Active beating modes of two clamped filaments driven by molecular motors

Biological cilia pump the surrounding fluid by asymmetric beating that is driven by dynein motors between sliding microtubule doublets. The complexity of biological cilia raises the question about minimal systems that can re-create similar patterns of motion. One such system consists of a pair of microtubules that are clamped at the proximal end. They interact through dynein motors that cover one of the filaments and pull against the other one. Here, we study theoretically the static shapes and the active dynamics of such a system. Using the theory of elastica, we analyse the shapes of two filaments of different lengths with clamped ends. Starting from equal lengths, we observe a transition similar to Euler buckling leading to a planar shape. When further increasing the length ratio, the system assumes a non-planar shape with spontaneously broken chiral symmetry after a secondary bifurcation and then transitions to planar again. The predicted curves agree with experimentally observed shapes of microtubule pairs. The dynamical system can have a stable fixed point, with either bent or straight filaments, or limit cycle oscillations. The latter match many properties of ciliary motility, demonstrating that a two-filament system can serve as a minimal actively beating model.

Self-Organized PT-Symmetry of Exciton-Polariton Condensate in a Double-Well Potential

We investigate the dynamics and stationary states of a semiconductor exciton–polariton condensate in a double-well potential. We find that upon the population build-up of the polaritons by above-threshold laser pumping, coherence relaxation due to the phase fluctuations in the polaritons drives the system into a stable fixed point corresponding to a self-organized PT-symmetric phase.

Parrondo's paradox for homoeomorphisms

We construct two planar homoeomorphisms $f$ and $g$ for which the origin is a globally asymptotically stable fixed point whereas for $f \circ g$ and $g \circ f$ the origin is a global repeller. Furthermore, the origin remains a global repeller for the iterated function system generated by $f$ and $g$ where each of the maps appears with a certain probability. This planar construction is also extended to any dimension $>$ 2 and proves for first time the appearance of the dynamical Parrondo's paradox in odd dimensions.

Controlling Hidden Dynamics and Multistability of a Class of Two-Dimensional Maps via Linear Augmentation

This paper reports the complex dynamics of a class of two-dimensional maps containing hidden attractors via linear augmentation. Firstly, the method of linear augmentation for continuous dynamical systems is generalized to discrete dynamical systems. Then three cases of a class of two-dimensional maps that exhibit hidden dynamics, the maps with no fixed point and the maps with one stable fixed point, are studied. Our numerical simulations show the effectiveness of the linear augmentation method. As the coupling strength of the controller increases or decreases, hidden attractor can be annihilated or altered to be self-excited, and multistability of the map can be controlled to being bistable or monostable.

The impact of travel and timing in eliminating COVID-19

While the spread of communicable diseases such as coronavirus disease 2019 (COVID-19) is often analyzed assuming a well-mixed population, more realistic models distinguish between transmission within and between geographic regions. A disease can be eliminated if the region-to-region reproductive number—i.e., the average number of other regions to which a single infected region will transmit the disease—is reduced to less than one. Here we show that this region-to-region reproductive number is proportional to the travel rate between regions and exponential in the length of the time-delay before region-level control measures are imposed. If, on average, infected regions (including those that become re-infected in the future) impose social distancing measures shortly after experiencing community transmission, the number of infected regions, and thus the number of regions in which such measures are required, will exponentially decrease over time. Elimination will in this case be a stable fixed point even after the social distancing measures have been lifted from most of the regions.

On the UV completion of the O(N) model in 6 − ϵ dimensions: a stable large-charge sector

We study large charge sectors in the O(N) model in 6 − ϵ dimensions. For 4 < d < 6, in perturbation theory, the quartic O(N) theory has a UV stable fixed point at large N . It was recently argued that this fixed point can be described in terms of an IR fixed point of a cubic O(N) model. By considering a double scaling limit of large charge and weak couplings, we compute two-point and all “extremal” higher-point correlation functions for large charge operators and find a precise equivalence between both pictures. Instanton instabilities are found to be exponentially suppressed at large charge. We also consider correlation function of U(1)-invariant meson operators in the O(2N) ⊃ U(1) × SU(N) theory, as a first step towards tests of (higher spin) AdS/CFT.

Reducing SARS-CoV-2 infectious spreading patterns by removing S and R compartments from SIR model equation

This research points to the asymptotic instability of SIR model and its variants to predict the behavior of SARS-CoV-2 infection spreading patterns over the population and time aspects. Mainly for the “S” and “R” terms of the equation, the predictive results fail due to confounding environment of variables that sustain the virus contagion within population complex network basis of analysis. While “S” and “R” are not homologous data of analysis, thus with improper topological metrics used in many researches, these terms leads to the asymptotic feature of “I” term as the most stable point of analysis to achieve proper predictive methods. Having in its basis of formulation the policies adopted by countries, “I” therefore presents a stable fixed point orientation in order to be used as a predictive analysis of nearby future patterns of SARS-CoV-2 infection. New metrics using a Weinbull approach for “I” are presented and fixed point orientation (sensitivity of the method) are demonstrated empirically by worldwide statistical data.

Dynamics of a Discrete Prey–Predator Model with Mixed Functional Response

In this paper, we propose a discrete Lotka–Volterra predator–prey model with Holling type-I and -II functional responses. We investigate the stability of the fixed points of this model. Also, we study the effects of changing each control parameter on the long-time behavior of the model. This model contains a lot of complex dynamical behaviors ranging from a stable fixed point to chaotic attractors. Finally, we illustrate the analytical results by some numerical simulations.