Nonlocalized clustering and evolution of cluster structure in nuclei

We explain various facets of the THSR(Tohsaki-Horiuchi Schuck-Ropke)wave function.We first discuss the THSR,wave function as a wave function of cluster-gas state,since the THSR,wave function was originally introduced to elucidate the 3a-condensate-like character of the Hoyle state(O2^+ state)of 12C.We briefly review the cluster-model studies of the Hoyle state in 1970’s in order to explain how there emerged the idea to assign the a condensate character to the Hoyle state.We then explain that the THSR wave function can describe very well also non-gaslike ordinary cluster states with spatial localization of clusters.This fact means that the dynamical motion of clusters is of nonlocalized nature just as in gas-like states of clusters and the localization of clusters is due to the inter-cluster Pauli principle which is against the close approach of two clusters.The nonlocalized cluster dynamics is formulated by the container model of cluster dynamics.The container model describes gas-like state and non-gaslike states as the solutions of the Hill Wheeler equation with respect to the size parameter of THSR wave function which is just the size parameter of the container.When we notice that fact that the THSR wave function with the smallest value of size parameter is equivalent to the shell-model wave function,we see that the container model describes the evolution of cluster structure from the ground state with shell-model structure up to the gas-like cluster state via ordinary non-gaslike cluster states.For the description of various cluster structure,more generation of THSR wave function have been introduced and we review some typical examples with their actual applications.

Verifying hierarchical network nonlocality in general quantum networks

Recently, a class of innovative notions on quantum network nonlocality(QNN), called full quantum network nonlocality(FQNN), have been proposed in Phys. Rev. Lett. 128 010403(2022). As the generalization of full network nonlocality(FNN), l-level quantum network nonlocality(l-QNN) was defined in arxiv. 2306.15717 quant-ph(2024). FQNN is a NN that can be generated only from a network with all sources being non-classical. This is beyond the existing standard network nonlocality, which may be generated from a network with only a non-classical source. One of the challenging tasks is to establish corresponding Bell-like inequalities to demonstrate the FQNN or l-QNN. Up to now, the inequality criteria for FQNN and l-QNN have only been established for star and chain networks. In this paper, we devote ourselves to establishing Bell-like inequalities for networks with more complex structures. Note that star and chain networks are special kinds of tree-shaped networks. We first establish the Bell-like inequalities for verifying l-QNN in k-forked tree-shaped networks. Such results generalize the existing inequalities for star and chain networks. Furthermore, we find the Bell-like inequality criteria for l-QNN for general acyclic and cyclic networks. Finally, we discuss the demonstration of l-QNN in the well-known butterfly networks.

THE PERSISTENCE OF SOLUTIONS IN A NONLOCAL PREDATOR-PREY SYSTEM WITH A SHIFTING HABITAT

In this paper,we mainly study the propagation properties of a nonlocal dispersal predator-prey system in a shifting environment.It is known that Choi et al.[J Differ Equ,2021,302:807-853]studied the persistence or extinction of the prey and of the predator separately in various moving frames.In particular,they achieved a complete picture in the local diffusion case.However,the question of the persistence of the prey and of the predator in some intermediate moving frames in the nonlocal diffusion case was left open in Choi et al.'s paper.By using some a prior estimates,the Arzelà-Ascoli theorem and a diagonal extraction process,we can extend and improve the main results of Choi et al.to achieve a complete picture in the nonlocal diffusion case.

A nonlocal dispersal and time delayed HIV infection model with general incidences

Biologically,because of the impact of reproduction period and nonlocal dispersal of HIV-infected cells,time delay and spatial heterogeneity should be considered.In this paper,we establish an HIV infection model with nonlocal dispersal and infection age.Moreover,applying the theory of Fourier transformation and von Foerster rule,we transform the model to an integrodifferential equation with nonlocal time delay and dispersal.The well-posedness,positivity,and boundedness of the solution for the model are studied.

Sharing quantum nonlocality in the noisy scenario

It was showed in [Phys. Rev. Lett. 125 090401(2020)] that there exist unbounded number of independent Bobs who can share quantum nonlocality with a single Alice by performing sequentially measurements on the Bob's half of the maximally entangled pure two-qubit state. However, from practical perspectives, errors in entanglement generation and noises in quantum measurements will result in the decay of nonlocality in the scenario. In this paper, we analyze the persistency and termination of sharing nonlocality in the noisy scenario. We first obtain the two sufficient conditions under which there exist n independent Bobs who can share nonlocality with a single Alice under noisy measurements and the noisy initial two qubit entangled state. Analyzing the two conditions, we find that the influences on persistency under different kinds of noises can cancel each other out. Furthermore, we describe the change patterns of the maximal nonlocality-sharing number under the influence of different noises. Finally, we extend our investigation to the case of arbitrary finite-dimensional systems.

A STRONG POSITIVITY PROPERTY AND A RELATED INVERSE SOURCE PROBLEM FOR MULTI-TERM TIME-FRACTIONAL DIFFUSION EQUATIONS

In this article,we consider the diffusion equation with multi-term time-fractional derivatives.We first derive,by a subordination principle for the solution,that the solution is positive when the initial value is non-negative.As an application,we prove the uniqueness of solution to an inverse problem of determination of the temporally varying source term by integral type information in a subdomain.Finally,several numerical experiments are presented to show the accuracy and efficiency of the algorithm.

Nonlinear phenomena in vibrations of embedded carbon nanotubes conveying viscous fluid

Various nonlinear phenomena such as bifurcations and chaos in the responses of carbon nanotubes(CNTs)are recognized as being major contributors to the inaccuracy and instability of nanoscale mechanical systems.Therefore,the main purpose of this paper is to predict the nonlinear dynamic behavior of a CNT conveying viscousfluid and supported on a nonlinear elastic foundation.The proposed model is based on nonlocal Euler–Bernoulli beam theory.The Galerkin method and perturbation analysis are used to discretize the partial differential equation of motion and obtain the frequency-response equation,respectively.A detailed parametric study is reported into how the nonlocal parameter,foundation coefficients,fluid viscosity,and amplitude and frequency of the external force influence the nonlinear dynamics of the system.Subharmonic,quasi-periodic,and chaotic behaviors and hardening nonlinearity are revealed by means of the vibration time histories,frequency-response curves,bifurcation diagrams,phase portraits,power spectra,and Poincarémaps.Also,the results show that it is possible to eliminate irregular motion in the whole range of external force amplitude by selecting appropriate parameters.

Qualitative Analysis of a Diffusive Predator-prey Model with Nonlcoal Fear Effect

In this paper,we establish a delayed predator-prey model with nonlocal fear effect.Firstly,the existence,uniqueness,and persistence of solutions of the model are studied.Then,the local stability,Turing bifurcation,and Hopf bifurcation of the constant equilibrium state are analyzed by examining the characteristic equation.The global asymptotic stability of the positive equilibrium point is investigated using the Lyapunov function method.Finally,the correctness of the theoretical analysis results is verified through numerical simulations.

Global Existence and Decay of Solutions for a Class of a Pseudo-Parabolic Equation with Singular Potential and Logarithmic Nonlocal Source

This article investigates the well posedness and asymptotic behavior of Neumann initial boundary value problems for a class of pseudo-parabolic equations with singular potential and logarithmic nonlinearity. By utilizing cut-off techniques and combining with the Faedo Galerkin approximation method, local solvability was established. Based on the potential well method and Hardy Sobolev inequality, derive the global existence of the solution. In addition, we also obtained the results of decay.

Einstein-Podolsky-Rosen Steering and Nonlocality in Open Quantum Systems

We investigate the dynamical behavior of quantum steering (QS), Bell nonlocality, and entanglement in open quantum systems. We focus on a two-qubit system evolving within the framework of Kossakowski-type quantum dynamical semigroups. Our findings reveal that the measures of quantumness for the asymptotic states rely on the primary parameter of the quantum model. Furthermore, control over these measures can be achieved through a careful selection of these parameters. Our analysis encompasses various cases, including Bell states, Werner states, and Horodecki states, demonstrating that the asymptotic states can exhibit steering, entanglement, and Bell nonlocality. Additionally, we find that these three quantum measures of correlations can withstand the influence of the environment, maintaining their properties even over extended periods.

Quantization of Action for Elementary Particles and the Principle of Least Action

The uncertainty principle is a fundamental principle of quantum mechanics, but its exact mathematical expression cannot obtain correct results when used to solve theoretical problems such as the energy levels of hydrogen atoms, one-dimensional deep potential wells, one-dimensional harmonic oscillators, and double-slit experiments. Even after approximate treatment, the results obtained are not completely consistent with those obtained by solving Schrödinger’s equation. This indicates that further research on the uncertainty principle is necessary. Therefore, using the de Broglie matter wave hypothesis, we quantize the action of an elementary particle in natural coordinates and obtain the quantization condition and a new deterministic relation. Using this quantization condition, we obtain the energy level formulas of an elementary particle in different conditions in a classical way that is completely consistent with the results obtained by solving Schrödinger’s equation. A new physical interpretation is given for the particle eigenfunction independence of probability for an elementary particle: an elementary particle is in a particle state at the space-time point where the action is quantized, and in a wave state in the rest of the space-time region. The space-time points of particle nature and the wave regions of particle motion constitute the continuous trajectory of particle motion. When an elementary particle is in a particle state, it is localized, whereas in the wave state region, it is nonlocalized.

Propagation Dynamics of Forced Pulsating Waves for a Time Periodic Lotka-Volterra Cooperative System with Nonlocal Effects in Shifting Habitats

In this paper, we will concern the existence, asymptotic behaviors and stability of forced pulsating waves for a Lotka-Volterra cooperative system with nonlocal effects under shifting habitats. By using the alternatively-coupling upper-lower solution method, we establish the existence of forced pulsating waves, as long as the shifting speed falls in a finite interval where the endpoints are obtained from KPP-Fisher speeds. The asymptotic behaviors of the forced pulsating waves are derived. Finally, with proper initial, the stability of the forced pulsating waves is studied by the squeezing technique based on the comparison principle.

基于ResNet50的水稻病虫害识别

为了准确识别水稻病虫害,收集8种水稻病虫害图像和健康水稻图像,构建水稻病虫害数据集。将残差网络ResNet50用于水稻病虫害识别,在原模型基础上引入了迁移学习和NonLocal注意力机制。实验结果表明,改进模型的准确率、精确率、召回率、F1-score分别达到99.12%、99.31%、99.27%、99.28%,相比于原模型分别提升了2.92%、2.91%、4.05%、3.60%。与模型DenseNet121、InceptionV3、ShuffleNetV2、MobileVit-small、ResNext50相比,改进模型的准确率、精确率、召回率、F1-score至少高出2%。实验验证了所提模型的有效性,该模型可以准确识别这几种水稻病虫害。

Dynamic stability analysis of porous functionally graded beams under hygro-thermal loading using nonlocal strain gradient integral model

We present a study on the dynamic stability of porous functionally graded(PFG)beams under hygro-thermal loading.The variations of the properties of the beams across the beam thicknesses are described by the power-law model.Unlike most studies on this topic,we consider both the bending deformation of the beams and the hygro-thermal load as size-dependent,simultaneously,by adopting the equivalent differential forms of the well-posed nonlocal strain gradient integral theory(NSGIT)which are strictly equipped with a set of constitutive boundary conditions(CBCs),and through which both the stiffness-hardening and stiffness-softening effects of the structures can be observed with the length-scale parameters changed.All the variables presented in the differential problem formulation are discretized.The numerical solution of the dynamic instability region(DIR)of various bounded beams is then developed via the generalized differential quadrature method(GDQM).After verifying the present formulation and results,we examine the effects of different parameters such as the nonlocal/gradient length-scale parameters,the static force factor,the functionally graded(FG)parameter,and the porosity parameter on the DIR.Furthermore,the influence of considering the size-dependent hygro-thermal load is also presented.

Towards a unified nonlocal, peridynamics framework for the coarse-graining of molecular dynamics data with fractures

Molecular dynamics(MD)has served as a powerful tool for designing materials with reduced reliance on laboratory testing.However,the use of MD directly to treat the deformation and failure of materials at the mesoscale is still largely beyond reach.In this work,we propose a learning framework to extract a peridynamics model as a mesoscale continuum surrogate from MD simulated material fracture data sets.Firstly,we develop a novel coarse-graining method,to automatically handle the material fracture and its corresponding discontinuities in the MD displacement data sets.Inspired by the weighted essentially non-oscillatory(WENO)scheme,the key idea lies at an adaptive procedure to automatically choose the locally smoothest stencil,then reconstruct the coarse-grained material displacement field as the piecewise smooth solutions containing discontinuities.Then,based on the coarse-grained MD data,a two-phase optimizationbased learning approach is proposed to infer the optimal peridynamics model with damage criterion.In the first phase,we identify the optimal nonlocal kernel function from the data sets without material damage to capture the material stiffness properties.Then,in the second phase,the material damage criterion is learnt as a smoothed step function from the data with fractures.As a result,a peridynamics surrogate is obtained.As a continuum model,our peridynamics surrogate model can be employed in further prediction tasks with different grid resolutions from training,and hence allows for substantial reductions in computational cost compared with MD.We illustrate the efficacy of the proposed approach with several numerical tests for the dynamic crack propagation problem in a single-layer graphene.Our tests show that the proposed data-driven model is robust and generalizable,in the sense that it is capable of modeling the initialization and growth of fractures under discretization and loading settings that are different from the ones used during training.

Unified two-phase nonlocal formulation for vibration of functionally graded beams resting on nonlocal viscoelastic Winkler-Pasternak foundation

A nonlocal study of the vibration responses of functionally graded(FG)beams supported by a viscoelastic Winkler-Pasternak foundation is presented.The damping responses of both the Winkler and Pasternak layers of the foundation are considered in the formulation,which were not considered in most literature on this subject,and the bending deformation of the beams and the elastic and damping responses of the foundation as nonlocal by uniting the equivalently differential formulation of well-posed strain-driven(ε-D)and stress-driven(σ-D)two-phase local/nonlocal integral models with constitutive constraints are comprehensively considered,which can address both the stiffness softening and toughing effects due to scale reduction.The generalized differential quadrature method(GDQM)is used to solve the complex eigenvalue problem.After verifying the solution procedure,a series of benchmark results for the vibration frequency of different bounded FG beams supported by the foundation are obtained.Subsequently,the effects of the nonlocality of the foundation on the undamped/damping vibration frequency of the beams are examined.

Fault rupture propagation in soil with intercalation using nonlocal model and softening modulus modification

Fault rupture propagation is more complex in the overlying soil with intercalation than in homogeneous soil,and it is challenging to simulate this phenomenon accurately using the finite element method.To address this issue,an improved nonlocal model that incorporates softening modulus modification is proposed.The methodology has the advantage that the solutions are independent of both mesh sizes and characteristic lengths,while maintaining objective softening rates of materials.Using the proposed methodology,a series of numerical simulations are conducted to investigate the effects of different mechanical parameters,such as elastic modulus,friction angle and dilation angle of the soil within the intercalation,as well as the impact of geometries,such as the depth and thickness of the intercalation,on the fault rupture progress.This study not only provides significant insights into the mechanisms of fault rupture propagation,specifically in relation to intercalations,but also shows a great value in promoting the current research on fault rupture.

Estimates on the eigenvalues of complex nonlocal Sturm-Liouville problems

The present paper deals with the eigenvalues of complex nonlocal Sturm-Liouville boundary value problems.The bounds of the real and imaginary parts of eigenvalues for the nonlocal Sturm-Liouville differential equation involving complex nonlocal potential terms associated with nonlocal boundary conditions are obtained in terms of the integrable conditions of coefficients and the real part of the eigenvalues.

ENTIRE SOLUTIONS OF LOTKA-VOLTERRA COMPETITION SYSTEMS WITH NONLOCAL DISPERSAL

This paper is mainly concerned with entire solutions of the following two-species Lotka-Volterra competition system with nonlocal(convolution)dispersals:{u_(t)=k*u-u+u(1-u-av),x∈R,t∈R,vt=d(k*v-v)+rv(1-v-bu),c∈R,t∈R.(0.1)Here a≠1,b≠1,d,and r are positive constants.By studying the eigenvalue problem of(0.1)linearized at(ϕc(ξ),0),we construct a pair of super-and sub-solutions for(0.1),and then establish the existence of entire solutions originating from(ϕc(ξ),0)as t→−∞,whereϕc denotes the traveling wave solution of the nonlocal Fisher-KPP equation ut=k*u−u+u(1−u).Moreover,we give a detailed description on the long-time behavior of such entire solutions as t→∞.Compared to the known works on the Lotka-Volterra competition system with classical diffusions,this paper overcomes many difficulties due to the appearance of nonlocal dispersal operators.

Analytical determination of non-local parameter value to investigate the axial buckling of nanoshells affected by the passing nanofluids and their velocities considering various modified cylindrical shell theories

We analytically determine the nonlocal parameter value to achieve a more accurate axial-buckling response of carbon nanoshells conveying nanofluids. To this end, the four plates/shells' classical theories of Love, Fl ¨ugge, Donnell, and Sanders are generalized using Eringen's nonlocal elasticity theory. By combining these theories in cylindrical coordinates,a modified motion equation is presented to investigate the buckling behavior of the nanofluid-nanostructure-interaction problem. Herein, in addition to the small-scale effect of the structure and the passing fluid on the critical buckling strain,we discuss the effects of nanoflow velocity, fluid density(nano-liquid/nano-gas), half-wave numbers, aspect ratio, and nanoshell flexural rigidity. The analytical approach is used to discretize and solve the obtained relations to study the mentioned cases.