Peristalsis by actively generated waves of muscle contraction is one of the most fundamental ways of producing motion in living systems. We show that peristalsis can be modeled by a train of rectangular-shaped solitary waves of localized activity propagating through otherwise passive matter. Our analysis is based on the Fermi-Pasta-Ulam (FPU) type discrete model accounting for active stresses and we reveal the existence in this problem of a critical regime which we argue to be physiologically advantageous.We consider the extended Hubbard diamond chain with an arbitrary number of particles driven by chemical potential. The interaction between dimer diamond chain and nodal couplings is considered in the atomic limit (no hopping), whereas the dimer interaction includes the hopping term. We demonstrate that this model exhibits a pseudo-transition effect in the low-temperature regime. Here, we explore the pseudo-transition rigorously by analyzing several physical quantities. The internal energy and entropy depict sudden, although continuous, jumps which closely resembles discontinuous or first-order phase-transition. At the same time, the correlation length and specific heat exhibit astonishing strong sharp peaks quite similar to a second-order phase-transition. We associate the ascending and descending parts of the peak with power-law “pseudo-critical” exponents. We determine the pseudo-critical exponents in the temperature range where these peaks are developed, namely, ν=1 for the correlation length and α=3 for the specific heat. We also study the behavior of the electron density and isothermal compressibility around the pseudo-critical temperature.We consider the laser rate equations describing the evolution of a semiconductor laser subject to an optoelectronic feedback. We concentrate on the first Hopf bifurcation induced by a short delay and develop an asymptotic theory where the delayed variable is Taylor expanded. SB239063 purchase We determine a nearly vertical branch of strongly nonlinear oscillations and derive ordinary differential equations that capture the bifurcation properties of the original delay differential equations. An unexpected result is the need for Taylor expanding the delayed variable up to third order rather than first order. We discuss recent laser experiments where sustained oscillations have been clearly observed with a short-delayed feedback.We consider a one-dimensional model allowing analytical derivation of the effective interactions between two charged colloids. We evaluate exactly the partition function for an electroneutral salt-free suspension with dielectric jumps at the colloids’ position. We derive a contact relation with the pressure that shows there is like-charge attraction, whether or not the counterions are confined between the colloids. In contrast to the homogeneous dielectric case, there is the possibility for the colloids to attract despite the number of counterions (N) being even. The results are shown to recover the mean-field prediction in the limit N→∞.We study numerically a system of athermal, overdamped, frictionless spheres, as in a non-Brownian suspension, in two and three dimensions. Compressing the system isotropically at a fixed rate ε[over ̇], we investigate the critical behavior at the jamming transition. The finite compression rate introduces a control timescale, which allows one to probe the critical timescale associated with jamming. As was found previously for steady-state shear-driven jamming, we find for compression-driven jamming that pressure obeys a critical scaling relation as a function of packing fraction ϕ and compression rate ε[over ̇], and that the bulk viscosity p/ε[over ̇] diverges upon jamming. A scaling analysis determines the critical exponents associated with the compression-driven jamming transition. Our results suggest that stress-isotropic, compression-driven jamming may be in the same universality class as stress-anisotropic, shear-driven jamming.Elevators can be regarded as oscillators driven by the calls of passengers who arrive randomly. We study the dynamic behavior of elevators during the down peak period numerically and analytically. We assume that new passengers arrive at each floor according to a Poisson process and call the elevators to go down to the ground floor. We numerically examine how the round-trip time of a single elevator depends on the inflow rate of passengers at each floor and reproduce it by a self-consistent equation considering the combination of floors where the call occurs. By setting an order parameter, we show that the synchronization of two elevators occurs irrespective of final destination (whether the elevators did or did not go to the top floor). It indicates that the spontaneous ordering of elevators emerges from the Poisson noise. We also reproduce the round-trip time of two elevators by a self-consistent equation considering the interaction through the existence of passengers and the absence of volume exclusion. Those results suggest that such interaction stabilizes and characterizes the spontaneous ordering of elevators.Biochemical reactions in living cells often produce stochastic trajectories due to the fluctuations of the finite number of the macromolecular species present inside the cell. A significant number of computational and theoretical studies have previously investigated stochasticity in small regulatory networks to understand its origin and regulation. At the systems level regulatory networks have been determined to be hierarchical resembling social networks. In order to determine the stochasticity in networks with hierarchical architecture, here we computationally investigated intrinsic noise in an autocratic reaction network in which only the upstream regulators regulate the downstream regulators. We studied the effects of the qualitative and quantitative nature of regulatory interactions on the stochasticity in the network. We established an unconventional scaling of noise with average abundance in which the noise passes through a minimum indicating that the network can be noisy both in the low and high abundance regimes.