Nonlocal Propagation Research Articles

The cosmological collider in R 2 inflation

Starobinsky's R 2 inflation manifests a best-fit scenario for the power spectrum of primordial density fluctuations. Observables derived from the slow-roll picture of the R 2 model in the Einstein frame relies on the conformal transformation of the metric, which inevitably induces a unique exponential-type couplings of the rolling scalaron with all matter fields during inflation. The “large-field” nature of the R 2 model further invokes non-negligible time and scale dependence to the matter sector through such an exponential coupling, modifying not only the dynamics of matter perturbations on superhorizon scales but also their decay rates. In this work, we identify the simplest observable of the cosmological collider physics built in the background of R 2 inflation, focusing on the so-called “quantum primordial clock” signals created by the non-local propagation of massive scalar perturbations. Our numerical formalism based on the unique conformal coupling can have extended applications to (quasi-)single-field inflationary models with non-trivial couplings to gravity or models that originated from the f(R) modification of gravity.

I-FENN with Temporal Convolutional Networks: Expediting the load-history analysis of non-local gradient damage propagation

In this paper, we demonstrate for the first time how the Integrated Finite Element Neural Network (I-FENN) framework, previously proposed by the authors [1,2], can efficiently simulate the entire loading history of non-local gradient damage propagation. To achieve this goal, we first adopt a Temporal Convolutional Network (TCN) as the neural network of choice to capture the history-dependent evolution of the non-local strain in a coarsely meshed domain. The quality of the network predictions governs the computational performance of I-FENN, and therefore we perform an extended investigation aimed at enhancing them. We explore a data-driven vs. physics-informed TCN setup to arrive at an optimum network training, evaluating the network based on a coherent set of relevant performance metrics. We address the crucial issue of training a physics-informed network with input data that span vastly different length scales by proposing a systematic way of input normalization and output un-normalization. We then integrate the trained TCN within the nonlinear iterative FEM solver and apply I-FENN to simulate the damage propagation analysis. I-FENN is always applied in mesh idealizations different from the one used for the TCN training, showcasing the framework’s ability to be used at progressively refined mesh resolutions. We illustrate several cases that I-FENN completes the simulation using either a modified or a full Newton–Raphson scheme, and we showcase its computational savings compared to both the classical monolithic and staggered FEM solvers. We underline that we satisfy very strict convergence criteria for every increment across the entire simulation, providing clear evidence of the robustness and accuracy of I-FENN. All the code and data used in this work will be made publicly available upon publication of the article.

Cascading Failure Propagation and Mitigation Strategies in Power Systems

In this article, we investigate the local and nonlocal failure propagation patterns in power systems and propose effective mitigation strategies. It is widely acknowledged that the sequence of failure events of component overloading is determined by power flow redistribution. To understand the power flow redistribution process, we analyze the prefault power flow condition using network flow theory and by clustering the system into several regions with balanced local power flow. We observe that faults triggering local power imbalance would lead to remote power transfer and faults causing no local power imbalance would lead to local power redistribution. The improved understanding of the failure process permits us to develop effective mitigating strategies consisting of adaptive power balance restoration and selective edge protection for cascading failure propagation. In addition, we propose a set of indexes to measure the local and nonlocal propagation risks of cascading failures. Numerical simulations on the IEEE 118- and 300-bus systems demonstrate that the proposed mitigation strategies can significantly reduce the blackout sizes and are tolerant to incorrect transmission line tripping.

Nonlocal state-space strain gradient wave propagation of magneto thermo piezoelectric functionally graded nanobeam

Abstract In this work, the state -space nonlocal strain gradient theory is used for the vibration analysis of magneto thermo piezoelectric functionally graded material (FGM) nanobeam. An analysis of FGM constituent properties is stated by using the power law relations. The refined higher order beam theory and Hamilton’s principle have been used to obtain the motion equations. Besides, the governing equations of the magneto thermo piezoelectric nanobeam are extracted by developed nonlocal state-space theory. And to solve the wave propagation problems, the analytical wave dispersion method is used. The effect of magnetic potential, temperature gradient, and electric voltage in variant parameters are presented in graph.

Diagnostics of nonergodic extended states and many body localization proximity effect through real-space and Fock-space excitations

We provide real-space and Fock-space (FS) characterizations of ergodic, nonergodic extended (NEE) and many-body localized (MBL) phases in an interacting quasiperiodic system, namely, the generalized Aubry-Andr\'e-Harper model, which possesses a mobility edge in the noninteracting limit. We show that a mobility edge in the single-particle (SP) excitations survives even in the presence of interaction in the NEE phase. In contrast, all single-particle excitations get localized in the MBL phase due to the MBL proximity effect. We give complementary insights into the distinction of the NEE states from the ergodic and MBL states by computing local FS self-energies and decay length associated, respectively, with the local and the nonlocal FS propagators. Based on a finite-size scaling analysis of the typical local self-energy across the NEE to ergodic transition, we show that MBL and NEE states exhibit qualitatively similar multifractal character. However, we find that the NEE and MBL states can be distinguished in terms of the distribution of local self-energy and the decay of the nonlocal propagator in the FS, whereas the typical local FS self-energy cannot tell them apart.

A three-dimensional (3D) micro-potential-based peridynamics model for deformation and fracture in solid materials

In this work, an innovative three-dimensional (3D) micro-potential-based peridynamics model is developed, and its applications for modeling deformation and fracture of solid materials are studied. In the present micro-potential-based peridynamics, a square measure of bond deformation is considered within peridynamics framework, and a 3D nonlocal strain tensor is constructed, including the nonlocal shear strain and the nonlocal volumetric strain. We assume that the micro potential energy generated by particle deformation conforms to the Xu–Needleman potential function, then the micro-potential-based peridynamics constitutive model is established. A bond failure criterion based on the energy release rate is established for the three-dimensional micro-potential-based peridynamics model and the critical stretch of bonds is derived, then the discrete form of the numerical implementation of the model is given. The bond force models obtained by present micro-potential-based peridynamics and existing peridynamics models are compared and investigated. Finally, Mode I, II, and III cracks are selected to verify the current 3D micro-potential-based peridynamics model in the simulation of deformation and fracture, as the nonlocal strain, crack nucleation, and propagation characteristics.

Nonlocal wave propagation analysis of a rotating nanobeam on a Pasternak foundation

In this paper, the wave propagation analysis of a cantilever rotating nanobeam modeled as a thin beam based on the Euler–Bernoulli theory on a Pasternak foundation has been investigated using the nonlocal theory of elasticity. The governing partial differential equation of motion for a uniform rotating nanobeam is derived using the Hamilton principle considering the nonlocal parameter of small scale effect. The Spectrum and dispersion relations of non-dimensional wave number are obtained analytically. The effect of changes of different parameters including nonlocal scale parameter, non-dimensional rotational speed, non-dimensional rotational wave frequency ratio, and shear stiffness of the Pasternak foundation on the wave dispersion behavior of the non-dimensional wave number and phase and group speeds dispersions for the rotating nanotube have been studied. It is observed that the wave dispersion characteristics of the rotating nanobeam are extremely influenced by rotational speed, wave number, nonlocal length scale parameter, and shear stiffness of the Pasternak foundation. Moreover, the propagated flexural wave has been shown to exhibit non-dispersive behavior at very high rotational speeds.

Prediction and mitigation of nonlocal cascading failures using graph neural networks.

Cascading failures in electrical power grids, comprising nodes and links, propagate nonlocally. After a local disturbance, successive resultant can be distant from the source. Since avalanche failures can propagate unexpectedly, care must be taken when formulating a mitigation strategy. Herein, we propose a strategy for mitigating such cascading failures. First, to characterize the impact of each node on the avalanche dynamics, we propose a novel measure, that of Avalanche Centrality (AC). Then, based on the ACs, nodes potentially needing reinforcement are identified and selected for mitigation. Compared with heuristic measures, AC has proven to be efficient at reducing avalanche size; however, due to nonlocal propagation, calculating ACs can be computationally burdensome. To resolve this problem, we use a graph neural network (GNN). We begin by training a GNN using a large number of small networks; then, once trained, the GNN can predict ACs efficiently in large networks and real-world topological power grids in manageable computational time. Thus, under our strategy, mitigation in large networks is achieved by reinforcing nodes with large ACs. The framework developed in this study can be implemented in other complex processes that require longer computational time to simulate large networks.

Majorana-like end states in one-dimensional dimerized Kitaev topolectrical circuit

Majorana zero modes (MZMs) have attracted tremendous attention in condensed matter and materials physics communities due to the implications in topological quantum computation. One-dimensional (1D) dimerized Kitaev chain is a prototype model for MZMs, but its realization remains a challenge in material systems. Here, we develop a distinctive approach to achieve Majorana-like end states (MESs) by implementing practical dimerized Kitaev topolectrical circuits. Specifically, two arrays of inductors are arranged to simulate particles and antiparticles, while intra- and inter-array capacitive connections are used to model hopping and superconducting pairing. Three topological phases can be achieved by tuning the capacitance, i.e. the trivial phase, Su–Schrieffer–Heeger topological phase and Kitaev phase, with distinct field strength distributions in real space. Majorana splitting is observed around a domain wall in the circuit, and we propose an efficient experimental observable-edge distance-to characterize the process as premonition of topological phase transition. Remarkably, dynamics of the Gaussian wave packet in time domain provide an excellent signal to detect MESs in experiments, as only MESs allow nonlocal propagation in circuit network. Our results not only manifest the superiorities of topolectrical circuits for exotic topological states, but also pave the way for possible applications in electrical engineering and signal processing.

Event-triggered boundary control of a continuum model of highly re-entrant manufacturing systems

We design an event-triggered boundary controller for a continuum model of highly re-entrant manufacturing systems for which the influx rate of products is the controlled quantity. Mathematically, the governing equation of the process is a nonlinear hyperbolic partial differential equation with a nonlinearity arising from the nonlocal propagation speed and the positivity state constraint. The nonlinearity makes highly non-trivial the proof of well-posedness of the closed-loop system under ETC, and the design of the triggering mechanism requires novelty because standard triggering schemes proposed in the literature of linear PDEs do not work. The designed controller can potentially operate in networked control systems subject to limited information sharing resources. A Lyapunov argument is utilized to derive the boundary controller together with a feasible event generator that avoids the occurrence of Zeno behavior for the closed-loop system. The global stability estimate is established using the logarithmic norm of the state due to the system’s nonlinearity and positivity of the density. Furthermore, robustness of the proposed controller with respect to the sampling schedule and sampled-data stabilization results are established. Consistent simulation results that support the proposed theoretical statements are provided.

Light propagation in a three-dimensional Rydberg gas with a nonlocal optical response.

We theoretically investigate the linear susceptibility and propagation of light in a three-dimensional (3-D) Rydberg gas under conditions of electromagnetically induced transparency. Rydberg atoms with two relevant S states are coupled via exchange interactions. When the gas is initially prepared in an entangled spin-wave state, this coupling induces a strong, nonlocal susceptibility whereby the photon field at one point of the medium acts as a source at a distant position. The nonlocal propagation occurs not only in the propagation direction but also in the paraxial direction. We discuss the absorption features and numerically simulate the 3-D propagation of probe laser light. Combined with the long-range exchange interaction, we show that the 3-D Rydberg gas is an ideal medium for studying nonlocal wave phenomena, in which the strength, range, and sign of the nonlocal interaction kernel can be widely tuned.

A non-local propagation filtering scheme for edge-preserving in variational optical flow computation

The median filtering heuristic is considered to be an indispensable tool for the currently popular variational optical flow computation. Its attractive advantages are that outliers reduction is attained while image edges and motion boundaries are preserved. However, it still may generate blurring at image edges and motion boundaries caused by large displacement, motion occlusion, complex texture, and illumination change. In this paper, we present a non-local propagation filtering scheme to deal with the above problem during the coarse-to-fine optical flow computation. First, we analyze the connection between the weighted median filtering and the blurring of image edge and motion boundary under the coarse-to-fine optical flow computing scheme. Second, to improve the quality of the initial flow field, we introduce a non-local propagation filter to reduce outliers while preserving context information of the flow field. Furthermore, we present an optimization combination of non-local propagation filtering and weighted median filtering for the flow field estimation under the coarse-to-fine scheme. Extensive experiments on public optical flow benchmarks demonstrate that the proposed scheme can effectively improve the accuracy and robustness of optical flow estimation.

Abrupt transition due to non-local cascade propagation in multiplex systems

Multilayer systems are coupled networks characterized by different contexts (layers) of interaction and have gained much attention recently due to their suitability to describe a broad spectrum of empirical complex systems. They are very fragile to percolation and first-neighbor failure propagation, but little is known about how they respond to non-local disruptions, as it occurs in failures induced by flow redistribution, for example. Acknowledging that many socio-technical and biological systems sustain a flow of some physical quantity, such as energy or information, across the their components, it becomes crucial to understand when the flow redistribution can cause global cascades of failures in order to design robust systems, to increase their resilience or to learn how to efficiently dismantle them. In this paper we study the impact that different multiplex topological features have on the robustness of the system when subjected to non-local cascade propagation. We first numerically demonstrate that this dynamics has a critical value at which a small initial perturbation effectively dismantles the entire network, and that the transition appears abruptly. Then we identify that the excess of flow caused by a failure is, in general, more homogeneously distributed the networks in which the average distance between nodes is small. Using this information we find that aggregated versions of multiplex networks tend to overestimate robustness, even though to make the system more robust can be achieved by increasing the number of layers. Our predictions are confirmed by simulated cascading failures in a real multilayer system.

Thermo magnetic response of nonlocal propagation of waves in rotating graphene tubules

Thermo magnetic response of propagation of waves in rotating graphene tubules is studied with the aid of nonlocal Euler–Bernoulli beam theory within the framework of spectral analysis. The governing dynamic equation of nonlocal rotating graphene tubules under thermo magnetic response is formulated with the help of equation of thermal force, centrifugal force and electromagnetic force. The dispersion equation of nonlocal rotating graphene tubules under thermo magnetic field is derived. The numerical value of non-dimensional wave number is computed and is represented in terms of scattered curves. The scattered curves of graphene tubules at different rotating speed, nonlocal parameter, temperature and magnetic field strength are also drawn. The results give useful information in the study and design of rotary nano-devices such as nano motors, nanoturbines, nano robots etc. The dispersion curves of non-rotating graphene tubules in the absence of thermal and magnetic field are drawn and are compared with the existing literature.

On the Choice of Kernel Function in Nonlocal Wave Propagation

It is a challenge to choose the appropriate kernel function in nonlocal problems. We tackle this challenge from the aspect of nonlocal wave propagation and study the dispersion relation at the analytical level. The kernel function enters the formulation as an input. Any effort to narrow down this function family is valuable. Dispersion relations of the nonlocal governing operators are identified. Using a Taylor expansion, a selection criterion is devised to determine the kernel function that provides the best approximation to the classical (linear) dispersion relation. The criterion is based on selecting the smallest coefficient in magnitude of the dominant term in the Taylor expansion after the constant term. The governing operators are constructed using functional calculus, which provides the explicit expression of the eigenvalues of the operators. The ability to express eigenvalues explicitly allows us to obtain dispersion relations at the analytical level, thereby isolating the effect of discretization on the dispersion relation. With the presence of expressions of eigenvalues of the governing operator, the analysis is clear and accessible. The choices made to obtain the best approximation to the classical dispersion relation become completely transparent. We find that the truncated Gaussian family is the most effective compared to power and rational function families.

Magnetic electron collimation in three-dimensional semi-metals

While electrons moving perpendicular to a magnetic field are confined to cyclotron orbits, they can move freely parallel to the field. This simple fact leads to complex current flow in clean, low carrier density semi-metals, such as long-ranged current jets forming along the magnetic field when currents pass through point-like constrictions. Occurring accidentally at imperfect current injection contacts, the phenomenon of "current jetting" plagues the research of longitudinal magneto-resistance, which is particularly important in topological conductors. Here we demonstrate the controlled generation of tightly focused electron beams in a new class of micro-devices machined from crystals of the Dirac semi-metal Cd3As2. The current beams can be guided by tilting a magnetic field and their range tuned by the field strength. Finite element simulations quantitatively capture the voltage induced at faraway contacts when the beams are steered towards them, supporting the picture of controlled electron jets. These experiments demonstrate direct control over the highly non-local signal propagation unique to 3D semi-metals in the current jetting regime, and may lead to applications akin to electron optics in free space.

Magnetic electron collimation in three-dimensional semi-metals

While electrons moving perpendicular to a magnetic field are confined to cyclotron orbits, they can move freely parallel to the field. This simple fact leads to complex flow in clean, low carrier density semi-metals, such as long-ranged jets forming along the magnetic field when currents pass through point-like constrictions. Occurring accidentally at imperfect injection contacts, the phenomenon of current plagues the research of longitudinal magneto-resistance which is particularly important in topological conductors. Here we demonstrate the controlled generation of tightly focused electron beams in a new class of micro-devices machined from crystals of the Dirac semi-metal Cd3As2. The beams can be guided by tilting a magnetic field and their range tuned by the field strength. Finite element simulations quantitatively capture the voltage induced at faraway contacts when the beams are steered towards them, supporting the picture of controlled electron jets. These experiments demonstrate the first direct control over the highly nonlocal signal propagation unique to 3D semi-metals in the jetting regime, and may lead to novel applications akin to electron optics in free space.

Analysis of the nonlocal wave propagation problem with volume constraints

Analysis of the nonlocal wave propagation problem with volume constraints

Efficient Segmentation-Based PatchMatch for Large Displacement Optical Flow Estimation

Efficient optical flow estimation with high accuracy is a challenging problem in computer vision. In this paper, we present a simple but efficient segmentation-based PatchMatch framework to address this issue. Specifically, it firstly generates sparse seeds without losing important motion information by over-segmentation, and then yields sparse matches by adopting a coarse-to-fine PatchMatch with sparse seeds. Such a scheme enhances the robustness of global regularization and yields better matching results compared with the existing NNF techniques while leading to a significant speed-up due to the sparsity of these seeds. Simultaneously, we introduce an extended nonlocal propagation and adaptive random search to address the basic limitation of the traditional coarse-to-fine framework in handing motion details that often vanish at coarser levels. Finally, we obtain dense matches at the finest level through an efficient sparse-to-dense matching according to the cues of over-segmentation. While performing an efficient approximation for over-segmentation, the proposed algorithm runs significantly fast and is robust to large displacements while preserving important motion details. It also achieves good performance on the challenging MPI-Sintel and Kitti flow 2015 datasets.

Peridynamic micromechanical prediction of nonlocal damage initiation and propagation in DP steels based on real microstructure

Dual phase steels are the complex heterogeneous materials that are widely used in various automobile industries. It is important to develop numerical methods to enhance the capability of the damage mechanism prediction. Dual phase steels consist of soft ferrite and hard martensite phases and the grain boundaries play the main role as the important location with possible occurrence of damage in these materials. In this study, a microstructure-based approach using representative volume elements is utilized to evaluate the damage initiation and propagation. The material is modeled at the microscopic scale using real microstructural SEM images. A two-dimensional model is developed and the damage mechanisms of dual phase steels are simulated using a bond based peridynamic microstructural model. According to the peridynamic simulation, no mesh refinement is necessary, as damage is inherently characterized by bond breakages and the obtained damage patterns are compared with experimental SEM images. Finally, a sensitivity analysis is conducted to understand the effect of peridynamic discretization, real microstructure, horizon size and interface behavior on the damage pattern of the proposed model under tension static loading. It is shown that the obtained damage initiation and propagation patterns are in good agreement with the experimental results.