The results are relevant to various quantum systems, including exciton diffusion in photosynthesis and electronic transport in solid-state physics.
