Nonlocal Model Research Articles

Public transport across models and scales: A case study of the munich network

Abstract The use of public transport systems is a striking example of complex human behavior. Modeling, planning, and managing public transport is a major future challenge considering the drastically accelerated population growth in many urban areas. The desire to design sustainable cities that can cope with a dynamically increasing demand requires models for transport networks since we are not able to perform real-life experiments before constructing additional infrastructure. Yet, there is a fundamental challenge in the modeling process: we have to understand which basic principles apply to the design of transit networks. In this work, we are going to compare three scientific methods to understand human behavior in public transport modeling: agent-based models, centralized optimization-based models, and minimal physicsbased models. As a case study, we focus on the transport network in Munich, Germany. We show that there are certain universal macroscopic emergent features of public transport that arise regardless of the model chosen. In particular, we can obtain with minimal basic assumptions a common and robust distribution for the individual passenger in-vehicle time as well as for several other distributions. Yet, there are other more microscopic features that differ between the individual and centralized organization and/or that cannot be reproduced by a minimal non-local random-walk type model. Finally, we cross-validate our results with observed public transport data. In summary, our results provide a key understanding of the basic assumptions that have to underlie transport modeling for human behavior in future sustainable cities.

Neutron skins: A perspective from dispersive optical models

An overview of neutron skin predictions obtained using an empirical nonlocal dispersive optical model (DOM) is presented. The DOM links both scattering and bound-state experimental data through a subtracted dispersion relation which allows for fully consistent, data-informed predictions for nuclei where such data exist. Large skins were predicted for both 48Ca (Rskin48=0.25±0.023 fm in 2017) and 208Pb (Rskin208=0.25±0.05 fm in 2020). Whereas the DOM prediction in 208Pb is within 1σ of the subsequent PREX-2 measurement, the DOM prediction in 48Ca is over 2σ larger than the thin neutron skin resulting from CREX. From the moment it was revealed, the thin skin in 48Ca has puzzled the nuclear-physics community as no adequate theories simultaneously predict both a large skin in 208Pb and a small skin in 48Ca. The DOM is unique in its ability to treat both structure and reaction data on the same footing, providing a unique perspective on this Rskin puzzle. It appears vital that more neutron data be measured in both the scattering and bound-state domain for 48Ca to clarify the situation.

Yukawa theory in non-perturbative regimes: towards confinement, exact β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document}-function and conformal phase

We study possible hints towards confinement in a Z2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {Z}_2$$\\end{document}-invariant Yukawa system with massless fermions and a real scalar field in the strongly-coupled regime. Using the tools developed for studying non-perturbative physics via Jacobi elliptical functions, for a given but not unique choice of the vacuum state, we find the exact Green’s function for the scalar sector so that, after integrating out the scalar degrees of freedom, we are able to recover the low-energy limit of the theory that is a fully non-local Nambu–Jona–Lasinio (NJL) model. We provide an analytical result for the renormalization group (RG) running of the self-interaction coupling in the scalar sector in the strongly-coupled regime. In the fermion sector, we provide some clues towards confinement, after deriving the gap equation with the non-local NJL model, a property which is well-known to not emerge in the local limit of this model. We conclude that, for the scalar-Yukawa theory in the non-perturbative domain with our choice of the vacuum state, the fundamental fermions of the theory form bound states and cannot be observed as asymptotic states.

Nonlinear Structures of Dispersive Electrostatic Solitary Waves in a Multi‐Ion Partially Ionized Plasma

ABSTRACTThe nonlinear structure and dynamics of dispersive solitons and breather waves described by Korteweg‐de Vries and nonlinear Schrödinger equations are studied. The theoretical and numerical study of the generalized hydrodynamic equations, accounting for wave dissipation and particle production‐loss mechanism, are considered. The reductive expansion method has been used in the context of the instability problem of multi‐fluid dynamics, applied to the study of electrostatic solitons and ion‐acoustic waves. A nonlocal model of interacting solitary‐breather waves has been presented. Applications of the theory, concerning the ion streaming instability in the framework of plasma physics, are presented.

An efficient nonlocal integral method based on the octree algorithm

The nonlocal integral method typically requires a very high computing cost to search neighborhood integration points for calculating the nonlocal variable, which limits its application in large-scale problems. This paper proposes an efficient nonlocal integral method based on the octree algorithm, in which the integration point information is stored in the tree data structure to accelerate the search task. Firstly, the fundamental principles and implementation details of using the octree algorithm to search neighborhood integration points are described in detail. Subsequently, a Mohr-Coulomb nonlocal damage plastic model is presented as the application object of the proposed method. The model is implemented further in the ABAQUS using the octree-based nonlocal method and the return mapping algorithm enhanced by a line search method. Finally, two typical boundary value problems are simulated to verify the effectiveness and to assess the computational efficiency of the proposed nonlocal method. For the given test environment, the octree algorithm can achieve up to 100 times speedup at the integration point level compared to the traversal algorithm, and the developed efficient nonlocal method can achieve up to 7.9 times speedup at the boundary value problem level compared to the original nonlocal method.

A nonlocal kernel-based continuum damage model for compaction band formation in porous sedimentary rock

A nonlocal kernel-based continuum damage model for compaction band formation in porous sedimentary rock

Stress-driven nonlocal homogenization method for cellular structures

Strong size-dependent mechanical behaviors can be observed in cellular structures violating the principle of scale separation and cannot be captured by classical homogenization methods. This paper proposes a stress-driven nonlocal homogenization method to capture the size-dependent mechanical behavior due to the nonlocal force of cellular structures. A nonlocal discrete element model is proposed first to describe the nonlocal deformation mechanism of cellular structures. Then, a continuum stress-driven nonlocal homogenization method is calibrated by deriving the continuum limit from the nonlocal discrete element model. The continuum homogenization method releases the assumption of scale separation by introducing an intrinsic length, which can be calibrated by high throughput numerical computation. Also, for efficient prediction of size-dependent mechanical behaviors, an offline dataset of the intrinsic length is constructed for different unit cells. With the help of the offline dataset, the proposed homogenization method improves the accuracy of the classic homogenization method and reduces the computational cost of the high-fidelity finite element method. Finally, a cellular rod under tension is used as an application to illustrate the efficiency and accuracy of the proposed homogenization method. Results indicate that compared with the classic homogenization method, the relative error of the proposed homogenization method is less than 1% which has a good consistency with the high-fidelity method. Moreover, the computational efficiency of the proposed homogenization method is more than five times that of the high-fidelity finite element method.

The TRUNC element in any dimension and application to a modified Poisson equation

AbstractWe introduce a novel TRUNC finite element in dimensions, encompassing the traditional TRUNC triangle as a particular instance. By establishing the weak continuity identity, we identify it as crucial for error estimate. This element is utilized to approximate a modified Poisson equation defined on a convex polytope, originating from the nonlocal electrostatics model. We have substantiated a uniform error estimate and conducted numerical tests on both the smooth solution and the solution with a sharp boundary layer, which align with the theoretical predictions.

Nonlocal combined nonlinear Schrödinger–Gerdjikov–Ivanov model: Integrability, Riemann–Hilbert problem with simple and double poles, Cauchy problem with step-like initial data

In this paper, we propose three new types of the integrable nonlocal combined nonlinear Schrödinger–Gerdjikov–Ivanov (NLS-GI) models. By the Riemann–Hilbert approach, we discuss the Cauchy problem of the reverse-space-time nonlocal combined NLS-GI model with step-like initial data: u(z, 0) = o(1) for z → −∞ and u(z, 0) = A + o(1) for z → +∞, where A is an arbitrary positive constant. First of all, we give an integrable nonlocal combined NLS-GI model and its Lax pair. Then, we consider the analytical and asymptotic behaviors, symmetries, and scattering matrix of the Jost solutions. Finally, we discuss the Cauchy problem for the nonlocal combined NLS-GI model with step-like initial data.

Two-step global sensitivity analysis of a non-local integro-differential model for Cancer-on-Chip experiments.

The present work focuses on a non-local integro-differential model reproducing Cancer-on-chip experiments where tumor cells, treated with chemotherapy drugs, secrete chemical signals stimulating the immune response. The reliability of the model in reproducing the phenomenon of interest is investigated through a global sensitivity analysis, rather than a local one, to have global information about the role of parameters, and by examining potential non-linear effects in greater detail. Focusing on a region in the parameter space, the effect of 13 model parameters on the in silico outcome is investigated by considering 11 different target outputs, properly selected to monitor the spatial distribution and the dynamics of immune cells along the period of observation. In order to cope with the large number of model parameters to be investigated and the computational cost of each numerical simulation, a two-step global sensitivity analysis is performed. First, the screening Morris method is applied to rank the effect of the 13 model parameters on each target output and it emerges that all the output targets are mainly affected by the same 6 parameters. The extended Fourier Amplitude Sensitivity Test (eFAST) method is then used to quantify the role of these 6 parameters. As a result, the proposed analysis highlights the feasibility of the considered space of parameters, and indicates that the most relevant parameters are those related to the chemical field and cell-substrate adhesion. In turn, it suggests how to possibly improve the model description as well as the calibration procedure, in order to better capture the observed phenomena and, at the same time, reduce the complexity of the simulation algorithm. On one hand, the model could be simplified by neglecting cell-cell alignment effects unless clear empirical evidences of their importance emerge. On the other hand, the best way to increase the accuracy and reliability of our model predictions would be to have experimental data/information to reduce the uncertainty of the more relevant parameters.

A generalization of the Exner law for sediment nonlocal transport at bedform scale

Recent researches have highlighted the significance of nonlocal processes in understanding the morphodynamics and sediment transport across landscapes. Nonlocal processes in sediment transport refer to the influence of landscape properties beyond the immediate vicinity of a given point on the sediment flux. Existing nonlocal models, employing fractional operators, aim to capture global correlated nonlocality using a global convolution operator. Nevertheless, such models tend to disregard nonlocal phenomena occurring at regional scales, potentially resulting in substantial inaccuracies due to an inadequate representation of sediment transport processes at these scales. This study presents a novel and more comprehensive mathematical formulation of the nonlocal Exner law, leveraging the peridynamic differential operator (PDDO). The proposed regional nonlocal model incorporates nonlocal sediment transport processes by utilizing a pre-defined weight function and interaction domain within the framework of the PDDO. The novel regional nonlocal model effectively bridges the gap between local and global models by integrating both short-range and long-range interactions in sediment transport. Application reveals that that the regional nonlocal model provides a significantly enhanced accuracy in depicting profiles at the bedform scale compared to the local and the global models.

Performance assessment of SiGe extended four corner source TFET for biosensing applications

In this paper, the performance of a novel SiGe extended four corner source tunneling field–effect transistor (SiGe EFCS TFET) based dielectrically modulated label-free biosensor has been investigated for biosensing applications. Using a combination of heterostructure (SiGe/Si) and extended four corner source (EFCS) lead to increased band–to–band tunneling (BTBT) probability, improved gate control and superior drain current sensitivity for biomolecule conjugation in comparison with a conventional TFET and Si EFCS TFET structures of similar dimensions. The influence of both the charge–neutral and charged biomolecules on the sensitivity performance is investigated using the Silvaco TCAD ATLAS semiconductor device simulator with a calibrated nonlocal BTBT model. Four different kinds of biomolecules such as Streptavidin, Ferro–cytochrome c, Keratin and Gelatin with various charge density values were used for this purpose. In order to model steric hindrance effects in partially filled cavities, in addition to various fill factors, four different step profile patterns have considered such as convex, concave, decreasing and increasing step profiles. Also, the dependence of the nanogap cavity properties on the sensing performance in terms of the length and thickness is investigated. A maximum drain current sensitivity of 1.69 × 105 is achieved in SiGe EFCS TFET for Gelatin biomolecules in a fully filled nanogap cavity at overdrive and drain voltages of 0.5 V.

Verification of the kinetic electron role in the microinstabilities in a negative triangularity model equilibrium

Effect of kinetic electrons on negative triangularity plasmas has been investigated and compared against the corresponding positive triangularity plasmas, using the global gyrokinetic code X-point Gyrokinetic Code with scale-separated delta-f option without Coulomb collisions. Our model magnetic equilibria have strong positive and negative triangularities and weak magnetic shear. However, unusually large ρi/a and low density plasmas are chosen to maximize the nonlocal effect to investigate the finite ρi effect and to be clearly away from kinetic ballooning modes. Similar conclusions to previous flux tube and global simulations have been obtained in this highly nonlocal model plasma: it is essential to include kinetic electrons in the micro-instability study of negative triangularity plasmas. Most physics findings agree with existing reports, with some disagreement. We offer a new “effective trapping fraction” concept that can add to the explanation of the growth rate difference between NT and PT plasmas, pointing to the significant variation in trapped particle fractions that have turning points in the mode growth regions.

Dynamics of a generalized nonlocal dispersion SIS epidemic model

Dynamics of a generalized nonlocal dispersion SIS epidemic model

How Cells Stay Together: A Mechanism for Maintenance of a Robust Cluster Explored by Local and Non-local Continuum Models.

Formation of organs and specialized tissues in embryonic development requires migration of cells to specific targets. In some instances, such cells migrate as a robust cluster. We here explore a recent local approximation of non-local continuum models by Falcó et al. (SIAM J Appl Math 84:17-42, 2023). We apply their theoretical results by specifying biologically-based cell-cell interactions, showing how such cell communication results in an effective attraction-repulsion Morse potential. We then explore the clustering instability, the existence and size of the cluster, and its stability. For attractant-repellent chemotaxis, we derive an explicit condition on cell and chemical properties that guarantee the existence of robust clusters. We also extend their work by investigating the accuracy of the local approximation relative to the full non-local model.

3D coupled vibrations of asymmetric nano-particle mass sensors: Two-phase integral nonlocal strain gradient model and MD simulation

Since it is possible for the nano-particle to have any asymmetric shape and may attach to every position of the resonator-based mass sensors, any type of mass eccentricity and subsequently coupled vibrations are possible. So, in the present work, the 3D coupled axial-torsional-flexural vibrations of the mass nano-sensors are investigated considering both in-plane and out-of-plane bending as well as axial and torsional vibrations. In addition, the integral form of the two-phase local/nonlocal strain gradient (LNSG), as the consistent type of the common nonlocal strain gradient (NSG) elasticity theory, is employed for the first time to consider the size effects in the mass nano-sensors. A quasi-3D coupled FE model is constructed with no shear-locking within the complicated environment of the integral LNSG. The impacts of the LNSG elasticity and diverse types of possible coupling in changing the vibrational behavior of the mass nano-sensor are scrutinized and their crucial role in modeling of the nano-sensors is indicated. Furthermore, molecular dynamic (MD) simulations are implemented to identify and analyze the coupled vibrations of a mass nano-sensor consisting of a fixed-free carbon nanotube. Comparison between the MD results with those of the present coupled FE model reveals that considering the coupling effects reduces the modeling error, especially in the cases in which the coupling influences intensify. The present work can help to provide more accurate models of mechanical resonance-based nanosensors to detect nanoparticles with different shapes, larger sizes, and high mass ratios, which can lead to achieving sensors with higher sensitivity.

Dynamics for a nonlocal diffusive SIR epidemic model with double free boundaries

In this paper, we study an SIR epidemic model with nonlocal diffusion and double free boundaries, which can be used to describe a class of biological phenomena: the depletion of native resources by all individuals, the infected individuals do not lose their fertility completely, the recovered individuals are immune and no longer infected, the infected and recovered individuals spread along the same free boundary. We first investigate the existence and uniqueness of global solution, long time behaviors and some sufficient conditions for spreading and vanishing. Then we estimate the spreading speed and derive that accelerated spreading could happen when the kernel function does not satisfy a threshold condition.

Computational and analytical studies of a new nonlocal phase-field crystal model in two dimensions

A nonlocal phase-field crystal (NPFC) model is presented as a nonlocal counterpart of the local phase-field crystal (LPFC) model and a special case of the structural PFC (XPFC) derived from classical field theory for crystal growth and phase transition. The NPFC incorporates a finite range of spatial nonlocal interactions that can account for both repulsive and attractive effects. The specific form is data-driven and determined by a fitting to the materials structure factor, which can be much more accurate than the LPFC and previously proposed fractional variant. In particular, it is able to match the experimental data of the structure factor up to the second peak, an achievement not possible with other PFC variants studied in the literature. Both LPFC and fractional PFC (FPFC) are also shown to be distinct scaling limits of the NPFC, which reflects the generality. The advantage of NPFC in retaining material properties suggests that it may be more suitable for characterizing liquid–solid transition systems. Moreover, we study numerical discretizations using Fourier spectral methods, which are shown to be convergent and asymptotically compatible, making them robust numerical discretizations across different parameter ranges. Numerical experiments are given in the two-dimensional case to demonstrate the effectiveness of the NPFC in simulating crystal structures and grain boundaries.

Propagation dynamics of a nonlocal dispersal Zika transmission model with general incidence

In this paper, we are interested in propagation dynamics of a nonlocal dispersal Zika transmission model with general incidence. When the threshold is greater than one, we prove that there is a wave speed such that the model has a traveling wave solution with speed , and there is no traveling wave solution with speed less than . When the threshold is less than or equal to one, we show that there is no nontrivial traveling wave solution. The approaches we use here are Schauder's fixed point theorem with an explicit construction of a pair of upper and lower solutions, the contradictory approach, and the two‐sided Laplace transform.

Stability of the Ionic Parameters of a Nonlocal FitzHugh-Nagumo Model of Cardiac Electrophysiology

Stability of the Ionic Parameters of a Nonlocal FitzHugh-Nagumo Model of Cardiac Electrophysiology