Mobility edges and localization characteristics in one-dimensional quasiperiodic quantum walk

We construct a one-dimensional quasiperiodic quantum walk to investigate the localization–delocalization transition.The inverse participation ratio and Lyapunov exponent are employed as two indexes to determine the mobility edge, a critical energy to distinguish the energy regions of extended and localized states. The analytical solution of mobility edge is obtained by the Lyapunov exponents in global theory, and the consistency of the two indexes is confirmed. We further study the dynamic characteristics of the quantum walk and show that the probabilities are localized to some specific lattice sites with time evolution. This phenomenon is explained by the effective potential of the Hamiltonian which corresponds to the phase in the coin operator of the quantum walk.

Mobility edges in one-dimensional finite-sized models with large quasi-periodic disorders

We study the one-dimensional tight-binding model with quasi-periodic disorders,where the quasi-period is tuned to be large compared to the system size.It is found that this type of model with large quasi-periodic disorders can also support the mobility edges,which is very similar to the models with slowly varying quasi-periodic disorders.The energy-matching method is employed to determine the locations of mobility edges in both types of models.These results of mobility edges are verified by numerical calculations in various examples.We also provide qualitative arguments to support the fact that large quasi-periodic disorders will lead to the existence of mobility edges.

Sensitivity of forest phenology in China varies with proximity to forest edges

Background:Shifts in forest phenological events serve as strong indicators of climate change.However,the sensitivity of phenology events to climate change in relation to forest origins has received limited attention.Moreover,it is unknown whether forest phenology changes with the proximity to forest edge.Methods:This study examined the green-up dates,dormancy dates,time-integrated NDVI(LiNDVI,a measure of vegetation productivity in growing season),and their sensitivities to climatic factors along the gradients of distance(i.e.proximity)to forest edge(0–2 km)in China's natural forests(NF)and planted forests(PF).For the analysis,field-surveyed data were integrated with Moderate Resolution Imaging Spectroradiometer(MODIS)NDVI from 2000 to 2022.Results:Our results reveal that PF had earlier green-up dates,later dormancy dates,and higher LiNDVI than NF.However,green-up sensitivities to temperature were higher at the edges of NF,whereas no such pattern was observed in PF.Conversely,the sensitivity of dormancy dates remains relatively stable from the inner to the edge of both NF and PF,except for a quadratic change in dormancy date sensitivity to precipitation found in NF.Additionally,we found that the green-up sensitivity to temperature increased with decreasing proximity to edge in NF evergreen forests,while it showed the opposite trend in PF evergreen forests.Furthermore,we observed that the precipitation impact on green-up dates shifts from postponing to advancing from the inner to the edge of NF,whereas precipitation dominantly postpones PF's green-up dates regardless of the proximity to edge.The LiNDVI exhibits higher sensitivity to precipitation at the edge areas,a phenomenon observed in NF but not in PF.Conclusions:These results suggest that the responses of forests to climate change vary with the distance to the edge.With increasing edge forests,which results from fragmentation caused by global changes,we anticipate that desynchronized phenological events along the distance to the edge could alter biogeochemical cycles and reshape ecosystem services such as energy flows,pollination duration,and the tourism industry.Therefore,we advocate for further investigations of edge effects to improve ecosystem modelling,enhance forest stability,and promote sustainable tourism.

Mobility edges generated by the non-Hermitian flatband lattice

We study the cross-stitch flatband lattice subject to the quasiperiodic complex potential exp(ix). We firstly identify the exact expression of quadratic mobility edges through analytical calculation, then verify the theoretical predictions by numerically calculating the inverse participation ratio. Further more, we study the relationship between the real–complex spectrum transition and the localization–delocalization transition, and demonstrate that mobility edges in this non-Hermitian model not only separate localized from extended states but also indicate the coexistence of complex and real spectrum.

General mapping of one-dimensional non-Hermitian mosaic models to non-mosaic counterparts:Mobility edges and Lyapunov exponents

We establish a general mapping from one-dimensional non-Hermitian mosaic models to their non-mosaic counterparts.This mapping can give rise to mobility edges and even Lyapunov exponents in the mosaic models if critical points of localization or Lyapunov exponents of localized states in the corresponding non-mosaic models have already been analytically solved.To demonstrate the validity of this mapping,we apply it to two non-Hermitian localization models:an Aubry-Andre-like model with nonreciprocal hopping and complex quasiperiodic potentials,and the Ganeshan-Pixley-Das Sarma model with nonreciprocal hopping.We successfully obtain the mobility edges and Lyapunov exponents in their mosaic models.This general mapping may catalyze further studies on mobility edges,Lyapunov exponents,and other significant quantities pertaining to localization in non-Hermitian mosaic models.

THE METHOD OF THE RECIPROCAL THEOREM OF FORCED VIBRATION FOR THE ELASTIC THIN RECTANGULAR PLATES(Ⅰ)—RECTANGULAR PLATES WITH FOUR CLAMPED EDGES AND WITH THREE CLAMPED EDGES

In this paper the method of the reciprocal theorem (MRT) is extended to solve the steady state responses of rectangular plater under harmonic disturbing forces. A series of the closed solutions of rectangular plates with various boundary conditions are given and the tables and figures which have practical value are provided.MRT is a simple, convenient and general method for solving the steady stale responses of rectangular plates under various harmonic disturbing forces.The paper contains three parts: (I) rectangular plates with four damped edges and with three clamped edges; (II) rectangular plates with two adjacent clamped edges; (III) cantilever plates.We arc going to publish them one after another.

Aggregation of ferromagnetic and paramagnetic atoms at edges of graphenes and graphite

In this work we report that when ferromagnetic metals （Fe, Co and Ni） are thermMly evaporated onto n-layer graphenes and graphite, a metal nanowire and adjacent nanogaps can be found along the edges regardless of its zigzag or armchair structure. Similar features can also be observed for paramagnetic metals, such as Mn, Al and Pd. Meanwhile, metal nanowires and adjacent nanogaps cannot be found for diamagnetic metals （Au and Ag）. An external magnetic field during the evaporation of metals can make these unique features disappear for ferromagnetic and paramagnetic metal; and the morphologies of diamagnetic metal do not change after the application of an external magnetic field. We discuss the possible reasons for these novel and interesting results, which include possible one-dimensional ferromagnets along the edge and edge-related binding energy.

Element-free Galerkin method for free vibration of rectangular plates with interior elastic point supports and elastically restrained edges

The element-free Galerkin method is proposed to solve free vibration of rectangular plates with finite interior elastic point supports and elastically restrained edges.Based on the extended Hamilton＇s principle for the elastic dynamics system,the dimensionless equations of motion of rectangular plates with finite interior elastic point supports and the edge elastically restrained are established using the element-free Galerkin method.Through numerical calculation,curves of the natural frequency of thin plates with three edges simply supported and one edge elastically restrained,and three edges clamped and the other edge elastically restrained versus the spring constant,locations of elastic point support and the elastic stiffness of edge elastically restrained are obtained.Effects of elastic point supports and edge elastically restrained on the free vibration characteristics of the thin plates are analyzed.

Evolutionary dynamics analysis of complex network with fusion nodes and overlap edges

Multiple complex networks, each with different properties and mutually fused, have the problems that the evolving process is time varying and non-equilibrium, network structures are layered and interlacing, and evolving characteristics are difficult to be measured. On that account, a dynamic evolving model of complex network with fusion nodes and overlap edges（CNFNOEs） is proposed. Firstly, we define some related concepts of CNFNOEs, and analyze the conversion process of fusion relationship and hierarchy relationship. According to the property difference of various nodes and edges, fusion nodes and overlap edges are subsequently split, and then the CNFNOEs is transformed to interlacing layered complex networks（ILCN）. Secondly,the node degree saturation and attraction factors are defined. On that basis, the evolution algorithm and the local world evolution model for ILCN are put forward. Moreover, four typical situations of nodes evolution are discussed, and the degree distribution law during evolution is analyzed by means of the mean field method.Numerical simulation results show that nodes unreached degree saturation follow the exponential distribution with an error of no more than 6%; nodes reached degree saturation follow the distribution of their connection capacities with an error of no more than 3%; network weaving coefficients have a positive correlation with the highest probability of new node and initial number of connected edges. The results have verified the feasibility and effectiveness of the model, which provides a new idea and method for exploring CNFNOE＇s evolving process and law. Also, the model has good application prospects in structure and dynamics research of transportation network, communication network, social contact network,etc.

The edges and terrace effect of Ag particles on optical resonance absorption property

Alternative Ag and Si02 multilayers are prepared by using radio frequency magnetron sputtering. The Ag particles are found to diffuse toward and mostly accumulate near the surface of the Ag-SiO2 composite film via a rapid thermal treatment. Different shapes of the Ag particles are obtained by changing the thickness of each Ag and SiO2 layer. The response absorption property of the Ag composite film is also investigated. We relate the resonance absorption to the surface level and the Fermi level. To induce the obvious resonance absorption in an Ag composite film, it is necessary to maintain special shapes with sharp edges and wide terraces and to maintain the particle sizes ranging from 0 nm to

A Simple Empirical Formula for Predicting the Ultimate Strength of Ship Plates with Elastically Restrained Edges in Axial Compression

An investigation is conducted on the static ultimate limit state assessment of ship hull plates with elastically restrained edges subjected to axial compression.Both material and geometric non-linearities were considered in finite element(FE)analysis.The initial geometric imperfection of the plate was considered,while the residual stress introduced by welding was not considered.The ultimate strength of simply supported ship hull plates compared well with the existing empirical formula to validate the correctness of the applied boundary conditions,initial imperfection and mesh size.The extensive FE calculations on the ultimate strength of ship hull plates with elastically restrained edges are presented.Then a new simple empirical formula for plate ultimate strength is developed,which includes the effect of the rotational restraint stiffness,rotational restraint stiffness,and aspect ratios.By applying the new formula and FE method to ship hull plates in real ships,a good coincidence of the results between these two methods is obtained,which indicates that the new formula can accurately predict the ultimate strength of ship hull plates with elastically restrained edges.

Mobility edges and reentrant localization in one-dimensional dimerized non-Hermitian quasiperiodic lattice

The mobility edges and reentrant localization transitions are studied in one-dimensional dimerized lattice with non-Hermitian either uniform or staggered quasiperiodic potentials.We find that the non-Hermitian uniform quasiperiodic disorder can induce an intermediate phase where the extended states coexist with the localized ones,which implies that the system has mobility edges.The localization transition is accompanied by the PT symmetry breaking transition.While if the non-Hermitian quasiperiodic disorder is staggered,we demonstrate the existence of multiple intermediate phases and multiple reentrant localization transitions based on the finite size scaling analysis.Interestingly,some already localized states will become extended states and can also be localized again for certain non-Hermitian parameters.The reentrant localization transitions are associated with the intermediate phases hosting mobility edges.Besides,we also find that the non-Hermiticity can break the reentrant localization transition where only one intermediate phase survives.More detailed information about the mobility edges and reentrant localization transitions are presented by analyzing the eigenenergy spectrum,inverse participation ratio,and normalized participation ratio.

BENDING OF UNIFORMLY LOADED RECTANGULAR PLATES WITH TWO ADJACENT EDGES CLAMPED, ONE EDGE SIMPLY SUPPORTED AND THE OTHER EDGE FREE

In this paper, an exact solution for an uniformly loaded rectangular plate with two adjacent edges clamped, one edge simply supported and the other edge free, was given by using the concept of generalized simply supported edges and superposition method. The numerical results were given for the deflections along the free edge and bending moments along the clamped edges of a square plate.

TRANSVERSE VIBRATION OF RECTANGULAR PLATES ELASTICALLY SUPPORTED AT POINTS ON EDGES

This paper studies transverse vibration of rectangular plates with two opposite edges simply supperted other two edges arbitrarily supported and free edges elaslically supported at points,A highly accurate solution is presented for calculating inherent frequencies and mode shape of rectangular platen elaslically supported at points. The number and location of these points on free edges may be completely arbitrary. This paper uses impulse function to represent reaction and moment at points. Fourter series is used to expand the impulse function along the edges. Characteristic equations satisfying all boundary conditions are given.Inherent frequencies and mode shape with any accutacy can be gained.

One Dimensional Random Motion on Segment with Reflecting Edges and Dependent Increments

In previous papers, the author considered the model of anomalous diffusion, defined by stable random process on an interval with reflecting edges. Estimates of the rate convergence of this process distribution to a uniform distribution are constructed. However, recent physical studies require consideration of models of diffusion, defined not only by stable random process with independent increments but multivariate fractional Brownian motion with dependent increments. This task requires the development of special mathematical techniques evaluation of the rate of convergence of the distribution of multivariate Brownian motion in a segment with reflecting boundaries to the limit. In the present work, this technology is developed and a power estimate of the rate of convergence to the limiting uniform distribution is built.

BENDING OF RECTANGULAR THIN PLATES WITH FREE EDGES LAID ON TENSIONLESS WINKLER FOUNDATION

In this paper, the bending problem of rectangular thin plates with free edges laid on tensionless Winkler foundation has been solved by employing Fourier series with supplementary terms. By assuming proper form of series for deflection, the basic differential equation with given boundary conditions can be transformed into a set of infinite algebraic equations. Because the boundary of contact region cannot bedetermined in advance, these equations are weak nonlinear ones. They can be solved by using iterative procedures.

A New Delay-Constrained Multicast Routing Algorithm Based on Shared Edges

In this paper, we made a detail analysis for the ESAMPH algorithm, and proposed ESAMPH_D algorithm according to the insufficient of ESAMPH algorithm. The ESAMPH_D algorithm does not consider those paths that do not satisfy the delay constraint, so we can ensure that all paths be taken into account will meet the limit of delay constraint, then we find the least costly path in order to build a minimum cost multicast tree. Simulation results show that the algorithm is better than ESAMPH algorithm in performance.

A Non-Conventional Coloring of the Edges of a Graph

Coloring the nodes of a graph is a commonly used technique to speed up clique search algorithms. Coloring the edges of the graph as a preconditioning method can also be used to speed up computations. In this paper we will show that an unconventional coloring scheme of the edges leads to an NP-complete problem when one intends to determine the optimal number of colors.

THE APPLICATION OF WEINSTEIN-CHIEN′S METHOD——THE UPPER AND LOWER LIMITS OF FUNDAMENTAL FREQUENCY OF RECTANGULAR PLATES WITH EDGES ARE THE MIXTURE OF SIMPLY SUPPORTED PORTIONS AND CLAMPED PORTIONS

In this paper, the method of relaxed boundary conditions is applied to rectangular plates with edges which are a sort of the mixture of simply supported portions and clamped portions, so that the lower limit of fundamental frequency of such plates is evaluated. A kind of polynomial satisfying the displacement boundary conditions is designed, os that it is enabled to evaluate the upper limit of fundamental frequency by Ritz' method. The practical calculation examples solved by these methods have given satisfactory results. At the end of this paper, it is pointed out that the socalled exact solution of such plates usually evaluated by the force superposition method is essentially a kind of lower limit of solution, if the truncated error of series which occurs in actual calculation is considered.

EXACT SOLUTION FOR RECTANGULAR SLAB WITH THREE EDGES SIMPLY-SUPPORTED AND OTHER FREE

In this paper,we give all-sided pastic analysis of the rectangular slab with three edges simply-supported and other free.Here we discuss the following four cases:(1)The uniformly distributedload over the area a slab.(2).A concentrated load act at midpoint of free edges slab.(3)A concen-trated load act at the center a slab.(4)The line load act along free edge of slab.