Two-dimensional System Research Articles

Linear quadratic optimal control of stochastic 2-D Roesser models

This paper investigates the linear quadratic (LQ) optimal control problem for the stochastic two-dimensional (2-D) systems governed by Roesser models with multiplicative noise. The main contribution is to give the necessary and sufficient optimality condition by proposing a set of novel forward and backward stochastic partial difference equations (FBSPDE), and to further present the explicitly optimal feedback control laws on the finite horizon and on the infinite horizon based on the Riccati-like difference equations and the algebraic equation, respectively. Several numerical simulations are provided to illustrate the performance of the designed controllers.

On solvability of a two-dimensional symmetric nonlinear system of difference equations

We show that the system of difference equations xn+k=xn+lyn−efxn+l+yn−e−f,yn+k=yn+lxn−efyn+l+xn−e−f,n∈N0,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ x_{n+k}=\\frac{x_{n+l}y_{n}-ef}{x_{n+l}+y_{n}-e-f},\\quad y_{n+k}= \\frac{y_{n+l}x_{n}-ef}{y_{n+l}+x_{n}-e-f},\\quad n\\in {\\mathbb{N}}_{0}, $$\\end{document} where k∈N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$k\\in {\\mathbb{N}}$\\end{document}, l∈N0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$l\\in {\\mathbb{N}}_{0}$\\end{document}, l<k\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$l< k$\\end{document}, e,f∈C\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$e, f\\in {\\mathbb{C}}$\\end{document}, and xj,yj∈C\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$x_{j}, y_{j}\\in {\\mathbb{C}}$\\end{document}, j=0,k−1‾\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$j=\\overline{0,k-1}$\\end{document}, is theoretically solvable and present some cases of the system when the general solutions can be found in a closed form.

Pseudospin Quantum Hall Ferromagnetism Probed by Electron Spin Resonance.

We study the effect of the pseudospin ferromagnetism with the aid of an electrically detected electron spin resonance in a wide AlAs quantum well containing a high quality two-dimensional electron system. Here, pseudospin emerges as a two-component degree of freedom, that labels degenerate energy minima in momentum space populated by electrons. The built-in mechanical strain in the sample studied imposes a finite "Zeeman" splitting between the pseudospin "up" and "down" states. Because of the anisotropy of the electron spin splitting we were able to independently measure the electron spin resonances originating from the two in-plane valleys. By analyzing the relative resonance amplitudes, we were able to investigate the ferromagnetic phase transitions taking place at integer filling factors of the quantum Hall effect when the magnetic field is tilted. The pseudospin nature of these transitions is demonstrated.

Conformity Experiment on Inelastic Scattering Exponent of Electrons in Two Dimensions.

The quantum Hall (QH) effect is one of the most widely studied physical phenomenon in two dimensions. The plateau-plateau transition within this effect can be comprehensively described by the scaling theory, which encompasses three pivotal exponents: the critical exponent κ, the inelastic scattering exponent p, and the universal exponent γ. Prior studies have focused on measuring κ and estimating γ, assuming a constant p value of 2 across magnetic fields. Here, our work marks a significant advancement by measuring all three exponents within a single graphene device and a conventional two-dimensional electron system. This study uniquely determines p at low magnetic fields (weak localization region and well outside the QH regime) and high magnetic fields (in the vicinity of the QH regime). Employing a comprehensive analytical approach that includes weak localization, plateau-plateau transitions, and variable range hopping, we have directly determined κ, p, and γ. Our findings reveal a distinct variation in p, shifting from 1 in the low magnetic field regime to 2 in the QH regime in graphene.

Liquid-Liquid Transition in a Bose Fluid near Collapse.

Discovering novel emergent behavior in quantum many-body systems is a main objective of contemporary research. In this Letter, we explore the effects on phases and phase transitions of the proximity to a Ruelle-Fisher instability, marking the transition to a collapsed state. To accomplish this, we study by quantum MonteCarlo simulations a two-dimensional system of soft-core bosons interacting through an isotropic finite-ranged attraction, with a parameter η describing its strength. If η exceeds a characteristic value η_{c}, the thermodynamic limit is lost, as the system becomes unstable against collapse. We investigate the phase diagram of the model for η≲η_{c}, finding-in addition to a liquid-vapor transition-a first-order transition between two liquid phases. Upon cooling, the high-density liquid turns superfluid, possibly above the vapor-liquid-liquid triple temperature. As η approaches η_{c}, the stability region of the high-density liquid is shifted to increasingly higher densities, a behavior at variance with distinguishable quantum or classical particles. Finally, for η larger than η_{c} our simulations yield evidence of collapse of the low-temperature fluid for any density; the collapsed system forms a circular cluster whose radius is insensitive to the number of particles.

Pair correlations and freezing transitions in a two-dimensional system of tilted axially symmetric quadrupoles

We study the pair structure and the transition from the liquid to the solid state in a system of axially symmetric charged particles confined to a two-dimensional plane and characterised by only one non-zero component of the electric quadrupole moment, which we assume to be inclined with respect to the perpendicular to the confining plane. The particles interact via anisotropic repulsive quadrupole–quadrupole interactions. The pair correlation functions (PCF) were calculated by solving the hypernetted chain integral equation (HNC) theory in the range of the tilt angle 75.0 ∘ ≤ 90 ∘ − ϕ ≤ 90 ∘ . NVT Monte Carlo (MC) simulations were also performed to test the accuracy of the PCFs. We find that the PCFs calculated with the HNC theory agree well with those of the MC simulation at smaller tilt angles and show anomalous behaviour with respect to the in-plane angular variation. The PCFs obtained with the HNC theory were used in the Ramakrishnan-Yussouff (RY) density functional theory (DFT) to investigate the transition between liquid and solid freezing. It was found that the RY DFT stabilises the triangular solid only for tilt angles ≥ 80 ∘ . When the tilt angle is decreased compared to the normal orientation of the quadrupoles, the transition density increases.

Removal of sulfadiazine from water by a three-dimensional electrochemical system coupled with persulfate: Enhancement effect of ball-milled CuO-Fe3O4@biochar

The CuO-Fe3O4@biochar (CFB) composite, synthesized via an eco-friendly mechanical ball milling, was employed as a particle electrode in a three-dimensional (3D) electrochemical reactor to investigate its efficiency in removing sulfadiazine (SD) from antibiotic wastewater. The study revealed that the addition of 5 g/L CFB into the 3D electrochemical system significantly enhanced SD removal, achieving a removal rate of 96.2 % compared to 33.5 % in a two-dimensional system, under optimal conditions of pH 7, persulfate concentration of 4 mM, and current density of 8 mA/cm2. The CFB particle electrode demonstrated superior catalytic activity compared to CuB, FeB, and CuFe particle electrodes. The ball milling process effectively reduced the agglomeration of CuO and Fe3O4, thereby increasing the active sites of the particle electrodes. The SD displayed remarkable removal efficiency across a broad pH spectrum ranging from 2 to 9. Scavenging experiments and electron paramagnetic resonance techniques suggested that SD removal primarily occurred via a non-radical pathway involving singlet oxygen (1O2). The synergistic effect between bimetallic ions and the reduction reaction at the cathode accelerated the cycling of Fe2⁺/Fe3⁺ and Cu⁺/Cu2⁺, thereby promoting PDS activation. Additionally, the positively charged surface of CFB facilitated contact with PDS through electrostatic attraction. The E-CFB-PDS system demonstrated excellent efficiency in removing antibiotics, and its stability and reusability make it a promising approach for treating organic pollutant wastewater.

Chern numbers in two-dimensional systems with spiral boundary conditions

Chern numbers in two-dimensional systems with spiral boundary conditions

Quantitative Disorder Effects in Low-Dimensional Spin Systems

The Imry–Ma phenomenon, predicted in 1975 by Imry and Ma and rigorously established in 1989 by Aizenman and Wehr, states that first-order phase transitions of low-dimensional spin systems are ‘rounded’ by the addition of a quenched random field coupled to the quantity undergoing the transition. The phenomenon applies to a wide class of spin systems in dimensions d≤2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d\\le 2$$\\end{document} and to spin systems possessing a continuous symmetry in dimensions d≤4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d\\le 4$$\\end{document}. This work provides quantitative estimates for the Imry–Ma phenomenon: in a cubic domain of side length L, we study the effect of the boundary conditions on the spatial and thermal average of the quantity coupled to the random field. We show that the boundary effect diminishes at least as fast as an inverse power of loglogL\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\log \\log L$$\\end{document} in general two-dimensional spin systems. For systems possessing a continuous symmetry, we show that the boundary effect diminishes at least as fast as an inverse power of L in two and three dimensions and at least as fast as an inverse power of loglogL\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\log \\log L$$\\end{document} in four dimensions. Finally, we establish a partial uniqueness results for translation-covariant Gibbs states, and prove that, for almost every realization of the random field, all such states must agree on the thermally-averaged value of the quantity coupled to the random field. Specific models of interest for the obtained results include the random-field q-state Potts model, the Edwards-Anderson spin glass model, and the random-field spin O(n) models.

Reliability modeling and optimization of a two-dimensional system considering performance sharing mechanism

Photovoltaic (PV) power generation systems are increasingly installed on the factory rooftop. The installed PV power generation system exits a two-dimensional structure since the factories are usually designed to be square or rectangular. Motivated by real industry practice, this research proposes a two-dimensional performance sharing reliability model for the factory rooftop PV power generation system, where a common bus exists in each row and across all rows. The component availability is affected by both internal failure and external impacts. The system reliability is the probability that each component can meet its own demand and each row can meet its required demand after performance sharing. To mitigate external impacts, the factory rooftop PV power generation system employs both overarching protection and individual protection measures. We extend the universal generating function (UGF) technique to propose a reliability evaluation algorithm and use the genetic algorithm (GA) to determine optimal protection resource allocation to improve system reliability. Further, the proposed two-dimensional performance sharing reliability model is extended to consider multiple phased-mission. Numerical studies indicate that both expanding common bus capacity and optimizing the protection allocation strategy are effective ways to improve the factory rooftop PV power generation system reliability.

Decoherence Channels Effects on Thermal Quantum Correlations Within a Two-Dimensional Graphene System

Decoherence Channels Effects on Thermal Quantum Correlations Within a Two-Dimensional Graphene System

Influence of sand layer thickness on the collapse mechanism of tunnels in soil-sand-rock composite strata

Collapse is a severe event during metro tunnel construction, particularly in soil-sand-rock composite strata. Variations in the thickness of sand layers, owing to their high compressibility, flowability, and thixotropic properties, significantly impact the mechanical response and deformation of strata, which also directly determine the stability of tunnel excavation processes. Regarding the complexity of the engineering response of the soil-sand-rock composite strata, a series of model tests were conducted to reveal the collapse mechanism of the metro tunnel in the soil-sand-rock composite strata subjected to varying sand layer thickness in this paper. Meanwhile, the influence of sand thickness on the evolution of collapse form, the response of strata stress, and the variation of the displacement and strain fields were systematically discussed by the monitoring data from the miniature earth pressure cells and a two-dimensional full-field deformation measurement system. Moreover, the collapse evolution process was recorded by the industrial camera. The test results indicated that the horizontal displacement of the tunnel shoulders was more affected by the increase in sand layer thickness than the horizontal displacement of the haunches before the tunnel collapse. The high compressibility of the sand layer resisted the transmission of surcharge load to the rock layer. Once the overlying rock layer above the tunnel vault lost its bearing capacity, the thixotropy and flowability properties of the sand layer caused the collapse face to expand funnel-shaped to both sides. The collapse width of the sand-soil interface was proportional to the sand layer thickness. The greater the sand layer thickness, the weaker the ability to provide stable support for the foot of the temporary stratigraphic arch, further reducing the stability of the temporary stratigraphic arch and leading to a faster collapse rate of the composite strata. In general, the results of this research offer valuable guidance for preventing and controlling tunnel collapse in soil-sand-rock composite strata.

The chaotic behavior and traveling wave solutions of the conformable extended Korteweg–de-Vries model

Abstract In this article, the phase portraits, chaotic patterns, and traveling wave solutions of the conformable extended Korteweg–de-Vries (KdV) model are investigated. First, the conformal fractional order extended KdV model is transformed into ordinary differential equation through traveling wave transformation. Second, two-dimensional (2D) planar dynamical system is presented and its chaotic behavior is studied by using the planar dynamical system method. Moreover, some three-dimensional (3D), 2D phase portraits and the Lyapunov exponent diagram are drawn. Finally, many meaningful solutions are constructed by using the complete discriminant system method, which include rational, trigonometric, hyperbolic, and Jacobi elliptic function solutions. In order to facilitate readers to see the impact of fractional order changes more intuitively, Maple software is used to draw 2D graphics, 3D graphics, density plots, contour plots, and comparison charts of some obtained solutions.

General Relations between Stress Fluctuations and Viscoelasticity in Amorphous Polymer and Glass-Forming Systems.

Mechanical stress governs the dynamics of viscoelastic polymer systems and supercooled glass-forming fluids. It was recently established that liquids with long terminal relaxation times are characterized by transiently frozen stress fields, which, moreover, exhibit long-range correlations contributing to the dynamically heterogeneous nature of such systems. Recent studies show that stress correlations and relaxation elastic moduli are intimately related in isotropic viscoelastic systems. However, the origin of these relations (involving spatially resolved material relaxation functions) is non-trivial: some relations are based on the fluctuation-dissipation theorem (FDT), while others involve approximations. Generalizing our recent results on 2D systems, we here rigorously derive three exact FDT relations (already established in our recent investigations and, partially, in classical studies) between spatio-temporal stress correlations and generalized relaxation moduli, and a couple of new exact relations. We also derive several new approximate relations valid in the hydrodynamic regime, taking into account the effects of thermal conductivity and composition fluctuations for arbitrary space dimension. One approximate relation was heuristically obtained in our previous studies and verified using our extended simulation data on two-dimensional (2D) glass-forming systems. As a result, we provide the means to obtain, in any spatial dimension, all stress-correlation functions in terms of relaxation moduli and vice versa. The new approximate relations are tested using simulation data on 2D systems of polydisperse Lennard-Jones particles.

An image encryption approach based on a novel two-dimensional chaotic system

An image encryption approach based on a novel two-dimensional chaotic system

A novel control approach for discrete-time 2D Roesser systems under input saturation and intrinsic nonlinearity: A region of stability investigation

This paper presents the control system design for the nonlinear discrete-time Roesser systems under saturated control input. A deficiency in the existing literature has been addressed in this study for the control of two-dimensional (2D) systems. A generalized boundary condition analysis is presented in the form of tractable invariant sets for the derivation of region of stability to design a suitable state feedback control. A mechanism for the evaluation of controller parameters is presented by considering the generalized structure of 2D Lyapunov function. The work has been extended when external disturbances are present in the 2D systems, and a robust design condition by accounting the perturbations as well as the input saturation has been established. In comparison to the existing works, a control system design for 2D Roesser systems under input saturation and intrinsic nonlinearity by application of a generalized Lyapunov function has been revealed. Furthermore, a tractable 2D region of stability for the local control of the 2D systems is achieved, rather than the conventional global controllers. Furthermore, a method has also been studied for obtainment of the controller gain matrix through convex optimization regarding the complete structure of the 2D Lyapunov function. Simulation results are provided for the stabilization of an unstable nonlinear 2D system under input saturation.

Constructing condylar cartilage organoid to explore primary cilia functions

An organoid culture system better recapitulates the cellular structure, function, and interaction between cells and the extracellular matrix (ECM) than a two-dimensional (2D) culture system. We here constructed a condylar cartilage organoid to explore the regulatory role of primary cilia. Similar to the natural condylar cartilage, the condylar cartilage organoid exhibited abundant ECM and comprised superficial, proliferative, and hypertrophic zones. Primary cilia in the condylar cartilage organoid were shorter on average than those in the 2D culture chondrocytes, but their average length was equivalent to those in the natural condylar cartilage. Notably, primary cilia in each zone of the condylar cartilage organoid had an average length similar to that of primary cilia in the natural condylar cartilage. According to transcriptomic and biochemical analyses, the expression of cilia-related genes and cilia-related Hedgehog (HH) signaling differed between the condylar cartilage organoid and 2D culture systems. IFT88 knockdown promoted the protein levels of COL-Ⅹ, TRPV4, and HH signaling molecules in the condylar cartilage organoid, but decreased them in the 2D culture system. Notably, the protein levels of COL-Ⅹ, TRPV4, and HH signaling molecules increased in the superficial zone of the si IFT88 condylar cartilage organoid compared with the condylar cartilage organoid. However, the protein levels of aforementioned molecules were not significantly different in proliferative and hypertrophic zones. Collectively, we successfully constructed the condylar cartilage organoid with a better tissue structure and abundant ECM. Moreover, the condylar cartilage organoid is more suitable for exploring primary cilia functions.

Patterns of forearm lymphatic drainage to the epitrochlear lymph nodes in 1400 cutaneous melanoma patients.

Variations of hand and forearm lymphatic drainage to upper-arm lymphatic pathways may impact the route of melanoma metastasis. This study compared rates of lymphatic drainage to epitrochlear nodes between anatomic divisions of the hand and forearm to determine whether the anatomic distribution of hand and forearm melanomas affects the likelihood of drainage to epitrochlear lymph nodes. Using a single-institution lymphoscintigraphy database, we identified all patients with cutaneous melanoma on the hand and forearm. A body-map two-dimensional coordinate system was used to classify cutaneous melanoma sites between radial-ulnar and dorsal-volar divisions. Sentinel lymph nodes (SLNs) visualized on lymphoscintigraphy were recorded. Proportions of patients with epitrochlear SLNs were compared between anatomic divisions using χ2 analysis. Of 3628 upper extremity cutaneous melanoma patients who underwent lymphatic mapping with lymphoscintigraphy, 1400 met inclusion criteria. Twenty-one percent of patients demonstrated epitrochlear SLNs. Epitrochlear SLNs were observed in 27% of dorsal forearm melanomas and 15% of volar forearm melanomas (p < 0.001). Epitrochlear SLNs were observed in 31% of ulnar forearm melanomas and 17% of radial forearm melanomas (p < 0.001). Higher proportions of dorsal and ulnar forearm melanomas have epitrochlear SLNs. Metastasis to epitrochlear SLNs may be more likely from melanomas in these respective forearm regions.

Entanglement asymmetry and quantum Mpemba effect in two-dimensional free-fermion systems

Entanglement asymmetry and quantum Mpemba effect in two-dimensional free-fermion systems

First-Principles Studies of the Electronic and Optical Properties of Two-Dimensional Arsenic-Phosphorus (2D As-P) Compounds.

In this work, we propose the construction of a two-dimensional system based on the stable phases previously reported for the 2D arsenic and phosphorus compounds, with hexagonal and orthorhombic symmetries. Therefore, we have modeled one hexagonal and three possible orthorhombic structures. To ensure the dynamical stability, we performed phonon spectra calculations for each system. We found that all phases are dynamically stable. To ensure the thermodynamic and mechanical stabilities, we have calculated cohesive energies and elastic constants. Our results show that the criteria for the stabilities are all fulfilled. For these stable structures, we computed the electronic and optical properties from first-principles studies based on density functional theory. The computation of electronic band gaps was performed by using the GW approximation to overcome the underestimation of the results obtained from standard DFT approaches. To study the optical properties, we have computed the dielectric function imaginary part within the BSE approach, which takes into account the excitonic effects and allows us to calculate the exciton binding energies of each system. The study was complemented by the computation of the absorption coefficient. From our calculations, it can be established that the 2D As-P systems are good candidates for several technological applications.