Nonlocal Interactions Research Articles

Nonlocal Cable-Network Metamaterials.

Metamaterials are artificial materials in which the atoms of ordinary solids are replaced by tailored functional building blocks. Therefore, previous work has emphasized tailoring the inside of the building blocks, for example, by exploiting local resonances, to realize unusual effective metamaterial properties. However, the wave properties of a metamaterial are not only determined by its building blocks but also by the interactions between these building blocks. Here, reconfigurable "plug-and-play" electromagnetic metamaterials are introduced for which the building blocks are essentially trivial standard bayonet Neill-Concelman (BNC) connectors and the effective metamaterial properties are solely achieved by tailoring the local and especially the nonlocal interactions mediated by standard coaxial cables. Unprecedented dispersion relations of the lowest band with multiple regions of slow waves and backward waves are demonstrated. Importantly, the dispersion relation of such metamaterials dominated by nonlocal interactions is not limited by the principle of causality in the same way as for metamaterials designed by local resonances of building blocks.

Nonlocal symmetries and interaction solutions for the (n + 1)-dimensional generalized Korteweg–de Vries equation

The (n + 1)-dimensional generalized KdV equation is presented in this paper, and we further investigate its nonlocal symmetries by different methods. It can be seen that the symmetrical transformations obtained by different nonlocal symmetries are usually equivalent. Based on the obtained Lie point symmetry as well as the mth finite symmetrical transformations, we obtain its soliton molecules and multiple soliton solutions. Additionally, for the case of n = 4 various types of interaction solutions among solitons and periodic waves are obtained by the similarity reduction method.

Quantum approximate optimization algorithm applied to the binary perceptron

We apply digitized quantum annealing (QA) and quantum approximate optimization algorithm (QAOA) to a paradigmatic task of supervised learning in artificial neural networks: the optimization of synaptic weights for the binary perceptron. At variance with the usual QAOA applications to MaxCut, or to quantum spin-chains ground-state preparation, here the classical cost function is characterized by highly nonlocal multispin interactions. Yet, we provide evidence for the existence of optimal smooth solutions for the QAOA parameters, which are transferable among typical instances of the same problem, and we prove numerically an enhanced performance of QAOA over traditional QA. We also investigate on the role of the classical cost-function landscape geometry in this problem. By artificially breaking this geometrical structure, we show that the detrimental effect of a gap-closing transition, encountered in QA, is also negatively affecting the performance of our QAOA implementation.

Achieving any desirable dispersion curves using non-local phononic crystals

Phononic crystals and vibro-elastic metamaterials are characterized by their dispersion relations—how frequency changes with wave number/vector. While there are many existing methods to solve the forward problem of obtaining the dispersion relation from any arbitrarily given design. The inverse problem of obtaining a design for any arbitrarily given dispersion bands has only had very limited success so far. Here, we report a new design scheme for arbitrary dispersion relations by incorporating non-local interactions between unit cells. Considering discrete models of one-dimensional mass-spring chains, we investigate the effects of both local (i.e., springs between the nearest neighbors) and non-local (i.e., springs between the next nearest neighbors and other longer-range springs) interactions. First, we derive the general governing equations of non-local phononic chains. Next, we examine all design constraints for a linear, periodic, passive, statically stable, non-gyroscopic, and free-standing system. Finally, we perform analytical calculations and numerical simulations to solve the inverse problem. The results illuminate a new path toward novel wave manipulation functionalities, such as ordinary and higher-order critical points with zero-group-velocity (ZGV) modes, as well as multi-wavelength and multi-speed propagations of the same mode at the same frequency.

Machine Learning Interatomic Potentials and Long-Range Physics.

Advances in machine learned interatomic potentials (MLIPs), such as those using neural networks, have resulted in short-range models that can infer interaction energies with near ab initio accuracy and orders of magnitude reduced computational cost. For many atom systems, including macromolecules, biomolecules, and condensed matter, model accuracy can become reliant on the description of short- and long-range physical interactions. The latter terms can be difficult to incorporate into an MLIP framework. Recent research has produced numerous models with considerations for nonlocal electrostatic and dispersion interactions, leading to a large range of applications that can be addressed using MLIPs. In light of this, we present a Perspective focused on key methodologies and models being used where the presence of nonlocal physics and chemistry are crucial for describing system properties. The strategies covered include MLIPs augmented with dispersion corrections, electrostatics calculated with charges predicted from atomic environment descriptors, the use of self-consistency and message passing iterations to propagated nonlocal system information, and charges obtained via equilibration schemes. We aim to provide a pointed discussion to support the development of machine learning-based interatomic potentials for systems where contributions from only nearsighted terms are deficient.

An unsupervised latent/output physics-informed convolutional-LSTM network for solving partial differential equations using peridynamic differential operator

This study presents a novel unsupervised convolutional Neural Network (NN) architecture with nonlocal interactions for solving Partial Differential Equations (PDEs). The nonlocal Peridynamic Differential Operator (PDDO) is employed as a convolutional filter for evaluating derivatives the field variable. The NN captures the time-dynamics in smaller latent space through encoder–decoder layers with a Convolutional Long–short Term Memory (ConvLSTM) layer between them. The ConvLSTM architecture is modified by employing a novel activation function to improve the predictive capability of the learning architecture for physics with periodic behavior. The physics is invoked in the form of governing equations at the output of the NN and in the latent (reduced) space. By considering a few benchmark PDEs, we demonstrate the training performance and extrapolation capability of this novel NN architecture by comparing against Physics Informed Neural Networks (PINN) type solvers. It is more capable of extrapolating the solution for future timesteps than the other existing architectures.

Monitoring Land Degradation through Vegetation Dynamics Mathematical Modeling: Case of Jornada Basin (in the U.S.)

Arid ecosystems are known to be sensitive to climate change. The Jornada Basin in the USA, as one representative of arid land, has suffered from land degradation in recent decades. In order to disentangle the climate–vegetation feedback, we analyzed the vegetation dynamics under the effects of climate change via a mathematical model based on the reaction–diffusion mechanism. Using this model, we conducted a sensitive analysis of climate factors and concluded that the ecosystem might experience a catastrophic shift with the climatic deterioration. We considered the non-local interaction term to explain the competition among plants. Additionally, the PLR (power law range) metric was used to quantify the extent of the degradation and to compare the results of the vegetation patterns from the remote sensing data and the simulations. From the results, this model could simulate the trends of land degradation in this area. We found that the land degradation could be mainly attributed to climate changes in recent years. This approach suggests that vegetation patterns can provide hints as to whether the ecosystem is approaching desertification. These results can help with mapping vulnerable arid areas around the world through model simulation and satellite images.

Ultrathin Acoustic Holography

AbstractHow to realize acoustic holography via ultradeep‐subwavelength structures is a challenging problem in the past decades, which is thought impossible due to the linear proportional relationship between the structural thickness and acoustic wavelength. In this article, the methodology of ultrathin holography by patterning holes in an acoustic insulation plate with an ultradeep‐subwavelength thickness is introduced. The transmitted sound field can be manipulated arbitrarily to form a desired shape by designing the ultrathin pattern based on the nonlocal wave interaction theory. The physical mechanism of the nonlocal behavior to achieve a sophisticated hologram is revealed due to the interaction among the sound wave components themselves. Furthermore, the experiments are designed to map out the pressure amplitude field of a “sun” pattern in air and water, respectively. The work demonstrates the advantage of nonlocal ultrathin holography in the applications of ultrathin acoustic devices and provides inspiration for the holographic wave manipulation.

Phase transitions in TGFT: a Landau-Ginzburg analysis of Lorentzian quantum geometric models

In the tensorial group field theory (TGFT) approach to quantum gravity, the basic quanta of the theory correspond to discrete building blocks of geometry. It is expected that their collective dynamics gives rise to continuum spacetime at a coarse grained level, via a process involving a phase transition. In this work we show for the first time how phase transitions for realistic TGFT models can be realized using Landau-Ginzburg mean-field theory. More precisely, we consider models generating 4-dimensional Lorentzian triangulations formed by spacelike tetrahedra the quantum geometry of which is encoded in non-local degrees of freedom on the non-compact group SL(2, ℂ) and subject to gauge and simplicity constraints. Further we include ℝ-valued variables which may be interpreted as discretized scalar fields typically employed as a matter reference frame. We apply the Ginzburg criterion finding that fluctuations around the non-vanishing mean-field vacuum remain small at large correlation lengths regardless of the combinatorics of the non-local interaction validating the mean-field theory description of the phase transition. This work represents a first crucial step to understand phase transitions in compelling TGFT models for quantum gravity and paves the way for a more complete analysis via functional renormalization group techniques. Moreover, it supports the recent extraction of effective cosmological dynamics from TGFTs in the context of a mean-field approximation.

A quantum-based approach for offensive security against cyber attacks in electrical infrastructure

Deciding the correct offensive security strategy for safeguarding the electrical physical infrastructures of smart grids is a challenging task. The offensive security training against various cyber-attacks focuses on a multitude of electrical subsystems and measurement systems like the Load Frequency Control(LFC) system. Primarily, the principal challenge is to categorize and parameterize the various possible cyber-attacks on electrical infrastructures. This is done by specifying and selecting cyber-attacks considering various main and subsystem blocks of the power structural system within each area of major installations. In this research investigation, formal modeling of security strategy is proposed using Lambda calculus with both classical and quantum perspectives. Furthermore, using a Quantum Machine Learning (QML) technique, the procedure for correct vulnerability prediction, exploitation, and execution strategy is presented with an approximated likelihood of attack and its mode. The local and non-local interactions are introduced as quantum threats and entanglement threats similar to False Data Injection (FDI) methods to induce the attack and counter-attack events through quantum causality connections. Finally, the Quirk simulator is used to validate the proposed quantum design of offensive and defensive attack models considering scenarios of exogenous and scaling attacks on the LFC systems that support the feasibility of the present research work to address the issue of cyber-attacks on the power system networks.

Postcritical Behavior of Nonlocal Strain Gradient Arches: Formulation and Differential Quadrature Solution

Arches are important components in nanostructures and systems. Because of the remarkable strength of nanomaterials, nanoarches are slender, thus enhancing their vulnerability to geometric instability, such as buckling. Although molecular simulations are often employed to analyze nanostructures, their use in routine analysis/design is formidable due to prohibitively exhaustive computation. Equivalent continuum models were developed as alternatives. The buckling and postcritical phenomena of the classical arch also form an important benchmark problem in nonlinear mechanics. This study investigates the buckling and the postcritical behavior of nanoarch subjected to inward pressure using nonlocal (NL), strain gradient (SG) continuum theory. The governing equations are derived in the form of a sixth-order nonlinear integrodifferential equation, unlike the fourth-order for a classical arch. The equation is then solved numerically using a differential quadrature (DQ) with appropriate boundary conditions. An incremental-iterative arc-length continuation is employed for the solution of the resulting algebraic system of equations. The equilibrium paths are traced for the possible instability modes, such as symmetric/antisymmetric bifurcations, snap-through and limit point instability, ascertained with the internal-external force diagrams. A particular instability mode is triggered at a certain threshold/range of the slenderness ratio of the arch, which is significantly influenced by the NL and SG interactions. These interactions not only cause quantitative changes in the instability behavior but also lead to qualitative changes, such as cessation, shift, and conversion of modes, more prominently for SG arches. Similar to classical arches, the prebuckling nonlinearity is shown to be significant.

Accelerated kinetic Monte Carlo methods for general nonlocal traffic flow models

This paper presents a class of one-dimensional cellular automata (CA) models on traffic flows, featuring nonlocal look-ahead interactions. We develop kinetic Monte Carlo (KMC) algorithms to simulate the dynamics. The standard KMC method can be inefficient for models with global interactions. We design an accelerated KMC method to reduce the computational complexity in the evaluation of the nonlocal transition rates. We investigate several numerical experiments to demonstrate the efficiency of the accelerated algorithm, and obtain the fundamental diagrams of the dynamics under various parameter settings.

A computational framework for modeling thermoelastic behavior of cubic crystals

In this paper, novel nonlocal reformulations of the conventional continuum-based models for modeling the thermoelastic behavior of cubic crystals based on a recently developed lattice particle method are presented. Like molecular dynamics simulation, the lattice particle method decomposes the grain domain into discrete material particles that are regularly packed according to the underlying atomic lattice. Nonlocal interactions are introduced between material particles and top-down approaches are used to relate model parameters to the material physical constants. Three equivalency assumptions are used in the top-down approach, namely, energy equivalency for the mechanical model, heat transfer rate equivalency for the thermal model, and thermal strain equivalency for the thermal-mechanical coupling model. Different from coordinates transformation used in the conventional continuum-based models, lattice rotation is adopted in the lattice particle method to equivalently represent the material anisotropy while explicitly capturing the crystallographic orientation. Two most common Bravais cubic lattices are studied, i.e., the body-centered cubic lattice and the face-center cubic lattice. The validity and prediction accuracy of the developed models are established by comparing the predicted displacements and temperature results with solutions of conventional continuum theories using the finite element method.

Transformable Metasurfaces Enabled by Twisting Induced Nonlocality

AbstractReconfigurable optical interfaces with low power cost are of tremendous interest in imaging and communication applications. This work reveals the nonlocal effect in twisted electric dipoles and demonstrates its capability of non‐volatile transformation on scattering. When electric dipoles are rotated to form a tilted array, the dipolar resonances yield nonlocal interactions tuned by the rotation angle. The collective polarizability transformation maps to a series of circles crossing the origin of coordinates in the complex plane, providing 2π phase coverage and continuous amplitude modulation beyond the theoretical limit of an electric surface. Based on this mechanism, a Bluetooth‐driven nonlocal metasurface is developed for remote switching on scattering channels. Due to the stability of mechanical deformation, the twisted metasurface retains the stored functionality even after the power is removed. Our results offer a nonlocal route to transformable planar optics.

Stochastic drift in discrete waves of nonlocally interacting particles.

In this paper, we investigate a generalized model of N particles undergoing second-order nonlocal interactions on a lattice. Our results have applications across many research areas, including the modeling of migration, information dynamics, and Muller's ratchet-the irreversible accumulation of deleterious mutations in an evolving population. Strikingly, numerical simulations of the model are observed to deviate significantly from its mean-field approximation even for large population sizes. We show that the disagreement between deterministic and stochastic solutions stems from finite-size effects that change the propagation speed and cause the position of the wave to fluctuate. These effects are shown to decay anomalously as (lnN)^{-2} and (lnN)^{-3}, respectively-much slower than the usual N^{-1/2} factor. Our results suggest that the accumulation of deleterious mutations in a Muller's ratchet and the loss of awareness in a population may occur much faster than predicted by the corresponding deterministic models. The general applicability of our model suggests that this unexpected scaling could be important in a wide range of real-world applications.

Accurate global machine learning force fields for molecules with hundreds of atoms.

Global machine learning force fields, with the capacity to capture collective interactions in molecular systems, now scale up to a few dozen atoms due to considerable growth of model complexity with system size. For larger molecules, locality assumptions are introduced, with the consequence that nonlocal interactions are not described. Here, we develop an exact iterative approach to train global symmetric gradient domain machine learning (sGDML) force fields (FFs) for several hundred atoms, without resorting to any potentially uncontrolled approximations. All atomic degrees of freedom remain correlated in the global sGDML FF, allowing the accurate description of complex molecules and materials that present phenomena with far-reaching characteristic correlation lengths. We assess the accuracy and efficiency of sGDML on a newly developed MD22 benchmark dataset containing molecules from 42 to 370 atoms. The robustness of our approach is demonstrated in nanosecond path-integral molecular dynamics simulations for supramolecular complexes in the MD22 dataset.

Analysis of a splitting scheme for a class of nonlinear stochastic Schrödinger equations

We analyze the qualitative properties and the order of convergence of a splitting scheme for a class of nonlinear stochastic Schrödinger equations driven by additive noise. The class of nonlinearities of interest includes nonlocal interaction cubic nonlinearities. We show that the numerical solution is symplectic and preserves the expected mass for all times (trace formula). On top of that, for the convergence analysis, some exponential moment bounds for the exact and numerical solutions are proved. This enables us to provide strong orders of convergence as well as orders of convergence in probability and almost surely. Finally, extensive numerical experiments illustrate the performance of the proposed numerical scheme.

Nonlocal transport of heat in equilibrium drift-diffusion systems

The amount of heat an integer quantum Hall edge state can carry in equilibrium is quantized in universal units of the heat flux quantum ${J}_{q}=\frac{\ensuremath{\pi}{k}_{B}^{2}}{12\ensuremath{\hbar}}{T}^{2}$ per edge state. We address the question of how heat transport in realistic one-dimensional devices can differ from the usual chiral Luttinger liquid theory. We show that a local measurement can reveal a nonquantized amount of heat carried by the edge states, despite a globally equilibrium situation. More specifically, we report a heat enhancement effect in edge states interacting with Ohmic reservoirs in the presence of nonlocal interactions or chirality-breaking diffusive currents. In contrast to a nonequilibrium, nonlinear drag effect, we report an equilibrium, linear phenomenon. The chirality of the edge states creates additional correlations between the reservoirs, reflected in a higher-than-quantum heat flux in the chiral channel. We show that for different types of coupling the enhancement can be understood as static or dynamical back action of the reservoirs on the chiral channel. We show that our results qualitatively hold by replacing the dissipative Ohmic reservoirs by an energy-conserving mesoscopic capacitor and consider the respective transmission lines for different types of interaction.

Ground state of Rydberg-dressed Bose gas confined in periodic moiré lattices

The experimental realization of Rydberg dressing and spin-orbit coupling greatly broadens the research field of ultracold atoms as a quantum simulation platform. Very recently, moiré lattices have attracted intensive study, ranging from condensed matter to ultracold physics. In this paper, the ground-state structure of Rydberg-dressed Bose gas with spin-orbit coupling and confined in moiré lattices is studied, and the effects of nonlocal Rydberg interaction and spin-orbit coupling on the ground state of the system are explored. Our results show that the system has no translational symmetry due to the presence of nonlocal Rydberg interaction, and more and more regular periodic structures present with the increases of the strength of nonlocal Rydberg interaction. In the presence of spin-orbit coupling, the Hamiltonian of the system has an imaginary part, and the phase of the system is not uniformly distributed. It is found that the ground state of the system with spin-orbit coupling present more abundant internal structure base on these periodic structures. The results pave the way for future study of moiré physics in ultracold atom system.

$ L^{p} $ compactness criteria with an application to variational convergence of some nonlocal energy functionals

<abstract><p>Motivated by some variational problems from a nonlocal model of mechanics, this work presents a set of sufficient conditions that guarantee a compact inclusion in the function space of $ L^{p} $ vector fields defined on a domain $ \Omega $ that is either a bounded domain in $ \mathbb{R}^{d} $ or $ \mathbb{R}^{d} $ itself. The criteria are nonlocal and are given with respect to nonlocal interaction kernels that may not be necessarily radially symmetric. Moreover, these criteria for vector fields are also different from those given for scalar fields in that the conditions are based on nonlocal interactions involving only parts of the components of the vector fields. The $ L^{p} $ compactness criteria are utilized in demonstrating the convergence of minimizers of parameterized nonlocal energy functionals.</p></abstract>