Low-dimensional Systems Research Articles

Development of a Machine Learning Potential to Study the Structure and Thermodynamics of Nickel Nanoclusters.

Machine learning (ML) potentials such as the Gaussian approximation potential (GAP) have demonstrated impressive capabilities in mapping structure to properties across diverse systems. Here, we introduce a GAP model for low-dimensional Ni nanoclusters and demonstrate its flexibility and effectiveness in capturing the energetics, structural diversity, and thermodynamic properties of Ni nanoclusters across a broad size range. Through a systematic approach encompassing model development, validation, and application, we evaluate the model's efficacy in representing energetics and configurational features in low-dimensional regimes while also examining its extrapolative nature to vastly different spatiotemporal regimes. Our analysis and discussion shed light on the data quality required to effectively train such models. Trajectories from large-scale MD simulations using the GAP model analyzed with data-driven models like graph neural networks reveal intriguing insights into the size-dependent phase behavior and thermomechanical stability characteristics of porous Ni nanoparticles. Overall, our work underscores the potential of ML models, which coupled with data-driven approaches serve as versatile tools for studying low-dimensional systems and complex material dynamics.

Atomically Sharp 1D Interfaces in 2D Lateral Heterostructures of VSe2─NbSe2 Monolayers.

van der Waals heterostructures have emerged as an ideal platform for creating engineered artificial electronic states. While vertical heterostructures have been extensively studied, realizing high-quality lateral heterostructures with atomically sharp interfaces remains a major experimental challenge. Here, we advance a one-pot two-step molecular beam lateral epitaxy approach and successfully synthesize atomically well-defined 1T-VSe2─1H-NbSe2 lateral heterostructures. We demonstrate the formation of defect-free lateral heterostructures and characterize their electronic structure by using scanning tunneling microscopy and spectroscopy together with density functional theory calculations. We find additional electronic states at the 1D interface as well as signatures of Kondo resonances in a side-coupled geometry. Our experiments explored the full potential of lateral heterostructures for realizing exotic electronic states in low-dimensional systems for further studies of artificial designer quantum materials.

Effective methods for quantifying complexity based on improved ordinal partition networks: Topological dispersion entropy and weighted topological dispersion entropy

Topological permutation entropy is based on ordinal partition networks (OPNs) to approximate topological entropy of low-dimensional chaotic systems. But the ordinal patterns of OPN ignore the magnitude of the amplitude value. To solve the problem, we propose topological dispersion entropy (TDE) and weighted topological dispersion entropy (WTDE) based on dispersion patterns to characterize the complexity of a system. Furthermore, WTDE strengthens the topological structure analysis of complex networks by weighting the adjacency matrix of the improved ordinal partition networks, thereby more accurately capturing the dynamic evolution of time series. The proposed methods are comprehensively evaluated by numerical experiments. The results show that the performance of both TDE and WTDE is significantly better than TPE. Especially, WTDE has good stability to parameters, data length, and noise. Finally, combining support vector machines and K-Nearest Neighbor, TDE and WTDE are applied to the classification of physiological data and mechanical failure data.

ZnO Nanowall Network-Based Tactile/Gesture Sensors and Prediction with Machine Learning.

In low-dimensional material systems, augmented physical and chemical properties may be witnessed through a unique morphological evolution. Here, we report the development of an optimized nanowall network of ZnO for the fabrication of a flexible single-electrode triboelectric nanogenerator (STENG)-based tactile and gesture sensors. The chemically grown nanowall network with an adequate pore area endows superior triboelectric output (current ∼0.6 μA and power ∼20 μW/cm2) by offering an optimum surface area and dielectric constant for pressure sensing applications. The rational comparison of the triboelectric properties of nanowall and nanorod structures of ZnO reveals that the higher surface area offered by the hollow walls leads to superior output characteristics. The demonstration of pressure sensitivity of the STENG ∼1 V/N is promising for self-powered tactile sensing applications. The array of STENG sensors, when attached to a user hand, generates distinguishable signals while holding objects of varying curvature and mass. Again, the observation of sensitivity of ∼0.1 V per degree during finger movement activity indicates the gesture sensing ability of the nanowall-based TENG system, facilitating sign language expression through the movement of fingers. Further, the generated electrical signals during tactile and gesture sensing can be classified and recognized through the deployment of machine learning (ML) techniques. In fact, the implementation of Random Forest and K-Nearest Neighbor models has offered an accuracy of 96% while recognizing the output signals generated by the sensor arrays. The demonstration of superior sensing characteristics with the optimized nanowall network may be advantageous in innovating prototype sensors for the differently abled people to distinguish or classify objects on the basis of material, morphology, and mass during their regular activities.

Orthogonality catastrophe beyond bosonization from post-selection

We show that the dynamics induced by post-selected measurements can serve as a controlled route to access physical processes beyond the boundaries of Luttinger liquid physics. We consider a one-dimensional fermionic wire whose dynamics results from a sequence of weak measurements of the fermionic density at a given site, interspersed with unitary hopping dynamics. This realizes a non-Hermitian variant of the celebrated instance of a local scatterer in a fermionic system and its ensuing orthogonality catastrophe. We observe a distinct crossover in the system's time evolution as a function of the fermion density. In the high-density regime, reminiscent of the Hermitian case, a bosonized version of the model properly describes the dynamics while, as we delve into the low-density regime, the validity of bosonization breaks down, giving rise to irreversible behavior. Notably, this crossover from reversible to irreversible dynamics is nonperturbative in the measurement rate and can manifest itself even with relatively shallow measurement rates, provided that the system's density remains below the crossover threshold. Our results render a conceptually transparent model for exploring nonperturbative effects beyond bosonization, which could be used as a stepping stone to explore novel routes for the control of nonlinear dynamics in low-dimensional quantum systems. Published by the American Physical Society 2024

Low-dimensional projection of reactivity classes in chemical reaction dynamics using supervised dimensionality reduction.

Transition state theory (TST) provides a framework to estimate the rate of chemical reactions. Despite its great success with many reaction systems, the underlying assumptions such as local equilibrium and nonrecrossing do not necessarily hold in all cases. Although dynamical systems theory can provide the mathematical foundation of reaction tubes existing in phase space that enables us to predict the fate of reactions free from the assumptions of TST, numerical demonstrations for large systems have been yet one of the challenges. Here, we propose a dimensionality reduction algorithm to demonstrate structures in phase space (called reactive islands) that predict reactivity in systems with many degrees of freedom. The core of this method is the application of supervised principal component analysis, where a coordinate transformation is performed to preserve the dynamical information on reactivity (i.e., to which potential basin the system moves from a region of interest) as much as possible. The reactive island structures are expected to be reflected in the transformed, low-dimensional phase space. As an illustrative example, the algorithm is scrutinized using a modified Hénon-Heiles Hamiltonian system extended to many degrees of freedom, which has three channels leading to three different products from one stable potential basin. It is shown that our algorithm can predict the reactivity in the transformed, low-dimensional coordinate system better than a naïve coordinate system and that the reactivity distribution in the transformed low-dimensional space is considered to reflect the underlying reactive islands.

Study on the effects of strain and electrostatic doping on the magnetic anisotropy of GaN/VTe2 van der waals heterostructure

Using a first-principles approach, this study delves into the effects of strain and electrostatic doping on the electronic and magnetic properties of the GaN/VTe2van der Waals (vdW) heterostructure. The results reveal that when the GaN/VTe2vdW heterostructure is doped with 0.1h/0.2hof electrostatic charge, its magnetization direction undergoes a remarkable reversal, shifting from out-of-plane orientation to in-plane direction. Therefore, we conduct a thorough investigation into the influence of electron orbitals on magnetic anisotropy energy. In addition, as the strain changes from -1% to 1%, the 100% spin polarization region of the GaN/VTe2vdW heterostructure becomes smaller. It is worth noting that at a doping concentration of 0.1h, the GaN/VTe2vdW heterostructure has a Curie temperature of 30 K above room temperature. This comprehensive study provides valuable insights and provides a reference for analyzing the electronic and magnetic properties of low-dimensional systems.

Stacking Fault Nucleation in Films of Vertically Oriented Multiwall Carbon Nanotubes by Pyrolysis of Ferrocene and Dimethyl Ferrocene at a Low Vapor Flow Rate

Recent observations of superconductivity in low-dimensional systems composed of twisted, untwisted, or rhombohedral graphene have attracted significant attention. One-dimensional moiré superlattices and flat bands have interestingly been identified in collapsed chiral carbon nanotubes (CNTs), opening up new avenues for the tunability of the electronic properties in these systems. The nucleation of hexagonal moiré superlattices and other types of stacking faults has also been demonstrated in partially collapsed and uncollapsed carbon nano-onions (CNOs). Here, we report a novel investigation on the dynamics of stacking fault nucleation within the multilayered lattices of micrometer-scale vertically oriented films of multiwall CNTs (MWCNTs), resulting from the pyrolysis of molecular precursors consisting of ferrocene or dimethyl ferrocene, at low vapor flow rates of ~5–20 mL/min. Interestingly, local nucleation of moiré-like superlattices (as stacking faults) was found when employing dimethyl ferrocene as the pyrolysis precursor. The morphological and structural properties of these systems were investigated with the aid of scanning and transmission electron microscopies, namely SEM, TEM, and HRTEM, as well as X-ray diffraction (XRD) and Raman point/mapping spectroscopy. Deconvolution analyses of the Raman spectra also demonstrated a local surface oxidation, possibly occurring on defect-rich interfaces, frequently identified within or in proximity of bamboo-like graphitic caps. By employing high-temperature Raman spectroscopy, we demonstrate a post-growth re-graphitization, which may also be visualized as an alternative way of depleting the oxygen content within the MWCNTs’ interfaces through recrystallization.

Learning quantum properties from short-range correlations using multi-task networks

Characterizing multipartite quantum systems is crucial for quantum computing and many-body physics. The problem, however, becomes challenging when the system size is large and the properties of interest involve correlations among a large number of particles. Here we introduce a neural network model that can predict various quantum properties of many-body quantum states with constant correlation length, using only measurement data from a small number of neighboring sites. The model is based on the technique of multi-task learning, which we show to offer several advantages over traditional single-task approaches. Through numerical experiments, we show that multi-task learning can be applied to sufficiently regular states to predict global properties, like string order parameters, from the observation of short-range correlations, and to distinguish between quantum phases that cannot be distinguished by single-task networks. Remarkably, our model appears to be able to transfer information learnt from lower dimensional quantum systems to higher dimensional ones, and to make accurate predictions for Hamiltonians that were not seen in the training.

Model and Energy Bounds for a Two-Dimensional System of Electrons Localized in Concentric Rings.

We study a two-dimensional system of interacting electrons confined in equidistant planar circular rings. The electrons are considered spinless and each of them is localized in one ring. While confined to such ring orbits, each electron interacts with the remaining ones by means of a standard Coulomb interaction potential. The classical version of this two-dimensional quantum model can be viewed as representing a system of electrons orbiting planar equidistant concentric rings where the kinetic energy may be discarded when one is searching for the lowest possible energy. Within this framework, the lowest possible energy of the system is the one that minimizes the total Coulomb interaction energy. This is the equilibrium energy that is numerically determined with high accuracy by using the simulated annealing method. This process allows us to obtain both the equilibrium energy and position configuration for different system sizes. The adopted semi-classical approach allows us to provide reliable approximations for the quantum ground state energy of the corresponding quantum system. The model considered in this work represents an interesting problem for studies of low-dimensional systems, with echoes that resonate with developments in nanoscience and nanomaterials.

The origin of broadband blue emission in zero-dimensional organic lead iodine perovskites: A first-principles study.

Broadband blue emission in zero-dimensional perovskites has received considerable attention, which is very important for the realization of stable blue-light emitters; however, the underlying formation mechanism remains unclear. Based on first-principles calculations, we have systematically studied the self-trapped excitons (STEs) behavior and luminescence properties in 0D-(DMA)4PbI6 perovskite. Our calculations show that there is a significant difference between the intrinsic STE luminescence mechanism (∼2.51eV) and experimental observations (∼2.70eV). In contrast, we found that the iodine vacancy (VI) is energetically accessible and exhibits a shallow charge transition level at ∼2.69eV (0/+1) above the valence band maximum, which provides the initial local well for the STEs formation. Moreover, the low electronic dimension synergistic Jahn-Teller distortion facilitates the formation of extrinsic excitons self-trapping. Further excited state electronic structure analysis and configuration coordinate diagram calculations confirmed that the broadband blue emission in 0D-(DMA)4PbI6 is the origin of VI-induced extrinsic STEs instead of intrinsic STEs. Therefore, our simulation results rationalize the experimental phenomena and provide important insights into the formation mechanism of STEs in low-dimensional perovskite systems.

Investigation of Tandem Queuing Systems Using Machine Learning Methods

This paper considers tandem queuing systems with limited buffer sizes in each phase. The system handles an incoming correlated MAP flow and the service time obeys a PH-distribution. Models of such systems and methods for their investigation are briefly reviewed from the historical perspective. According to the review, the problem statement presented below, the methods proposed for solving this problem, and the corresponding results are novel. An accurate algorithm for calculating the performance characteristics of low-dimensional tandem queuing systems is described, including an estimate of the algorithm’s complexity. An approach using both machine learning and simulation modeling is suggested for the investigation of high-dimensional tandem queuing systems. Numerical analysis results are provided to show the effectiveness of machine learning methods for estimating the performance of tandem queuing systems.

Reduced Markovian models of dynamical systems

Leveraging recent work on data-driven methods for constructing a finite state space Markov process from dynamical systems, we address two problems for obtaining further reduced statistical representations. The first problem is to extract the most salient reduced-order dynamics for a given timescale by using a modified clustering algorithm from network theory. The second problem is to provide an alternative construction for the infinitesimal generator of a Markov process that respects statistical features over a large range of time scales. We demonstrate the methodology on three low-dimensional dynamical systems with stochastic and chaotic dynamics. We then apply the method to two high-dimensional dynamical systems, the Kuramoto-Sivashinky equations and data sampled from fluid-flow experiments via Particle Image Velocimetry. We show that the methodology presented herein provides a robust reduced-order statistical representation of the underlying system.

Posterior comparison of model dynamics in several hybrid turbulence model forms

Hybrid turbulence models that can accurately reproduce unsteady three-dimensional flow physics across the entire range of grid scales and turbulence dynamics from Reynolds-averaged Navier–Stokes (RANS), through large-eddy simulation (LES), down to direct numerical simulations (DNS) are of increasing interest to the turbulence modeling community. However, despite decades of research and development, the basic tasks of eliminating poor-performing hybrid RANS-LES models and accelerating adoption of superior models through well-designed validation and verification have yet to occur. As a step in this direction, in this work we evaluate thirteen different hybrid RANS-LES models via systematic grid refinement of decaying homogeneous isotropic turbulence. We further derive a novel mathematical framework for assessing the energy partitioning dynamics of each Hybrid RANS-LES model, wherein model-to-model variations in energy partitioning can be interpreted as different feedback mechanisms operating on a low-dimensional nonlinear dynamical system. We found that model forms similar to the flow simulation methodology—also often termed very-large eddy simulation—are dynamically inconsistent with DNS at all resolutions. Additionally, we found a strong dynamical similarity in the feedback mechanisms of all models related to detached eddy simulation and partially averaged Navier–Stokes that is inherent to their general model forms.

Adjoint-Based Design Optimization of Stability Constrained Systems

A partial differential equation (PDE) constrained design optimization problem usually optimizes a characteristic of a dynamical system around an equilibrium point. However, a commonly omitted constraint is the linear stability constraint at the equilibrium point, which undermines the optimized solution’s applicability. To enforce the linear stability constraint in practical gradient-based optimization, the derivatives must be computed accurately, and their computational cost must scale favorably with the number of design variables. In this paper, we propose an algorithm based on the coupled adjoint method and the algorithmic differentiation method that can compute the derivative of such constraint accurately and efficiently. We verify the proposed method using several simple low-dimensional dynamical systems. The relative difference between the adjoint method and the finite differences is between 10−6 to 10−8. The proposed method is demonstrated through several optimizations, including a nonlinear aeroelastic optimization. The proposed algorithm has the potential to be applied to more complex problems involving large-scale nonlinear PDEs, such as aircraft flutter and buffet suppression.

A Novel Parameter-Variabled and Coupled Chaotic System and Its Application in Image Encryption with Plaintext-Related Key Concealment.

The design of a chaotic system and pseudo-random sequence generation method with excellent performance and its application in image encryption have always been attractive and challenging research fields. In this paper, a new model of parameter-variabled coupled chaotic system (PVCCS) is established by interaction coupling between parameters and states of multiple low-dimensional chaotic systems, and a new way to construct more complex hyperchaotic systems from simple low-dimensional systems is obtained. At the same time, based on this model and dynamical DNA codings and operations, a new pseudo-random sequence generation method (PSGM-3DPVCCS/DNA) is proposed, and it is verified that the generated pseudo-random sequence of PSGM-3DPVCCS/DNA has excellent random characteristics. Furthermore, this paper designs a novel pixel chain diffusion image encryption algorithm based on the proposed parameter-variabled coupled chaotic system (PVCCS) in which the hash value of plaintext image is associated with the initial key to participate in the encryption process so that the encryption key is closely associated with plaintext, which improves the security of the algorithm and effectively resists the differential cryptanalysis risk. In addition, an information hiding method is designed to hide the hash value of plaintext image in ciphertext image so that the hash value does not need to be transmitted in each encryption, and the initial key can be reused, which solves the key management problem in application and improves the application efficiency of the encryption algorithm. The experimental analysis shows that the chaotic system constructed in this paper is creative and universal and has more excellent chaotic characteristics than the original low-dimensional system. The sequence generated by the pseudo-random sequence generation method has excellent pseudo-random characteristics and security, and the image encryption algorithm can effectively resist differential cryptanalysis risk, showing advanced encryption performance.

Model order reduction for the input–output behavior of a geothermal energy storage

In this article, we consider a geothermal energy storage system in which the spatio-temporal temperature distribution is modeled by a heat equation with a time-dependent convection term. Such storage systems are often embedded in residential heating systems. The control and management of such systems requires knowledge of aggregated characteristics of the temperature distribution in the storage. These describe the input–output behavior of the storage, the associated energy flows, and their response to charging and discharging processes. Our aim is to derive an efficient, approximate description of these characteristics by using low-dimensional systems of ordinary differential equations (ODEs). This leads to a model order reduction problem for a large-scale linear system of ODEs resulting from the semidiscretization of the heat equation combined with a linear algebraic output equation. In a first step, we approximated the nonautonomous system of ODEs by a linear time-invariant system. Then, we applied Lyapunov balanced truncation model order reduction to approximate the output by a reduced-order system that has only a few state equations but almost the same input–output behavior. The results of our extensive numerical experiments show the efficiency of the applied model order reduction method. We found that only a few suitably chosen ODEs are sufficient to achieve good approximations of the input–output behavior of the storage.

Applying the Expectation-Maximization Algorithm to Multivariate Signal Extraction

Understanding time series signal extraction is vital for federal agencies, especially as data collection accelerates. One natural extension is moving from univariate to multivariate signal extraction, which offers the promise of reducing extraction error by exploiting cross-sectional relationships. However, such an extension ushers in new computational challenges, viz. larger parameter spaces and more complicated objective functions. The Expectation-Maximization (EM) algorithm provides a methodology to implicitly compute (or approximate) maximum likelihood estimates (MLEs). This paper provides methodology for applying the EM algorithm to a class of latent component multivariate time series models that allow for a nuanced specification of the unobserved signal. We derive an explicit formula for the maximization step, which facilitates computation speed while also improving the stability of the algorithm. Numerical studies demonstrate EM’s ability to efficiently compute MLEs in low-dimensional systems, while also providing feasible estimates in moderate-dimensional systems where MLEs are infeasible to compute. Applications to monthly housing starts and daily immigration are provided.

Designer spin-orbit superlattices: symmetry-protected Dirac cones and spin Berry curvature in two-dimensional van der Waals metamaterials

The emergence of strong relativistic spin-orbit effects in low-dimensional systems provides a rich opportunity for exploring unconventional states of matter. Here, we present a route to realise tunable relativistic band structures based on the lateral patterning of proximity-induced spin-orbit coupling. The concept is illustrated on a patterned graphene–transition metal dichalcogenide heterostructure, where the spatially periodic spin-orbit coupling induces a rich mini-band structure featuring massless and massive Dirac bands carrying large spin Berry curvature. The envisaged systems support robust and gate-tunable spin Hall responses driven by the quantum geometry of mini-bands, which can be tailored through metasurface fabrication methods and twisting effects. These findings open pathways to two-dimensional quantum material design and low-power spintronic applications.

Probing multi-mobility edges in quasiperiodic mosaic lattices

The mobility edge (ME) is a crucial concept in understanding localization physics, marking the critical transition between extended and localized states in the energy spectrum. Anderson localization scaling theory predicts the absence of ME in lower dimensional systems. Hence, the search for exact MEs, particularly for single particles in lower dimensions, has recently garnered significant interest in both theoretical and experimental studies, resulting in notable progress. However, several open questions remain, including the possibility of a single system exhibiting multiple MEs and the continual existence of extended states, even within the strong disorder domain. Here, we provide experimental evidence to address these questions by utilizing a quasiperiodic mosaic lattice with meticulously designed nanophotonic circuits. Our observations demonstrate the coexistence of both extended and localized states in lattices with broken duality symmetry and varying modulation periods. By single site injection and scanning the disorder level, we could approximately probe the ME of the modulated lattice. These results corroborate recent theoretical predictions, introduce a new avenue for investigating ME physics, and offer inspiration for further exploration of ME physics in the quantum regime using hybrid integrated photonic devices.