Table of contents

We show that non-Hermitian biorthogonal many-body phase transitions can be characterized by the enhanced decay of Loschmidt echo. The quantum criticality is numerically investigated in a non-Hermitian transverse field Ising model by performing the finite-size dynamical scaling of Loschmidt echo. We determine the equilibrium correlation length critical exponents that are consistent with previous results from the exact diagonalization. More importantly, we introduce a simple method to detect quantum phase transitions with the short-time average of rate function motivated by the critically enhanced decay behavior of Loschmidt echo. Our studies show how to detect equilibrium many-body phase transitions with biorthogonal Loschmidt echo that can be observed in future experiments via quantum dynamics after a quench.

How to simulate the true pedestrians' psychology who face an emergency is an important issue that decides evacuation efficiency. Pedestrian psychology during the evacuation process is complex, abstract and difficult to quantify directly. Based on the typical social force model, this paper improves the pedestrian direction selection procedure and introduces a "weight factor" to adjust the degree of contribution of "the density factor" and "the distance factor" to pedestrians' choice of moving direction. In this model, pedestrians can not only roughly estimate the distance between themselves and each exit, but also judge the degree of crowd gathering near each exit by virtue of the electronic display screen in the center of the cross-shaped aisle. Simulation results show that, for a configuration with multi-rooms and multi-exits, when the pedestrian number reaches a certain level, only considering the distance factor will lead to uneven distribution of the crowd, therefore inducing obvious congestion. On the other hand, concentrating too much on the density factor makes pedestrians hesitate to choose the appropriate exit. In conclusion, we should comprehensively consider the impact of the "density factor" and the "distance factor", which helps to provide feasible evacuation strategies for emergency situations and to improve both evacuation efficiency and exit utilization.

Directed polymers on (1+1)-dimensional lattices coupled to a heat bath at temperature T are studied numerically for three new ensembles of the site disorder, plus a standard random ensemble. In particular correlations of the disorder as well as fractal patterning are considered for the new ensembles. Configurations are directly sampled in perfect thermal equilibrium for very large system sizes with up to $N=L^2= 32768 \times 32768 \approx 10^{9}$ sites. The phase-space structure is studied via the distribution of overlaps and hierarchical clustering of configurations. Two ensembles show a simple behavior basically like a ferromagnet. The other two ensembles exhibit indications for complex behavior strongly reminiscent of multiple replica-symmetry breaking (RSB). Also results for the ultrametricity of the phase space are presented. In total, the present model ensembles offer convenient numerical accesses to comprehensively studying complex behavior.

Many networks such as critical infrastructures exhibit a modular structure. One approach to increase the robustness of these systems is to reinforce a fraction of the nodes so that the reinforced nodes provide additional needed sources for themselves as well as for their nearby neighborhood. Since reinforcing a node can be expensive, the efficiency of the decentralization process by reinforced nodes is vital. Here we develop a model which combines both modularity and reinforced nodes and study the robustness of the system. Using tools from percolation theory, we derive an analytical solution for the robustness resulting from any partition of reinforced nodes; between nodes that have links that connect between modules and nodes which have links only within modules. We find that near the critical percolation threshold the robustness is greatly affected by the partition. In particular, we find a partition of reinforced nodes that yields optimal robustness and we show that the optimal partition remains constant for high average degrees.

Lake ecosystems exhibit nonlinear responses and may undergo catastrophic shifts to opposite states from which recovery is difficult. Recent theoretical and experimental developments have revealed that characterizing the resilience of ecosystems can provide a way to anticipate critical transitions. In this letter, we present a novel and practical approach that measures the resilience, i.e., the relaxation time as an indicator of a critical transition to a eutrophic lake state. Furthermore, the possible mechanisms underlying these findings are explored via stochastic resonance, namely, the signal-to-noise ratio as a function of the system parameter shows a maximum value when the noise intensity is fixed. The results show that relaxation time is an excellent indicator, and stochastic resonance occurs near a critical threshold. Our results offer a new perspective to anticipate critical transitions in ecosystems.

It is well known that the outbreak of infectious diseases is affected by the diffusion of the infected. However, the diffusion network is seldom considered in the network-organized SIR model. In this work, we investigate the effect of the maximum eigenvalue on Turing instability and show the role of network parameters (the network connection rate, the network's infection, etc.) on the outbreak of infectious diseases. Meanwhile, stability of network-organized SIR is given by using the maximum eigenvalue of the network matrix which is proportional to the network connection rate and the networks infection rate. The bridge between the two rates and Turing instability was also revealed which can explain the spread mechanism of infectious diseases. In the end, some measures to mitigate the spread of infectious diseases are proposed and the feasible strategies for prevention and control can be provided in our paper, the data from COVID-19 validated the above results.

Remarkably, we experimentally evidenced normal field instability-driven reversible transition from ferrofluid droplet to spikes, when a sessile ferrofluid drop is exposed to a varying magnetic field gradient due to an approaching magnet, without flipping its direction of motion. We find the reversible transition is attributed to the critical magnetization of the ferrofluid and a characteristic wavelength that control normal-field instability. We extend the theory of magnetic instability by including non-uniformity in the magnetic field in all directions to predict the critical condition for transition, which is in good agreement with experiments. The spacing between spikes and spike height, and the number of spikes measured from experiments are in agreement with existing theory.

Nano-patterned substrates offer possibilities for controlling the motion of fluids without external energy supply in novel technologies in microfluidics, coatings, etc. Here, we report on the rugotaxial motion of droplets on wrinkled substrates with gradient in the wavelength of the wrinkles by exploring a broad range of parameters, such as amplitude of the wrinkles, substrate wettability, droplet size and wavelength gradient. Adopting a theoretical and molecular dynamics approach, we determine the Cassie-Baxter and Wenzel states of the droplets, investigate the efficiency of rugotaxis as a function of different parameters, and discuss additional effects, such as pinning. We find that shallow wrinkles characterised by small wavelength gradients, and moderate adhesion of the droplet to the substrate favour the rugotaxis motion with growing droplet size, when pinning is avoided. We also find that the driving force in rugotaxis is the gain in interfacial energy between the droplet and the substrate as the droplet enters regions of denser wrinkles (smaller wavelengths of the wrinkles).

The effects of particle size on the agglomeration and spatial distribution of dust particles in unitary and binary dusty systems were experimentally studied. The agglomeration process of dust particles was characterized by direct micrograph image and the evolution of scattered light as time. The fractal dimension and average particle area in the steady state of the dust system changing as height were used to show the spatial distribution of dust particles. It shows that the binary system formed by dust particles with different sizes has more obvious agglomeration and the distribution range of particle size is wider.

By using both ray and wave optics, we show that a simple device which consists of a film of hyperbolic metamaterial on the surface of a catenoid can be used to trap light. From the study of the trajectories, we observe a tendency for the light rays to wrap, and eventually be trapped, around the neck of the device. The wave equation appears to have an effective attractive potential, and their solutions confirm the bound states suggested by the trajectories. The relevant equations are solved numerically using neural networks.

We study the humidity dependency of the adhesion (or pull-off) force between granite fragments and a silica glass plate. The particles bind to the glass plate via capillary bridges. The granite particles are produced by cracking a granite stone in a mortar and have self-affine fractal surface roughness. Theory shows that the surface roughness results in an interaction force between stone fragments and the glass plate which is independent of the size of the particles, in contrast to the linear size dependency expected for particles with smooth surfaces. We measure the adhesion force by depositing the granite particle powder, with particle sizes ranging from mm to μm (or less), on the glass plate. By turning the glass plate upside-down all particles with a gravitational force larger than the adhesion force will fall off the glass plate. By studying the size (and hence the mass) of biggest still attached particles we obtained the adhesion force, which is found to be in good agreement with the theory prediction.

Fatigue caused by cyclic bending of a piece of material, resulting in its mechanical failure, is a phenomenon that had been studied for ages by engineers and physicists alike. In this letter we study such fatigue in a strip of an athermal amorphous solid. On the basis of atomistic simulations we conclude that the crucial quantity to focus on is the accumulated damage. Although this quantity exhibits large sample-to-sample fluctuations, its dependence on the loading determines the statistics of the number of cycles to failure. Thus we can provide a scaling theory for the Wöhler plots of mean number of cycles for failure as a function of the loading amplitude.

Zr-Ti-X ternary alloys are striking materials of the latest technology because of their excellent and desired mechanical aspects. Therefore, electronic, elastic, mechanical and anisotropic properties of ZrTiX₄ (X = Cr, Mo, W) alloys were probed in this work for the first time via density functional theory (DFT) calculations. The computed electronic band structures disclose the metallic nature of all alloys. Further, the calculated elastic stiffness constants and linking mechanical data of all alloys demonstrate mechanical stability. All surveyed alloys display ductile mechanical character where ZrTiCr₄ and ZrTiMo₄ alloys are found to be more ductile than ZrTiW₄. On the other hand, ZrTiW₄ was determined to be approximately two times harder than the ZrTiCr₄ and ZrTiMo₄ alloys with a Vickers Hardness value of 8.47 GPa. Both numerical and three-dimensional (3D) analyses reveal the presence of elastic anisotropy in ZrTiX₄ (X = Cr, Mo, W) alloys.

In this letter, a two-dimensional (2D) gravity-scalar model is studied. This model supports interesting double-kink solutions, and the corresponding metric solutions can be derived analytically. Depending on a tunable parameter c, the metric can be symmetric or asymmetric. The Schrödinger-like equation for normal modes of the physical linear perturbation is derived. As c varies, the effective potential can have one or two singular barriers. If c is larger than a critical value, the zero mode will be normalizable, despite of the appearance of a strong repulsive singularity. The double-kink solution is always stable against linear perturbations.

It is claimed that, using the Boltzmann-Gibbs statistical mechanics together with the Bekenstein-Hawking area entropy law, it is possible to determine a value for the Barbero-Immirzi parameter, $\gamma=\ln (2)/(\pi \sqrt{3})$. In this letter, we have shown that if we use Barrow's entropy rather than Bekenstein-Hawking's area entropy law then the Barbero-Immirzi parameter will depend on the Δ parameter. As a consequence, the loop quantum gravity area element will also depend on the Δ parameter.