Two-dimensional Region Research Articles

Effects of Curvature on the Electronic States of a Two-Dimensional Mesoscopic Ring

We study the effects of curvature on an electron in a two-dimensional localized annular region in the presence of external magnetic fields. The approach follows the thin-layer quantization procedure. We verify that the most significant contribution of the mean curvature occurs in the state with \(m=0\), which tends to decrease the energies in null magnetic fields. The effects of curvature are also manifested in the cyclotron frequency as well as in the effective angular momentum through the \(\alpha \) parameter, which can be controlled in such a way that the magnitude of these effects becomes explicit. This is verified in the energies and wave functions of the system. A decrease in the number of occupied states in the Fermi energy is observed, which leads to an alteration in the radial range of the conducting region of the sample. This is confirmed by studying the variations in the radii of the states.

Turing-Turing bifurcation and multi-stable patterns in a Gierer-Meinhardt system

The classical Gierer-Meinhardt system portrays the formation process of a self-organizing pattern of vascular mesenchymal cells. In this paper, the coexistence of multi-stable patterns with different spatial responses and the superposition for patterns have been explored in theory from the perspective of Turing-Turing bifurcation. On the one-dimensional region, the system is simplified near the Turing-Turing singularity to obtain a third-order ordinary differential equation employing center manifold and normal form theory, which is locally topologically equivalent to the primitive system and its coefficients can be represented by the parameters of original equation. Especially, considering the simplified system, it is theoretically revealed that the system supports semi-stable patterns superimposed by two different spatial resonances and the coexistence of four stable steady states with different single characteristic wavelengths, indicating that different initial conditions may tent to completely different spatial patterns. Finally, some numerical simulations are given, which are consistent with the theoretical analysis. The multi-stable and superimposed modes of the system are also studied on a two-dimensional region, which shows that some experimental patterns of vascular mesenchymal cells in vitro can be interpreted as the superposition of different spatial modal patterns to a certain extent.

Correlated disorder induced anomalous transport in magnetically doped topological insulators

We examine the transport properties of magnetically doped topological insulator (TI) thin films subject to correlated non-magnetic disorder. For the disorder we choose a quasi-periodic potential with a random phase. We restrict the disorder to a central region, which is coupled to two leads in a clean quantum spin Hall insulator (QSHI) state and concentrate on different orientations of the quasi-periodicity in the two-dimensional central region. In the case of a diagonally oriented or purely longitudinal quasi-periodicity we find different topological Anderson insulator (TAI) phases, with a quantum anomalous Hall insulator (QAHI), a quantum spin Chern insulator (QSCI), or a QSHI phase being realized before the Anderson insulation takes over at large disorder strength. Quantized transport from extended bulk states is found for diagonal quasi-periodicity in addition to the above TAI phases that are also observed for the case of uncorrelated disorder. For a purely transverse orientation of the quasi-periodicity the emerging QSHI and QSCI phases persist to arbitrarily strong disorder potential. These topological phase transitions (except to the Anderson insulator phase), can be understood from a self consistent Born approximation.

Pervasive approximate periodic symmetry in organic P1 structures.

The goal of this project was to identify the prevalence of approximate symmetry in organic P1 structures. In the November 2019 version of the Cambridge Structural Database (CSD), there are 2592 organic, P1, R ≤ 0.050 structures; complete, unique entries are available for 1407 Z= Z'> 1 and 1049 Z= Z'= 1 structures. All the Z> 1 structures can have approximate symmetry; the Z= 1 structures were scanned to find those composed of molecules or ions that might lie on a special position and those that have two or more large molecules or ions that are very similar. The number of Z= 1 structures so identified was 285, of which 49 were grouped with the Z> 1 structures because Zeffective> 1. The packing in each of the 1407+285= 1692 structures was investigated. The 144 that should almost certainly have been described in a smaller or higher-symmetry unit cell were removed from the list; 120 of the 144 are composed of achiral or racemic material. (About half of the Z= 1 and 89% of the Z> 1 structures are composed of enantiopure material.) Approximate periodic symmetry was found in 86% of the 1337 remaining Z> 1 structures and in 72% of the 211 remaining Z= 1 structures. About a third of the enantiomerically pure structures mimic inversion symmetry; 38% have approximate rotational symmetry. For the structures of achiral and racemic material, distorted glide or mirror symmetry is more common than is distorted inversion symmetry. Approximate rotational and glide symmetry was found to be periodic in two dimensions considerably more often than in three. In 4% of the structures, different layer types alternate or layers are related by approximate local rotations, as well as by small translations. In 5% of the structures, different parts of the molecule are segregated into two-dimensional regions that have different approximate symmetries. More than a third of the structures that are a distorted version of a higher-symmetry structure were determined at T ≥ 288 K.

Two-dimensional multiphase batch process monitoring based on sparse canonical variate analysis

Most industrial batch processes involve inherent dynamic characteristics in both within-batch time direction and batch-wise direction. In order to ensure process safety and improve process performance, the two-dimensional dynamics should be analyzed during batch process monitoring. In this work, two-dimensional region of support (2D-ROS) is first constructed to select and preserve the relevant samples for the current measured sample by calculating autoregressive orders with Akaike information criterion (AIC) in time direction and measuring the similarity with the weighted Euclidean distance in batch-wise direction. Afterwards, sparse canonical variate analysis (SCVA) algorithm is performed to yield sparse canonical vectors, which is especially advantageous for eliminating the irrelevant variables and facilitating the interpretation of underlying relationships of process variables. Meanwhile, given most measurements are subject to the non-Gaussian distribution, the upper control limits (UCLs) in 2D-SCVA can be estimated using kernel density estimation (KDE). The achieved results obtained from a numerical dynamic example and the benchmark fed-batch penicillin fermentation process clearly verify that the proposed method performs well for detecting abnormal operation for the batch processes.

Kalman filter temperature estimation with a photoacoustic observation model during the hyperthermia treatment of cancer

Hyperthermia with laser heating can be a noninvasive treatment for tumors near the body surface. Thermal damage of tissues depends on temperature levels and time of exposure to high temperatures, thus requiring accurate techniques to measure the temperature in the target region of interest. In this computational work, we couple the laser hyperthermia treatment of cancer to the photoacoustic temperature measurement of internal tissues, by solving a state estimation problem with the Kalman filter. The region of interest is considered to be continuously heated by a laser for the hyperthermia treatment, while another laser is sequentially pulsed over the same heated surface to generate acoustic pressure waves. The observation model is derived from the photoacoustic problem, which is linear with respect to the local internal temperatures of the tissues. The evolution model given by the bioheat transfer problem is also supposed linear and uncertainties are modeled as additive and Gaussian. Therefore, the Kalman filter provides the optimal solution of the state estimation problem considered in this work. Simulated nonintrusive acoustic pressure measurements are used in inverse analyses for two test cases, with different dimensions and locations of a tumor in a two-dimensional region. The simulated tumors are supposed loaded with nanoparticles, in order to enhance the local absorption of the laser energy and to reduce thermal damage to healthy cells. The Kalman filter estimated accurate and stable temperature distributions, even in the tumor region that involved large gradients. Moreover, uncertainties in the Kalman filter estimates were smaller than those resulting from the direct simulation of the photoacoustic thermometry problem.

A Bivariate Post-Warranty Maintenance Model for the Product under a 2D Warranty

In this study, by integrating preventive maintenance (PM) into a two-dimensional warranty region, a two-dimensional warranty with customized PM (2D warranty with customized PM) is proposed from the manufacturer’s perspective to reduce the warranty cost. The warranty cost of a 2D warranty with customized PM is derived. The manufacturer’s tradeoff between PM cost and minimal repair cost saving is obtained by choosing the proper reliability threshold and the number of customized PMs, and the advantage of a 2D warranty with customized PM is illustrated. Second, by integrating PM into the post-warranty period, a bivariate post-warranty maintenance (BPWM) policy is proposed from the consumer’s perspective to ensure the reliability of the product through the 2D warranty with customized PM. The expected cost rate model of BPWM is derived. Optimal BPWM is obtained in the numerical experiments. It is shown that a 2D warranty with customized PM is beneficial for both the manufacturer and the consumer, since both the manufacturer’s warranty cost and the consumer’s total cost are reduced.

Thermal ablation effects on rotors that characterize functional re-entry cardiac arrhythmia.

Thermal ablation is a well-established successful treatment for cardiac arrhythmia, but it still presents limitations that require further studies and developments. In the rotor-driven functional re-entry arrhythmia, tissue heterogeneity results on the generation of spiral/scroll waves and wave break dynamics that may cause dangerous sustainable fibrillation. The selection of the target region to perform thermal ablation to mitigate this type of arrhythmia is challenging, since it considerably affects the local electrophysiology dynamics. This work deals with the numerical simulation of the thermal ablation of a cardiac muscle tissue and its effects on the dynamics of rotor-driven functional re-entry arrhythmia. A non-homogeneous two-dimensional rectangular region is used in the present numerical analysis, where radiofrequency ablation is performed. The electrophysiology problem for the propagation of the action potential in the cardiac tissue is simulated with the Fenton-Karma model. Thermal damage caused to the tissue by the radiofrequency heating is modeled by the Arrhenius equation. The effects of size and position of a heterogeneous region in the original muscle tissue were first analyzed, in order to verify the possible existence of the functional re-entry arrhythmia during the time period considered in the simulations. For each case that exhibited re-entry arrhythmia, six different ablation procedures were analyzed, depending on the position of the radiofrequency electrode and heating time. The obtained results revealed the effects of different model parameters on the existence and possible mitigation of the functional re-entry arrhythmia.

Quantum magnetic billiards: boundary conditions and gauge transformations

We study admissible boundary conditions for a charged quantum particle in a two-dimensional region subjected to an external magnetic field, i.e. a quantum magnetic billiard. After reviewing some physically interesting classes of admissible boundary conditions (magnetic Robin and chiral boundary conditions), we turn our attention to the role of gauge transformations in a magnetic billiard: in particular, we introduce gauge covariant boundary conditions, and find a sufficient condition for gauge covariance which is satisfied by all the aforementioned examples.

Bayesian Inference on the Bimodality of the Generalized von Mises Distribution

This article introduces Bayesian inference on the bimodality of the generalized von Mises (GvM) distribution for planar directions (Gatto and Jammalamadaka in Stat Methodol 4(3):341–353, 2007). The GvM distribution is a flexible model that can be axial symmetric or asymmetric, unimodal or bimodal. Two inferential approaches are analysed. The first is the test of null hypothesis of bimodality and Bayes factors are obtained. The second approach provides a two-dimensional highest posterior density (HPD) credible set for two parameters relevant to bimodality. Based on the identification of the two-dimensional parametric region associated with bimodality, the inclusion of the HPD credible set in that region allows us to infer on the bimodality of the underlying GvM distribution. A particular implementation of the Metropolis–Hastings algorithm allows for the computation of the Bayes factors and the HPD credible sets. A Monte Carlo study reveals that, whenever the samples are generated under a bimodal GvM, the Bayes factors and the HPD credible sets do clearly confirm the underlying bimodality.

The effect of geometry on survival and extinction in a moving-boundary problem motivated by the Fisher–KPP equation

The Fisher–Stefan model involves solving the Fisher–KPP equation on a domain whose boundary evolves according to a Stefan-like condition. The Fisher–Stefan model alleviates two practical limitations of the standard Fisher–KPP model when applied to biological invasion. First, unlike the Fisher–KPP equation, solutions to the Fisher–Stefan model have compact support, enabling one to define the interface between occupied and unoccupied regions unambiguously. Second, the Fisher–Stefan model admits solutions for which the population becomes extinct, which is not possible in the Fisher–KPP equation. Previous research showed that population survival or extinction in the Fisher–Stefan model depends on a critical length in one-dimensional Cartesian or radially-symmetric geometry. However, the survival and extinction behaviour for general two-dimensional regions remains unexplored. We combine analysis and level-set numerical simulations of the Fisher–Stefan model to investigate the survival–extinction conditions for rectangular-shaped initial conditions. We show that it is insufficient to generalise the critical length conditions to critical area in two-dimensions. Instead, knowledge of the region geometry is required to determine whether a population will survive or become extinct.

MeQryEP: A Texture Based Descriptor for Biomedical Image Retrieval.

Image texture analysis is a dynamic area of research in computer vision and image processing, with applications ranging from medical image analysis to image segmentation to content-based image retrieval and beyond. “Quinary encoding on mesh patterns (MeQryEP)” is a new approach to extracting texture features for indexing and retrieval of biomedical images, which is implemented in this work. An extension of the previous study, this research investigates the use of local quinary patterns (LQP) on mesh patterns in three different orientations. To encode the gray scale relationship between the central pixel and its surrounding neighbors in a two-dimensional (2D) local region of an image, binary and nonbinary coding, such as local binary patterns (LBP), local ternary patterns (LTP), and LQP, are used, while the proposed strategy uses three selected directions of mesh patterns to encode the gray scale relationship between the surrounding neighbors for a given center pixel in a 2D image. An innovative aspect of the proposed method is that it makes use of mesh image structure quinary pattern features to encode additional spatial structure information, resulting in better retrieval. On three different kinds of benchmark biomedical data sets, analyses have been completed to assess the viability of MeQryEP. LIDC-IDRI-CT and VIA/I–ELCAP-CT are the lung image databases based on computed tomography (CT), while OASIS-MRI is a brain database based on magnetic resonance imaging (MRI). This method outperforms state-of-the-art texture extraction methods, such as LBP, LQEP, LTP, LMeP, LMeTerP, DLTerQEP, LQEQryP, and so on in terms of average retrieval precision (ARP) and average retrieval rate (ARR).

Bone radiomics reproducibility: a three-centered study on the impacts of image contrast, edge enhancement, and latitude variations.

This study aims to measure the reproducibility of radiomics features in ankle bone radiography over changes in post-processing parameters including contrast, edge enhancement and latitude.Lateral ankle bone radiographies for sixty patients were obtained from three digital radiology centers. All images were acquired by same image acquisition settings. A two-dimensional region of interest was drawn in any image and 93 features from 6 feature sets including first and second order were extracted. The coefficient of variation (COV) and intraclass correlation coefficient (ICC) were calculated to assess feature reproducibility for each center and among all centers in three scenarios: Adams(Nat Rev Endocrinol 9(1):28, 2013) ten different contrast Brown et al. (J Med Imaging 5(1):011017, 2018) ten different edge enhancement and Hirvasniemi et al. (Osteoarthr Cartilage 27(6):906-914, 2019) ten different image latitude parameters.Based on ICC analysis, it is observed that 46-100-44% of Histogram, 54-72-42% of GLCM, 43-76-36% of GLDM, 60-90-17% of GLRLM, 33-19-21% of GLSZM and 13-20-0% of NGTDM radiomics features had 90% < ICC < 100% over changes in contrast-edge enhancement-latitude changes respectively. Based on COV, GLRLM was only feature set that 100% of their features had COV ≤ 5% over changes in contrast and edge enhancement.The results presented here, indicating that radiomics features extracted are vulnerable over changes in contrast, edge enhancement and latitude. The most reproducible features that introduced in this study could be used for further clinical decision making.

On Solving a Class of Continuous Traffic Equilibrium Problems and Planning Facility Location Under Congestion

This paper presents methods to obtain analytical solutions to a class of continuous traffic equilibrium problems, where continuously distributed customers from a bounded two-dimensional service region seek service from one of several discretely located facilities via the least congested travel path. We show that under certain conditions, the traffic flux at equilibrium, which is governed by a set of partial differential equations, can be decomposed with respect to each facility and solved analytically. This finding paves the foundation for an efficient solution scheme. Closed-form solution to the equilibrium problem can be obtained readily when the service region has a certain regular shape, or through an additional conformal mapping if the service region has an arbitrary simply connected shape. These results shed light on some interesting properties of traffic equilibrium in a continuous space. This paper also discusses how service facility locations can be easily optimized by incorporating analytical formulas for the total generalized cost of spatially distributed customers under congestion. Examples of application contexts include gates or booths for pedestrian traffic, as well as launching sites for air vehicles. Numerical examples are used to show the superiority of the proposed optimization framework, in terms of both solution quality and computation time, as compared with traditional approaches based on discrete mathematical programming and partial differential equation solution methods. An example with the metro station entrances at the Beijing Railway Station is also presented to illustrate the usefulness of the proposed traffic equilibrium and location design models.

Application of the Moment Method for Numerical Simulation of Homogeneous-Heterogeneous Condensation

The paper considers the numerical modeling of the processes of homogeneous and heterogeneous condensation and evaporation in multiphase flows using the method of moments. Nonstationary processes of gas dynamics and phase transitions in the two-dimensional plane and axisymmetric regions are described by a general system of equations. The system of equations is expanded by adding two equations. One describes the evolution of the total mass fraction of the condensing substance; the other describes the evolution of the mass fraction of solid particles. An instant wetting model is used to model heterogeneous nucleation. The Gyarmathy model is used for the approximation of the average droplet growth rate. Heterogeneous condensation is modeled based on the distribution function of foreign impurities. An approach to calculating evaporation in the heterogeneous case is proposed. A comparison of the proposed models with a numerical experiment is given. Numerical simulation of homogeneous-heterogeneous condensation in a gas-dynamic ejector is carried out.

Application of two-dimensional warped discrete Fourier transform to nonlinear two-dimensional amplitude demodulation

This study introduces a novel nonlinear two-dimensional (2D) warped discrete Fourier transform (WDFT) amplitude demodulation method that allows higher-resolution measurements on specific two-dimensional regions of interest. The specific application in this study addresses the need for the nonlinear 2D amplitude demodulation of fringe-wave fields acquired by a deformed Mach–Zehnder interferometer. The proposed method exploits the properties based on which the WDFT can obtain frequency spectra sampled at non-equidistant intervals and the symmetry of the Fourier transform. As a result, this 2D-WDFT-based method can be used to nonlinearly demodulate the amplitude of the 2D interference fringe wave field to obtain a high-resolution localized fringe envelope. This study describes the proposed analysis procedure and its application using this 2D WDFT-based demodulation scheme. Experimental verification of the proposed approach was conducted with the use of deformed Mach–Zehnder interferometry. The successful experimental validation proves the efficiency of the proposed algorithm for amplitude demodulation with dense sampling points located in the central part of the envelope. To the best of the authors’ knowledge, this is the first investigational report on a 2D nonlinear envelope demodulator.

Програмно-алгоритмічне забезпечення паралельного розрахунку неізотермічного вологоперенесення на підставі апарату похідних дробового порядку

A new mathematical model of the nonstationary process of heat and moisture transfer in the two-dimensional region is constructed on the basis of the use of Caputo and Grunwald- Letnikov derivatives. An implicit finite-difference scheme for approximation of a mathematical model of noisothermal moisture transfer taking into account the fractional integro-differential apparatus is developed. The given algorithm of numerical realization of model allows to receive values of function of temperature and humidity for all points of area of partition. The method of fractional steps is adapted for numerical realization of mathematical model. It allowed performing parallel calculations of two difference half-step taking into account the corresponding spatial coordinate. The implemented algorithm of parallel calculation of non- isothermal moisture transfer in materials of fractal structure makes it possible to obtain a reliable result without the need to conduct complex and expensive practical experiments. It is proposed to use the Model-View-Presenter design pattern for software development. The software a parallel algorithm using .Net threads and algorithmic features of the TPL library has developed. It has been tested on multi-core computer systems with CPUs of different capacities. The .NET Stopwatch class was used to measure the execution time of sequential and parallel algorithms. A two-dimensional case with a mesh partition is studied for three cases: a square shape, a wide rectangular shape, and a tall rectangular shape. Graphs of dynamics of acceleration and efficiency of algorithms are given, and their analysis is also carried out. To smooth the graphs of acceleration and efficiency of algorithms, we apply approximation of experimental data based on the obtained results.

On the construction of stress discontinuity lines for a two-dimensional plastic region

On the construction of stress discontinuity lines for a two-dimensional plastic region

Influence of the location of drilling fluid loss on wellbore temperature distribution during drilling

Circulation loss can occur at different positions during drilling, which has different effects on the wellbore temperature distribution. To ensure the safety and effectiveness of the drilling process, it is necessary to study the influence of circulation loss at different positions on the wellbore temperature distribution. In this study, we established mathematical models of wellbore temperature distribution corresponding to different situations in which circulation loss occurred and obtained the wellbore temperature distribution for each situation. When circulation loss occurred in the one-dimensional region, the annulus drilling fluid temperature at the circulation loss position changed suddenly; when it occurred in the two-dimensional region, the wellbore temperature at the circulation loss position was significantly disturbed. Under other conditions unchanged, as the circulation loss occurred closer to the bottom hole, the lower the wellbore temperature became at the same well depth. After circulation loss occurred, the formation temperature in the circulation loss area decreased significantly. The difference between the wellbore temperature distribution curve after circulation loss occurs and the wellbore temperature distribution curve when no circulation loss occurred can be used to monitor the location of the circulation loss in real time.

The Gravity Collective: A Search for the Electromagnetic Counterpart to the Neutron Star–Black Hole Merger GW190814

Abstract We present optical follow-up imaging obtained with the Katzman Automatic Imaging Telescope, Las Cumbres Observatory Global Telescope Network, Nickel Telescope, Swope Telescope, and Thacher Telescope of the LIGO/Virgo gravitational wave (GW) signal from the neutron star–black hole (NSBH) merger GW190814. We searched the GW190814 localization region (19 deg2 for the 90th percentile best localization), covering a total of 51 deg2 and 94.6% of the two-dimensional localization region. Analyzing the properties of 189 transients that we consider as candidate counterparts to the NSBH merger, including their localizations, discovery times from merger, optical spectra, likely host galaxy redshifts, and photometric evolution, we conclude that none of these objects are likely to be associated with GW190814. Based on this finding, we consider the likely optical properties of an electromagnetic counterpart to GW190814, including possible kilonovae and short gamma-ray burst afterglows. Using the joint limits from our follow-up imaging, we conclude that a counterpart with an r-band decline rate of 0.68 mag day−1, similar to the kilonova AT 2017gfo, could peak at an absolute magnitude of at most −17.8 mag (50% confidence). Our data are not constraining for “red” kilonovae and rule out “blue” kilonovae with M &gt; 0.5 M ⊙ (30% confidence). We strongly rule out all known types of short gamma-ray burst afterglows with viewing angles &lt;17° assuming an initial jet opening angle of ∼5.°2 and explosion energies and circumburst densities similar to afterglows explored in the literature. Finally, we explore the possibility that GW190814 merged in the disk of an active galactic nucleus, of which we find four in the localization region, but we do not find any candidate counterparts among these sources.