Periodic Systems Research Articles

Magic-angle twisted bilayer graphene under orthogonal and in-plane magnetic fields

We investigate the effect of a magnetic field on the band structure of bilayer graphene with a magic twist angle of 1.08∘. The coupling of a tight-binding model and the Peierls phase allows the calculation of the energy bands of periodic two-dimensional systems. For an orthogonal magnetic field, the Landau levels are dispersive, particularly for magnetic lengths comparable to or larger than the twisted bilayer cell size. A high in-plane magnetic field modifies the low-energy bands and gap, which we demonstrate to be a direct consequence of the minimal coupling.

Finite-time resilient control for uncertain periodic piecewise polynomial time-varying systems

This study explores the problem of finite-time resilient control for periodic piecewise polynomial time-varying systems in the face of parameter uncertainties, time-varying state delays and external disturbances. Particularly, the considered system is characterized by dividing the fundamental period of periodic systems into numerous subintervals, each of which can be expressed by using matrix polynomial functions. The foremost intention of this work is to lay out a resilient controller such that the resulting closed-loop system is finite-time bounded and satisfies a mixed [Formula: see text] and passivity performance index. Furthermore, by constructing a periodic piecewise time-varying Lyapunov–Krasovskii functional, a delay-dependent sufficient condition is established in line with Wiritinger’s inequality and matrix polynomial lemma to guarantee the needed outcomes of the system under study. Following this, the gain matrix of the devised controller can be calculated by solving the established constraints. As a final step, we conclude with a numerical example that validates the potential and importance of the theoretical discoveries and the developed control scheme.

Current density functional framework for spin-orbit coupling: Extension to periodic systems.

Spin-orbit coupling induces a current density in the ground state, which consequently requires a generalization for meta-generalized gradient approximations. That is, the exchange-correlation energy has to be constructed as an explicit functional of the current density, and a generalized kinetic energy density has to be formed to satisfy theoretical constraints. Herein, we generalize our previously presented formalism of spin-orbit current density functional theory [Holzer et al., J. Chem. Phys. 157, 204102 (2022)] to non-magnetic and magnetic periodic systems of arbitrary dimension. In addition to the ground-state exchange-correlation potential, analytical derivatives such as geometry gradients and stress tensors are implemented. The importance of the current density is assessed for band gaps, lattice constants, magnetic transitions, and Rashba splittings. In the latter, the impact of the current density may be larger than the deviation between different density functional approximations.

Exact closed forms for the transmittance of electromagnetic waves in one-dimensional anisotropic periodic media

In this work, we obtain closed expressions for the transfer matrix and the transmittance of electromagnetic waves propagating in finite one-dimensional anisotropic periodic stratified media with an arbitrary number of cells. By invoking the Cayley–Hamilton theorem on the transfer matrix for the electromagnetic field in a periodic stratified media formed by N cells, we obtain a fourth-order recursive relation for the matrix coefficients that defines the so-called Tetranacci polynomials (TPs). In the symmetric case, corresponding to a unit-cell transfer matrix with a characteristic polynomial where the coefficients of the linear and cubic terms are equal, closed expressions for the solutions to the recursive relation, known as symmetric TPs, have recently been derived, allowing us to write the transfer matrix and transmittance in a closed form. We show as sufficient conditions that the 4×4 differential propagation matrix of each layer in the binary unit cell, Δ , a) has eigenvalues of the form ±p1 , ±p2 , with p1≠p2 , and b) its off-diagonal 2×2 block matrices possess the same symmetric structure in both layers. Otherwise, the recursive relations are still solvable for any 4×4 matrix and provide an algorithm to compute the Nth power of the transfer matrix without carrying out explicitly the matrix multiplication of N matrices. We obtain analytical expressions for the dispersion relation and transmittance, in closed form, for two finite periodic systems: the first one consists of two birefringent uniaxial media with their optical axis perpendicular to the z-axis, and the second consists of two isotropic media subject to an external magnetic field oriented along the z-axis and exhibiting the Faraday effect. Our formalism applies also to lossy media, magnetic anisotropy or optical activity.

Interface state-based bound states in the continuum and below-continuum-resonance modes with high-Q factors in the rotational periodic system

Abstract In thispaper, we have introduced a new approach to calculate the orbital angular momentum (OAM) of bound states in the continuum (BICs) and below-continuum-resonance (BCR) modes in the rotational periodic system nested inside and outside by transforming the Bloch wave number from the translational periodic system. We extensively classify and study these BICs and BCR modes, which exhibit high-quality (high-Q) factors, in different regions relative to the interface of system. These BICs and BCR modes with high-Q factor have been studied in detail based on the distinctive structural parameters and scattering theory. Outcomes of this research break the periodic limitation of interface state-based BICs, and realize more and higher symmetry interface state-based BICs and BCR modes. Moreover, we can control the region that light captured by adjusting the frequency, and show that Q factor of BICs is more closely related to the ordinal number of rings and rotational symmetry number of the system.

Multiple heating loads participate in the system power regulation control strategy

With the addition of a high proportion of new energy and power electronic equipment, the power system has shown characteristics such as low inertia and significant energy output fluctuation, which has brought great challenges to power/frequency regulation and control of the power system. Therefore, this article uses the inertia characteristics of heat energy on the load side and exerts reasonable start-stop control to play a positive and beneficial role in the power regulation of the power system. Firstly, the room temperature variation process was transformed into a lumped parameter equivalent model. A lumped parameter heat transfer model of a single typical load was built in Simulink, and its dynamic characteristics were analyzed by symbolic calculation. Based on this, a time-domain simulation was carried out to explore the influence of the law of system parameters and external input on the change of system state quantity. Based on time domain simulation, the behavior of the heating load is analyzed. Then, the effects of typical and multiple loads on system power regulation at different outdoor temperatures are studied. It is found that when the average outdoor temperature decreases, the sustainable time of system power upturn will increase, and the sustainable time of downturn will decrease. The power curve of multiple loads simultaneously is more stable, and the adjustment ability is stronger. The reasonable and flexible control method of load switch setting, namely the coherent characteristic load power regulation strategy, realizes the sustainable power optimization of the load to the system in the specified period.

Discrete heat equation for a periodic layered system with allowance for the interfacial thermal resistance: General formulation and dispersion analysis

Discrete heat equation for a periodic layered system with allowance for the interfacial thermal resistance: General formulation and dispersion analysis

Preview controller synthesis for a class of linear parameter periodic systems

SummaryIn this study, the problem of preview tracking control (PTC) was considered with regard to the linear parameter periodic systems (LPPSs) subject to previewed signals. First, the difference operator approach was extended to derive an augmented error system (AES). As a result, the PTC problem was transformed into a stabilization problem via state/output feedback. Second, sufficient conditions guaranteeing the closed‐loop stability of the augmented error systems were derived, and the design of a periodic controller with preview actions was proposed through the approach of linear matrix inequalities (LMIs). Finally, a numerical simulation was performed to illustrate the effectiveness of the proposed periodic controller.

Restoration of non-Hermitian bulk-boundary correspondence by counterbalancing skin effect

In systems exhibiting the non-Hermitian skin effect (NHSE), the bulk spectrum under open boundary conditions (OBC) significantly differs from that of its periodic counterpart. This disparity renders the conventional bulk-boundary correspondence (BBC) inapplicable. Here we propose an intuitive approach called doubling and swapping to restore the BBC, using the non-Hermitian Su-Schrieffer-Heeger model as an example. Explicitly, we construct a modified system free of NHSE by swapping the asymmetric intracell hoppings in every second primitive unit cell. Importantly, this change does not alter the OBC spectrum. As a result, the modified periodic system can serve as the bulk for defining topological invariants that accurately predict edge states and topological phase transitions. The basic principle is applicable to many other systems. By extending the study to disordered systems in which the asymmetric hoppings are randomly swapped, we show that two types of winding numbers can also be defined to account for the NHSE and topological edge states, respectively.

Bordering the COVID-19 Pandemic Through Schengen Visa: Contested Policies and Persistent Effects for Mobility Rights

Visa regimes were key global mechanisms of the COVID-19 pandemic governance. Many nationals, both from the Global South and North, were subject to the several visa regulations during the pandemic. Whilst nationals of the Global North could regain their visa-free travel rights in the further phases, the others are still entrapped in the visa regimes, just like the pre-pandemic period. Considering visa’s global importance for border regulations in the (post-) pandemic period, what has changed for mobility rights of the visa applicants? This study examines changes in mobility rights for visa applicants during and after the pandemic, focusing on Schengen visa regime from March 2020 to June 2023. Our argument is twofold: first, the EU temporarily but substantially changed visa policies in the name securing the public health and free movement in(to) the Schengen area. However, these policies for securing mobility also created administrative gray zones that include new travel restrictions, confusions as well as strategic spaces for accessing to the mobility rights. Second, ongoing visa issuance practices and application process problems since the pandemic reveal a regression in the mobility rights lasting in the (post-)pandemic period. Hence, this article offers a more nuanced account of mobility rights by shedding light on the Schengen visa regime which will continue to play substantial roles in the EU’s border management system in the post-pandemic period.

Photocleavable Polymer Cubosomes: Synthesis, Self-Assembly, and Photorelease.

Polymer cubosomes (PCs) are a recent class of self-assembled block copolymer (BCP) microparticles with an accessible periodic channel system. Most reported PCs consist of a polystyrene scaffold, which provides mechanical stability for templating but has a limited intrinsic functionality. Here, we report the synthesis of photocleavable BCPs with compositions suitable for PC formation. We analyze the self-assembly mechanism and study the model release of dyes during irradiation, where the transition of the BCPs from amphiphilic to bishydrophilic causes the rapid disassembly of the PCs. A combination of modeling and experiment shows that the evolution of PCs proceeds first via liquid-liquid phase separation into polymer-rich droplets, followed by microphase separation within this droplet confinement, and finally, membrane reorganization into high internal order. This insight may encourage exploration of alternative preparation strategies to better control the size and homogeneity of PCs.

A Graph Neural Network Approach to the Inverse Design for Thermal Transparency with Periodic Interparticle System

Abstract Recent years have witnessed significant advancements in utilizing machine learningbased techniques for thermal metamaterial-based structures and devices to attain favorable thermal transport behavior. Among the various thermal transport behaviors, achieving thermal transparency stands out as particularly desirable and intriguing. Our earlier work demonstrated the use of a thermal metamaterial-based periodic interparticle system as the underlying structure for manipulating thermal transport behavior and achieving thermal transparency. In this paper, we introduce an approach based on graph neural network to address the complex inverse design problem of determining the design parameters for a thermal metamaterial-based periodic interparticle system with the desired thermal transport behavior. Our work demonstrates that combining graph neural network modeling and inference is an effective approach for solving inverse design problems associated with attaining desirable thermal transport behaviors using thermal metamaterials.

Chiral Spectroscopy of Bulk Systems with Propagated Localized Orbitals.

We present approaches for the simulation of electronic circular dichroism, Raman, and Raman optical activity (ROA) spectra for isolated and periodic systems as well as subsystem analysis thereof. The method is based on the use of time-dependent maximally localized Wannier functions in the CP2K package and accounts for origin dependencies inherent to the Gaussian and plane wave with pseudopotentials approach as well as the origin dependence of the magnetic dipole and electric quadrupole operators. Tests on the H-bonded enantiomers of alanine by harmonic normal-mode analysis and on an aqueous solution of l-alanine by ab initio molecular dynamics obeying periodic boundary conditions (PBCs) are presented as total and subsystem-resolved spectra. To our knowledge, this is the first instance of an ROA spectrum derived from real-time propagation obeying PBCs and the first ROA simulation considering off-, pre-, and on-resonance effects within PBCs.

Is It Salt, Cocrystal, or Continuum? Successes and Limitations of Computationally Efficient Periodic System Calculations

Is It Salt, Cocrystal, or Continuum? Successes and Limitations of Computationally Efficient Periodic System Calculations

Sampled-data controller synthesis using dissipative linear periodic jump-flow systems with design applications

In this paper, we will propose linear-matrix-inequality-based techniques for the design of sampled-data controllers that render the closed-loop system dissipative with respect to quadratic supply functions, which includes passivity and an upper-bound on the system’s H∞-norm as a special case. To arrive at these results, we model the sampled-data control system as a linear periodic jump-flow system, study dissipativity in terms of differential linear matrix inequalities (DLMIs) and then convert these DLMIs into a single linear matrix inequality. We will present three applications of these synthesis techniques: (1) passivity-based controller synthesis, as found in teleoperations, (2) input–output-response matching of a continuous-time filter with a discrete-time filter (by minimizing the H∞-norm of a generalized plant) and (3) a sampled-data controller redesign problem, where the objective is to find the best sampled-data controller, in the H∞-norm sense, for a given continuous-time controller. We will show that synthesizing sampled-data controllers leads to better closed-loop system behaviour than using a Tustin discretization of a continuous-time controller.

Iterative Learning with Adaptive Sliding Mode Control for Trajectory Tracking of Fast Tool Servo Systems

To address the tracking control problem of the periodic motion fast tool servo system (FTS), we propose a control method that combines adaptive sliding mode control with closed-loop iterative learning control. Adaptive sliding mode control enhances the system’s robustness to external non-repetitive disturbances, and exponential gain iterative learning control compensates for the influence of periodic disturbances such as cutting force. The experimental results show that the proposed iterative learning controller based on adaptive sliding mode control can effectively eliminate the influence of various interference factors, achieve accurate tracking of the FTS system’s motion trajectory within a limited number of iterations, and ensure the stability of the system, which has the advantages of a fast convergence speed, high tracking accuracy, and strong robustness.

Post-pandemic: outcomes and prospects of the digitalisation of higher education

The article attempts to analyse the interim results of digitalisation of the Russian higher education system in the post-pandemic period. The research methods include an analysis of regulatory documents, statistical analysis of data gathered by the Federal State Statistics Service, and a secondary analysis of results from research centres of the Higher School of Economics, Plekhanov Russian University of Economics, and others. The main findings are related to the analysis of dynamics of indicators responsible for transformation of the social space in the higher education system during digitalisation. The authors view the digitalisation of higher school as a factor that perpetuates social inequality and stimulates the development of its new forms. They conclude that maintaining distance learning in universities contributes to communication barriers within the student community and between students and faculty as well. Slow increase in the digital literacy of teachers is emphasised. During the analysis, the authors conclude that the transformation of higher school through digitalisation is progressing at quite slow rate due to unhurried provision of universities with financial, technical, and personnel resources necessary for the digital transition. The novelty of the work lies in documenting the results of the transformation of social relations within the higher education system during digitalisation and defining its characteristic features, including the readiness of participants of the educational process to implement specific state vectors of the transformation of the Russian higher education

Етична економіка як методологічний виклик постмодернізму

The article is devoted to the problem of the compatibility of the economic and ethical foundations of entrepreneurial activity. In the conditions of postmodernism, their connection is blurred by a complex interweaving of economic and ethical motives. The conclusions of researchers who study this issue often contradict actual practice. Moreover, in postmodern philosophy, ethics in the general theoretical sense was not only underestimated, but also not regarded as an acceptable phenomenon. That is why science has not developed a complex of intellectual actions that would have a universal character to neutralize the negative consequences of postmodernism. Considering the growing role of ethical issues in the modern society and their lack of development in the economic environment, it is reasonable to analyze the series of works of the German economist, philosopher and sociologist Peter Koslowski. In his studies, the issues of bridging the gap between ethics and economic rationality associated with postmodernism as a special historical era, which is characterized by a number of specific features that are critical to the emergence and deepening of socio-economic risks, are discussed in a balanced and objective manner. Due to this it is relevant to define the problems of the theory of ethical economy not in isolation, but in interaction and mutual influence with modern transformation processes of postmodernism. The productive attempt to consider these issues was made by Peter Koslowski in his fundamental works: «Postmodern Culture», «Principles of Ethical Economy», «Ethics of Banking». The purpose of this article is to consider, based on the conceptualization of Peter Koslowski’s methodological position, the theoretical concept of ethical economy as a potentially important factor in overcoming the ethical neutralization of the economic system in the postmodern period. The novelty is the definition of ethical economy as a universal theory of rational activity, which takes into account the interaction of various socio-economic factors — ethics, economy and finance, law, sociology, history — which allows it to be interpreted as a multi-subject scientific discipline, the semantic contexts of which determine behavioral choice of economic entities, consumer and humanitarian expectations of the population. The methods of hermeneutics, analysis and synthesis, comparison, abstraction and generalization were used in the research. The main conclusions of the article are characterized by theoretical innovations that can provoke methodological discussions and ultimately contribute to an in-depth study of the multifaceted issues of ethical economy. The detailed and logically consistent concept of ethical economy as a system of economic views on a fair economic order during the period of change of world history eras, change from modernity to postmodernity is presented. The normative side of ethical economy includes legal obligations, which can be properly implemented in laws. In the triad of law, ethics and economics, the principle of efficiency and social justice applies to both law itself and ethics and should be used in the development of adequate legislation.

JEDI: A versatile code for strain analysis of molecular and periodic systems under deformation.

Stretching or compression can induce significant energetic, geometric, and spectroscopic changes in materials. To fully exploit these effects in the design of mechano- or piezo-chromic materials, self-healing polymers, and other mechanoresponsive devices, a detailed knowledge about the distribution of mechanical strain in the material is essential. Within the past decade, Judgement of Energy DIstribution (JEDI) analysis has emerged as a useful tool for this purpose. Based on the harmonic approximation, the strain energy in each bond length, bond angle, and dihedral angle of the deformed system is calculated using quantum chemical methods. This allows the identification of the force-bearing scaffold of the system, leading to an understanding of mechanochemical processes at the most fundamental level. Here, we present a publicly available code that generalizes the JEDI analysis, which has previously only been available for isolated molecules. Now, the code has been extended to two- and three-dimensional periodic systems, supramolecular clusters, and substructures of chemical systems under various types of deformation. Due to the implementation of JEDI into the Atomic Simulation Environment, the JEDI analysis can be interfaced with a plethora of program packages that allow the calculation of electronic energies for molecular systems and systems with periodic boundary conditions. The automated generation of a color-coded three-dimensional structure via the Visual Molecular Dynamics program allows insightful visual analyses of the force-bearing scaffold of the strained system.

Generalized geometric pore size distribution code GPSD-3D for periodic systems composed of monodisperse spheres

The generalized geometric pore size distribution P(r;rp|rc) as function of pore radius r, probe sphere radius rp, and coating thickness rc for a periodic two-dimensional system composed of circles (GPSD-2D) had been defined recently. For rp=rc=0 it reduces to the widely accepted pore radius distribution P(r) introduced by Gelb and Gubbins. The three-dimensional counterpart GPSD-3D for periodic systems composed of spheres is implemented here using an efficient Voronoi-based semi-analytic strategy that offers significant advantages compared with both a grid-based implementation and constrained nonlinear optimization with respect to speed, precision and memory requirements. Moreover, GPSD-3D is fully parallelized using OpenMP. Program summaryProgram title:GPSD-3DCPC library link to program files:https://doi.org/10.17632/ntcr87fgr5.1Developers repository link:https://github.com/mkmat/CODE-GPSD-3DLicensing provisions: MITProgramming languages:fortran, c++, perlNature of problem: Calculation of a set of pore radii for a user-provided configuration of (material) spheres contained in a periodic three-dimensional, rectangular box. This set depends on the user-specified radius rp of a probe sphere, and a user-specified hypothetical coating thickness rc of the material spheres. The variable size of the set, and thus the resolution of the resulting generalized geometric pore size distribution increases linearly with computing time.Solution method: Analytic calculation of pore radii from the Voronoi faces for the case of monodisperse systems, constrained nonlinear optimization or grid-based approach for polydisperse systems.Additional comments: This code requires a c++ compiler such as g++, a OpenMP-supporting fortran compiler such as gfortran, perl, and the voro++ library. Download links will be automatically provided during installation of GPSD-3D.