Nonperiodic Systems Research Articles

Topological Photonic Alloy.

We present the new concept of photonic alloy as a nonperiodic topological material. By mixing nonmagnetized and magnetized rods in a nonperiodic 2D photonic crystal configuration, we realized photonic alloys in the microwave regime. Our experimental findings reveal that the photonic alloy sustains nonreciprocal chiral edge states even at very low concentration of magnetized rods. The nontrivial topology and the associated edge states of these nonperiodic systems can be characterized by the winding of the reflection phase. Our results indicate that the threshold concentrations for the investigated system within the first nontrivial band gap to exhibit topological behavior approach zero in the thermodynamic limit for substitutional alloys, while the threshold remains nonzero for interstitial alloys. At low concentration, the system exhibits an inhomogeneous structure characterized by isolated patches of nonpercolating magnetic domains that are spaced far apart within a topologically trivial photonic crystal. Surprisingly, the system manifests chiral edge states despite a local breakdown of time-reversal symmetry rather than a global one. Photonic alloys represent a new category of disordered topological materials, offering exciting opportunities for exploring topological materials with adjustable gaps.

Overcoming the barrier of orbital-free density functional theory for molecular systems using deep learning.

Orbital-free density functional theory (OFDFT) is a quantum chemistry formulation that has a lower cost scaling than the prevailing Kohn-Sham DFT, which is increasingly desired for contemporary molecular research. However, its accuracy is limited by the kinetic energy density functional, which is notoriously hard to approximate for non-periodic molecular systems. Here we propose M-OFDFT, an OFDFT approach capable of solving molecular systems using a deep learning functional model. We build the essential non-locality into the model, which is made affordable by the concise density representation as expansion coefficients under an atomic basis. With techniques to address unconventional learning challenges therein, M-OFDFT achieves a comparable accuracy to Kohn-Sham DFT on a wide range of molecules untouched by OFDFT before. More attractively, M-OFDFT extrapolates well to molecules much larger than those seen in training, which unleashes the appealing scaling of OFDFT for studying large molecules including proteins, representing an advancement of the accuracy-efficiency trade-off frontier in quantum chemistry.

Some insights on the COVID-19 pandemic from Fisher information

We explored the application of Fisher information to the study of pandemics and illustrated the insights that can be gained using the COVID-19 pandemic, as a test case. To do so, we applied the Fisher information theory previously applied to periodic systems, to non-periodic dynamic systems. The resulting mathematical machinery was then used to compute the Fisher information measure, as the amount of information extracted from the time series for COVID-19 confirmed infections and deaths. The analysis was performed for the World as a whole and five nation-states: India, USA, Japan, Germany, and Chile. Several insights resulted from the study: (1) the information content of the time series varied widely for different time periods, over the course of the pandemic, (2) it is advisable not to fit model parameters or make policy decisions based on data from time periods with low Fisher information, (3) the most information about a wave of infections comes towards the end of the wave where the time series data has the most information about the dynamics of the pandemic, and (4) the quality of the time series data significantly affects the Fisher information value, and, therefore, what can be learned from studying the time series.

Topological elastic interface states in hyperuniform pillared metabeams

Topological states have been receiving a great deal of interest in various wave problems, such as photonic, acoustic, and elastic waves. However, few studies of topological elastic waves in non-periodic systems have been reported. Recently, hyperuniform systems suppressing long-range order while partly maintaining short-range order have provided new opportunities to control waves. In this work, we study the elastic topological interface states appearing between two Su–Schrieffer–Heeger (SSH)-like pillared metabeams where each metabeam, is constituted by a mirror symmetric hyperuniform structure. The SSH-like model is constructed by combining two hyperuniform metabeams with inverted configurations. We demonstrate that this structure could open new bandgaps at low frequencies, of which some are nontrivial and can support topological interface modes. We further show that the number of low-frequency bandgaps supporting the topological modes increases with the level of randomness, hence providing a high number of interface modes in the same structure. The robustness of the topological interface states against random perturbations in the pillars’ positions is further verified. Our work offers a reliable platform for studying topological properties and hyperuniform metamaterials and designing wave control devices for low-frequency wave attenuation and robust energy localization.

Transition metal loaded carbon penta-belt SACs for hydrogen and oxygen evolution reactions and identification of systematic DFT method to characterize the main interacting orbital for non-periodic system

In the pursuit of efficient hydrogen and oxygen production via water electrolysis, the deployment of single atom catalysts (SACs) plays a pivotal role in reducing the overpotential of this process on a large scale. Hence, the quest for suitable support materials remains imperative for the design of superior SACs. In this study, we explored the potential of the recently proposed penta-belt structure as a support matrix for anchoring late first-row transition metals (Fe - Zn). The catalytic prowess of these engineered SACs in facilitating water electrolysis is assessed through density functional theory (DFT) calculations. Remarkably, the Cu@Penta-belt SACs exhibits the highest catalytic activity for the hydrogen evolution reaction (HER), with a remarkably low ΔGH value of 0.17 eV. Additionally, Ni@Penta-belt demonstrates a competitively moderate overpotential of 0.72 V for the oxygen evolution reaction (OER). To deepen our comprehension of the bonding interactions between the metal atoms and the support structure, we introduce and apply a systematic approach for identifying and analyzing the primary binding molecular orbital. This innovative methodology can be extended to diverse doping investigations that necessitate non-periodic DFT calculations.

DFT Calculation of Nonperiodic Small Molecular Systems to Predict the Reaction Mechanism of Advanced Oxidation Processes: Challenges and Perspectives

DFT Calculation of Nonperiodic Small Molecular Systems to Predict the Reaction Mechanism of Advanced Oxidation Processes: Challenges and Perspectives

Computational Analysis of Semi-Analytical Modeling Techniques for a Novel PM-Based Planar Actuator

A novel type of permanent magnet planar actuator is proposed which consists of a permanent magnet mover that interacts with individually mechanically controllable permanent magnets in the stator. A state of levitation and actuation is obtained by mechanically altering the orientation of the stator magnets to control the forces and torques on the mover. To design and control the actuator, fast and accurate electromagnetic models are required. In this study, the harmonic modeling technique is applied to rotating and translating cuboidal and cylindrical permanent magnets and is compared to the equivalent charge model in terms of accuracy and computational effort. The models are compared for a finite stator topology which demonstrates that the harmonic model has a substantial computational advantage over the equivalent charge method in a non-periodic system while both models are in good agreement in terms of accuracy.

Environmental theoretical calculation for non-periodic systems

Environmental theoretical calculation for non-periodic systems

TopIso3D Viewer: Enhancing Topological Analysis through 3D Isosurfaces.

We present TopIso3D Viewer, a software with a user-friendly graphical interface, that generates three-dimensional maps to analyze descriptors based on the Quantum Theory of Atoms in Molecules (QTAIM), applied in periodic and nonperiodic systems. The software also automates the launching of topological analysis calculations through the Topond package and generates a report that facilitates the identification of the values of the calculated descriptors, in the Bond Critical Points (BCP) and Critical Points of the Laplacian of the electron density (LCP), facilitating the classification of chemical interactions. The map projects created can be stored in the form of HTML files, for later consultation through any type of browser. For validation of the software, several systems with 0-3D dimensions were studied. In addition, the topology of urea molecular crystal and its isolated molecule were revisited.

Better Heisenberg Limits, Coherence Bounds, and Energy-Time Tradeoffs via Quantum Rényi Information.

An uncertainty relation for the Rényi entropies of conjugate quantum observables is used to obtain a strong Heisenberg limit of the form RMSE≥f(α)/(⟨N⟩+12), bounding the root mean square error of any estimate of a random optical phase shift in terms of average photon number, where f(α) is maximised for non-Shannon entropies. Related simple yet strong uncertainty relations linking phase uncertainty to the photon number distribution, such as ΔΦ≥maxnpn, are also obtained. These results are significantly strengthened via upper and lower bounds on the Rényi mutual information of quantum communication channels, related to asymmetry and convolution, and applied to the estimation (with prior information) of unitary shift parameters such as rotation angle and time, and to obtain strong bounds on measures of coherence. Sharper Rényi entropic uncertainty relations are also obtained, including time-energy uncertainty relations for Hamiltonians with discrete spectra. In the latter case almost-periodic Rényi entropies are introduced for nonperiodic systems.

Variationally consistent Hellmann–Feynman forces in the finite element formulation of Kohn–Sham density functional theory

Hellmann–Feynman forces are derived within the numerical framework of the finite element method for density functional theory in the Kohn–Sham formalism. The variational consistency of the force expressions in all-electron and pseudopotential settings are carefully examined, with a particular focus on the implications arising from different representations for interaction terms that are associated with electrostatics. Numerical investigations in nonperiodic systems which range from diatomic molecules to carbon allotropes demonstrate the systematic convergence that is offered by the finite element framework, not only for energy and force but also for geometric configuration and molecular statics parameters. A range of higher-order discretizations employing fixed meshes are invoked within these examples based on classical finite elements as well as on isogeometric analysis. Overall, this work contributes to recent advances which demonstrate the viability of the finite element method for carrying out ab initio molecular dynamics.

Localization of Generalized Wannier Bases Implies Chern Triviality in Non-periodic Insulators

We investigate the relation between the localization of generalized Wannier bases and the topological properties of two-dimensional gapped quantum systems of independent electrons in a disordered background, including magnetic fields, as in the case of Chern insulators and quantum Hall systems. We prove that the existence of a well-localized generalized Wannier basis for the Fermi projection implies the vanishing of the Chern character, which is proportional to the Hall conductivity in the linear response regime. Moreover, we state a localization dichotomy conjecture for general non-periodic gapped quantum systems.

Towards Ab-Initio Simulations of Crystalline Defects at the Exascale Using Spectral Quadrature Density Functional Theory

Defects in crystalline solids play a crucial role in determining properties of materials at the nano, meso- and macroscales, such as the coalescence of vacancies at the nanoscale to form voids and prismatic dislocation loops or diffusion and segregation of solutes to nucleate precipitates, phase transitions in magnetic materials via disorder and doping. First principles Density Functional Theory (DFT) simulations can provide a detailed understanding of these phenomena. However, the number of atoms needed to correctly simulate these systems is often beyond the reach of many widely used DFT codes. The aim of this article is to discuss recent advances in first principles modeling of crystal defects using the spectral quadrature method. The spectral quadrature method is linear scaling with respect to the number of atoms, permits spatial coarse-graining, and is capable of simulating non-periodic systems embedded in a bulk environment, which allows the application of appropriate boundary conditions for simulations of crystalline defects. In this article, we discuss the state-of-the-art in ab-initio modeling of large metallic systems of the order of several thousand atoms that are suitable for utilizing exascale computing resourses.

Control of time-varying systems based on forward Riccati formulation in hybrid functions domain

In this paper, the time-varying system control is resolved with the aid of forward Riccati formulation and hybrid functions. The applied Riccati equations need neither advanced knowledge of the system dynamics nor the assumption of the future information of system matrices. Herein, the state space equation of LTV system is rewritten in the Hybrid functions (HF) domain where results a set of linear discrete equations instead of having a complex Forward-in-time Propagating Riccati Equation (FPRE). The HF evolve from the synthesis of sample-and-hold functions (SHF) and triangular functions (TF) that can estimate any functions based on the summation of two series. The feasibility of the proposed method is investigated by various numerical control cases. Numerical results demonstrated that the proposed method is usable in both periodic and non-periodic systems with less control effort and significant damping time.

Orbital angular momentum driven anomalous Hall effect

Orbital angular momentum (OAM) plays a central role in regulating the magnetic state of electrons in nonperiodic systems such as atoms and molecules. In solids, on the other hand, OAM is usually quenched by the crystal field, and thus has a negligible effect on magnetization. Accordingly, it is generally neglected in discussions around band topology such as Berry curvature and intrinsic anomalous Hall effect (AHE). Here, we present a theoretical framework demonstrating that crystalline OAM can be directionally unquenched in transition metal oxides via energetic proximity of the conducting $d$ electrons to the local magnetic moments. We show that this leads to ``composite'' Fermi pockets with topologically nontrivial OAM textures. This enables a giant Berry curvature and a resultant intrinsic nonmonotonic AHE, even in collinearly ordered spin states. We use this model to explain the origin of the giant AHE observed in the forced ferromagnetic state of ${\mathrm{EuTiO}}_{3}$ and propose it as a general scheme for OAM driven AHE.

Finding critical points and reconstruction of electron densities on grids.

The quantum theory of atoms in molecules (QTAIM), developed by Bader and co-workers, is one of the most popular ways of extracting chemical insight from the results of quantum mechanical calculations. One of the basic tasks in QTAIM is to locate the critical points of the electron density and calculate various quantities (density, Laplacian, etc.) on them since these have been found to correlate with molecular properties of interest. If the electron density is given analytically, this process is relatively straightforward. However, locating the critical points is more challenging if the density is known only on a three-dimensional uniform grid. A density grid is common in periodic solids because it is the natural expression for the electron density in plane-wave calculations. In this article, we explore the reconstruction of the electron density from a grid and its use in critical point localization. The proposed reconstruction method employs polyharmonic spline interpolation combined with a smoothing function based on the promolecular density. The critical point search based on this reconstruction is accurate, trivially parallelizable, works for periodic and non-periodic systems, does not present directional lattice bias when the grid is non-orthogonal, and locates all critical points of the underlying electron density in all tests studied. The proposed method also provides an accurate reconstruction of the electron density over the space spanned by the grid, which may be useful in other contexts besides critical point localization.

Dynamics of meandering rivers in finite-length channels: linear theory

Meandering channels are dynamic landforms that arise as a result of fluid mechanic and sedimentary processes. Their evolution has been described by the meander-morphodynamic equations, which dictate that channel curvature and bed topography give rise to local perturbations in streamwise fluid velocity, prompting the preferential erosion and sediment deposition that constitute meander behaviour. Novel mathematical conditions are presented to guarantee unique solutions for the linearized equations in non-periodic domains with finite boundaries. With the boundary condition specification sufficient for the uniqueness proof one finds a well-posed initial-boundary-value problem amenable to standard numerical techniques for partial differential equations. This provides a pathway for improved numerical algorithms for simulations of meandering river dynamics. Previous theoretical analysis for linear stability theory in meandering dynamics has been restricted to spatially periodic systems. The present effort develops new results for linear stability theory in non-periodic systems with temporal driving at system boundaries as well as non-homogeneous initial conditions. Predictions for temporal driving at the inlets for non-periodic finite domains provide clarification for observed behaviour in laboratory flumes where driven conditions at the inlet avoids the long-term decay of all meanders observed in flumes with fixed entry conditions. Linear stability theory for finite domains confirms that a continuous perturbation is required for sustained meandering. Original scaling arguments are presented for the dependence of the meander migration rate on geological parameters, showing that the rate of channel migration increases with increased width, downreach slope and bank erodibility, and decreases with increased volumetric flow rate.

Spectral quadrature for the first principles study of crystal defects: Application to magnesium

We present an accurate and efficient finite-difference formulation and parallel implementation of Kohn-Sham Density (Operator) Functional Theory (DFT) for non periodic systems embedded in a bulk environment. Specifically, employing non-local pseudopotentials, local reformulation of electrostatics, and truncation of the spatial Kohn-Sham Hamiltonian, and the Linear Scaling Spectral Quadrature method to solve for the pointwise electronic fields in real-space and the non-local component of the atomic force, we develop a parallel finite difference framework suitable for distributed memory computing architectures to simulate non-periodic systems embedded in a bulk environment. Choosing examples from magnesium-aluminum alloys, we first demonstrate the convergence of energies and forces with respect to spectral quadrature polynomial order, and the width of the spatially truncated Hamiltonian. Next, we demonstrate the parallel scaling of our framework, and show that the computation time and memory scale linearly with respect to the number of atoms. Next, we use the developed framework to simulate isolated point defects and their interactions in magnesium-aluminum alloys. Our findings conclude that the binding energies of divacancies, Al solute-vacancy and two Al solute atoms are anisotropic and are dependent on cell size. Furthermore, the binding is favorable in all three cases.

Existence and Computation of Generalized Wannier Functions for Non-Periodic Systems in Two Dimensions and Higher

Exponentially-localized Wannier functions (ELWFs) are an orthonormal basis of the Fermi projection of a material consisting of functions which decay exponentially fast away from their maxima. When the material is insulating and crystalline, conditions which guarantee existence of ELWFs in dimensions one, two, and three are well-known, and methods for constructing the ELWFs numerically are well-developed. We consider the case where the material is insulating but not necessarily crystalline, where much less is known. In one spatial dimension, Kivelson and Nenciu-Nenciu have proved ELWFs can be constructed as the eigenfunctions of a self-adjoint operator acting on the Fermi projection. In this work, we identify an assumption under which we can generalize the Kivelson-Nenciu-Nenciu result to two dimensions and higher. Under this assumption, we prove that ELWFs can be constructed as the eigenfunctions of a sequence of self-adjoint operators acting on the Fermi projection. We conjecture that the assumption we make is equivalent to vanishing of topological obstructions to the existence of ELWFs in the special case where the material is crystalline. We numerically verify that our construction yields ELWFs in various cases where our assumption holds and provide numerical evidence for our conjecture.

Analytic Approximation of Non-Periodic Dynamical System by Perturbation Method

Analytic Approximation of Non-Periodic Dynamical System by Perturbation Method