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In general, a stationary, periodic structure is also left behind the moving front. If the periodicity of the boundary kinetics agrees with the allowed range of the stable-periodic solutions, the pattern formed tends to persist. Otherwise, it evolves to a nearby energy-minimum either by peak-splitting, peak-decay, or by settling down to a spatially homogeneous state.Birds are known for their extremely acute sense of vision. The very peculiar structural distribution of five different types of cones in the retina underlies this exquisite ability to sample light. It was recently found that each cone population as well as their total population display a disordered pattern in which long-wavelength density fluctuations vanish [Jiao et al., Phys. Rev. E 89, 022721 (2014)PLEEE81539-375510.1103/PhysRevE.89.022721]. This property, known as hyperuniformity, is also present in perfect crystals. In situations like the avian retina in which both the global structure and that of each component display hyperuniformity, the system is said to be multihyperuniform. In this work, we aim at devising a minimal statistical-mechanical model that can reproduce the main features of the spatial distribution of photoreceptors in avian retina, namely the presence of disorder, multihyperuniformity, and local heterocoordination. This last feature is key to avoiding local clustering of the same type of photoreceptors, an undesirable feature for the efficient sampling of light. For this purpose, we formulate a minimal statistical-mechanical model that definitively exhibits the required structural properties an equimolar three-component mixture (one component to sample each primary color red, green, and blue) of nonadditive hard disks to which a long-range logarithmic repulsion is added between like particles. Interestingly, a Voronoi analysis of our idealized system of photoreceptors shows that the space-filling Voronoi polygons display a rather uniform area distribution, symmetrically centered around that of a regular lattice, a structural property also found in human retina. Disordered multihyperuniformity offers an alternative to generate photoreceptor patterns with minimal long-range concentration and density fluctuations. This is the key to overcoming the difficulties in devising an efficient visual system in which crystal-like order is absent.Here we show that, although quantum fidelity can truly identify two quantum phase transitions of a one-dimensional spin-1/2 quantum Ising model with competing nearest and next-nearest neighbor interactions in a transverse magnetic field, it may not be a suitable approach for analyzing its ground-state phase diagram.The subharmonic acoustic emission of a stable oscillating bubble inside a rigid tube is investigated by direct numerical simulation. The mechanisms of bubble-tube interaction on the acoustic wave emitted by the bubble are clarified. When the bubble is small compared to the tube diameter, a critical threshold for the pressure amplitude appears beyond the point which nonspherical effects become important and bubble breaks. For a finite tube diameter, the scattered wave by the bubble is shown to generate a plane wave where the intensity of the subharmonic component becomes maximum for an optimal distance between the bubble and the tube wall. This effect seems to be directly related to the appearance of local resonance phenomena and a bubble resonance shift where liquid's compressibility plays a major role.We disagree with the objections raised by Nemati et al. regarding the phase transitions reported in our paper, where we used the fidelity method. Contrary to their claims, our fidelity calculations do not depend on energy level crossing between excited states. We obtain the same results just by analyzing the second derivative of the ground-state energy with respect to the interaction energy coupling J_2.The supersoft elasticity and slow dynamics of isotropic-genesis polydomain nematic elastomers are investigated by loading- and strain-rate-controlled tests. Loading-controlled tests reveal the stretching-driven polydomain-to-monodomain (PM) transition under true equilibrium condition without viscoelastic (time) effect. The equilibrium PM transition is observed as a discontinuous dimensional change at a threshold stress with extremely small magnitude (σ_PM^∞≈1kPa). The mechanical work required for 80% elongation of the elastomer accompanying the PM transition is only 2% of that required in the high-temperature isotropic state, reflecting the supersoft elasticity effect. The dimensional growth rate (R) under constant loading becomes low as the imposed stress (σ_0) approaches σ_PM^∞. The dependency of the dimension on the reduced time (Rt) is, however, independent of σ_0. In the strain-rate (ɛ[over ̇]) controlled tests, the stress-stretch curves show a plateau region characteristic of the PM transition in a finite range of stretch, which is equivalent to the discontinuous stretch in the loading-controlled tests. The plateau stress σ_pl significantly decreases with decreasing ɛ[over ̇], whereas the σ_pl at the practically accessible low strain rate (on the order of 10^-4s^-1 ) is still significantly higher than σ_PM^∞. The dependency of σ_pl on ɛ[over ̇] is almost similar to the dependency of σ_0 on R in the loading-controlled tests. This similarity signifies that the two types of tests with different controlled stimuli are governed by the same dynamics of the local director.The fast-forward (FF) scheme proposed by Masuda and Nakamura [Proc. R. [https://www.selleckchem.com/products/MLN8237.html Alisertib] Soc. A 466, 1135 (2010)1364-502110.1098/rspa.2009.0446] in the context of conservative quantum dynamics can reproduce a quasistatic dynamics in an arbitrarily short time. We apply the FF scheme to the classical stochastic Carnot-like heat engine which is driven by a Brownian particle coupled with a time-dependent harmonic potential and working between the high- (T_h) and low- (T_c) temperature heat reservoirs. Concentrating on the underdamped case where momentum degree of freedom is included, we find the explicit expressions for the FF protocols necessary to accelerate both the isothermal and thermally adiabatic processes and obtain the reversible and irreversible works. The irreversible work is shown to consist of two terms with one proportional to and the other inversely proportional to the friction coefficient. The optimal value of efficiency η at the maximum power of this engine is found to be η^*=1/21+1/2(T_c/T_h)^1/2-5/4T_c/T_h+O[(T_c/T_h)^3/2] and η^*=1-(T_c/T_h)^1/2, respectively, in the cases of strong and weak dissipation.